COMPUTATIONAL STUDIES OF GAS-PHASE RADICAL REACTIONS WITH
VOLATILE ORGANIC COMPOUNDS OF RELEVANCE TO COMBUSTION AND
ATMOSPHERIC CHEMISTRY
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
John Kenneth Merle, A.S., B.S.
*****
The Ohio State University
2005
Dissertation Committee:
Approved by
Professor Christopher M. Hadad, Advisor
Professor Sherwin J. Singer
Professor Heather C. Allen
_________________________________
Advisor
Graduate Program in Chemistry
ABSTRACT
The focus of this dissertation is to improve our understanding of chemical
reactions which are important in both combustion and atmospheric environments. The
following paragraphs describe the studies carried out and reported in this dissertation.
Density functional theory was utilized to determine whether the addition of
O2(3Σg) to 2-oxepinoxy radical, a proposed intermediate in the unimolecular
decomposition of phenylperoxy radical, followed by unimolecular rearrangement and
decomposition results in the formation of experimentally detected C1−C5 products via
oxidative combustion of benzene. Pathways resulting from the initial formation of 1,2dioxetanyl, 1,3-peroxy, 1,4-peroxy, hydroperoxy, and peroxy moiety scission
intermediates were calculated. At temperatures between 500-750 K, the formation of
peroxyoxepinone radicals and their decomposition pathways and products are
competitive with those proposed by Fadden for the unimolecular decomposition of 2oxepinoxy radical.
The conformational distribution and unimolecular decomposition pathways for npropylperoxy radical have been generated at the CBS-QB3, B3LYP/6-31+G** and
mPW1K/6-31+G** levels of theory. At the CBS-QB3 level, the 298 K distribution of
rotamers is predicted to be 28.1, 26.4, 19.6, 14.0, and 11.9 % for the gG, tG, gT, gG’, and
tT conformations, respectively. The detailed CBS-QB3 potential energy surface for the
ii
unimolecular decomposition of n-propylperoxy radical indicates that important
bimolecular products could be derived from two 1,4-H transfer mechanisms available at
T < 500K, primarily via an activated n-propylperoxy adduct.
Substituent effects on the bond dissociation enthalpies (BDEs) and hydroxyl
radical addition reactions for a series of mono-substituted ethenes and benzenes have
been studied using density functional theory (DFT). In each case, a hydrogen atom on the
ethene and benzene has been replaced by the following series of substituents: F, Cl, CF3,
CH3, CN, CHO, OCH3, OH, NH2, NO2, SCH3, and SH. BDEs for the cis ethene and ortho
benzene C–H bonds are shown to correlate well with the atoms in molecule (AIM)
derived charge localized on the substituent of the parent molecule when steric
interactions are minimized. When the ethene β-addition and benzene ortho and para
addition barrier heights are compared with the adiabatic ionization energies, a good
correlation is obtained.
The C–H bond dissociation energies and H-atom abstraction and radical addition
reactions of hydrogen atom and hydroxyl radical with naphthalene, anthracene,
phenanthrene, 4H-cyclopenta[d,e,f]phenanthrene, benzo[c]phenanthrene,
benzo[g,h,i]fluoranthene, and corannulene have been studied using density functional
theory. Thermodynamically, hydrogen atom and hydroxyl radical addition reactions with
PAHs are more favorable than H-atom abstraction reactions. The bond dissociation
energies for the PAHs studied here are typical for aromatic C–H bonds (~111 kcal/mol).
We have calculated detailed thermochemical and kinetic data for the reaction of
the simplest unsaturated aldehyde, acrolein, with hydroxyl radical, over an expanded
temperature range of 200–2000 K, for comparison and extension of the current
iii
experimental temperature range of 243–372 K. Conventional transition state theory
(TST) was used to determine the rate coefficients. Furthermore, Wigner corrections were
utilized to determine the contribution of quantum mechanical tunneling to the rate
coefficient for the H-abstraction mechanism. Our best estimate of the rate coefficients at
the high-pressure limit for the reaction of acrolein with hydroxyl radical, based on the
mPW1K PES over the 200–2000 K temperature range in 3–parameter Arrhenius form, is
k(T) = 4.00 x 10–20 T 2.66 exp(1322/T) cm3 molecule–1 s–1.
We have calculated the stationary points for H-atom abstraction reactions of
dimethyl ether (DME) and tetrahydrofuran (THF) by OH radical via ab initio and DFT
methods. From these energy surfaces conventional transition state theory (TST) rate
coefficients were generated with tunneling corrections based on Eckart potentials. The
mPW1K/6-31+G** rate coefficients from 200 to 2000 K have been fit to a 3-parameter
Arrhenius equation to yield the following expression: k(T) = 1.29 x 10–19 T2.73
exp(868.9/T) cm3 molecule–1 s–1.
iv
ACKNOWLEDGMENTS
I would like to thank, first and foremost, my advisor Christopher M. Hadad for
providing an example as a tremendous scientist and an even better human being.
I would like to thank my mother and father, Shari and Roger Merle, for their
unconditional support and love and for providing within me the guidance and character to
accomplish all that I have. My brother, Stephen Merle, I thank you for your efforts in
keeping us close. I love you all very much.
I thank my wife, Cheryll Merle, for support, love, and understanding throughout
my long educational career. Finally, I thank my daughter, Sarah Merle, for providing a
tremendous joy in our life through her extraordinary cheerfulness and vitality. I love you
both from the bottom of my heart.
I would also like to thank the Environmental Molecular Science Institute funded
by the National Science Foundation at The Ohio State University, a GAANN fellowship,
and an Amoco fellowship for providing financial support for my graduate studies. I
would also like to thank the Ohio Supercomputer Center for computing resources.
v
VITA
March 24, 1967. . . . . . . . . . . . . . . . . . . . . .Born – Bethesda, Maryland USA
December, 1999. . . . . . . . . . . . . . . . . . . . . B. S., Chemistry
California State University, Sacramento.
2000–2002. . . . . . . . . . . . . . . . . . . . . . . . GAANN Fellow
The Ohio State University.
2000–2005. . . . . . . . . . . . . . . . . . . . . . . . Research Asst.
The Ohio State University.
2004–2005. . . . . . . . . . . . . . . . . . . . . . . . Amoco Fellow
The Ohio State University.
PUBLICATIONS
Research Publications
1.
Merle, J. K.; Hadad, C. M. “Computational Study of the Oxygen Initiated
Decomposition of 2-Oxepinoxy Radical: A Key Intermediate in the Oxidation of
Benzene,” J. Phys. Chem. A 2004, 108, 8419–8433.
2.
Hommel, E. L.; Merle, J. K.; Ma, G.; Allen, H.; Hadad, C. M. “Spectroscopic and
Computational Studies of Aqueous Ethylene Glycol Solution Surfaces,” J. Phys. Chem. B
2005, 109, 811–818.
3.
Zalyubovsky, S. J.; Glover, B. J.; Miller, T. A.; Hayes, C. J.; Merle, J. K.; Hadad,
C. M. “Observation of the A - X Electronic Transition of the 1-C3H7O2 and 2-C3H7O2
Radicals Using Cavity Ringdown Spectroscopy,” J. Phys. Chem. A 2005, 109,
1308–1315.
vi
4.
Merle, J. K.; Hayes, C. J.; Zalyubovsky, S. J.; Glover, B. J.; Miller, T. A.; Hadad,
C. M. “Computational Study of the Unimolecular Decomposition of Propylperoxyl
Radical,” J. Phys. Chem. A 2005, 109, 3637–3646.
5. Villamena, F. A.; Merle, J. K.; Hadad, C. M.; Zweier, J. L. “Superoxide Radical Anion
Adduct of 5,5-Dimethyl-1-pyrroline N-Oxide (DMPO). 1. The Thermodynamics of
Formation and Its Acidity,” J. Phys. Chem. A 2005, 109, 6083–6088.
6. Villamena, F. A.; Merle, J. K.; Hadad, C. M.; Zweier, J. L. “Superoxide Radical Anion
Adduct of 5,5-Dimethyl-1-pyrroline N-Oxide (DMPO). 1. The Thermodynamics of
Decay and the EPR Spectral Properties,” J. Phys. Chem. A 2005, 109, 6089–6098.
FIELDS OF STUDY
Major Field: Chemistry
vii
TABLE OF CONTENTS
Page
Abstract. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .v
Vita . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vi
List of Tables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
Chapters:
1.
Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.1 Combustion Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
1.1.1 Low Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
1.1.2 High Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 PAH and Soot Formation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 Atmospheric Chemistry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .17
2.
Computational Study of the Oxygen Initiated Decomposition of 2-Oxepinoxy
Radical: A Key Intermediate in the Oxidation of Benzene. . . . . . . . . . . . . . . . . .20
2.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
2.2 Computational Details. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
2.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
2.3.1. Oxygen Addition to 2-Oxepinoxy Radical. . . . . . . . . . . . . . . . . . . 26
2.3.1.1 2-Addition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
2.3.1.2 4-Addition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
2.3.1.3 6-Addition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
viii
2.3.2 Reaction Mechanism and Products of Peroxyoxepinone (1a, 1b, 1c)
Decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .30
2.3.2.1 2-Peroxyoxepinone Radical (1a). . . . . . . . . . . . . . . . . . . .31
2.3.2.2 4-Peroxyoxepinone Radical (1b) . . . . . . . . . . . . . . . . . . . 36
2.3.2.3 6-Peroxyoxepinone Radical (1c) . . . . . . . . . . . . . . . . . . . 40
2.3.3. Comparison of Decomposition Pathways from 298 K to 1250 K. .44
2.3.4. Comparison of DFT energetics. . . . . . . . . . . . . . . . . . . . . . . . . . . .62
2.4 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .66
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .67
3.
Theoretical Determinations of the Ambient Conformational Distribution and
Unimolecular Decomposition of n-Propylperoxy Radical. . . . . . . . . . . . . . . . . . 70
3.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
3.2 Computational Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .76
3.3 Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.4. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .101
4.
Study of Substituent Effects on the Bond Dissociation Enthalpies and Hydroxyl
Radical Reactions of Ethenes and Benzenes. . . . . . . . . . . . . . . . . . . . . . . . . . . .106
4.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106
4.2 Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
4.3. Bond Dissociation Enthalpies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
4.3.1. Substituted Ethenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .111
4.3.2. Substituted Benzenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
4.4. Hydroxyl Radical Addition Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
4.4.1. Substituted Ethenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .119
4.4.2. Substituted Benzenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
4.5 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .130
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .132
5.
DFT Study of the Reactions of H and OH Radicals with Polycyclic Aromatic
Hydrocarbons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136
5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .136
5.2 Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .139
5.3 Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3.1 Bond Dissociation Energies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .141
5.3.2 Reactions with H and OH Radicals. . . . . . . . . . . . . . . . . . . . . . . . 145
5.3.2.1 Radical Additions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
5.3.2.2 H-atom Abstractions. . . . . . . . . . . . . . . . . . . . . . . . . . . .156
5.4 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .157
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .159
ix
6.
Ab Initio and DFT Study of the Atmospheric Reactions of Acrolein with
Hydroxyl Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163
6.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163
6.2. Computational and Theoretical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . .167
6.3. Results and Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .169
6.3.1. Potential Energy Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .174
6.3.2. Rate Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .181
6.4. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .190
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
7.
Computational Study of the Hydrogen-Atom Abstraction Reactions of Ethers by
Hydroxyl Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .196
7.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .196
7.2 Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .200
7.3 Potential Energy Surfaces. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .204
7.3.1 DME + OH Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
7.3.2 THF + OH Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .208
7.4 Rate Calculations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .215
7.4.1 DME + OH Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
7.4.2 THF + OH Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .219
7.5 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .224
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .227
List of References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
x
LIST OF TABLES
Table
Page
2.1
Relative Gibbs free energies for all intermediates and transition states (298 to
1250 K) at the B3LYP/6-311+G**//B3LYP/6-31G* level related to 1a
decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
2.2
Relative Gibbs free energies for all intermediates and transition states (298 to
1250 K) at the B3LYP/6-311+G**//B3LYP/6-31G* level related to 1b
decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
2.3
Relative Gibbs free energies for all intermediates and transition states (298 to
1250 K) at the B3LYP/6-311+G**//B3LYP/6-31G* level related to 1c
decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
2.4
Relative energies (kcal/mol) of selected intermediates at the B3LYP/6311+G**//B3LYP/6-31G* and CBS-QB3 levels. . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1
CBS-QB3 energies (ΔH (0 K), Δ H (298 K) and Δ G (298 K) relative to npropylperoxy radical) for species involved in possible unimolecular
decomposition pathways of n-propylperoxyl radical. . . . . . . . . . . . . . . . . . . . . . .80
3.2
B3LYP/6-31+G** energies (ΔH(0 K), ΔH(298 K) and ΔG(298 K) relative to npropylperoxy radical) for species involved in possible unimolecular
decomposition pathways of n-propylperoxyl radical. . . . . . . . . . . . . . . . . . . . . . .81
3.3
mPW1K/6-31+G** energies (ΔH(0 K), ΔH(298 K) and ΔG(298 K) relative to npropylperoxy radical) for species involved in possible unimolecular
decomposition pathways of n-propylperoxyl radical. . . . . . . . . . . . . . . . . . . . . . 82
3.4
Comparison of B3LYP, mPW1K, and CBS-QB3 alkylperoxy radical R–OO
bond dissociation energies (ΔH (298 K), kcal/mol) to experimentally derived
values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
xi
3.5
Boltzmann distributions for each of the five rotamers at the CBS-QB3,
B3LYP/6-31+G** and mPW1K/6-31+G** levels with the relative free energies
(ΔG (298 K), kcal/mol) and rotamer degeneracy. . . . . . . . . . . . . . . . . . . . . . . . .87
3.6
Energies, ΔH(0 K) kcal/mol, for each barrier and reaction step relative to the
reactant for that step at the CBS-QB3, B3LYP/6-31+G** and mPW1K/6-31+G**
levels and available theoretical literature values. . . . . . . . . . . . . . . . . . . . . . . . . 89
3.7
Thermodynamic values, ΔH≠ (298 K) and ΔG≠ (298 K) kcal/mol, at the B3LYP/631+G** level relative to n-propylperoxy radical (gG) for the transition states
involving 1,4-H transfer treating internal rotors and frequencies as both harmonic
and anharmonic oscillators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.1
Summary of Bond Dissociation enthalpies (BDEs, ΔH(298 K) kcal/mol), Spin
Densities (Populations), and AIM Substituent Charges for mono-Substituted
Ethenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .113
4.2
Summary of Bond Dissociation Enthalpies (BDEs, ΔH(298 K) kcal/mol), Spin
Densities (Populations), and AIM Substituent Charges for mono-Substituted
Benzenes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .117
4.3
Summary of Hydroxyl Radical Addition to mono-Substituted Ethenes Reaction
Barrier Heights, Reaction Energies (ΔH(298 K), kcal/mol), and Ionization
Energies (ΔH(0 K), kcal/mol) at the BH&HLYP/6-31+G** level. . . . . . . . . . . 121
4.4
Summary of Hydroxyl Radical Addition to mono-Substituted Benzenes Reaction
Barrier Heights, Reaction Energies (ΔH(298 K), kcal/mol), and Ionization
Energies (ΔH(0 K), kcal/mol) at the BH&HLYP/6-31+G** level. . . . . . . . . . .126
5.1
List of homolytic C–H bond dissociation energies (ΔH298, kcal/mol) for the PAHs
shown in Figure 5.2. See text for the limited experimental values. . . . . . . . . . . 144
5.2
List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to reactants
at infinite separation) for the addition and H-atom abstraction reactions for
naphthalene with hydrogen atom and hydroxyl radical. . . . . . . . . . . . . . . . . . . .146
5.3
List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to reactants
at infinite separation) for the addition and H-atom abstraction reactions for
anthracene with hydrogen atom and hydroxyl radical. . . . . . . . . . . . . . . . . . . . .147
5.4
List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to reactants
at infinite separation) for the addition and H-atom abstraction reactions for
phenanthrene with hydrogen atom and hydroxyl radical. . . . . . . . . . . . . . . . . . .148
xii
5.5
List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to reactants
at infinite separation) for the addition and H-atom abstraction reactions for 4Hcyclopenta[d,e,f]phenanthrene with hydrogen atom and hydroxyl radical. . . . . 149
5.6
List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to reactants
at infinite separation) for the addition and H-atom abstraction reactions for
benzo[g,h,i]fluoranthene with hydrogen atom and hydroxyl radical. . . . . . . . . .150
5.7
List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to reactants
at infinite separation) for the addition and H-atom abstraction reactions for
benzo[c]phenanthrene with hydrogen atom and hydroxyl radical. . . . . . . . . . . .151
5.8
List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to reactants
at infinite separation) for the addition and H-atom abstraction reactions for
corannulene with hydrogen atom and hydroxyl radical. . . . . . . . . . . . . . . . . . . .152
6.1
Relative energies (ΔH0, kcal/mol) for the stationary points on the energy surface
for aldehydic H–atom abstraction and C=C addition reactions of E–acrolein and
OH radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
6.2
The total rate coefficients for the reaction of acrolein with hydroxyl radical at
each level of theory and for experiment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 180
7.1
Relative Energies (ΔH0‡, kcal/mol) of Stationary Points for the Reaction of
Dimethyl Ether and Hydroxyl Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
7.2
Relative Energies (ΔH, 0 K kcal/mol) of Stationary Points for the Reaction of
THF (THF-d8) and Hydroxyl Radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
7.3
Total TST/Eckart rate coefficients (cm3 molecule–1 s–1) for the DME + OH
reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .217
7.4
Total TST/Eckart and experimental rate coefficients (molecules cm–3 s–1) for the
THF + OH reaction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .221
xiii
LIST OF FIGURES
Figure
Page
1.1
Examples of radicals for sp3, sp2, and sp hybridized carbon centers of methyl,
ethenyl, and acetylenyl radicals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
1.2
Mechanisms for small radical aggregation that yield the seed benzene leading to
PAH formation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . 10
1.3
Reaction scheme for the successive addition of acetylene to phenyl radical to
yield PAH (naphthalene). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.4
General reaction scheme for the atmospheric degradation of an alkane VOC. . . 14
2.1
Reaction scheme for the generation of 2-oxepinoxy radical (1). Energies are at the
B3LYP/6-311+G**//B3LYP/6-31G* level ΔG(298 K) relative to phenylperoxy
radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
2.2
Reaction scheme for the addition of molecular oxygen (3Σg) to 2-oxepinoxy
radical (1). Free energies (298 K) are at the B3LYP/6-311+G**//B3LYP/6-31G*
level, relative to O2 and 2-oxepinoxy radical at infinite separation . . . . . . . . . . . 28
2.3
Unimolecular decomposition pathways of 2-peroxyoxepinone radical (1a). The
relative free energies (kcal/mol, 298 K) at the B3LYP/6-311+G**//B3LYP/631G* level are shown for each intermediate relative to 1 (Figure 2.2), and each
free energy of activation is relative to the reactant for that specific step. . . . . . . 32
2.4
Unimolecular decomposition pathways of 4-peroxyoxepinone radical (1b). The
relative free energies (kcal/mol, 298 K) at the B3LYP/6-311+G**//B3LYP/631G* level are shown for each intermediate relative to 1 (Figure 2.2), and each
free energy of activation is relative to the reactant for that specific step. . . . . . . 37
xiv
2.5
Unimolecular decomposition pathways of 6-peroxyoxepinone radical (1c). The
relative free energies (kcal/mol, 298 K) at the B3LYP/6-311+G**//B3LYP/631G* level are shown for each intermediate relative to 1 (Figure 2.2), and each
free energy of activation is relative to the reactant for that specific step. . . . . . .41
2.6
Unimolecular decomposition pathways of 2-peroxy-oxepinone radical (1a) from
298 (a), 500 (b), 750 (c), 1000 (d), and 1250 (e) K using the mechanistic
pathways shown in Figure 2.3. The relative Gibbs free energies at the B3LYP/6311+G**//B3LYP/6-31G* level are shown relative to 2-oxepinoxy radical and
O2(3Σg) at infinite separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
2.7
Unimolecular decomposition pathways of 4-peroxy-oxepinone radical (1b) from
298 (a), 500 (b), 750 (c), 1000 (d), and 1250 (e) K using the mechanistic
pathways shown in Figure 2.4. The relative Gibbs free energies at the B3LYP/6311+G**//B3LYP/6-31G* level are shown relative to 2-oxepinoxy radical and
O2(3Σg) at infinite separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.8
Unimolecular decomposition pathways of 6-peroxy-oxepinone radical (1c) from
298 (a), 500 (b), 750 (c), 1000 (d), and 1250 (e) K using the mechanistic
pathways shown in Figure 2.5. The relative Gibbs free energies at the B3LYP/6311+G**//B3LYP/6-31G* level are shown relative to 2-oxepinoxy radical and
O2(3Σg) at infinite separation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.9
Potential energy surfaces (Δ H, kcal/mol at 0 K) at the B3LYP/6311+G**//B3LYP/6-31G* and CBS-QB3 (parentheses) levels for the lowest
energy pathway for the oxygen initiated decomposition of 2-oxepinoxy radical
(1). The energies for each intermediate are relative to 1 and each barrier is relative
to the reactant for that specific step. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
3.1
Potential initiation mechanisms for the unimolecular decomposition of npropylperoxy radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.2
Potential energy diagram (ΔH298, kcal/mol) at the CBS-QB3 level for the
formation and unimolecular decomposition of n-propylperoxy radical. . . . . . . . 79
3.3
Five possible rotamers of n-propylperoxy radical. . . . . . . . . . . . . . . . . . . . . . . . .86
3.4
Energies, ΔH(298 K) kcal/mol, and typical structures for the transition states
involved in the initiation of unimolecular decomposition of n-propylperoxy
radical. The B3LYP/6-31+G** (top), mPW1K/6-31+G** (middle), and
CBS-QB3 (bottom) relative energies are provided for the respective stationary
points. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .90
3.5
Schematic representation of the possible mechanisms for unimolecular
decomposition for Q(1,5p)OOH and Q(1,4s)OOH. . . . . . . . . . . . . . . . . . . . . . . .91
xv
4.1
Correlation plots for cis C–H BDEs of mono-substituted ethenes verses AIM
charge on the substituent of the parent ethene. All conformations considered (top)
and with syn orientations removed (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . .114
4.2
Correlation plots for the ortho B3LYP/6-311++G**//B3LYP/6-31G* C–H BDEs
of the mono-substituted benzenes verses AIM charge on the substituent of the
parent benzene. All conformations are considered (top) and with syn orientations
omitted (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .118
4.3
BH&HLYP/6-31+G** transition state structures for OH radical addition to the βcarbons of some mono-substituted ethenes. When applicable, the syn-oriented
substituent is on top. Distances are given in angstroms. . . . . . . . . . . . . . . . . . . .122
4.4
Plot correlating the BH&HLYP/6-31+G** barrier heights for OH radical addition
to the β-carbon (top) and α-carbon (bottom) of the mono-substituted ethenes with
the calculated ionization energies of the ethene precursor. . . . . . . . . . . . . . . . . 123
4.5
BH&HLYP/6-31+G** transition state structures for OH radical addition to the
ortho positions of some mono-substituted benzenes. Distances are given in
angstroms and dihedral angles given in degrees. . . . . . . . . . . . . . . . . . . . . . . . .127
4.6
Plots correlating the barrier heights for OH radical addition to mono-substituted
ethenes with ionization energies. Ortho addition (top) and para addition (bottom).
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .128
4.7
Plots correlating the barrier heights for OH radical addition to mono-substituted
benzenes with the calculated ionization energy. Meta addition (top) and ipso
addition (bottom). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .129
5.1
Reaction scheme for the successive addition of acetylene to phenyl radical to
yield a PAH (naphthalene). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .137
5.2
Structures and relevant carbon labels for the polycyclic aromatic hydrocarbons
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .140
6.1
Potential energy diagram (ΔH0, kcal/mol) for the aldehydic and vinyl H–atom
abstraction and C=C addition reactions of E–acrolein and OH radical based on the
mPW1K/6–311G** energies. See Figures 6.2 and 6.3 for the structures. . . . . . 171
6.2
Structures for each of the stationary points in Figure 6.1 along with select
geometric parameters. The parameters are listed according to mPW1K/6–311G**
(top), BH&HLYP/6–311G** (second), MP2/6–311++G** (third),
QCISD/6–31G** (fourth), and QCISD/6–311G** (fifth). Distances are provided
in angstrom (Å) and torsion angles in degrees. . . . . . . . . . . . . . . . . . . . . . . . . . 173
xvi
6.3
Structures for the transition states and radical products of the vinylic H–atom
abstraction reactions of E –acrolein and hydroxyl radical at the
mPW1K/6–311G** level. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
6.4
Arrhenius plots of the total theoretical TST rate coefficients for the reaction of
E–acrolein with OH radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
6.5
Plot of the branching ratios for the aldehydic H–abstraction and OH addition
mechanisms contribution to the total rate coefficients for the reaction of
E–acrolein with OH radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
6.6
Minimum energy pathways (MEPs) for the aldehydic H–abstraction reaction of
E–acrolein and OH radical. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
7.1.
Structures and parameters (bond lengths in angstrom and bond angles in degrees)
for reactants and products involved in the hydrogen-atom abstraction of dimethyl
ether (DME) and tetrahydrofuran (THF) by hydroxyl radical at the B3LYP/631G* (top), MP2/6-31G* (middle), and mPW1K/6-31+G** (bottom) levels. . 203
7.2.
Structures and parameters (bond lengths in angstrom and imaginary vibrational
frequencies in cm–1) for intermediates involved in the hydrogen-atom abstraction
of dimethyl ether by hydroxyl radical at the B3LYP/6-31G* (top), MP2/6-31G*
(middle), and mPW1K/6-31+G** (bottom) levels. . . . . . . . . . . . . . . . . . . . . . . 206
7.3.
Structures and parameters (bond lengths in angstrom and imaginary vibrational
frequencies in cm-1) for intermediates involved in the hydrogen-atom abstraction
of THF by hydroxyl radical at the B3LYP/6-31G* (top), MP2/6-31G* (middle),
and mPW1K/6-31+G** (bottom) levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .210
7.4.
Pseudorotational itinerary for tetrahydrofuran (THF). . . . . . . . . . . . . . . . . . . . .211
7.5.
Arrhenius plots of the TST/Eckart and literature rate coefficients between 200 and
2000 K for the H-atom abstraction reaction of DME + OH radical . . . . . . . . . .218
7.6.
Arrhenius plots of the TST/Eckart and experimental rate coefficients between 200
and 2000 K for the H-atom abstraction reaction of THF (THF-d8) + OH radical
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
xvii
CHAPTER 1
INTRODUCTION
Combustion and atmospheric chemistry processes comprise the primary focus of
this dissertation. The quality of human life is greatly affected by the chemistry of our
environment, yet there is still an extraordinary amount of information still to be learned
in this area. A primary source for our incomplete understanding of these processes is their
immense complexity. Current methods for studying combustion and atmospheric
processes include elaborate modeling schemes that depend on the knowledge of a large
number of individual chemical reaction rates and thermodynamics. Experimental
techniques are capable of providing accurate chemical reaction rates, thermodynamics
and product distributions. However, often times, experimental results are conflicting,
thereby creating significant doubts in the accuracy of the data. In addition, even the best
of experimental techniques typically do not provide a detailed mechanistic picture of a
chemical reaction. With the significant gains in computer hardware and software
development in the past decade, it is now possible for chemists to obtain a detailed
quantum mechanical picture of the potential energy surfaces for complex chemical
reactions. Computational chemistry along with theoretical chemical methods provides a
powerful means to complement experimental data. These theoretical tools are also the
1
means used in this work to study systems relevant to combustion and atmospheric
chemistry.
The areas of combustion and atmospheric chemistry are intimately connected.
Oxidation (combustion) of fossil fuels and their derivatives converts chemical energy into
heat energy that can be used, for example, to power electrical generators and
automobiles. Under ideal conditions, the combustion of a hydrocarbon-based fuel will
consume oxygen molecules and produce carbon dioxide and water. For example, the
combustion of methane consumes two oxygen molecules and yields one CO2 and two
water molecules.
CH4 + 2 O2  CO2 + 2 H2O
However, to extract the maximum utility from the chemical energy of the fuel, the
ideality of the combustion system is compromised in order to maximize power
production. Typical fuels contain a variety of aromatic and alkane combinations, and
incomplete fuel combustion in power-producing systems and their by-products are
emitted into the atmosphere.1,2,3 Emission from fossil fuel and gasoline power-producing
systems contain volatile organic compounds (VOCs); these sources are known as
anthropogenic (man-made) sources of VOCs. These anthropogenic VOC sources can
reach significant levels in highly developed regions, resulting in regionally localized
photochemical smog and high ozone levels. VOCs with low atmospheric reactivity can
potentially diffuse significant distances within the troposphere, incorporate into
atmospheric aerosols, or undergo wet and dry deposition. Clearly, a thorough
2
understanding of chemical processes in fuel combustion can help increase combustion
efficiency for maximum power generation and minimize VOC emission.
The chemistry in both combustion and atmospheric environments is dominated by
radicals (often called free radicals). Radicals are highly reactive species which contain an
unpaired electron centered on an atom, typically carbon, violating the octet rule. Figure
1.1 shows examples of radicals on the sp3, sp2, and sp hybridized carbons as the radical
centers of methyl, ethenyl, and acetylenyl radicals, respectively.
H2 C
CH3
H
C
H
H
H
HC
CH
H
H
H
sp3
sp2
sp
Figure 1.1. Examples of radicals for sp3, sp2, and sp hybridized carbon centers as the
methyl, ethenyl, and acetylenyl radicals.
Radicals are most commonly formed from homolytic bond scission which can occur via
hydrogen-atom abstraction by other radicals, addition of a radical to an unsaturated
molecule, or unimolecular decomposition. In combustion, radical chemistry is primarily
initiated thermally by providing sufficient heat energy for unimolecular homolytic bond
scission to occur, whereas atmospherically, radical chemistry is initiated as the result of
3
photolytic processes in which high-energy light from the sun is used to break chemical
bonds. In both cases, specific radicals are very important as they constitute the dominant
components of the radical pool, responsible for the interconversion of intermediates.
1.1 Combustion Chemistry
Hydrocarbon combustion is initiated by the oxidation of a fuel molecule
producing a reactive radical species. Initiation within a particular fuel/air mixture
typically results from high-energy collisions with other molecules in the system (M), or
hydrogen-atom abstraction by O2, as expressed in reactions 1.1–1.3:
R–H + M → R• + H• + M*
(1.1)
R–R' + M → R• + R'• + M*
(1.2)
R–H + O2 → R• + HO2•
(1.3)
The particular mechanism responsible for the initiation reaction is strongly dependent on
the fuel’s characteristics as well as temperature and pressure. Reactions 1.1 and 1.2
require considerable temperature and pressure in order to provide sufficient collisional
force and frequency for bond breaking. These reaction mechanisms are dominant at high
temperature when sufficient energy is available for unimolecular homolytic bond
scissions. The particular bond that is broken is primarily dependent on the strength of the
bond. Hydrogen-atom abstraction reactions with O2 (reaction 1.3) are significant in low
and moderate temperature regimes in which insufficient thermal energy is available.
4
Following radical initiation, radical propagation reactions are typically required to
generate a pool of radicals. The larger the radical pool is, then the higher is the
probability that a chain-branching reaction can occur. In a chain-branching reaction, the
number of radical species in the reaction is doubled. It is the rapid increase of highly
reactive radicals in the reaction system that leads to combustion and the rapid flame
propagation.
1.1.1. Low Temperature
Semenov proposed the first general mechanism for low-temperature (~ 600 K or
less) hydrocarbon combustion.4,5 Following initiation via hydrogen-atom abstraction
(reaction 1.3), radical-chain propagation, and chain-branching reactions can proceed as
follows:
R• + O2 → alkene + HO2•
(1.4)
R• + O2 → RO2•
(1.5)
RO2•+ RH → RO2H + R•
(1.6)
RO2• → R'CH(=O) + R"O•
(1.7)
HO2•+ RH → H2O2 + R•
(1.8)
RO2H → RO• + •OH
(1.9)
R'CH(=O) + O2 → R'C•(=O) + HO2•
(1.10)
Reactions 1.4–1.8 are chain-propagating reactions responsible for building and
maintaining the pool of radicals. Reactions 1.9 and 1.10 are chain-branching processes,
5
since in each reaction, the number of radical species becomes doubled. These reactions
cause an exponential increase in the number of radicals in the system and leads to
uncontrolled reactivity and combustion at low temperatures. The persistence of
alkylperoxy (RO2•) radicals (reaction 1.5) at lower temperatures is significant in order for
chain branching to occur, and is both pressure and temperature dependent.5,7 The pressure
dependence results from the energy-rich alkylperoxy radical formed in the O2 addition
step (typically ~25 kcal/mol exothermic), thereby requiring collisional stabilization to
prevent return to reactants and allow later reactions to occur:
R + O2
RO2* + M
RO2 + M*
Products
Thermally, alkylperoxy radicals can become unstable as temperatures approach ~ 600 K,
for which equilibrium favors reactants.6 As temperatures increase further, high
temperature oxidation mechanisms will prevail. One of the most important lowtemperature combustion events is auto-ignition, which in automobiles, can lead to engine
knock resulting in engine damage as well as poor fuel efficiency.7 Chapters 2 and 3 of
this thesis focus on the reactions of some peroxy radicals that are important in the lowtemperature oxidation of benzene and n-propane. In these chapters, the potential energy
surfaces for the possible pathways for the unimolecular decomposition of 2-, 4-, 6peroxyoxepinone (Chapter 2) and n-propylperoxy (Chapter 3) radicals are generated
6
using density functional theory (DFT) and ab initio quantum mechanical methods.
Peroxyoxepinone radicals may be important intermediates in benzene oxidation and npropylperoxy radical are the smallest alkylperoxy radicals which can undergo a facile 6membered ring intramolecular 1,5-H transfer, possibly leading to auto-ignition. Each
pathway is evaluated based on the thermodynamic and kinetic parameters obtained.
1.1.2. High Temperature
Under high-temperature conditions, enough thermal energy is available to allow
chain-branching reactions, which were unavailable at lower temperatures, to occur
without a significant radical pool. After radical generation via initiation, chain-branching
is immediately accessible via subsequent reactions with O2:
H• + O2 → O(3P) + HO•
(1.11)
R• + O2 → O(3P) + RO•
(1.12)
Reaction 1.11 is not accessible at lower temperatures, where instead formation of HO2
radical is preferred. In fact, it is often the competition between reaction 1.11 and the
thermal stability of HO2 radical that determines the line between the high and low
temperature regimes for a particular fuel. The availability of the initial hydrogen atom or
alkyl radical is dependent on the strength of the chemical bonds contained in the fuel
molecule. The aldehydic C–H bond, for example, has a relatively low bond dissociation
energy (~ 87 kcal/mol) and can readily provide the initial H atom. On the other hand,
benzene contains C–H bonds with a bond dissociation energy of 113.5 kcal/mol and
7
require higher temperatures to yield hydrogen atoms. Typical C–H bond strengths in
alkanes range from ~ 90 to 100 kcal/mol, and C–C bond strengths range from ~80 to 90
kcal/mol.
Studying the chemical combustion of even a single component fuel can involve
an immense number of atomic and molecular species reacting via a complex array of
chemical reactions, which is very demanding. Given the chaotic nature of combustion,
turbulence, and the variety of intermediate species involved, there is significant difficulty
in constructing experiments capable of predicting intermediates and products under real
combustion conditions. Several popular methods for analyzing high-temperature
oxidation reaction intermediates and products are shock tubes8 and flow reactors.9 Single
reaction experimental studies are also important for filling in the gaps and providing
high-quality thermodynamic and kinetic data. However, even the best of experimental
techniques typically does not provide a detailed mechanistic picture of a chemical
reaction. Computational quantum chemical methods allow for chemists to obtain a
detailed picture of reaction potential energy surfaces. Computational chemistry along
with theoretical chemical methods provides a powerful means to complement
experimental data.
A very powerful approach for studying combustion is by means of computational
modeling. Computational modeling provides detailed analysis of combustion systems.
Mechanisms are constructed which account for the kinetic and thermodynamic properties
of the important species and reactions for the combustion of a particular fuel.
Furthermore, these data are used to construct a set of differential equations constrained to
a set of conditions, such as detailed mass balance under isothermal, isobaric, isochoric, or
8
adiabatic conditions. Other factors unique to the characteristics of the system being
studied may also be included as constraints. However, reliable solutions require a wealth
of accurate thermodynamic and kinetic information for the suspected species and
chemical reactions involved in the combustion system. The current state of the art
mechanism for modeling natural gas (methane) combustion includes 325 chemical
reactions and 53 atomic and molecular species.10 Fuels containing larger molecular
species can require an exponentially increased amount of thermochemical and kinetic
data. In order to make a problem more tractable, researchers will often determine the
sensitivity of the model toward a species or specific steps of a reaction mechanism and
refine these data. Alternatively, a group of similar species can be assigned the same
thermodynamic and kinetic data (lumping) to greatly reduce a model’s complexity.
1.2 PAH and Soot Formation
One of the more significant classes of compounds emitted from combustion sources
include polycyclic aromatic hydrocarbons (PAHs). PAHs are also known to be the
building blocks for soot generation. Past studies have concluded that 85% of airborne
PAHs are in the form of particles, which are less than 5µm in diameter.11 Particles of this
size can readily be inhaled into the respiratory airways and enter the lungs. PAHs are
known inducers of the CYP1 family of cytochrome P450 enzymes,12,13 and CYP1A2
levels have been identified as biomarkers for PAH exposure and have also provided a
link to increased risk of prostate, breast and bladder cancers.12,13,14
A topic of strong debate is the reaction mechanism responsible for yielding the first
seed benzene molecule in a pyrolytic environment to allow PAH formation.15,16,17,18,19
9
Much of this pioneering work has been based on experimental and modeling studies for
acetylene (HC≡CH) oxidation. Figure 1.2 shows the three foremost mechanisms for the
generation of benzene in an acetylene flame. When acetylene reacts with either 1,2buten-2-yl or 3-acetyl-1-buten-1-yl radicals, unsaturated 6-carbon acyclic radials are
formed which can cyclize to yield benzene. Alternatively, two propargyl radicals can
combine and undergo H-atom transfers, followed by cyclization, to yield benzene.
H
H
C
H
C
C
H
H
C
H
H
H
C
C
C
C
H
C
C
+H
C
C
H
H
H
H
H
C
C
H
C
C
H
H
H
H
C
C
C
C
C
H
C
C
H
H
C
H
H
2 H2C
C
CH
propargyl radical
Figure 1.2. Mechanisms for small radical aggregation that yield the seed benzene leading
to PAH formation.
10
Once benzene is formed, hydrogen abstraction and subsequent reactions with
acetylene are thought to be responsible for continued PAH growth.15,20 In fact, several
intermediates have been isolated in benzene oxidations studies, including
phenylacetylene, vinylbenzene, and naphthalene.21 Frenklach and Wang have delineated a
mechanism for this growth called the H-abstraction-C2H2-addition (HACA)
mechanism.15,22 Figure 1.3 shows the successive acetylene addition steps that occur after
H-atom abstraction from benzene to form naphthalene. Further PAH growth can be
attained via PAH–PAH radical recombination and addition reactions.23 Chapters 4 and 5
of this thesis discuss theoretically determined C–H bond dissociation enthalpies for
mono-substituted ethenes, and benzenes as well as a series of polycyclic aromatic
hydrocarbons. Knowledge of aromatic C–H bond energies can help to predict growth
characteristics for PAHs.
HC
CH
CH
C2H2
+ H
CH
Figure 1.3. Reaction scheme for the successive addition of acetylene to phenyl radical to
yield a PAH (naphthalene).
11
When PAHs grow to molecular weights of 500–1000 amu, they are thought to
begin to take the form of particles. These particles serve as nuclei to facilitate further
particle growth. The particle size increases via the addition of gas-phase molecules to the
particle possibly by radical mechanisms.23 Eventually, these large particles undergo
collisions and stick together in a coagulation phase to form soot.
1.3 Atmospheric Chemistry
Primary volatile organic compounds (VOCs) are emitted into the atmosphere via
anthropogenic and biogenic (natural) sources. The fate and persistence of a VOC is
largely determined by its reactivity with a group of reactive radicals present in the
troposphere (OH, O(3P), O3, and NO3). Hydroxyl radical (OH) is the most significant
tropospheric oxidizer of VOCs and is active during daylight hours, while NO3 radicals,
which are less reactive, predominate at night.24 Hydroxyl radicals result from the
photolysis of ozone (O3) at wavelengths of 350 nm or less.25,26
O3 + hv (λ ≤ 350 nm) → O(1D) + O2
(1.13)
O(1D) + M → O(3P) + M*
(1.14)
O(1D) + H2O → 2 •OH
(1.15)
12
Photolysis of O3 yields O2 and electronically excited O(1D), which can be collisionally
stabilized or react with a water molecule to yield two hydroxyl radicals. Atmospheric
concentrations of hydroxyl radical on a 24-hour seasonal average basis are estimated at
1 x 106 molecules cm–3, while peak daytime measurements of 46 x 106 molecules cm–3
have been made.26,27
Hydroxyl radical reacts with VOCs via either an H-atom abstraction or radical
addition mechanism. The nascent radical is transformed via ensuing reactions with other
abundant atmospheric radicals to yield secondary VOCs in most cases. Figure 1.4 shows
a general reaction scheme for the atmospheric oxidation of an alkane VOC to secondary
products. The scheme is similar for unsaturated molecules, for which hydroxyl radical
addition reactions dominate over H-atom abstraction so as to yield a hydroxy-substituted
alkyl radical. Molecular oxygen, due to high atmospheric concentrations, is the first
species to react with the VOC radical, typically via an addition mechanism to form a
peroxy radical. The persistence of peroxy radicals formed via the radical addition process
is pressure dependent, relying on collisional stabilization by other gas molecules;
otherwise regeneration of reactants is possible.
13
VOC
OH
RCH2 + H2O
O2
products + O2
R'O2
RCH2OO
HO2
RCH2OOH + O2
NO
RCH2ONO2
RCH2O + NO2
β–scission products
(e.g. R + CH2=O)
H-atom shift products
O2
RCHO
Figure 1.4. General reaction scheme for the atmospheric degradation of an alkane VOC.
14
A peroxy radical can react with other peroxy species; however, reaction with
nitric oxide (NO) is most significant when considering atmospheric air quality. Peroxy
radicals are integral components in the processes, leading to the formation of
photochemical smog from anthropogenic VOCs. Peroxy radicals react with NO,
produced from high temperature combustion sources and formed in auto engine exhaust,
in the lower troposphere to produce excess NO2. Photolysis of NO2 produces O(3P) and
regenerates NO. The oxygen atoms then combine with O2 resulting in increased ozone
(O3) concentration according to reactions 1.16 and 1.17:25,28
NO2 + hv (λ < 430 nm)  NO + O(3P)
(1.16)
O(3P) + O2 + M  O3 + M*
(1.17)
In a clean troposphere, ozone instead would react with NO molecules, resulting in no net
generation of ozone.
The other products of the reaction of peroxy radicals with NO are oxy radicals
and molecular nitrates. Oxy radicals react with O2 via abstraction of an H-atom β to the
oxy radical center to yield an aldehyde and a secondary VOC. Furthermore, an oxy
radical can react unimolecularly via β-scission or H-atom shift reactions to form
decomposition or isomerization products, respectively. Alkylnitrates can act as reservoirs
for nitrate radicals, allowing for their transport away from their origin source for later
release. Furthermore, nitrates formed from aldehydic VOCs, which are common
secondary VOCs (Figure 1.4), are peroxyacylnitrates (PANs) which are known to be
15
lachrymators.29
Chapters 4 through 7 are applicable to chemical reactions relevant to atmospheric
oxidation of VOCs by hydroxyl radical. Chapters 4–7 discuss OH radical addition
reactions to mono-substituted ethenes and benzenes as well as a series of PAHs. Chapters
5–7 include H-atom abstraction reactions for the PAHs, acrolein, dimethyl ether, and
tetrahydrofuran. Furthermore, the unimolecular decomposition studies of Chapters 2 and
3 are relevant to the atmospheric decomposition of peroxy radicals.
16
References for Chapter 1
1
Gorches, R.; Olivella, M. A.; de las Heras, F. X. M. Org. Geochem. 2003, 34, 1627.
2
Pankow, J. F.; Luo, W.; Bender, D. A.; Isabelle, L. I.; Hollingsworth, J. S.; Chen, C.;
Asher, W. E.; Zogorski, J. S. Atmos. Environ. 2003, 37, 5023.
3
Heeb, N. V.; Forss, A.-M.; Saxer, C. J.; Wilhelm, P. Atmos. Environ. 2003, 37, 5185.
4
Semenov, N. N. Some Problems in Chemical Kinetics and Reactivity, Chap. 7.
Princeton Univ. Press, Princeton, New Jersey, 1958.
5
Glassman, I. Combustion, Academic Press, San Diego, California, 1996.
6
Benson, S. W. J. Am. Chem. Soc. 1965, 87, 972.
7
Compton, R. G.; Hancock, G. Comprehensive Chemical Kinetics, Low-Temperature
Combustion and Autoignition, Vol. 35 Pilling, M. J., Ed., Elsevier, Amsterdam, 1997.
8
Fujii, N.; Asaba, T. Proc. Combust. Inst. 1973, 14, 433.
9
Venkat, C.; Brezinsky, K.; Glassman, I. Proc. Combust. Inst. 1982, 19, 143.
10
Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.;
Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S.; Gardiner, W. C., Jr.;
Lissianski, V. V.; Qin, Z. http://www.me.berkeley.edu/gri_mech/.
11
Albagli, A.; Oja, H.; Dubois, L. Environ. Lett. 1974, 6, 241.
12
Pavanello, S.; Simioli, P.; Lupi, S.; Gregorio, P.; Clinfero, E. Cancer Epidemiology,
Biomarkers & Prevention 2002, 11, 998.
13
Williams, J. A., Martin, F. L.; Muir, G. H.; Hewer, A.; Grover, P.L.; Phillips, D. H.
Carcinogenesis 2000, 21, 1683-1689.
17
14
WHO (1997) The World Health Report. World Health Organization, Geneva,
Switzerland.
15
Frenklach, M. Phys. Chem. Chem. Phys. 2002, 4, 2028.
16
Bittner, J. D.; Howard, J. B. Proc. Combust. Inst. 1981, 18, 1105.
17
Westmoreland, P. R.; Dean, A. M.; Howard, J. B.; Longwell, J. P. J. Phys. Chem. 1989,
93, 8171.
18
Miller, J. A.; Melius, C. F. Combust. Flame 1992, 91, 21.
19
Melius, C. F.; Colvin, M. E.; Marinov, N. M.; Pitz, W. J.; Senkin, S. M. Proc.
Combust. Inst. 1996, 26, 685.
20
Glassman, I. Combustion, 3rd Ed.; Academic Press, San Diego, CA, 1996.
21
Chai, Y.; Pfefferle, L. D. Fuel, 1998, 77, 313.
22
Frenklach, M.; Wang. H. Proc. Combust. Inst. 1991, 23, 1559.
23
Richter, H.; Howard, J. B. Prog. Energy Combust. Sci. 2000, 26, 565.
24
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Madronich, S.; Moortgat, G. K.; Wallington,
T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the Alkenes, Oxford
University Press, New York, 2000.
25
Finlayson-Pitts, B. J.; Pitts, J. N., Jr. Chemistry of the Upper and Lower Atmosphere:
Theory, Experiments, and Applications; Academic Press, San Diego, California, 2000.
26
Atkinson, R.; Arey, J. Atmos. Environ. 2003, 37 (Supp. 2), S197.
27
George, L. A.; Hard, T. M.; O’Brien, R. J. J. Geophys. Res. 1999, 104, 11643.
28
Wallington, T. J.; Dagaut, P.; Kurylo, M. Chem. Rev. 1992, 92, 667-710.
18
29
Andrew, L. S.; Snyder, R. Casarett and Doull’s Toxicology: The Basic Science of
Poisons; Amdur, O. A.; Doull, J.; Klaassen, D. K. (Eds.), Pergamon Press, New York,
1991.
19
CHAPTER 2
COMPUTATIONAL STUDY OF THE OXYGEN INITIATED DECOMPOSITION OF
2-OXEPINOXY RADICAL: A KEY INTERMEDIATE IN THE OXIDATION OF
BENZENE
This chapter is reproduced with permission from the Journal of Physical Chemistry A
2004, 108, 8419–8433 copyright 2004 American Chemical Society.
2.1. Introduction
For years, chemists have been working toward an understanding of the oxidation
of aromatic compounds. Aromatic compounds are major constituents in various fuels,
including coal and gasoline, thereby consumed by combustion processes to generate
energy for numerous uses.1,2 Benzene, as well as toluene and other mono and dialkyl
benzenes, have been shown to be present in air masses around industrial regions in
significant amounts.1,3 Most of their presence can be attributed to incomplete
decomposition of the fuel during combustion. 3,4 Benzene and benzene derivatives have
also been shown to aggregate into polycyclic aromatic hydrocarbons (PAHs) in pyrolysis
environments. Heavy PAHs, in turn, can act as seeds for the formation of particles of
soot, which leads to poor local and regional air quality and has adverse effects on human
health.5,6 An understanding of the processes involved during the combustion and
20
oxidation of aromatic compounds is necessary in order to control their emission and
influence on air quality.
Due to the prominence of aromatics in fuels, the oxidation of benzene, the most
basic aromatic compound, has been the subject of numerous studies. Experimental
studies using mass spectrometric detection7,8,9,10,11 at high to intermediate temperatures
and various fuel/oxidant ratios indicate that the most common products of benzene
oxidation are CO2, CO, C2H2 (acetylene), cyclopentadienyl radical, and various
unsaturated C2Ox and C3Ox species. The commonly accepted high-temperature
mechanism for the initiation reaction of benzene oxidation with molecular oxygen results
in the generation of phenyl radical and hydroperoxyl radical (eqn. 1.1)7,10 followed by the
addition of molecular oxygen and concomitant or simultaneous loss of oxygen atom (3P)
(eqn. 1.2)7,8,9
C6H6 + O2 → C6H5 + HO2
(1.1)
C6H5 + O2 → C6H5O + O(3P)
(1.2)
Yu and Lin,12 however, successfully performed kinetic studies to determine the rate of
reaction of phenyl radical with O2 using cavity-ring down (CRD) spectroscopy and
detected phenylperoxy radical at temperatures as high as 473 K. Using a flow system to
analyze the reaction of benzene and O2 in a nitrogen diluent at 685 K, Norrish and
Taylor13 predicted that phenylperoxy radical was a probable intermediate by
identification of ortho and para dihydroxybenzenes formed as products.
21
Computational methods have also been utilized in order to determine the most
thermodynamically and kinetically viable mechanistic pathways involved in benzene
oxidation.14,15,16,17,18,19,20 Theoretical studies by this group,15 based on B3LYP/611+G**//B3LYP/6-31G* free energies, predicted that the phenylperoxy radical is the
more thermodynamically favored intermediate, relative to phenoxy radical, at T ≤ ~ 450
K, while at T > 450 K, entropy dominates thereby making phenoxy radical the preferred
intermediate based on free energies. However, kinetic barriers were significant. This
implies that under low temperature combustion and atmospheric conditions, the
phenylperoxy radical is likely to play an important role in the decomposition of phenyl
radical.
Carpenter14 utilized PM3/UHF semiempirical calculations to elucidate possible
decomposition pathways for phenylperoxy radical to form cyclopentadienyl radical and
CO2. He considered a pathway in which phenylperoxy radical rearranges to form a
spirodioxiranyl radical intermediate, with an enthalpic barrier of 26.1 kcal/mol, to form a
thermodynamically stable seven-membered ring radical, 2-oxepinoxy (1), as shown in
Figure 1.1. Barckholtz et.al. and Fadden et. al. have refined Carpenter pathway energies
using density functional theory and high-level ab initio calculations to study this
decomposition process as well as to probe for the formation of a dioxetanyl radical
intermediate leading to the 2-oxepinoxy radical (1).15,16 Decomposition through the
spirodioxiranyl radical was shown to be the most viable reaction path leading to 2oxepinoxy radical, with a free energy barrier of ~41.6 kcal/mol at 298 K, due to the
inclusion of an additional high energy triradical intermediate (Figure 1.1).16 Despite the
inclusion of the high-energy triradical species, the spirodioxiranyl pathway exhibited a
22
lower barrier than that for the formation of phenoxy radical and oxygen atom which has a
free energy barrier of ~51.0 kcal/mol.16 These barriers are rough estimates, however,
because of spin contamination in the wavefunctions of these key intermediates. At the
B3LYP/6-311+G**//B3LYP/6-31G* level, 2-oxepinoxy radical was calculated to have a
ΔG(298 K) energy of −79.9 kcal/mol with respect to infinitely separated phenyl radical
and O2(3Σg) reactants.16 Consistent values were obtained with UMP4(SDQ)/6-31G** and
UCCSD(T)/6-31G** energy calculations in the same study. Mebel and Lin18 in a
theoretical study of C6H5O2 geometrical isomers estimated 2-oxepinoxy radical (1) to
have a ΔH(0 K) of -91.8 kcal/mol, with respect to phenyl radical and molecular oxygen,
based on PUMP3/6-31G*//UHF/6-31G* energies. The stability of 2-oxepinoxy radical
indicates that it should be relatively long-lived after its initial formation and therefore
potentially susceptible to further oxidation by reactive species with appreciable
concentration contained in a typical radical pool.
23
O O
O
O
O
11.3
(-10.5)
27.2
46.2
O
O
(46.1)
22.6
0.0
O
O
O
O
11.1
H
H -0.3
44.8
O
-48.1
(1)
-18.0
Figure 2.1. Reaction scheme for the generation of 2-oxepinoxy radical (1). Energies are
at the B3LYP/6-311+G**//B3LYP/6-31G* level ΔG(298 K) relative to phenylperoxy
radical.
In this study, we utilized the B3LYP hybrid density functional theory method to
analyze the potential energy surface for the decomposition of 2-oxepinoxy radical after
further addition of O2 (3Σg). The energies of stationary points for these decomposition
pathways following the initial formation of 1,2-dioxetanyl, 1,3-peroxy and 1,4-peroxy
intermediates, as well as scission of the O−O peroxy bond and abstraction of an H-atom
by the geminal peroxy moiety were examined. The energies for these surfaces were
evaluated from T = 298-1250 K, the range in which phenylperoxy radical has been shown
to be a viable combustion component in order to determine the viability of these
pathways.
24
2.2. Computational Details
All geometry optimizations, energy and frequency calculations were performed
using Gaussian9821 at the Ohio Supercomputer Center or on our IBM RS/6000
workstations. Stationary points were determined using B3LYP hybrid density functional
theory (DFT) with the 6-31G* basis set.22,23,24 The B3LYP functional has been shown to
evaluate aromatic C−H and other homolytic bond dissociation energies accurately
relative to more expensive high-level ab initio methods with minimal cost and spin
contamination.17,20,25 In general, <S2> values were as expected and typically were 0.75 ≤
<S2> ≤ 0.80, except were noted in the text. Frequency calculations were performed on all
stationary points to confirm the nature of the geometry. Minima were confirmed to have
all real vibrational frequencies. All transition state geometries were confirmed to have a
single imaginary vibrational frequency corresponding to motion along the reaction
coordinate and were further shown to connect the proper reactant and product by
displacement along the transition vector for the imaginary frequency in both the positive
and negative direction (typically 10%), followed by careful optimization using either of
the calcfc or calcall options. Alternatively, intrinsic reaction coordinate (IRC)26
calculations were performed for the more difficult cases. Single-point energy calculations
on each stationary point were calculated at the B3LYP/6-311+G** level with the scf =
tight option. All basis sets for these B3LYP calculations used six Cartesian d functions.
The Thermo9427 program was used to determine the thermal contributions to the
Gibbs free energy in the temperature range from 298-1250 K. (The supporting
information provides all of the enthalpic and free energy corrections at different
temperatures.) All thermal contributions were calculated using unscaled28 harmonic
25
vibrational frequencies and rotational constants derived from the B3LYP/6-31G*
geometries and assuming an ideal gas at 1 atm of pressure, and such assumptions may
create some uncertainty for a true combustion flame All low frequency modes were
treated as harmonic oscillators. Zero-point vibrational energy (ZPE) corrections were
scaled by 0.9806.29 To account for the thermal contribution of the radical species, a factor
of RTln 2 was added to the Thermo94 free energy corrections. All energies discussed in
this paper are Gibbs free energies derived from the B3LYP/6-311+G**//B3LYP/6-31G*
energies and thermal and entropic corrections as stated above, unless otherwise noted.
The CBS-QB330 composite method was used to recalculate the geometries and
energies for the addition of O2 to 2-oxepinoxy radical as well as the most favored
pathway, in order to render a comparison to the energetics of our B3LYP/6311+G**//B3LYP/6-31G* surface.
2.3. Results
2.3.1. Oxygen Addition to 2-Oxepinoxy Radical
The addition of O2 to 2-oxepinoxy radical (1) can occur at three different
positions on the 2-oxepinoxy radical ring, forming three distinctive peroxyoxepinone
radicals (1a, 1b, or 1c, Figure 2.2), due to delocalization of the free electron within the π
network of the ring carbons. Addition of O2 to 1 can occur at the 2−, 4− and 6−ring
carbon positions (see Figure 2.2), numbered relative to the carbonyl carbon as position 1.
moving counterclockwise (1). Also shown in Figure 2.2 are the 298 K free energies
(ΔG(298 K)) for each intermediate and transition state relative to reactants at infinite
26
separation. Each free energy of activation barrier is relative to the reactant for that
individual step.
2.3.1.1. 2-Addition
Three unique transition state (TS) structures for the formation of 2peroxyoxepinone radical (1a) were found. In each transition state, the oxygen molecule
approaches perpendicular to the ring plane and differs in the orientation of the O−O bond
relative to the forming C−O bond. All three TS wavefunctions have considerable spin
contamination, giving 〈S2〉 values of ~ 1.0, rendering the transition state barriers to be
suspect. This level of spin contamination is not surprising since the separated reactants
form a quartet state but the product is a doublet. Regardless, the 298 K free energy barrier
(ΔG‡(298 K)) for the lowest energy TS structure, with the O−O oxygen bond setting
above the C1−C2 ring bond, is 17.7 kcal/mol with an 〈S2〉 value of 0.96, the least spin
contaminated of the three TS wavefunctions. The 298 K reaction is endoergic by 10.4
kcal/mol with a reverse ΔG‡(298 K) of only 7.3 kcal/mol.
27
O
O
O
O
O
17.7
1
2
O2 +
O
O
3
6
4
1a
O
17.5
5
O
1c
9.0
1
0.0
10.4
O
17.0
O
O
O
O
1b
13.2
Figure 2.2. Reaction scheme for the addition of molecular oxygen (3Σg) to 2-oxepinoxy
radical (1). Free energies (298 K) are at the B3LYP/6-311+G**//B3LYP/6-31G* level,
relative to O2 and 2-oxepinoxy radical at infinite separation.
28
2.3.1.2. 4-Addition
Two TS structures were found for addition of oxygen to the 4-carbon to form 4peroxy-oxepinone radical (1b). In both transition structures, the oxygen molecule
approaches perpendicular to the ring plane. In the lower energy TS, the O−O bond adds
anti to the C−H bond at the 4-position while the higher energy structure has the O−O
bond almost eclipsing the C−H bond. Spin contamination for both transition states was
also significant, (〈S2〉 ~ 1.0). The ΔG‡(298 K) for the lowest energy transition structure
was 17.0 kcal/mol. This barrier is the lowest for molecular oxygen addition at either of
the three carbon positions. A simple Hückel MO analysis for the 5-carbon ring π system
for 1 would indicate that most of the electron density should be localized on the
4−carbon, allowing for the relative ease of oxygen addition. Examination of the C−C
bond lengths on the ring are consistent with Hückel theory, as the two C−C bonds
containing the 4-carbon are 1.40 and 1.42 Å, bond lengths intermediate between typical
C–C single and double bond character. The adjacent C−C bonds have lengths of 1.38 and
1.36 Å, exhibiting more pure C=C character. Formation of 1b, however, is endoergic by
13.2 kcal/mol and is the most unstable addition product, due to disruption of resonance
interaction between the double bonds of the π system. Re-crossing back to reactants costs
a mere 3.8 kcal/mol.
2.3.1.3. 6-Addition
Three transition state structures for the formation of 6-peroxy-oxepinone radical
(1c) were also found. Each TS structure has the oxygen molecule approaching
perpendicular to the ring plane and differs only by a rotation of the O−O bond about the
forming C−O bond. All three TS wavefunctions have considerable spin contamination,
29
〈S2〉 values of ~ 1.0, making the TS energies to be suspect. The ΔG‡(298 K) for the lowest
energy TS, with the O−O oxygen bond residing above the C−O ring bond, is 17.5
kcal/mol and with an 〈S2〉 value of 1.1. The reaction is endoergic by 9.0 kcal/mol, making
1c the most stable of the peroxyoxepinone radical species. Return to reactants has a
ΔG‡(298 K) of 8.5 kcal/mol, the largest of the return barriers.
2.3.2. Reaction Mechanism and Products of Peroxyoxepinone (1a, 1b, 1c)
Decomposition
Following the formation of each peroxyoxepinone radical (1a, 1b, 1c),
rearrangement to several isomers leading to decomposition are possible. Five general
rearrangement intermediates have been explored to include the formation of a dioxetanyl
(1,2-peroxy), 1,3-peroxy, 1,4-peroxy, and an abstraction intermediate. Furthermore,
scission of the peroxy O−O bond prior to decomposition was considered. Figures 2.3, 2.4
and 2.5 show the possible decomposition pathways calculated for 1a, 1b and 1c,
respectively. The ΔG(298 K) energies for each intermediate relative to 2-oxepinoxy
radical and O2(3Σg) at infinite separation and ΔG‡(298 K) for each individual step relative
to the reactant(s) for that step at the B3LYP/6-311+G**//B3LYP/6-31G* level are given
in each figure.
30
2.3.2.1. 2-Peroxyoxepinone Radical (1a)
Abstraction by the peroxy group, on 2-peroxyoxepinone, of the hydrogen on the
2-carbon gives 2-hydroperoxyoxepin-1-one-2-yl radical (2a). The abstraction product
(2a) is the most stable of the initial intermediates with an exoergicity of 12.4 kcal/mol
relative to 2-peroxyoxepinone (1a). The barrier to formation of 2a is one of the largest
due to a strained 4-membered ring TS geometry. Facile loss of hydroxyl radical forms
oxepin-1,2-dione (3a). The formation of 3a is exoergic by 25.9 kcal/mol relative to 2a.
The cumulative free energy barrier relative to 1 and O2 is +47.7 kcal/mol. This pathway
leads to a stable, closed-shell species and further decomposition of 3a was not examined.
Isomerization of 2-peroxyoxepinone radical (1a) by addition of the free end of the
peroxy moiety to carbon 3 forms the radical derived from 3,8,9-trioxa-bicyclo[5.2.0]non4-ene-2-one (4a). Scission of the shared ring C−C bond of 4a is followed by O−O bond
breakage to form, in a highly exoergic process, a radical derived from 4-oxo-but-1-enyl
oxoacetate (5a). Breaking the ester carbonyl-oxygen bond of 5a gives 1,4-but-2-enedial
and the 1,2-ethanedial radical (6a). Further decomposition of the 1,2-ethanedial radical
gives formyl radical and carbon monoxide (7a). Completion of this pathway is exoergic
by 45.0 kcal/mol with a total free energy barrier of 44.6 kcal/mol. Alternatively, 5a can
cyclize and form furanyl oxoacetate radical (8a). After two facile bond scissions, this
pathway results in the generation of furan, CO2 and formyl radical (10a). The pathway
from 5a leading to 10a has the same overall free energy barrier as the pathway leading to
7a; however, 5a  8a  9a  10a is much more thermodynamically favored with an
overall exoergicity of −84.9 kcal/mol.
31
O
O
O
O(3P)
O
4.1
O
O(3P)
8.0
+ CO2 +
18a −6.4
O
O(3P) +
7.6
O
O
O
21.0
+
18.7
O
O
25.7
O
O
22a 32.2
O
O
O
O
O
6a −39.5
O
12a 52.7
27a 23.9
14.5
O
O(3P)
4.6
9.1
O O
O
O
O
2.4
O
O
O
O
8a −52.8
+ CO +HCO
7a −45.0
40.8
6.6
O
O
O
0.6
O
13a 52.9
28a −32.9
+ CO2 + HCO
10a −84.9
9a −41.9
+ C2H2
+ CO
O
O
O
O
O
O
CO2 +
+
24a 28.2
25a 58.8
O
O
5a −53.1
CO2 + C2H2 +O(3P) +
+ HCO + O(3P) + CO
19.5
O O
31.0
O
34.6
26a 26.4
22.2
+ O(3P) + CO
21a 30.2
11a 27.0
O
O
23a 50.9
O
O
OO
O
O O
O
15a 6.4
O
O
OH +
O
O
O
O
3a −27.9
16.4
0.3
O(3P)
-0.4
O
O
O O
4a 28.2
+ O(3P) + CO
O
O
22.9
O
19a 58.2
O
2a −2.0
18.6
O
O
20a 28.8
37.3
O
O
O
HO O
35.9
27.8
O
O(3P)
O
1a 10.4
16a 57.0
17a 32.4
11.3
O
O O
O
−0.5
O
O
+ C2H2 + CO2
14a −44.7
Figure 2.3. Unimolecular decomposition pathways of 2-peroxyoxepinone radical (1a).
The relative free energies (kcal/mol, 298 K) at the B3LYP/6-311+G**//B3LYP/6-31G*
level are shown for each intermediate relative to 1 (Figure 2.2), and each free energy of
activation is relative to the reactant for that specific step.
32
2-Peroxyoxepinone radical (1a) can rearrange to form a 1,3-peroxy bicyclic
intermediate by addition of the free end of the peroxy group to carbon 4 resulting in
3,7,8-trioxa-bicyclo[4.2.1]non-4-ene-3-one-9-yl radical (11a). Two pathways for
decomposition of 11a are considered. One is discussed here and shown in Figure 2.3. The
second will be discussed, and shown in Figure 2.4, with relation to 4-peroxyoxepinone
decomposition, since 11a is also formed by rearrangement of 1b. Decomposition of 11a
can result from breaking the bond between a bridge carbon and the 5-carbon leaving a
high energy vinyl radical intermediate (12a). Subsequent loss of C2H2, followed by CO2,
results in CO2, C2H2 and 3-oxopropanal-2-yl radical (14a) as products. The step from 13a
to 14a, corresponding to loss of CO2, is extremely exoergic (~ 98 kcal/mol) and is
possible to be a barrierless reaction, given a ΔG‡(298 K) of only –0.5 kcal/mol for the
step. The overall reaction is exoergic by 44.7 kcal/mol with a free energy of activation of
+61.6 kcal/mol due to the formation of 14a.
Two 1,4-peroxy intermediates can be formed from 1a. The formation of 2,6peroxyoxepinone radical (15a) has a relatively low ΔG‡(298 K) of 18.6 kcal/mol and is
the least endoergic of the peroxy ring intermediates at ΔG(298 K) of only 6.4 kcal/mol.
Decomposition of 15a is discussed in the section for 1c and shown on Figure 2.5, as 6peroxyoxepinone radical also forms the 1,4-peroxy intermediate 15a. Rearrangement to
form 2,5-peroxyoxepinone radical (26a) from 1a is also possible. Scission of the ester
linkage of 26a results in 3-formyl-6-carbonyl-1,2-oxo-cyclohex-4-ene radical (27a).
Upon extrusion of CO from 27a, the O−O ring bond can break resulting in 5-formyl-4oxy-pentenal radical (28a) which can easily lose the formyl group to form 7a. This
33
pathway has an overall ΔG‡(298 K) of 45.9 kcal/mol due to breakage of the ester linkage
to form 27a and a ΔG(298 K) of –45.0 kcal/mol.
The final pathway examined for the decomposition of 2-peroxyoxepinone radical
(1a) involves O−O bond scission and therefore release of an oxygen atom from the
peroxy group to form 2-oxy-oxepinone radical (16a). This reaction is analogous to the
proposed mechanism for formation of phenoxy radical and oxygen atom in the high
temperature reaction between phenyl radical and molecular oxygen. A reliable TS for this
O−O scission step has not been found. First-order saddle points have been located but
each suffers from excess spin-contamination and do not feature a normal coordinate
displacement vector which connects the correct reactant/product pair. However, this 1a to
16a step is highly endoergic, and the TS barrier has to be at least that value.
Rearrangement of 16a by addition of the oxy moiety across the ring to the 6 carbon forms
a bicyclic pyranyl lactone radical (17a). Liberation of CO2 from 17a gives pyranyl
radical, CO2 and oxygen atom (18a) with a total path exoergicity of −6.4 kcal/mol.
Cleavage of the C1−C2 bond of 16a gives the radical derived from 5-oxo-penta-scis-1,3-dien-formate radical (19a). Two pathways for the decomposition of 19a were
considered. Extrusion of CO from 19a results in the radical derived from 5-oxo-2pentenal (20a) which can cyclize (21a) and then extrude formyl radical, thereby forming
furan, CO, formyl radical, and oxygen atom as eventual products (22a). Formation of 22a
is endoergic by 31.8 kcal/mol. Alternatively, isomerization of the dienyl moiety of 19a
from a cis to a trans orientation results in 5-oxo-penta-s-trans-1,3-dien-formate radical
(23a) with a trivial barrier of 0.3 kcal/mol. Extrusion of CO2 from 23a gives 5-oxo-pentas-trans-2,4-dienyl radical (24a), CO2 and oxygen atom. Further decomposition via
34
extrusion of acetylene, from 24a, gives 3-oxo-1-propenyl radical (25a). Decomposition
via this pathway is considerably endoergic at 298 K with a free energy of +58.8 kcal/mol.
The overall activation free energy for reaction is +81.9 kcal/mol due to the loss of CO2
from 23a to 24a. If it is assumed that the addition of O(3P) to 16a, the reverse of O−O
scission, is barrierless, then the ΔG‡(298 K) to form 16a would be ~60 kcal/mol and
would not be the rate-limiting step for pathways passing through 16a.
The rotation of 5-oxo-penta-s-trans-2,4-dienyl radical (24a), resulting in the 5oxo-penta-s-cis-2,4-dienyl radical rotamer, is an intermediate in a previous study by this
group of the unimolecular decomposition of 2-oxepinoxy radical (1).31 Fadden et al.
showed that 5-oxo-penta-s-cis-2,4-dienyl radical can possibly rearrange to form pyranyl
radical and 2-cyclopentenone-1-yl radical as well as decompose to vinyl radical,
acetylene and 2 CO molecules. The thermodynamically most favorable products of those
unimolecular “Fadden” pathways is 2-cyclopentenone-1-yl radical with a ΔG(298 K) of
−50.5 kcal/mol relative to the cis isomer of 24a. Pyranyl radical has a ΔG(298 K) of
–38.7 kcal/mol, while the decomposition products have a ΔG(298 K) of +15.4 kcal/mol
relative to the cis isomer of 24a. Formation of all of the “Fadden” products are more
exoergic than formation of 25a via Figure 2.3.
35
2.3.2.2. 4-Peroxyoxepinone Radical (1b)
The pathways considered for the decomposition of 4-peroxyoxepinone (1b) are
given in Figure 2.4. Abstraction of the hydrogen on carbon-4 of 1b gives 4hydroperoxyoxepin-1-one-4-yl radical (2b). Loss of hydroxyl radical forms oxepin-1,4dione (3b) and proceeds without a barrier. The formation of 3b is exoergic at 298 K by
33.3 kcal/mol relative to reactants with an activation barrier of +47.1 kcal/mol, owing to
the strained hydrogen-abstraction TS. This pathway leads to a stable closed-shell species,
and the further decomposition of 3b was not considered.
Addition of the free end of the peroxy moiety of 1b to carbon-5 forms one
possible dioxetanyl intermediate, 3,8,9-trioxa-bicyclo[5.2.0]non-4-en-3-one-2-yl radical
(4b). Scission of the dioxetane’s O−O bond results in the immediate cleavage of the C−C
ring fusion to yield an acyclic radical derived from 2-oxoethyl-4-oxo-butan-2-enoate
(5b). Scission of the C−O bond of the ester linkage leads to 4-oxo-but-3-enal-2-yl radical
and trans-ethanedial (6b). Rotation around C1−C2 bond of 6b results in the formation of
γ-butyrolactonyl radical and trans-ethanedial (7b). The overall pathway is exoergic
having a 298 K free energy of reaction of −67.9 kcal/mol, and an overall ΔG‡(298 K) of
+49.3 kcal/mol, due to the formation of 5b and endoergicity of 4b formation.
36
+
O
O
O
O
O(3P)
13.9
O
O
O 17b 62.6
O 1b 13.2
O
O(3P) +
18b 31.2
O
+ O(3P)
O(3P) +
O
O
O
O
O
O O
O
5b −46.5
O
O
21b 29.5
33.1
O
O
O
7b −67.9
O
C
O
O
O
10b −39.8
−7.6
10.0
O O
CO2 + C2H2 +
O O
+ CO2
+ CO
O
22b 8.2
24b 8.7
O
O
2.4
O
O
+ CO +HCO
7a −45.0
6.6
16b −68.7
32.4
O
14a −44.7
O
CO +
14.4
O
+ C2H2 + CO2
22.9
37.4
12.2
O
O
15b −16.7
14.3
O +
O
9b −41.8
O 8b 35.2
10.0
8.4
O
O
19.3
O
O
24a 28.2
O
C +
O
6b −52.5
O
O
O
14.1
11a 27.0
11.5
CO2 + O(3P) +
18a −6.4
O
OO
O
O O
4b 37.8
O
+ CO2 + O(3P)
29.2
O
13c 21.4
6.7
8.6
O 3b -33.3
O
O
20b 43.1
19b 53.0
O 2b -3.3
OH
33.2
O
OH +
−1.0
O
O
O
33.9
34.2
O
O
O
O
29.7
19.9
27.9
O
O
+ CO
OH
CO +
13b −34.0
O
O
O
O
11b −39.1
14b −53.1
29.4
H
−2.4
O
OH
12b −54.2
23b −32.9
Figure 2.4. Unimolecular decomposition pathways of 4-peroxyoxepinone radical (1b).
The relative free energies (kcal/mol, 298 K) at the B3LYP/6-311+G**//B3LYP/6-31G*
level are shown for each intermediate relative to 1 (Figure 2.2), and each free energy of
activation is relative to the reactant for that specific step.
37
Formation of another dioxetanyl intermediate is possible via the addition of the
free end of the peroxy moiety of 4-peroxyoxepinone radical (1b) to carbon-3 forming
4,8,9-trioxa-bicyclo[5.2.0]non-4-en-3-one-2-yl radical (8b). Cleavage of the C−C fusion
is followed by concomitant breakage of the dioxetane’s O−O bond, in a process with a
ΔG(298 K) of −78 kcal/mol, thereby forming 3-oxo-propenyl 3-oxo-propenoate radical
(9b). Scission of the ester’s C−O linkage results in the formation of two intermediates, 3oxo-propenal and propan-1,3-dial-2-yl radical (10b). Decomposition pathways of both
10b species have been calculated yielding 2-oxo-ethanyl radical, carbon monoxide,
carbon dioxide, and acetylene (16b). The energies listed in Figure 2.4 for these separate
branching paths correspond to that of the intermediate shown and the individual
component of 10b. 3-Oxo-propenal can cyclize to form β-propenolactone (15b) which
can break apart to form acetylene and carbon dioxide. Decomposition of propan-1,3-dial2-yl radical is initiated by bond rotation and a 1,4-hydrogen-atom transfer resulting in 3hydroxy-1-oxo-prop-2-eneyl radical (12b). From 12b, two pathways have been
considered. Bond scission gives CO and 2-hydroxy-ethenyl radical (13b). 2-Hydroxyethenyl radical can undergo a 1,3-hydrogen shift to form 2-oxo-ethanyl radical (16b).
Rearrangement to form the tautomer of 12b (14b) affords a more facile CO extrusion to
give the same products. The overall free energy of activation for this pathway is +49.3
kcal/mol, due to the formation of 9b, and is exoergic by 68.7 kcal/mol.
Two 1,3-peroxy intermediates resulting from the rearrangement of 1b include
11a, which was introduced as an intermediate for 1a decomposition, and 2,7,8-trioxabicyclo[4.2.1]non-4-ene-3-one-9-yl radical (13c), an intermediate also generated by 6peroxyoxepinone radical (1c). One pathway for decomposition of 11a was discussed in
38
the previous section, and a second set will be discussed here. (The decomposition of 13c
will be presented within the discussion of the 6-peroxyoxepinone radical (1c) pathways,
shown in Figure 2.5.) Bond scission of C1−C2 bond of 11a results in the radical derived
from 2-(3H-[1,2]dioxol-3-yl)-vinyl formate (21b). Expulsion of CO has a relatively low
free energy barrier at 298 K of 10 kcal/mol, yielding 22b. Scission of the O−O bond of
22b causes a rearrangement of the carbon backbone of 22b, forming a transitory 2,3diformyl-1-oxy-cyclopropane radical intermediate which undergoes ring opening,
yielding 3,3-diformyl-propanal radical (23b). Facile loss of one of the formyl groups at
the 3-position of 23b gives 1,4-butendial, CO and formyl radical (7a). This pathway has a
ΔG(298 K) of –45.0 kcal/mol. The largest barrier for this pathway results from formation
of 21b from 11a. Instead, if 21b extrudes CO2 as an initial fragmentation, then 24b can
lose acetylene which is followed by ring opening to yield 3-oxo-propenal radical, CO2
and C2H2 (14a). The CO2 extrusion pathway has a similar exoergicity, at 298 K, to the
CO extrusion pathway (ΔG = −44.7 kcal/mol). The largest barrier for this path comes
from CO2 extrusion with a 298 K free energy barrier of +62.4 kcal/mol.
The final pathways calculated for 1b decomposition include the O−O peroxy
bond scission intermediate 17b. Formation of 17b is endoergic at 298 K by +62.6
kcal/mol, and the barrier for O–O bond scission has not been determined since a
legitimate TS has not been found. Further decomposition of 17b can be initiated by attack
at the carbonyl carbon by the oxy moiety causing simultaneous breakage of the C−O ester
linkage resulting in a ring contraction (18b). From 18b, two decomposition pathways
have been examined. If the exocyclic oxygen of 18b adds to the ring carbon α to the
carbonyl carbon, the bicyclic structure 19b is generated, which can easily eliminate CO2
39
to yield pyranyl radical 18a. If the ring C-O bond of 18b is broken, the radical derived
from 1,6-oxo-hex-2,4-en-1-oxy radical (20b) is formed which can easily extrude CO2,
thereby generating 24a. As shown for 2-peroxyoxepinone radical (1a) (Figure 2.2), 24a
can decompose to form C2H2, CO2, O(3P), and 3-oxo-1-propenyl radical (25a). Bond
rotation of 24a allows an intersection with pathways for the unimolecular decomposition
of 2-oxepinoxy,31 as mentioned in the previous section. Neither of the oxygen atom
extrusion products are the most thermodynamically favored at low temperatures.
Formation of pyranyl radical (18a) is exoergic only by −6.4 kcal/mol, and formation of
25a is endoergic by 58.8 kcal/mol. The 298 K free energy barrier for both pathways is at
least 76.5 kcal/mol due to the formation of 18b from 17b.
2.3.2.3. 6-Peroxyoxepinone Radical (1c)
The pathways considered for the decomposition of 6-peroxyoxepinone radical
(1c) are shown in Figure 2.5. Abstraction of the hydrogen on carbon-6 by the terminal
oxygen of the peroxy moiety gives 6-hydroperoxyoxepin-1-one-6-yl radical (2c).
Barrierless fragmentation of hydroxyl radical forms oxepin-1,6-dione (3c). The
formation of 3c is exoergic at 298 K by 41.4 kcal/mol relative to 2-oxepinoxy and oxygen
with a free energy barrier of +46.0 kcal/mol due to the tight H-atom-abstraction TS
geometry. This pathway leads to a stable closed-shell species and further decomposition
steps from 3c were not examined.
40
O
O(3P) +
O
O
17a 32.4
6.6
O(3P) +
O
O
23.2
21.2
5.1
O
+
O(3P)
O
O
O
4c 20.9
O
10c −57.3
O
8.4
O
O
+ CO2
8c −32.4
6.9
5.1
O
O
O O
CO2 +
O
O 6c −21.1
8.4
O
O
+ C 2H 2
+ CO
8.1
O
O
O
OH
18c −59.4
+ C2H2 + CO2
14a −44.7
CO2+ HCO +
7c −35.5
O
21c −86.9
O
+ CO2
O
15c 48.6
18.7
O
30.0
2.8
O
OH
17c −47.9
22.4
O
O
O
14c 46.6
21.0
12.6
23c −16.4
9c −35.5
O
O
O
O
20c −88.3
O
O
5c −12.9
+ CO2 + C2H2
+ CO2
CO2 +
O
8.2
9.5
O
O O
OO
O
24c −44.0
+ CO2
O
17.5
<S2>=1.0
+ CO2 + C2H2
16c −35.8
13c 21.4
23.7
12.7
O
O
O
15a 6.4
11c −55.1
O
O
9.2
OO
O
O
O O
O
+ CO2 + CO
O
O
3c −41.4
O
O
20b 43.1
14.4
OH +
29.8
17.5
O
O
18a −6.4
O
−1.0
O
2c −6.9 OH
O
O
+ CO2 + O(3P)
O
O
37.0
O
O
1c 9.0
22c 52.1
11.3
O
O
O
O + CO + CO
2
12c −104.5
O
O
10a −84.9
11.7
O
O
+ CO + OH
19c −54.7
Figure 2.5. Unimolecular decomposition pathways of 6-peroxyoxepinone radical (1c).
The relative free energies (kcal/mol, 298 K) at the B3LYP/6-311+G**//B3LYP/6-31G*
level are shown for each intermediate relative to 1 (Figure 2.2), and each free energy of
activation is relative to the reactant for that specific step.
41
Ring closure of 6-peroxyoxepinone radical (1c) by addition of the free end of the
peroxy moiety to carbon-5 forms the 3,8,9-trioxa-bicyclo[5.2.0]non-4-ene-2-one-3-yl
radical (4c). A greater degree of delocalization for the unpaired electron in 4c makes it
the most stable dioxetanyl intermediate considered here. Cleavage of the dioxetane’s
O–O bond leads to the formation of a bicyclic oxiranyl structure, 2-oxy-3,8-dioxabicyclo[5.1.0]oct-5-en-4-one radical (5c). The transition state leading to formation of 5c
from 4c suffers from excess spin contamination (〈S2〉 =1.0), rendering it to be suspect.
Breaking the C−O ester linkage of 5c opens the ring of the oxepinone, while maintaining
the epoxide ring, to give 3-(3-formyl-oxiranyl)-acrylic carboxy radical (6c), which can
easily eliminate CO2 and form 7c. Following two bond rotations, via 8c and 9c, a 1,5hydrogen shift yielding 10c allows for the extrusion of CO to form 1,2-epoxy-3-buten-1yl radical (11c). Facile opening of the epoxide ring gives 1-oxo-3-buten-2-yl radical
along with CO2 and CO (12c). Formation of 12c is extremely exoergic due to the relief of
ring strain and increased delocalization. The overall process is exoergic at 298 K by
−104.5 kcal/mol with an overall 298 K activation free energy of +33.6 kcal/mol relative
to reactants (1), due to the barrier for the 4c  5c transformation. Additionally, expulsion
of acetylene from 7c gives formyl-oxiranyl radical (23c) which can undergo facile ring
opening to form an s-trans isomer of 14a, s-trans-3-oxa-propanal radical (24c).
6-Peroxyoxepinone radical (1c) can undergo ring closure to form a 1,3-peroxy
intermediate by addition of the free end of the peroxy group to carbon-4 to give 2,8,9trioxa-bicyclo[4.2.1]non-4-ene-3-one-9-yl radical (13c). The 1,3-peroxy intermediate
(13c) is also formed, in a similar fashion, from 1b. Bond scission of the C2−C3 bond of
13c results in the radical derived from 3H-[1,2]dioxol-3-yl-acrylate (14c). Loss of C2H2
42
(15c) followed by CO2 results in 3-oxopropanal-2-yl radical (14a). The barrier for loss of
CO2 from 15c  14a is very small. This may be attributed to the exoergicity of the step
which is aided by opening of the ring (ΔG(298 K) = −93.3 kcal/mol). The overall
pathway is exoergic at 298 K by −44.7 kcal/mol with a 298 K free energy of activation of
69.0 kcal/mol due to the barrier to expel C2H2.
Alternatively, upon scission of the C6−O bond on the oxepinone ring of 13c, the
oxygen may form a bond with C5, and the peroxy bond is broken to yield 2-formyl-6keto-3-oxy-1-oxa-cyclohex-4-ene radical (16c). Following an exocyclic 1,4-hydrogen
transfer from the formyl group to the oxy moiety of 16c to generate 17c, CO can be
extruded (18c), allowing for further fragmentation of OH radical, resulting in 2H-pyran2-one (19c). The overall pathway is exoergic at 298 K by 54.7 kcal/mol with a 298 K free
energy of activation of 38.8 kcal/mol due to the formation of the 1,3-peroxy intermediate
(13c).
6-Peroxyoxepinone radical (1c) can also rearrange to form the 1,4-peroxy
intermediate 15a by addition of the free end of the peroxy moiety to carbon-2. This
intermediate is also formed via rearrangement of 2-peroxyoxepinone radical (1a) (Figure
2.3). Loss of CO2 from 15a, by breaking the C6−O oxepinone bond, results in
simultaneous scission of the peroxy O−O bond to give 5-oxo-3-pentenal radical (20c).
Further, decomposition of 20c can proceed by the same mechanism as that for
decomposition from 20a to 22a (cyclization followed by formyl extrusion, 20c to 10a,
Figure 2.3). Unlike the 20a to 22a steps, however, the 20c to 10a intermediates have a
thermodynamically favorable 298 K free energy relative to 2-oxepinoxy radical and
oxygen. This pathway is highly exoergic at 298 K at –84.9 kcal/mol with a 298 K free
43
energy barrier of 26.5 kcal/mol resulting from the formation of 15a. This pathway has the
lowest 298 K free energy barrier of all examined steps.
The final pathways examined for the decomposition of 6-peroxyoxepinone radical
(1c) involve the release of an oxygen atom from the peroxy group to form 6-oxyoxepinone radical (22c). From 22c, two possible pathways have been calculated.
Rearrangement, by addition of the oxy moiety to carbon-2, results in 17a which can then
form pyranyl radical upon loss of the bridging CO2 (18a). The second possible pathway
for 22c decomposition involves scission of the C6−O bond to provide 1,6-oxo-hex-2,4en-1-oxy radical (20b). After expulsion of CO2 from 20b, 24a is formed, providing
another intersection with a 2-peroxyoxepinone radical (1a) process (Figure 2.3), which
has CO2, C2H2, O(3P) and 3-oxo-1-propen-1-yl radical (25a) as products.
2.3.3. Comparison of Decomposition Pathways from 298 K to 1250 K
To contrast all of the proposed decomposition pathways (Figures 2.3–2.5) as a
function of temperature, the free energies profiles for all intermediates and transition
states in each pathway at 298, 500, 750, 1000, and 1250 K have been plotted and are
shown in Figures 2.6–2.8 for the decomposition of 1a, 1b and 1c, respectively.
Additionally, the bottom-of-the-well electronic energies and Gibbs free energies at 298,
500, 750, 1000, and 1250 K for all intermediates and transition states, relative to 1, as
well as the 〈S2〉 value, point group, electronic state, and number of imaginary vibrational
frequencies are listed in Tables 2.1−2.3 for decomposition of 1a, 1b and 1c, respectively.
44
(a)
100
4a
75
Free Energy (kcal/mol), 298 K
12a
13a
23a
20a
25
0
19a
16a
50
26a
1
21a
17a
15a 11a
1a
22a
24a
27a
2a
25a
18a
-25
28a
3a
9a
6a
-50
5a
7a 14a
8a
-75
10a
-100
-125
-150
100
(b)
75
Free Energy (kcal/mol), 500 K
50
26a
1a
17a
1
22a
24a
20a
2a
25a
21a
27a
15a 11a
18a
-25
-50
13a
23a
4a
25
0
12a
19a
16a
3a
28a
6a
5a
8a
9a
7a 14a
-75
10a
-100
-125
-150
Continued
Figure 2.6. Unimolecular decomposition pathways of 2-peroxy-oxepinone radical (1a)
from 298 (a), 500 (b), 750 (c), 1000 (d), and 1250 (e) K using the mechanistic pathways
shown in Figure 2.3. The relative Gibbs free energies at the B3LYP/
6-311+G**//B3LYP/6-31G* level are shown relative to 2-oxepinoxy radical and O2(3Σg)
at infinite separation.
45
Figure 2.6. continued
(c)
100
75
4a 19a
12a
16a
50
Free Energy (kcal/mol), 750 K
26a 11a
25
0
15a
1a
13a
23a
17a
27a
25a
21a
2a
20a
24a
1
22a
3a
-25
18a
5a
-50
28a
9a
8a
6a
-75
7a
14a
-100
10a
-125
-150
100
(d)
11a
12a
75
4a
Free Energy (kcal/mol), 1000 K
50
26a
1a
25
0
-25
19a
15a 17a
16a
27a
2a
21a
20a
25a
24a
1
8a
3a
18a
5a
-50
13a
23a
28a
22a
9a
6a
-75
7a
14a
-100
10a
-125
-150
Continued
46
Figure 2.6. continued
100
(e)
4a 11a
12a
75
19a
26a
15a
16a
50
Free Energy (kcal/mol), 1250 K
1a
27a
13a
23a
2a
25
17a
0
21a
1
28a
-25
3a
5a
18a
24a
8a
-50
6a
20a
25a
22a
9a
-75
-100
-125
oxygen addition
hydroperoxy
dioxetanyl
1,3-peroxy
1,4-peroxy A
1,4-peroxy B
7a
14a
10a
oxy
-150
47
100
(a)
4b
75
17b
19b
8b
50
Free Energy (kcal/mol), 298 K
25c
25
0
1b
1
11a
13c
18b
24a
21b
22b 24b
2b
18a
15b
-25
10b
3b
9b
-50
5b
23b
6b
11b
-75
7a
13b
12b
14b
14a
7b
16b
-100
-125
-150
100
(b)
4b
75
17b
8b
19b
Free Energy (kcal/mol), 500 K
50
11a
13c 18b
25
21b
25c
1b
0
-25
-50
1
24a
22b
2b
24b 18a
3b
15b
23b
9b
5b
10b
6b
-75
14a
11b
7a
13b
12b
14b
7b
16b
-100
-125
-150
Continued
Figure 2.7. Unimolecular decomposition pathways of 4-peroxy-oxepinone radical (1b)
from 298 (a), 500 (b), 750 (c), 1000 (d), and 1250 (e) K using the mechanistic pathways
shown in Figure 2.4. The relative Gibbs free energies at the B3LYP/
6-311+G**//B3LYP/6-31G* level are shown relative to 2-oxepinoxy radical and O2(3Σg)
at infinite separation.
48
Figure 2.7. continued
100
(c)
75
4b
17b
8b
19b
Free Energy (kcal/mol), 750 K
50
11a
13c
25
1b
18b
22b
2b
0
24a
21b 25c
1
24b
9b
-25
18a
23b
3b 5b
-50
15b
12b
10b
6b
-75
11b
14a
7b
7a
13b
14b
-100
16b
-125
-150
100
(d)
4b
8b
75
19b
Free Energy (kcal/mol), 1000 K
50
17b 13c
1b
25
11a
21b
25c
18b
2b
0
-25
1
22b
3b
-50
-75
24a
24b
9b
18a
23b
5b
10b
15b
7b
6b
11b
14a
14b
12b
13b
7a
-100
-125
16b
-150
Continued
49
Figure 2.7. continued
100
8b
(e)
21b
75
4b
17b 13c
50
Free Energy (kcal/mol), 1250 K
1b
25
0
11a
19b
18b
25c
2b
1
22b
9b
-25
24b
5b
18a 23b
3b
-50
24a
15b
10b
14b
6b
-75
14a
-100
-125
-150
11b
7b
oxygen addition
hydroperoxy
dioxetanyl A
dioxetanyl B
1,3-peroxy A
1,3-peroxy B
oxy
50
12b
13b
7a
16b
(a)
100
75
22c
50
14c
Free Energy (kcal/mol), 298 K
20b
25
1c
0
1
4c 13c
15a
2c
-25
15c
17a 24a
5c
6c
3c
-50
23c
7c
17c
14a
18c
-75
20c
-100
9c
8c
16c
21c
24c
19c
10c
11c
10a
12c
-125
-150
100
(b)
20b
75
22c
Free Energy (kcal/mol), 500 K
50
14c
25
4c 13c
1c
0
1
17a
15c
24a
15a
2c
5c
6c
-25
23c
7c
9c
16c
-50
3c
18c
-75
-100
14a
17c
20c
21c
8c
19c
24c
10c
11c
10a
12c
-125
-150
Continued
Figure 2.8. Unimolecular decomposition pathways of 6-peroxy-oxepinone radical (1c)
from 298 (a), 500 (b), 750 (c), 1000 (d), and 1250 (e) K using the mechanistic pathways
shown in Figure 2.5. The relative Gibbs free energies at the B3LYP/
6-311+G**//B3LYP/6-31G* level are shown relative to 2-oxepinoxy radical and O2(3Σg)
at infinite separation.
51
Figure 2.8 continued
100
75
(c)
13c
22c
14c
50
Free Energy (kcal/mol), 750 K
25
0
1c
15c
17a
4c
15a
2c
24a
5c
1
6c
20b
-25
8c
16c
17c
3c
-50
23c
7c
14a
-75
19c
24c
10c
21c
20c
-100
18c
11c
9c
10a
-125
12c
-150
100
(d)
4c
13c
75
14c
Free Energy (kcal/mol), 1000 K
50
17a
22c
1c
25
2c
0
-25
-50
1
15c
15a
5c
20b
6c
16c 24a
8c
17c
7c
3c
23c
18c
-75
-100
9c
14a
20c
21c
10c
19c
24c
11c
10a
-125
12c
-150
Continued
52
Figure 2.8. continued
100
(e)
4c
13c
75
14c
50
22c
Free Energy (kcal/mol), 1250 K
1c
25
0
1
16c
6c
24a
17c
-125
8c
7c
3c
18c
-75
-100
1,3-peroxy
oxy
15c
5c
-25
-50
hydroperoxy
dioxetanyl
1,4-peroxy
17a
15a
20b
2c
oxygen addition
20c
21c
14a
9c
23c
19c
10c
24c
11c
10a
12c
-150
53
The free energy of activation barriers for the addition of molecular oxygen to 2oxepinoxy radical (1) increase from ~17 kcal/mol at 298 K to ~50 kcal/mol at 1250 K.
The relative ordering of the free energies of activation remains unchanged through this
temperature regime with TS (1-1b) being the lowest energy barrier throughout the
temperature range (Table 2.1). The barrier for formation of either of the peroxyoxepinone
radicals is not the highest point on the free energy surface for any of the proposed
decomposition pathways at any of the temperatures considered. Despite the large barrier
for O2 addition and small endoergicity of formation of each of the peroxyoxepinone
radicals, their free energies are still well below that of phenyl radical and 2 O2(3Σg)
molecules at temperatures < 1250 K due to the large exoergic formation of 2-oxepinoxy
radical (1). The free energy of phenyl radical and two molecular oxygens, relative to 1
and O2, are +80.4, +73.3, +64.7, +56.3, and +48.0 kcal/mol at 298, 500, 750, 1000, and
1250 K, respectively.
Figure 2.6 shows the free energy profiles for the decomposition pathways of 1a.
At 298 K, the unimolecular decomposition of 1a through 15a is the lowest energy
process. The complete free energy profile for decomposition of 15a is shown in Figure
2.8, where 15a also emanates from 1c. Regardless, the free energy barrier for 1a or 1b to
form 15a is the highest point on the energy profile, irrespective of whether the reactant is
1a or 1b. Thermodynamically, furan, CO2 and formyl radical (10a) as products represent
the most exoergic pathway (ΔG(298 K) = −84.9 kcal/mol) formed from the dioxetanyl
intermediate (4a) via 1b  4a  5a  8a  9a  10a. Pathways resulting from the
peroxy O−O bond scission intermediate lie near the top of the 298 K free energy profile
for 1a decomposition. Furthermore, the only exoergic intermediate or product at 298 K is
54
18a starting from the decomposition of 16a. The high-energy profile for decomposition
of 16a can be attributed to the unfavorability of generating free oxygen atom at low
temperatures. Next to the formation of 15a, the lowest profile is through 4a followed by
26a. With increasing temperature through to 1250 K, the free energy profiles for the
rearrangement pathways increase steadily, with the ordering between pathways remaining
generally consistent. The increasing height of the 1a free energy profiles is due to a small
negative value for the entropy of the addition step of molecular oxygen to 2-oxepinoxy
radical (1). In contrast, the free energy profiles for 1a decomposition through 16a remain
approximately constant through the first few steps, after which they become exoergic,
due to an increased influence of entropy, resulting from breaking the peroxy O−O bond
to generate the oxygen atom. At 1250 K, the decomposition pathways through the O−O
scission intermediate 16a have lower overall free energy profiles than those through
rearrangement intermediates. However, the profile through 15a remains the lowest of the
rearrangement profiles. The formation of 10a (furan, CO2 and formyl radical) is the most
stable overall product of 1a decomposition throughout the 298-1250 K temperature
range. Between 500 and 750 K, the free energies for rearrangement and decomposition
through the chosen intermediates start to become uncompetitive with respect to the
energy of phenyl radical and 2 oxygen molecules as well as the “Fadden” pathways for
unimolecular decomposition of 1.31
The free energy profiles for the decomposition pathways of 1b and 1c (Figures
2.7 and 2.8, respectively) are qualitatively similar to those for 1a. At 298 K, the lowest
overall profile for decomposition of 1b is through 11a, resulting in formation of 7a
(Figure 2.7). The highest free energy profile at 298 K is for decomposition through
55
peroxy O−O bond scission (17b). Thermodynamically, 16b products, formed via the
dioxetanyl intermediate 8b, provide the most exoergic pathway for the decomposition of
1b at all temperatures. While the profile trends for 1b are consistent with those of 1a as
the temperature is increased, pathways through 17b become lower in energy and
sufficiently competitive with the other pathways at 1250 K. The lowest overall free
energy pathway at 298 K is for the profile 1c  15a  20c  21c  10a (Figure 2.8)
and remains the lowest profile up to 1250 K, wherein the pathway of 1c  22c  17a 
18a is slightly lower (ΔG‡(1250 K) = 68.6 kcal/mol vs. 69 kcal/mol). The overall most
exoergic pathway at all temperatures corresponds to formation of 12c followed by 10a.
56
Structurea
phenyl + 2(O2)
1d
TS (1-1a)
1a
TS (1a-2a)
2a
TS (2a-3a)
3ae
TS (1a-4a)
4a
TS (4a-5a)
5a
TS (5a-6a)
6a
TS (6a-7a)
7a
TS (5a-8a)
8a
TS (8a-9a)
9af
TS (9a-10a)f
10ag
TS (1a-11a)
11a
TS (11a-12a)
12a
TS (12a-13a)
13ah
TS (13a-14a)h
14ai
TS (1a-15a)
15a
TS (1a-16a)
16aj
TS (16a-17a)j
17aj
TS (17a-18a)j
18ak
TS (16a-19a)j
19aj
TS (19a-20a)j
20al
TS (20a-21a)l
21al
TS (21a-22a)l
22am
TS (19a-23a)j
23aj
TS (23a-24a)j
24ak
TS (24a-25a)k
25an
TS (1a-26a)
26a
TS (26a-27a)
27a
TS (27a-28a)
28ao
TS (28a-7a)o
Eb
(hartrees/part)
-532.36918
-532.51741
-532.50807
-532.52289
-532.45727
-532.54115
-532.53925
-532.56069
-532.48181
-532.49525
-532.46631
-532.61728
-532.57070
-532.57062
-532.55145
-532.55835
-532.58376
-532.62024
-532.60612
-532.58120
-532.57821
-532.63164
-532.46386
-532.49746
-532.43741
-532.44987
-532.42110
-532.39614
-532.39573
-532.53108
-532.49401
-532.53186
p
-532.40029
-532.39419
-532.44296
-532.42239
-532.48249
-532.38418
-532.39411
-532.37773
-532.41811
-532.38547
-532.41807
-532.38567
-532.39388
-532.39262
-532.40440
-532.35038
-532.42135
-532.34789
-532.31748
-532.48693
-532.49847
-532.46471
-532.49695
-532.48577
-532.56351
-532.55745
ΔG (298 K)
(kcal/mol)
80.4
0.0
17.7
10.4
47.7
-2.0
-2.3
-27.9
36.2
28.2
44.6
-53.1
-27.3
-39.5
-30.4
-45.0
-30.9
-52.8
-46.3
-41.9
-41.3
-84.9
46.3
27.0
61.6
52.7
67.2
52.9
52.3
-44.7
29.0
6.4
ΔG (500 K)
(kcal/mol)
73.3
0.0
25.2
18.4
55.6
5.7
5.1
-27.9
44.9
36.5
53.3
-47.5
-22.8
-42.7
-34.3
-55.0
-23.7
-46.1
-40.2
-42.8
-42.0
-92.3
54.6
35.8
69.7
59.3
72.8
52.1
62.3
-53.4
38.2
15.5
ΔG (750 K)
(kcal/mol)
64.7
0.0
34.4
28.1
65.3
14.9
14.2
-28.0
55.8
46.7
64.0
-40.8
-17.5
-46.7
-39.1
-67.4
-14.9
-37.9
-32.8
-43.8
-42.7
-101.1
64.9
46.5
79.6
67.1
79.4
50.8
65.5
-64.4
49.6
26.7
ΔG (1000 K)
(kcal/mol)
56.3
0.0
43.6
37.6
74.9
23.8
23.2
-28.3
66.7
56.7
74.7
-34.3
-12.2
-50.6
-43.7
-79.5
-6.2
-29.9
-25.4
-44.6
-43.2
-109.8
75.2
57.0
89.3
74.7
85.7
49.3
66.0
-75.3
61.0
37.8
ΔG (1250 K)
(kcal/mol)
48.0
0.0
52.7
47.0
84.4
32.6
32.1
-28.5
77.6
66.6
85.2
-28.0
-7.0
-54.5
-48.2
-91.4
2.5
-22.0
-18.1
-45.5
-43.5
-118.1
85.4
67.4
99.0
82.1
91.9
47.8
66.3
-86.0
72.3
48.6
<S 2>
57.1
61.1
32.4
43.7
-6.4
65.1
58.2
65.8
28.8
49.7
30.2
48.9
32.2
58.4
50.9
81.9
28.2
69.0
58.8
33.2
26.4
45.9
23.9
28.5
-32.9
-30.5
58.3
63.4
34.8
45.9
-12.2
65.9
57.8
65.0
20.9
42.8
23.0
41.5
17.7
58.3
49.8
80.6
20.5
59.5
43.4
42.4
35.1
54.6
30.7
34.8
-34.2
-31.9
59.6
66.2
37.7
48.6
-19.5
66.9
57.0
63.7
10.9
34.1
13.9
32.3
-0.2
58.0
48.2
78.6
11.2
47.8
24.0
53.7
45.8
65.5
38.9
42.4
-36.2
-33.8
60.7
68.9
40.4
51.3
-26.8
67.8
56.1
62.4
0.8
25.5
4.7
23.1
-17.8
57.7
46.5
76.5
1.8
36.1
4.7
65.0
56.3
76.2
46.9
50.0
-38.2
-35.6
61.7
71.6
43.0
54.0
-34.0
68.6
55.0
61.0
-9.3
17.1
-4.5
14.0
-35.3
57.3
44.5
74.4
-7.6
24.5
-14.5
76.2
66.6
86.9
54.8
57.4
-40.2
-37.3
0.75
0.76
0.78
0.96
0.75
0.78
0.78
0.81
0.00
0.78
0.78
0.80
0.78
0.76
0.76
0.76
0.00
0.76
0.77
0.76
0.76
0.75
0.75
0.80
0.75
0.78
0.76
0.77
0.76
0.76
0.78
0.80
0.78
0.77
0.78
0.77
0.78
0.76
0.75
0.78
0.79
0.76
0.77
0.77
0.75
0.76
0.75
0.76
0.77
0.78
0.76
0.77
0.76
0.76
0.75
0.77
0.75
0.76
Other
(PG, ES, Nimag)c
C2V, 2A1,0
C1, 0
C1, 1
C1, 0
C1, 1
C1, 0
C1, 1
C1, 0
C1,1
C1,0
C1,1
C1,0
C1,1
Cs,2A",0; C2,1A,0
C2,1A,0
C1, 0
C1,1
C1, 0
C1,1
C1, 0
C1,1
C2V, 1A1,0
C1,1
C1, 0
C1,1
C1,0
C1,1
C1,0
C1,1
C2V,2B1,0
C1,1
C1,0
C1,0
C1,1
C1,0
C1,1
C2V, 2B1,0
C1,1
C1,0
C1,1
C2,2A,0
C1,1
C1,0
C1,1
C2V,1A1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
Continued
Table 2.1. Relative Gibbs free energies for all intermediates and transition states (298 to 1250
K) at the B3LYP/6-311+G**//B3LYP/6-31G* level related to 1a decomposition.
57
Table 2.1 continued
a
See Figure 2.3 for structures. bBottom-of-the-well energy. cPoint group (PG), Electronic
state (ES), Number of imaginary vibrational frequencies (Nimag). dE and ΔG(T) values
include E and G(T) of O2. eE and ΔG(T) values include E and G(T) of OH. fE and ΔG(T)
values include E and G(T) of furan. gE and ΔG(T) values include E and G(T) of furan,
CO2 and formyl radical. hE and ΔG(T) values include E and G(T) of C2H2. iE and ΔG(T)
values include E and G(T) of CO2 and C2H2. jE and ΔG(T) values include E and G(T) of
O(3P). kE and ΔG(T) values include E and G(T) of CO2 and O(3P). lE and ΔG(T) values
include E and G(T) of CO and O(3P). mE and ΔG(T) values include E and G(T) of furan,
CO, O(3P), and formyl radical. nE and ΔG(T) values include E and G(T) of CO2, O(3P)
and C2H2. oE and ΔG(T) values include E and G(T) of CO. pA reliable transition state was
not found for this process.
58
Structurea
TS (1-1b)
1b
TS (1b-2b)
2b
TS (2b-3b)
3bd
TS (1b-4b)
4b
TS (4b-5b)
5b
TS (5b-6b)
6be
TS (6b-7b)e
7be
TS (1b-8b)
8b
TS (8b-9b)
9b
TS (9b-10b)
10b
TS (10b-11b)f
11bf
TS (11b-12b)f
12bf
TS (12b-13b)f
13bg
TS (13b-16b)g
14bf
TS (14b-16b)f
TS (10b-15b)h
15bh
TS (15b-16b)h
16bi
TS (1b-17b)
17bj
TS (17b-18b)j
18bj
TS (18b-19b)j
19bj
TS (19b-18a)j
TS (18b-20b)j
20bj
TS (20b-24a)j
TS (1b-11a)
TS (11a-21b)
21b
TS (21b-22b)
22bk
TS (22b-23b)k
23bk
TS (23b-7a)k
TS (1b-13c)
Eb
(hartrees/part)
-532.508515
-532.516912
-532.45786
-532.54148
-532.54198
-532.57036
-532.47045
-532.47919
-532.45734
-532.60706
-532.58222
-532.59294
-532.56801
-532.62256
-532.47086
-532.48332
-532.45816
-532.59941
-532.58112
-532.57167
-532.58372
-532.57139
-532.57281
-532.59788
-532.54312
-532.54207
-532.48523
-532.59198
-532.57817
-532.53593
-532.54824
-532.47124
-532.54899
l
-532.39077
-532.36886
-532.43907
-532.39713
-532.40935
-532.39317
-532.40485
-532.41667
-532.40230
-532.46518
-532.46387
-532.48731
-532.46737
-532.49938
-532.47251
-532.60598
-532.56878
-532.46387
ΔG (298 K)
(kcal/mol)
17.0
13.2
47.2
-3.3
-4.3
-33.3
42.9
37.8
49.3
-46.5
-34.2
-52.5
-38.2
-67.9
42.4
35.2
49.2
-41.8
-31.9
-39.8
-47.4
-39.1
-41.5
-54.2
-24.8
-34.0
-1.6
-53.1
-46.5
-17.3
-16.7
20.3
-68.7
ΔG (500 K)
(kcal/mol)
24.0
20.4
54.9
3.4
2.8
-33.0
51.4
46.1
57.6
-40.8
-29.4
-55.7
-41.4
-69.4
50.9
43.2
57.6
-36.1
-26.1
-42.7
-49.6
-41.8
-43.3
-56.5
-28.8
-43.9
-11.4
-56.5
-50.3
-19.4
-18.8
17.2
-84.4
ΔG (750 K)
(kcal/mol)
32.7
29.1
64.3
11.4
11.6
-32.8
62.0
56.2
67.7
-34.0
-23.8
-59.2
-44.7
-70.6
61.4
53.1
67.9
-29.3
-19.2
-46.2
-52.2
-45.1
-45.4
-59.4
-33.9
-56.4
-23.4
-60.8
-55.0
-21.8
-21.5
13.4
-104.0
ΔG (1000 K)
(kcal/mol)
41.4
37.6
73.6
19.2
20.3
-32.7
72.6
66.1
77.8
-27.5
-18.2
-62.6
-47.9
-71.8
71.8
62.8
78.1
-22.6
-12.4
-49.7
-54.6
-48.3
-47.4
-62.3
-38.9
-68.7
-35.2
-65.1
-59.5
-24.1
-24.1
9.6
-123.4
ΔG (1250 K)
(kcal/mol)
50.0
46.1
82.8
26.8
28.8
-32.6
83.1
75.9
87.8
-21.1
-12.8
-66.0
-50.9
-72.9
82.2
72.3
88.2
-16.2
-5.6
-53.1
-56.9
-51.5
-49.2
-65.1
-43.8
-80.8
-46.7
-69.3
-63.9
-26.2
-26.7
6.0
-142.5
<S 2>
62.6
76.5
31.2
59.2
53.0
61.6
51.1
43.1
49.7
46.4
46.34
29.5
39.3
8.2
22.6
-59.6
-39.8
47.3
63.6
78.7
31.7
61.4
55.2
63.7
51.5
42.1
48.5
55.2
54.73
35.6
45.0
7.1
21.8
-61.4
-42.8
56.3
64.6
81.3
32.1
64.1
57.8
66.2
51.9
40.7
46.6
66.1
65.11
42.9
51.8
5.6
20.6
-63.7
-46.5
67.4
65.3
83.8
32.3
66.8
60.2
68.6
52.2
39.1
44.7
77.0
75.42
50.1
58.5
4.1
19.5
-66.1
-50.2
78.4
66.0
86.3
32.3
69.5
62.5
71.1
52.5
37.3
42.7
87.9
85.67
57.0
65.1
2.5
18.4
-68.5
-53.9
89.4
0.76
0.76
0.77
0.94
0.75
0.77
0.77
0.79
0
0.77
0.75
0.90
0.76
0.77
0.77
0.76
0.77
0.78
0.76
0.78
0.77
0.77
0.76
0.77
0.78
0.76
0.75
0.76
0.76
0.76
0.75
0.77
0
0
0
0.77
0.77
0.75
0.77
0.78
0.76
0.76
0.81
0.78
0.75
0.77
0.77
0.89
0.77
0.77
0.79
Other
(PG, ES, Nimag)c
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C2h,1Ag,0;Cs,2A",0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
Cs,1A',0; C2V,2B1,0
C1,1
C1,0
C1,1
C1,0
Cs,2A",0
Cs,2A",0
C1,1
C1,0
C1,1
C1,1
C1,0
C1,1
C1,0
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,1
C1,0
C1,1
C1,1
C1,1
C1, 0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,1
Continued
Table 2.2. Relative Gibbs free energies for all intermediates and transition states (298 to 1250
K) at the B3LYP/6-311+G**//B3LYP/6-31G* level related to 1b decomposition.
59
Table 2.2 continued
a
See Figure 2.4 for structures. bBottom-of-the-well energy. cPoint group (PG), Electronic
state (ES), Number of imaginary vibrational frequencies (Nimag). dE and ΔG(T) values
include E and G(T) of OH. eE and ΔG(T) values include E and G(T) of trans-glyoxal. fE
and ΔG(T) values include E and G(T) of formylketene. gE and ΔG(T) values include E
and G(T) of CO and formylketene. hE and ΔG(T) values include E and G(T) of 2malonaldehyde radical. iE and ΔG(T) values include E and G(T) of CO, CO2 and C2H2. jE
and ΔG(T) values include E and G(T) of O(3P). kE and ΔG(T) values include E and G(T)
of CO. lA reliable transition state was not found for this process.
60
Structurea
TS (1-1c)
1c
TS (1c-2c)
2c
TS (2c-3c)
3cd
TS (1c-4c)
4c
TS (4c-5c)
5c
TS (5c-6c)
6c
TS (6c-7c)
7ce
TS (7c-8c)e
8ce
TS (8c-9c)e
9ce
TS (9c-10c)e
10ce
TS (10c-11c)e
11cf
TS (11c-12c)f
12cf
TS (1c-13c)
13c
TS (13c-14c)
14c
TS (14c-15c)
15cg
TS (15c-14a)g
TS (13c-16c)
16c
TS (16c-17c)
17c
TS (17c-18c)
18ch
TS (18c-19c)h
19ci
TS (1c-15a)
TS (15a-20c)
20ce
TS (20c-21c)e
21ce
TS (21c-10a)e
TS (1c-22c)
22cj
TS (22c-17a)j
TS (22c-20b)j
Eb
(hartrees/part)
-532.50740
-532.52526
-532.46008
-532.54729
-532.54723
-532.58274
-532.49135
-532.50668
-532.48428
-532.56092
-532.53662
-532.56802
-532.55245
-532.57137
-532.56289
-532.56613
-532.56140
-532.57077
-532.55503
-532.60727
-532.57797
-532.58234
-532.57238
-532.66042
-532.47794
-532.50669
-532.46387
-532.45970
-532.41875
-532.40469
-532.38842
-532.48962
-532.59437
-532.57602
-532.61487
-532.59781
-532.61104
-532.58952
-532.58369
-532.49778
-532.50011
-532.65587
-532.62323
-532.65583
-532.62343
k
-532.40773
-532.39825
-532.36788
ΔG (298 K)
(kcal/mol)
17.5
9.0
46.0
-6.9
-7.9
-41.4
30.2
20.9
33.6
-12.9
-0.3
-21.1
-14.0
-35.5
-30.4
-32.4
-29.5
-35.5
-27.1
-57.3
-42.9
-55.1
-50.0
-104.5
38.8
21.4
45.1
46.6
68.9
48.6
56.7
30.5
-35.8
-26.3
-47.9
-39.5
-59.4
-47.7
-54.7
26.5
23.9
-88.3
-67.3
-86.9
-68.2
ΔG (500 K)
(kcal/mol)
24.7
17.0
53.9
0.1
-0.8
-41.3
38.9
29.2
41.8
-4.3
7.8
-14.7
-8.3
-36.2
-30.5
-33.0
-29.7
-36.4
-26.9
-58.1
-45.2
-63.2
-58.0
-112.9
47.8
30.1
53.1
53.3
74.6
48.1
56.0
39.1
-28.5
-18.4
-40.6
-32.7
-59.7
-48.2
-61.5
35.5
32.5
-89.1
-67.2
-87.0
-68.5
ΔG (750 K)
(kcal/mol)
33.6
26.7
63.6
8.5
7.9
-41.4
49.8
39.4
52.0
6.3
17.8
-7.0
-1.4
-37.1
-30.6
-34.0
-29.9
-37.7
-26.7
-59.2
-48.0
-27.8
-20.6
-123.3
59.0
40.8
62.9
61.2
81.2
47.2
54.8
49.7
-19.6
-8.6
-31.8
-24.4
-60.2
-48.8
-70.1
46.7
43.1
-90.1
-66.9
-87.1
-68.7
ΔG (1000 K)
(kcal/mol)
42.4
36.2
73.2
16.6
16.4
-41.5
60.7
49.5
62.2
16.7
27.8
0.5
5.5
-38.0
-30.5
-34.9
-29.9
-38.9
-26.4
-60.2
-50.7
-83.1
-77.1
-133.6
70.2
51.3
72.7
68.9
87.6
46.1
53.6
60.2
-10.8
1.1
-23.2
-16.2
-60.7
-49.4
-78.5
57.9
53.7
-91.1
-66.4
-87.2
-68.8
ΔG (1250 K)
(kcal/mol)
51.2
45.6
82.6
24.5
24.9
-41.5
71.5
59.4
72.4
26.9
37.6
7.8
12.2
-39.0
-30.3
-35.9
-29.8
-40.2
-26.1
-61.2
-53.2
-92.8
-86.3
-143.7
81.3
61.7
82.3
76.4
93.9
45.0
52.4
70.7
-2.2
10.7
-14.7
-8.0
-61.3
-49.9
-86.8
69.0
64.3
-92.1
-65.8
-87.3
-68.8
<S 2>
1.09
0.75
0.77
0.78
0.80
0
0.79
0.78
0.99
0.75
0.77
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.76
0.75
0.76
0.75
0.76
0.78
0.81
0.75
0.78
0.76
0.77
0.75
0.76
0.77
0.75
0.76
0.75
0.76
0.76
0.77
0
0.80
0.76
0.79
0.76
0.77
0.77
Other
(PG, ES, Nimag)c
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,0
C1,1
C1,1
C2,2A,0
C1,1
C1,0
C1,1
52.1
58.7
75.3
53.2
60.9
76.4
54.3
63.7
77.6
55.3
66.4
78.7
56.2
69.2
79.8
0.76
0.78
0.78
C1,0
C1,1
C1,1
Continued
Table 2.3. Relative Gibbs free energies for all intermediates and transition states (298 to
1250 K) at the B3LYP/6-311+G**//B3LYP/6-31G* level related to 1c decomposition.
61
Table 2.3 continued
a
See Figure 2.5 for structures. bBottom-of-the-well energy. cPoint group (PG), Electronic
state (ES), Number of imaginary vibrational frequencies (Nimag). dE and ΔG(T) values
include E and G(T) of OH. eE and ΔG(T) values include E and G(T) of CO2. fE and
ΔG(T) values include E and G(T) of CO and CO2. gE and ΔG(T) values include E and
G(T) of C2H2. hE and ΔG(T) values include E and G(T) of CO. iE and ΔG(T) values
include E and G(T) of CO and OH. jE and ΔG(T) values include E and G(T) of O(3P).
k
A reliable transition state was not found for this process.
2.3.4. Comparison of DFT energetics
Due to a lack of experimental data for the energetics of the intermediates
proposed in the preceding pathways, CBS-QB3 optimization and energy calculations
were performed on the three 2-oxepinoxy + O2 addition steps as well as the lowest energy
pathway, 1c  10a, via the 1,4-peroxy intermediate 15a. Table 2.4 lists the ΔH(298 K)
and ΔG(298 K) values for the intermediates and the transition states for the
interconversion of 1  1a, 1  1b, 1  1c and 1c  10a at the B3LYP/6311+G**//B3LYP/6-31G* and CBS-QB3 levels. Figure 2.9 illustrates the relative
ΔH(0K) values for the 1c  10a pathway. The ΔG‡(298 K) values for addition of
molecular oxygen at the CBS-QB3 level agree well with those obtained using our DFT
method, differing at most by 2 kcal/mol for addition of O2 to carbon-4 of 1. The three
peroxyoxepinone (1a, 1b and 1c) free energies at 298 K, on the other hand, appear to be
significantly underestimated by the B3LYP method. The difference in ΔG(298 K)
62
between the two methods, for the peroxyoxepinone intermediates, range from 8.1 to 9.8
kcal/mol, with CBS-QB3 method giving more exoergic values. The difference in ΔG(298
K) increases upon formation of 15a to 16.3 kcal/mol, approximately double that for the
O2 addition products (1a, 1b and 1c). This trend is conserved in the ΔH(0K) and
ΔH(298K) energy values, and this discrepancy is obviously not due to thermal and
entropic corrections alone. The origin of this discrepancy is not clear at this time. These
calculations have been performed with single-reference wavefunctions, and perhaps some
multi-configurational character is important for the peroxy species derived from
unsaturated radicals.
The agreement between the 298 K free energy of activation barrier heights for the
B3LYP and CBS methods is consistent, throughout the 1c  15a  20c  21c  10a
pathway, with values differing on average by 2.4 kcal/mol. There is a large discrepancy,
however, between the barrier heights for TS (15a-20c) of ~10 kcal/mol. Following
decomposition of the peroxy moiety, the ΔG(298 K) values fall into closer agreement.
Despite the discrepancy in reaction free energies, the qualitative nature of the B3LYP
decomposition paths are in very good agreement with the CBS-QB3 method.
63
Molecule
1
TS (1-1a)
TS (1-1b)
TS (1-1c)
1a
1b
1c
TS (1c-15a)
15a
TS (15a-20c)
20c
TS (20c-21c)
21c
TS (21c-10a)
10a
B3LYPa
ΔH(298 K)
ΔG(298 K)
0.0
0.0
7.5
17.7
7.2
17.0
7.5
17.6
–0.4
10.4
3.4
13.2
–1.7
9.0
14.8
26.5
–5.5
6.4
12.4
23.9
–87.9
–88.7
–67.4
–67.3
–86.8
–86.9
–67.8
–68.2
–74.6
–85.3
CBS-QB3
ΔH(298 K)
ΔG(298 K)
0.0
0.0
5.8
16.9
4.6
15.0
5.6
16.2
–11.1
0.7
–5.3
5.1
–12.5
–0.8
3.1
16.2
–23.3
–9.9
4.7
17.6
–90.5
–91.9
–71.4
–71.2
–94.1
–94.1
–72.7
–73.0
–77.5
–88.8
Table 2.4. Relative energies (kcal/mol) of selected intermediates at the B3LYP/
6-311+G**//B3LYP/6-31G* and CBS-QB3 levels.
a
Energies correspond to the B3LYP/6-311+G**//B3LYP/6-31G* level.
64
16.5
7.5
17.9
(6.2)
0.0
(27.8)
(16.1)
−1.7
−5.5
O
O
+ O2
(−11.6)
O
1
O
O
1c
O
(−21.8)
O
O
O O
15a
20.5
19.0
(19.8)
(21.4)
−74.6
(−78.3)
−87.9
−86.8
(−91.1)
OO
(−94.1)
CO2 +
20c
CO2 +
O
O
O
+ CO2+ HCO.
10a
21c
Figure 2.9. Potential energy surfaces (ΔH, kcal/mol at 0 K) at the B3LYP/
6-311+G**//B3LYP/6-31G* and CBS-QB3 (parentheses) levels for the lowest energy
pathway for the oxygen initiated decomposition of 2-oxepinoxy radical (1). The energies
for each intermediate are relative to 1 and each barrier is relative to the reactant for that
specific step.
65
2.4. Conclusions
Numerous possible pathways for the decomposition of 2-, 4-, and 6peroxyoxepinone radicals (1a, 1b and 1c), following addition of O2 to 2-oxepinoxy
radical (1) have been examined in the 298 through 1250 K temperature range. Pathways
initiated via rearrangement to a dioxetane (1,2-peroxy), 1,3-peroxy, 1,4-peroxy or by
intramolecular hydrogen-atom-abstraction are competitive at temperatures < 500 K with
the pathways proposed by Fadden31 for the unimolecular decomposition of 2-oxepinoxy
radical (1) in the high-pressure limit. For the decomposition of the peroxyoxepinone
radicals, the mechanistic sequence of 1c  15a  20c  21c  10a appears to be the
most viable pathway. Due to the large exoergicity associated with forming 2-oxepinoxy
radical, these rearrangement pathways all lie below the level of free energy to re-generate
phenyl radical and 2 O2 molecules. However, as the temperature becomes greater than
500 K, the overall barriers for the proposed pathways make them less competitive, as a
result of unfavorable entropy associated with the addition step of O2 to 2-oxepinoxy
radical as compared to previously calculated pathways for unimolecular decomposition
mechanisms.31
The present chapter reflects an attempt to estimate the competition of oxidative
interference on the unimolecular decomposition products of phenylperoxy radical that
generates the 2-oxepinoxy radical in a very exothermic reaction. Due to the complex
physical and chemical nature of combustion environments as well as the high
exothermicity for the initial generation of 2-oxepinoxy radical, a more thorough treatment
of the branching pathways via a multi-well master-equation analysis may also be
warranted.
66
References for Chapter 2
1
Santos, C. Y. M.; Almeida Azevedo, D.; Aquino Neto, F. R. Atmos. Environ. 2004, 38,
1247-1257.
2
Burri, J.; Crockett, R.; Hany, R.; Rentsch, D. Fuel 2004, 83, 187-193.
3
Yamada, E.; Hosokawa, Y.; Furuya, Y.; Matsushita, K.; Fuse, Y. Analytical Sciences
2004, 20, 107-112.
4
Schuetzle, D.; Siegl, W. O.; Jensen, T. E.; Dearth, M. A.; Kaiser, E. W.; Gorse, R.;
Kreucher, W.; Kulik, E. Environ. Health Persp. 1994, 102(S4), 3-12.
5
Richter, H.; Howard, J. B. Prog. Energy and Combust. Sci. 2000, 26, 565-608.
6
Marsh, N. D.; Ledesma, E. B.; Sandrowitz, A. K.; Wornat, M. J. Energy and Fuels
2004, 18, 209-217.
7
Venkat, C.; Brezinsky, K.; Glassman, I. Symp. (Int.) Combust., 19th 1982, 143-152.
8
Rotzoll, G. Int. J. Chem. Kinet. 1985, 17, 637-653.
9
Frank, P.; Herzler, J.; Just T.; Wahl, C. Symp. (Int.) Combust., 25th 1994, 833-840.
10
Bermudez, G.; Pfefferle, L. Combustion and Flame 1995, 100, 41-51.
11
Chai, Y.; Pfefferle, L. D. Fuel 1998, 77, 313-320.
12
Yu, T.; Lin, M. C. J. Am. Chem. Soc. 1994, 116, 9571-9576.
13
Norrish, R. G. W.; Taylor, G. W. Proc. R. Soc. 1965, A234, 160-177.
14
Carpenter, B. K. J. Am. Chem. Soc. 1993, 113, 9806-9807.
15
Barckholtz, C.; Fadden, M. J.; Hadad, C. M. J. Phys. Chem. A 1999, 103, 8108-8117.
16
Fadden, M. J.; Barckholtz, C.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 3004-3011.
67
17
Ruifeng, L.; Morokuma, K.; Mebel, A. M.; Lin, M. C. J. Phys. Chem. 1996, 100, 9314-
9322.
18
Mebel, A. M.; Lin, M. C. J. Am. Chem. Soc. 1994, 116, 9577-9584.
19
Cioslowski, J.; Liu, G.; Martinov, M.; Piskorz, P.; Moncrieff, D. J. Am. Chem. Soc.
1996, 118, 5261-5264.
20
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Am. Chem. Soc. 1999, 121, 491-
500.
21
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J.
C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.;
Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.;
Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.;
Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J.
V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;
Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98,
Revision A.7, Gaussian, Inc.; Pittsburgh, PA, 1998.
22
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
23
Lee, C.; Yang, W.; Parr, R.G. Phys. Rev. B 1998, 37, 785-789.
24
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital
Theory; John Wiley & Sons; New York, 1986.
68
25
Bauschlichter, C. W., Jr.; Langhoff, S. R. Mol. Phys. 1999, 96, 471.
26
(a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.;
Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523.
27
28
Rablen, P. R. Thermo94, Yale University: New Haven, CT, 1994.
Reference 29 recommends that B3LYP/6-31G(d) vibrational frequencies used for the
determination of ΔHvib(T) and ΔSvib(T) be scaled by 0.9989 and 1.0015, respectively.
However, considering how close those values are to 1, we have chosen to leave the
frequencies unscaled for simplicity.
29
30
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502-16513.
Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys.
1999, 110, 2822-2827.
31
Fadden, M. J.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 8121-8130.
69
CHAPTER 3
THEORETICAL DETERMINATIONS OF THE AMBIENT CONFORMATIONAL
DISTRIBUTION AND UNIMOLECULAR DECOMPOSITION OF
N-PROPYLPEROXY RADICAL
This chapter is reproduced with permission from the Journal of Physical Chemistry A
2005, 109, 3637–3646 copyright 2005 American Chemical Society.
3.1. Introduction
Peroxy radicals play an important role in the atmospheric and combustion oxidation
reactions of alkanes. In the daytime troposphere, alkane oxidation is typically initiated by
reaction with OH radicals to yield an alkyl radical and H2O via C–H abstraction.
Molecular oxygen can then add to the radical center of the alkyl radical, resulting in an
alkylperoxy radical. Peroxy radicals are integral components in the processes leading to
formation of photochemical smog. Peroxy radicals and NO, generated from combustion
sources and formed in auto engine exhaust, for example, react in the lower troposphere to
produce excess NO2, which upon photolysis results in an increased ozone (O3)
concentration via the following reaction sequence:1,2
RO2• + NO → RO• + NO2
NO2 + hv (λ < 430 nm) → NO + O
O + O2 + M → O3
70
In a clean troposphere, ozone would replace peroxy radicals in the above scheme
resulting in no net generation of ozone.
In combustion environments, alkane oxidation is initiated by loss of a hydrogen
atom, via abstraction or high-energy collisions, forming an alkyl radical that can yield an
alkylperoxy radical after the addition of O2. Low-temperature combustion environments
(T < 1000 K)3,4 are particularly important since mechanisms which lead to autoignition of
a fuel are more prominent at these lower temperatures. The persistence of alkylperoxy
radicals at lower temperatures is both pressure and temperature dependent. The pressure
dependence results from the energy-rich alkylperoxy radical formed in the O2 addition
step, thereby requiring collisional stabilization to prevent return to reactants or generation
of products:
R + O2
RO2* + M
RO2 + M*
Products
Thermally, alkylperoxy radicals can become unstable as temperatures approach ~ 600 K,
for which equilibrium favors reactants, thereby resulting in a negative temperature
coefficient regime. As temperatures increase further, high temperature oxidation
mechanisms predominate. At temperatures where alkylperoxy radicals are prominent,
several pathways are possible. Two important pathways include self-reaction and
isomerization via transfer of an alkyl hydrogen (C–H) to the terminal peroxy oxygen to
71
form a hydroperoxyalkyl radical, typically denoted QOOH, where Q represents an alkyl
group with a carbon-centered radical. Of course, by abstraction of unique primary and
secondary C–H bonds, different QOOH species can be generated. Each possible QOOH
species derived from a particular alkylperoxy radical can be differentiated by adding the
(1,xn) label to Q where x represents the numbered displacement of the new radical center
from the original radical center and n designates the type (primary, secondary) of carbon
from which the hydrogen is being abstracted (Figure 3.1). QOOH (Figure 3.1) radicals
may decompose unimolecularly resulting in radical propagation or react with O2 again
via addition to form a hydroperoxyalkylperoxy radical. The addition of O2 to a QOOH is
thought to be primarily responsible for chain-branching events.5,6 Such chain-branching
reactions derived from alkylperoxy radical formation under low-temperature oxidation
conditions lead to autoignition which can result in engine knock in an internal
combustion engine.3
72
+ O2
concerted
1,4-H transfer/elimination
O
1,5-H transfer
OH
O
Q(1,5p)OOH
O
n-propylperoxy radical
1,4-H transfer
+
OH
O
1,3-H transfer
OH
OH
O
O
Q(1,4s)OOH
Q(1,3s)OOH
Figure 3.1. Potential initiation mechanisms for the unimolecular decomposition of
n-propylperoxy radical.
The smallest alkylperoxy radical which can undergo an internal hydrogen transfer
of significant importance in either low-temperature combustion or atmospheric processes
.
is ethylperoxy (CH3CH2OO ) radical, and it has been studied extensively both
experimentally7,8,9,10,11,12,13,14 and theoretically.15,16,17,18,19,20,21,22,23,24,25 Theoretical
calculations by Ignatyev et al. were important in the elucidation of a 1,4-concerted
elimination transition state in ethylperoxy radical for which the abstraction of a primary
hydrogen by the terminal peroxy oxygen and simultaneous cleavage of the C–O bond to
.
form ethylene (H2C=CH2) and hydroperoxy radical (HO2 ) occurs with an energetic
barrier below the energy required to reform reactants, unlike that for the 1,4-transfer
73
isomerization.18 Prior to the study by Ignatyev et al., experimental observations had not
provided conclusive evidence to rule out the direct abstraction of a primary hydrogen by
O2.
.
n-Propylperoxy (CH3CH2CH2OO ) radical differs from ethylperoxy
.
(CH3CH2OO ) radical by an additional methylene (–CH2–) group. n-Propylperoxy radical
is capable of undergoing the 1,4-elimination/isomerization reactions as for ethylperoxy
radical and, additionally, due to the extra methylene group, can isomerize through a
potentially low-barrier 1,5-H transfer, via a six-member ring transition state to generate
the Q(1,5p)OOH species (Figure 3.1).
The reaction of propyl radical (normal and iso) with O2 has been studied
experimentally, and theoretical studies have examined several of the adduct’s
decomposition pathways.5,20,26,27,28,29,30,31,32,33,34 Most experimental studies involve a
mixture of iso- and n-propyl radicals reacting with O2. The primary products, whether
with mixed propyl radicals or isolated n-propyl radical, are propene and HO2, which
seemingly can derive from 1,4-isomerization or concerted 1,4-elimination processes.
Experimentally, products resulting from a 1,5-isomerization, primarily OH radical and
cyclic ethers, are negligible.7–14 The experimental production of propene and HO2
exhibits a pressure dependence similar to that seen in ethyl radical + O2 studies. The
pressure dependence is attributed to a mechanism by which the propene + HO2 are
derived from the chemically activated propylperoxy radical that proceeds through the
low-energy barrier of the 1,4-concerted isomerization/elimination channel.
Computationally, the 1,4-isomerization, concerted 1,4-elimination, and 1,5-isomerization
74
pathways of the n-propylperoxy radical have been studied.30,32,33 These studies reported
that the 1,5-H transfer transition state is lower in energy than both of the 1,4-H transfer
transition states and that all of these H-atom transfer barriers are calculated to be lower
then the energy required for regeneration of n-propyl radical + O2. DeSain et al.30 used
QCISD(T) energies for the 1,4- and 1,5-pathways to generate master equation rates to
model the production of HO2 and OH from the reactions of propyl, ethyl and butyl
radicals + O2. Niak et al.32 used (unspecified) potential energy surfaces to study the
production of HO2 in the ethyl and propyl + O2 systems. In each case, the 1,5-H transfer
intermediate was found to be of little import.
To this point, experimental studies of the oxidation of propyl radicals by O2 have
focused on the global mechanism:
R• + O2 → R' + HO2• (or •OH)
This chapter is intended as a computational companion to an experimental study which
utilized cavity ringdown spectroscopy (CRDS) for the direct detection and identification
of propylperoxy radicals via the A˜ − X˜ electronic transition.35 The CBS-QB3 composite
method as well as the B3LYP and mPW1K density functional theory (DFT) methods
€
with the 6-31+G** basis set will be used to generate the five unique conformers of n-
propylperoxy radical, as well as a complete and detailed high-level potential energy
surface for the unimolecular decomposition of n-propylperoxy radical to yield OH, HO2
and the closed-shell complementary species. The energetics obtained will be used to
estimate the ambient distribution of each of the n-propylperoxy conformers and,
75
furthermore, to predict the importance of pathways which may contribute to diminishing
the abundance of detectable n-propylperoxy radicals, particularly those which might
result from the low-energy 1,5-H transfer. We are also interested in calibrating the DFT
energies and surfaces as these methods are more applicable to larger peroxy radicals.
3.2. Computational Methods
All calculations were performed using the Gaussian 0336 suite of programs at the
Ohio Supercomputer Center. Geometries for all stationary points were optimized using
the B3LYP37,38 and mPW1K39 hybrid density functional theoretical methods with a 631+G** basis set and the composite CBS-QB340 method. The CBS-QB3 method
attempts to estimate the CCSD(T) energy at the infinite basis set limit for a B3LYP
geometry. Each stationary point was characterized via vibrational frequency calculations
using the same theoretical method and basis set from which the geometry was generated.
Minima were confirmed to have adequate convergence and zero imaginary vibrational
frequencies. Transition state (TS) structures were confirmed to have one imaginary
vibrational frequency and furthermore shown to be connected to the desired reactant and
product by displacement along the normal coordinate (typically 10%) for the imaginary
vibrational frequency in the positive and negative directions followed by careful
minimization using either opt = calcfc or opt = calcall. For reaction coordinates requiring
a more accurate treatment, an intrinsic reaction coordinate (IRC)41 calculation was
performed. In general, <S2> values for the optimized geometries were typically 0.75 ≤
<S2> ≤ 0.79, except where noted in the text. The CBS-QB3 method utilizes single-point
energy calculations from CCSD(T), MP4, and MP2 methods which are more susceptible
76
to spin contamination from an unrestricted Hartree-Fock wavefunction. For the geometry
optimization, the spin contamination is reasonable in most cases for the B3LYP
optimized geometries, and the CBS-QB3 method does include a spin contamination
correction term based on the deviation from the expected <S2> value. In the subsequent
text, the Hartree-Fock <S2> values are not discussed but are provided in the supporting
information.
Scaling factors of 0.980642 and 0.951543 were applied, respectively, to the B3LYP
and mPW1K zero-point vibrational energies. Thermal corrections were determined
utilizing the harmonic-oscillator/rigid-rotor approximations, using unscaled vibrational
frequencies, and assuming an ideal gas at 1.0 atm. The relative weighting of each npropylperoxy radical conformer was determined via a Boltzmann average as
gie
Ni =
−ΔGi



kB T 

∑g e
−ΔG j


kB T 

(3.1)
j
j
where ΔGi is the free energy at 298 K of structure i relative to the structure with the
€
lowest overall free energy set as zero, gi is the structural degeneracy, kB is Boltzmann’s
constant, T is temperature (298 K), and j runs over all five unique conformers of npropylperoxy radical. The structures, vibrational frequencies, energies, thermal
corrections to the enthalpy and free energy, <S2> values and rotational constants for all
stationary points can be found in the supporting information.
77
3.3. Results and Discussion
The complete CBS-QB3 potential energy surface (PES) (ΔH298, kcal/mol relative
to n-propylperoxy radical) for the formation and unimolecular decomposition of npropylperoxy radical through 1,5-, 1,4- and 1,3-isomerization intermediates, as well as
for direct formation of propene and hydroperoxy radical via a 1,4-concerted elimination
mechanism, is shown in Figure 3.2. Tables 3.1 through 3.3 list the relative enthalpies and
free energies in kcal/mol relative to n-propylperoxy radical for each of the stationary
points at the CBS-QB3, B3LYP/6-31+G**, and mPW1K/6-31+G** levels, respectively.
The discussion will focus on the energy surface as CBS-QB3 enthalpies at 298 K, unless
otherwise noted.
78
55
45
CH3CH2CH2 + O2
35
ΔH298 (kcal/mol)
cyclopropane + HO2
25
CH3CH=CH2 + HO2
15
CH2CH2CH2OOH
(Q(1,5p)OOH)
CH3CHCH2OOH
(Q(1,4s)OOH)
CH2O + C2H2 +
5
-5
CH3CH2CH2OO
oxetane + OH
methyloxirane
+ OH
-15
-25
propanal +
OH
Figure 3.2. Potential energy diagram (ΔH298, kcal/mol) at the CBS-QB3 level for the
formation and unimolecular decomposition of n-propylperoxy radical.
79
OH
molecule
propyl radical (Cs) + O2 (3Σg)
propyl radical + O2 (3Σg)
n–propylperoxy radical (gG)
n–propylperoxy radical (gG')
n–propylperoxy radical (tG)
n–propylperoxy radical (gT)
n–propylperoxy radical (tT)
TS (1,5)
Q(1,5p)OOHa
TS (Q(1,5p)OOH → oxetane)a
oxetane + OH
TS (Q(1,5p)OOH → ethene)a
ethene + formaldehyde + OH
TS (Q(1,4s)OOH → cyclopropane)b
cyclopropane + HO2
TS (Q(1,5p)OOH → Q(1,4s)OOH)a.b
Q(1,4s)OOH
TS (Q(1,4s)OOH → methyloxirane)b
methyloxirane + OH
TS (Q(1,4s)OOH → propene)b
propene + HO2
TS (1,4elim)c
TS (1,4)
TS (1,3)
propanal (Cs) + OH
propanal + OH
ΔH(0 K)
kcal/mol
35.1
34.8
0.0
0.5
0.3
0.2
0.4
23.9
15.9
35.6
–0.1
43.2
3.6
54.2
26.9
53.9
13.4
25.5
–4.0
28.7
18.2
30.9
32.1
40.9
–26.3
–25.2
ΔH(298 K)
kcal/mol
36.5
36.1
0.0
0.5
0.3
0.3
0.6
23.2
16.4
35.8
0.7
42.8
6.1
54.5
27.5
54.3
14.2
26.1
–3.0
29.2
19.3
30.8
31.7
40.8
–24.9
–23.8
ΔG(298 K)
kcal/mol
24.3
24.4
0.0
0.4
0.0
0.2
0.1
24.9
15.6
35.6
–7.9
42.1
–14.7
53.6
17.8
53.7
12.3
24.7
–12.1
28.1
7.6
31.2
32.8
41.0
–35.1
–34.2
Table 3.1. CBS-QB3 energies (ΔH(0 K), ΔH(298 K) and ΔG(298 K) relative to npropylperoxy radical) for species involved in possible unimolecular decomposition
pathways of n-propylperoxyl radical.
a
Q(1,5p) designates a propyl moiety with the radical centered on the primary carbon. b
Q(1,4s) designates a propyl moiety with the radical centered on the secondary carbon
adjacent to the primary carbon. c elim distinguishes the concerted TS which includes HO2
elimination from the formal 1,4-H transfer TS.
80
molecule
propyl radical (Cs) + O2 (3Σg)
propyl radical + O2 (3Σg)
n–propylperoxy radical (gG)
n–propylperoxy radical (gG')
n–propylperoxy radical (tG)
n–propylperoxy radical (gT)
n–propylperoxy radical (tT)
TS (1,5)
Q(1,5p)OOHa
TS (Q(1,5p)OOH → oxetane)a
oxetane + OH
TS (Q(1,5p)OOH → ethene)a
ethene + formaldehyde + OH
TS (Q(1,4s)OOH → cyclopropane)b
cyclopropane + HO2
TS (Q(1,5p)OOH →
Q(1,4s)OOH)a,b
Q(1,4s)OOH
TS (Q(1,4s)OOH →
methyloxirane)b
methyloxirane + OH
TS (Q(1,4s)OOH → propene)b
propene + HO2
TS (1,4elim)c
TS (1,4)
TS (1,3)
propanal (Cs) + OH
propanal + OH
ΔH(0 K)
kcal/mol
30.4
30.1
0.1
0.5
0.1
0.0
0.0
24.5
18.7
35.8
3.0
43.7
4.4
53.1
26.0
ΔH(298 K) ΔG(298 K)
kcal/mol
kcal/mol
31.8
19.8
31.4
19.8
0.0
0.1
0.5
0.5
0.1
–0.1
0.0
0.0
0.1
–0.2
23.8
25.6
19.3
18.0
35.9
35.9
3.8
–5.2
44.5
42.5
6.9
–13.4
53.4
52.8
26.6
17.0
55.3
55.6
55.2
15.4
16.0
14.5
24.4
25.0
23.7
–0.4
26.6
16.6
27.6
32.8
42.6
–24.3
–23.4
0.6
27.0
17.6
27.5
32.4
42.6
–22.9
–22.0
–8.5
26.0
6.0
27.9
33.5
42.8
–33.0
–32.4
Table 3.2. B3LYP/6-31+G** energies (ΔH(0 K), ΔH(298 K) and ΔG(298 K) relative to
n-propylperoxy radical) for species involved in possible unimolecular decomposition
pathways of n-propylperoxyl radical.
a
Q(1,5p) designates a propyl moiety with the radical centered on the primary carbon. b
Q(1,4s) designates a propyl moiety with the radical centered on the secondary carbon
adjacent to the primary carbon. c elim distinguishes the concerted TS which includes HO2
elimination from the formal 1,4-H transfer TS.
81
molecule
propyl radical (Cs) + O2 (3Σg)
propyl radical + O2 (3Σg)
n–propylperoxy radical (gG)
n–propylperoxy radical (gG')
n–propylperoxy radical (tG)
n–propylperoxy radical (gT)
n–propylperoxy radical (tT)
TS (1,5)
Q(1,5p)OOHa
TS (Q(1,5p)OOH → oxetane)a
oxetane + OH
TS (Q(1,5p)OOH → ethene)a
ethene + formaldehyde + OH
TS (Q(1,4s)OOH →
cyclopropane)b
cyclopropane + HO2
TS (Q(1,5p)OOH →
Q(1,4s)OOH)a,b
Q(1,4s)OOHb
TS (Q(1,4s)OOH →
methyloxirane)b
methyloxirane + OH
TS (Q(1,4s)OOH → propene)b
propene + HO2
TS (1,4elim)c
TS (1,4)
TS (1,3)
propanal (Cs) + OH
propanal + OH
ΔH(0 K)
kcal/mol
30.4
30.0
0.0
0.5
0.0
0.0
0.0
27.4
18.1
41.8
–2.4
51.2
11.3
ΔH(298 K) ΔG(298 K)
kcal/mol
kcal/mol
31.8
19.6
31.3
19.7
0.0
0.1
0.5
0.4
0.1
–0.1
0.0
0.0
0.1
–0.2
26.7
28.5
18.6
17.7
42.1
41.4
–1.6
–10.8
51.5
50.9
13.9
–6.6
59.6
25.3
59.8
26.0
59.4
16.2
57.2
15.5
57.4
16.2
57.2
14.5
30.6
–4.7
33.8
21.6
36.2
36.1
46.0
–25.4
–24.4
31.2
–3.7
34.2
22.7
37.0
35.7
45.9
–24.0
–23.0
29.9
–12.8
33.2
10.9
36.8
36.8
46.2
–34.2
–33.4
Table 3.3. mPW1K/6-31+G** energies (SCF and ΔH(0 K), ΔH(298 K) and ΔG(298 K)
relative to n-propylperoxy radical) for species involved in possible unimolecular
decomposition pathways of n-propylperoxyl radical.
a
Q(1,5p) designates a propyl moiety with the radical centered on the primary carbon. b
Q(1,4s) designates a propyl moiety with the radical centered on the secondary carbon
adjacent to the primary carbon. c elim distinguishes the concerted TS which includes HO2
elimination from the formal 1,4-H transfer TS.
82
Formation of n-propylperoxy radical by the addition of O2 (3Σg) to n-propyl
radical is exothermic by –36.1 kcal/mol. To our knowledge, the bond dissociation energy
for the C–O bond in n-propylperoxy radical has not been reported. Knyazev and Slegle44
have reported C–O bond dissociation energies for methyl, ethyl and isopropylperoxy
radicals using thermochemical methods and experimental data. Table 3.4 shows the
calculated B3LYP, mPW1K, and CBS-QB3 C–O bond dissociation energies for methyl,
ethyl, isopropyl, and n-propylperoxy radicals vis-à-vis the experimental values. The
CBS-QB3 values are in excellent agreement with the available experimental values;
therefore, we expect that the calculated C–O bond dissociation energy for n-propylperoxy
radical is correspondingly an excellent estimate. The B3LYP and mPW1K methods
appear to underestimate the BDE by ~5 kcal/mol predicting values of –31.4 and –31.3
kcal/mol, respectively.
R
methyl
ethyl
isopropyl
n–propyl
B3LYPa
–30.5
–31.4
–31.7
–31.4
mPW1Ka
–29.8
–31.2
–32.1
–31.3
CBS-QB3
–33.0
–35.5
–37.6
–36.1
Experimentb
–32.7
–35.5
–37.1
N/A
Table 3.4. Comparison of B3LYP, mPW1K, and CBS-QB3 alkylperoxy radical R–OO
bond dissociation energies (ΔH (298 K), kcal/mol) to experimentally derived values.
a
Geometries and energies derived from the 6-31+G** basis set. b See reference 44.
83
Five unique rotamers of n-propylperoxy radical can exist in thermal equilibrium.
Figure 3.3 shows the five possible n-propylperoxy radical rotamers. Each rotamer has
been labeled according to the rotational orientation of the O-O-C-C (designated first) and
O-C-C-C (designated second) dihedral angles in the O-O-C-C-C backbone. The two
dihedral angles can have either a trans (t), a clockwise gauche (g), or a counterclockwise
gauche (g') orientation. The O-O-C-C dihedral is given a lower case notation (i.e. t or g)
and the O-C-C-C dihedral an upper case notation (i.e. T or G) to differentiate each
rotamer.45 Therefore, the following unique conformations are possible: tT, tG, gG, gG',
and gT. Note that each of the conformers with a gauche orientation has an equivalent
mirror image. Of significant interest are the relative stabilities of the different rotamers
for n-propylperoxy radical and the relative contributions of each under ambient
conditions. This information will be helpful in identifying and assigning peaks in the
CRDS spectrum. Table 3.5 provides the ΔG(298 K), percentage based on Boltzmann
distribution, and degeneracy, as a result of the existence of non-superimposable mirror
images, for each of the five unique rotamers at the CBS-QB3, B3LYP/6-31+G** and
mPW1K/6-31+G** levels. The degeneracy due to methyl rotation has been ignored
because it is the same for all rotamers. At all levels of theory, each of the five unique
rotamers is consistently predicted to be present under ambient experimental conditions.
At 298 K, the gG conformation is predicted to be the major contributor to the
distribution, followed closely by the tG rotamer, with percentages of 28.1 and 26.4,
respectively. The B3LYP and mPW1K percentages and ordering are in good agreement
with each other; however, they differ from the CBS-QB3 results in this respect: favoring
84
the tG conformation followed by the gT conformation. We have also calculated the
rotational barriers (transition states) for interconversion between the different rotamers
(via rotation around the C–C and C–O bonds), and the rotational barriers are all lower
than 5 kcal/mol (see supporting information). Furthermore, at the CBS-QB3 level, the
largest energy difference between the different rotamers is ΔH(298 K) = 0.6 kcal/mol.
Recently, Zalyubovsky et al.46 have proposed assignments of the observed lines in the
CRDS spectrum to specific conformers. These assignments were made by comparing
experimental observations to computational results, particularly for the excited à states
of both n-propyl peroxy and isopropyl peroxy. The intensities of the assigned lines are
consistent with the predicted populations in Table 3.5. However the experimental results
are semi-quantitative at best due to partial overlap of conformer lines and unknown
rotational contours.
85
gT
tG
tT
gG’
gG
Figure 3.3. Five possible rotamers of n-propylperoxy radical.
86
CBS-QB3
B3LYP/6-31+G** mPW1K/6-31+G**
ΔG(298
K)
ΔG(298 K) % ΔG(298 K) %
%
Rotamer Degeneracy
gG'
2
0.41
14.0
0.62
11.8
0.57
11.7
gG
2
0.00
28.1
0.31
19.8
0.22
21.2
tG
2
0.04
26.4
0.11
27.8
0.06
28.0
gT
2
0.21
19.6
0.21
23.7
0.15
23.8
tT
1
0.10
11.9
0.00
16.8
0.00
15.4
a
b
Table 3.5. Boltzmann distributions for each of the five rotamers at the CBS-QB3,
B3LYP/6-31+G** and mPW1K/6-31+G** levels with the relative free energies (ΔG
(298 K), kcal/mol) and rotamer degeneracy.
a
See Figure 3.3 for structures. b The degeneracy for methyl rotation has been ignored
since it is the same for each rotamer.
The unimolecular decomposition of n-propylperoxy radical via pathways leading
to unimolecular decomposition products has been calculated and will be discussed
primarily with regard to the CBS-QB3 ΔH(0 K) values, unless otherwise specifically
stated. Figure 3.2 provides the completed potential energy surface for all of the possible
unimolecular pathways accessible to n-propylperoxy radical. Table 3.6 provides the ΔH(0
K) value for each barrier and reaction step relative to the reactant for that step at the
CBS-QB3, B3LYP/6-31+G** and mPW1K/6-31+G** levels, as well as the previously
calculated QCISD(T) and BH&HLYP theoretical values of DeSain et al.30 and Chan et
al.33, respectively. Figure 3.4 provides a more focused view of the initial barriers for
unimolecular decomposition of n-propylperoxy radical with each transition state structure
and ΔH(298 K) barrier height at the CBS-QB3, B3LYP/6-31+G** and mPW1K/6-
87
31+G** levels. Moreover, Figure 3.5 provides a schematic view of the mechanisms
studied subsequent to formation of the Q(1,5p)OOH and Q(1,4s)OOH intermediates.
The lowest barrier for isomerization of n-propylperoxy radical corresponds to the
1,5-H-atom transfer that has a barrier of +23.9 kcal/mol and results in the formation of
hydroperoxypropan-3-yl radical (Q(1,5p)OOH) with a reaction endothermicity of 15.9
kcal/mol. The B3LYP barrier is in good agreement, but the mPW1K value is ~3 kcal/mol
greater. Two other theoretical barrier heights and reaction energies have been reported for
the 1,5-H transfer in n-propylperoxy radical. At the QCISD(T)/6-311G**+(MP2/6311++G(2df,2pd) – MP2/6-311G**)//B3LYP/6-31G* level (hereafter just QCISD(T)),
DeSain et al. calculated the ΔH(0K) activation barrier and reaction energies to be +23.7
and +15.1 kcal/mol, respectively, and at the BH&HLYP/6-311G** level, Chan et al.
calculated values of +30.2 and +18.6 kcal/mol, respectively. This transition state benefits
from minimal strain as a result of the 6-member ring TS. This barrier height, however, is
significantly greater than those that have been estimated for the analogous 1,5-H-atom
transfers in the n-pentyl and n-butoxy radicals of +17.2 and +9.2 kcal/mol, respectively,
at the BAC-MP4 theoretical level.47,48 Furthermore, this series of 1,5-H-shift reactions
follows an Evans-Polanyi relationship: the n-butoxy, n-pentyl, and n-propylperoxy
radicals, respectively, have exoergic, isoergic, and endoergic 1,5-H-transfer reactions and
the barrier heights (9.2, 17.2, and 23.9 kcal/mol, respectively) follow the reaction
energies accordingly.
88
ΔH(0 K) ΔH(0 K)
molecule
CBS-QB3 B3LYPa
3
propyl radical + O2 ( Σg)
34.8
30.1
n-propylperoxy radical (gG)
0.0
0.0
TS (1,5)
23.9
24.5
Q(1,5p)OOHd
15.9
18.7
TS (Q(1,5p)OOH →
oxetane)d
19.7
17.1
Oxetane + OH
-16.0
-15.7
TS (Q(1,5p)OOH → ethene)d
27.3
25.1
ethene + formaldehyde + OH -12.3
-14.3
TS (Q(1,5p)OOH →
38.3
34.5
cylopropane)d
cyclopropane + HO2
11.0
7.3
TS (Q(1,5p)OOH →
Q(1,4s)OOH)d
38.0
36.6
Q(1,4s)OOH
13.4
15.4
TS (Q(1,4s)OOH →
12.1
9.0
methyloxirane)e
methyloxirane + OH
-17.4
-15.8
TS (Q(1,4s)OOH →
propene)e
15.3
11.2
propene + HO2
4.8
1.1
TS (1,4elim)f
30.9
27.6
TS (1,4)
32.1
32.8
TS (1,3)
40.9
42.6
propanal (Cs) + OH
-26.3
-24.3
ΔH(0 K)
mPW1Ka QCISD(T)b BH&HLYPc
30.0
34.9
0.0
0.0
27.4
23.7
30.2
18.1
15.1
18.6
23.7
-20.5
33.1
-6.8
23.4
41.5
7.2
41.7
39.1
15.5
15.0
-20.2
18.3
6.0
36.2
36.1
46.0
-25.4
23.8
-20.8
13.3
15.1
29.7
32.3
Table 3.6. Energies, ΔH(0 K) kcal/mol, for each barrier and reaction step relative to the
reactant for that step at the CBS-QB3, B3LYP/6-31+G** and mPW1K/6-31+G** levels
and available theoretical literature values.
a
Geometries and energies derived form the 6-31+G** basis set. b Reference 30, based on
basis set extrapolation scheme. c Reference 33, using the 6–311G** basis set. d Q(1,5p)
designates a propyl moiety with the radical centered on the primary carbon. e Q(1,4s)
designates a propyl moiety with the radical centered on the secondary carbon adjacent to
the primary carbon. f elim distinguishes the concerted TS which includes HO2 elimination
from the formal 1,4-H transfer TS.
89
1,3-H transfer TS
32.4
35.7
31.7
CH3CH2CH2 + O2
31.4
31.3
36.1
concerted
1,4-H transfer/elimination
42.6
45.9
40.8
27.5
37.0
30.8
23.8
26.7
23.2
1,4-H transfer TS
1,5-H transfer TS
0.0
0.0
0.0
B3LYP/6-31+G**
mPW1K/6-31+G**
CBS-QB3
Figure 3.4. Energies, ΔH(298 K) kcal/mol, and typical structures for the transition states
involved in the initiation of unimolecular decomposition of n-propylperoxy radical. The
B3LYP/6-31+G** (top), mPW1K/6-31+G** (middle), and CBS-QB3 (bottom) relative
energies are provided for the respective stationary points.
90
OH
O
cyclo-elimination
OH
O
+
Q(1,5p)OOH
oxetane
β-scission
C2H2 + H2CO + OH
1,2-H transfer
OH
O
Q(1,4s)OOH
cyclo-elimination
HO2
+
cyclopropane
O
OH cyclo-elimination
O
+
OH
methyloxirane
Q(1,4s)OOH
β-scission
+
HO2
Figure 3.5. Schematic representation of the possible mechanisms for unimolecular
decomposition for Q(1,5p)OOH and Q(1,4s)OOH.
91
The Q(1,5p)OOH radical can decompose by either β-scission, 1,2-H transfer
isomerization, or through one of two unique cyclo-elimination processes (Figure 3.5).
The most facile of these processes is a cyclo-elimination in which the terminal radical
carbon displaces hydroxyl radical to yield oxetane with a barrier of +19.7 kcal/mol and
an exothermicity of 16.0 kcal/mol (see Figure 3.2). This step provides the lowest overall
barrier to product formation through the Q(1,5p)OOH intermediate with an overall
pathway enthalpic barrier of +35.6 kcal/mol relative to n-propylperoxy radical, only 0.5
kcal/mol above the energy of n-propyl radical and O2 and slightly below their energy
when considering ΔH(298 K). The B3LYP method energy deviates with a barrier ~3
kcal/mol lower while the mPW1K, QCISD(T) and BH&HLYP methods all predict the
barrier to be larger by ~4 kcal/mol. The mPW1K TS wavefunction suffers from some
spin contamination with an <S2> value of 0.86, rendering it somewhat suspect. The <S2>
values for the previously reported QCISD(T) and BH&HLYP wavefunctions were not
reported. Furthermore, the mPW1K and BH&HLYP methods predict the reaction
products to be ~ 4 – 5 kcal/mol more stable than the CBS-QB3 method. Cycloelimination of Q(1,5p)OOH is also possible in which cyclopropane and HO2 are
generated. The CBS-QB3 barrier height for this process is +38.3 kcal/mol with a reaction
energy of +11.0 kcal/mol. The B3LYP and mPW1K barrier heights vary by ~ –4
kcal/mol and ~ +3 kcal/mol, respectively. The mPW1K transition state wavefunction also
suffers slightly from spin contamination with an <S2> value of 0.81. The QCISD(T) value
of DeSain et al. agrees closely with the mPW1K barrier height at +41.7 kcal/mol.
Two unique transition state geometries were found for the β-scission of
Q(1,5p)OOH (Figure 3.5). The first, and most favorable, involves coordination of the
92
hydroperoxy hydrogen with the terminal methylene moiety, resulting in a 6-membered
ring transition state. The second is an extended chain structure in which no
intramolecular coordination exists and is calculated to be ~1 kcal/mol higher in energy
than the coordinated TS. With a calculated barrier at +27.3 kcal/mol, the β-scission of
Q(1,5p)OOH yields ethane, formaldehyde, and hydroxyl radical with an exothermicity of
12.3 kcal/mol (Figure 3.2). The mPW1K method once again predicts a higher energy TS,
by ~ 6 kcal/mol, and the reaction exothermicity is smaller by ~ 5 kcal/mol. The β-scission
route, however, requires more energy (+43.2 kcal/mol) than that gained in the formation
of n-propylperoxy radical and is not expected to provide a viable route for either
activated or equilibrated n-propylperoxy radical to proceed to products.
The 1,2-H transfer isomerization of Q(1,5p)OOH has a barrier of +38.0 kcal/mol
resulting in the formation of hydroperoxypropan-2-yl radical (Q(1,4s)OOH) with an
exothermicity of 2.5 kcal/mol. The B3LYP and mPW1K barrier heights and reaction
energies are in good agreement, as is the QCISD(T) reaction energy.
The Q(1,4s)OOH intermediate can undergo two relatively facile decomposition
reactions. The first is a displacement of OH via cyclization that yields methyloxirane with
ΔH‡(0 K) = +12.1 kcal/mol and ΔH(0 K) = –17.4 kcal/mol. The B3LYP barrier height
and reaction energies are several kcal/mol below the CBS-QB3 values, while the
mPW1K values are several kcal/mol greater. Each of the TS geometry wavefunctions
suffers some spin contamination. The B3LYP/6-31+G** and B3LYP/CBSB7 (from the
CBS-QB3 geometry optimization step) wavefunction have <S2> values of 0.80 and 0.81,
respectively, and the mPW1K wavefunction is more suspect with a value of 0.89.49 The
QCISD(T) barrier height is in agreement with the mPW1K value at 15.1 kcal/mol. The
93
second available reaction for the Q(1,4s)OOH intermediate is a simple β-scission
resulting in propene and hydroperoxy radical with ΔH‡(0 K) = +15.3 kcal/mol and ΔH(0
K) = +4.8 kcal/mol. The B3LYP and mPW1K energies reflect the trends seen in the step
yielding methyloxirane, and the mPW1K wavefunction has an <S2> value of 0.82.
Overall, reaction pathways proceeding to products through the Q(1,5p)OOH intermediate
have formidable barrier heights with respect to the energetic barrier required (ΔH‡(0 K) =
+8.0 kcal/mol) to return to n-propylperoxy radical. The relatively lower barrier to
regenerate n-propylperoxy radical (ΔH(0 K) = +35.1 kcal/mol) makes other isomerization
pathways preferable. An additional unimolecular isomerization from the Q(1,5p)OOH
intermediate has been calculated by Green et al.50 at the CBS-QB3 level in which the OH
moiety is transferred to the carbon radical center. The barrier was calculated to be 27.5
kcal/mol with a considerable reaction exothermicity of 50.4 kcal/mol.
The most favorable of the two 1,4-hydrogen transfer TSs, at the CBS-QB3 level,
is that of the concerted elimination in which the C−O peroxy bond breaks, while
simultaneously abstracting a hydrogen atom on the 2-carbon of the propyl moiety with
the distal end of the peroxy radical, resulting in the direct formation of propene and
hydroperoxy radical. This mechanism is analogous to the 1,4-concerted mechanism
isolated in computational studies of ethylperoxy radical.18 The barrier for this reaction
step is +30.9 kcal/mol, and the reaction is endothermic by 18.2 kcal/mol. The B3LYP
values are several kcal/mol lower in energy and the mPW1K values are several kcal/mol
greater than the CBS-QB3 energies. On the other hand, the previously reported
QCISD(T)30 barrier is in good agreement at ΔH‡(0 K) = +29.7 kcal/mol. The 1,4-H
transfer isomerization mechanism, resulting in the formation of Q(1,4s)OOH, has a
94
slightly greater barrier than the concerted elimination mechanism, at 32.1 kcal/mol.
Q(1,4s)OOH was shown to be derived from Q(1,5p)OOH with a barrier height ~6
kcal/mol greater that for 1,4-isomerization. Q(1,4s)OOH, furthermore, must undergo an
endothermic β-scission to yield propene and hydroperoxy radical. On the other hand, the
Q(1,4s)OOH → methyloxirane + OH reaction is thermodynamically and kinetically more
favorable. The B3LYP and QCISD(T) barrier heights for the 1,4-H transfer isomerization
TS are in very good agreement with the CBS-QB3 values; however, the mPW1K method
predicts a barrier height ~4 kcal/mol greater.
The final pathway calculated for the unimolecular decomposition of npropylperoxy radical involves a 1,3-H transfer isomerization mechanism to directly yield
propanal and hydroxyl radical. The transfer of a 1-carbon hydrogen to the terminal
oxygen-centered radical simultaneously causes an OH radical to be extruded instead of a
stable hydroperoxypropan-1-yl radical. The 1,3-H transfer mechanism requires a highenergy four-member ring TS with ΔH‡(298 K) = +40.9 kcal/mol relative to npropylperoxy radical. Propanal and hydroxyl radical are the most thermodynamically
stable products obtained from the unimolecular decomposition pathways studied with an
exothermicity of 25.2 kcal/mol. The B3LYP and mPW1K values are in fair agreement
with only the mPW1K method predicting a barrier height 5.1 kcal/mol greater than the
CBS-QB3 value. Despite the favorable reaction energy, the barrier for 1,3-H transfer is
too formidable to be of significant consequence.
In summary, the most favorable kinetic process is the 1,4-H transfer that occurs
concomitantly with elimination to directly generate propene and HO2. At the CBS-QB3
level, the activation barrier is 30.8 kcal/mol (ΔH298). Experimentally, Taatjes et al.29
95
studied the reaction of propyl radicals with O2 and examined the HO2 and OH yields.29,30
Two HO2 source components over the 296-683 K temperature range were observed. HO2
was found to have a minor, prompt source between 296-550 K, with a percent yield from
1 to 16, and a major, separate source above 550 K. The prompt production was attributed
to excited propylperoxy radical and the other, commencing at just over 500 K, to
thermalized propylperoxy radical with an activation energy for HO2 production of 26
kcal/mol. The production of OH radical at various temperatures was shown to have a
small prompt source with a sharp increase in production above 600K, similar to HO2.
These experimental observations are consistent with the CBS-QB3 potential energy
surface that we have generated. Activated n-propylperoxy radical can react through the
two 1,4-H transition states which lie below the energy of n-propyl radical and O2, with
the concerted elimination yielding HO2 and the isomerization yielding OH radical. These
barriers as well as the other calculated barriers, however, are too considerable to be of
consequence at lower temperatures (< 500 K).
In order to estimate potential errors in the thermodynamics associated with the
harmonic-oscillator rigid-rotor approximation, the anharmonic vibrational frequencies
were calculated and low-energy torsions were treated as hindered rotors to determine the
corrected reaction barrier energetics for both the 1,4-H transfer and concerted 1,4-H
transfer/elimination reactions at the B3LYP/6-31+G** level. These two transition states
provide the most competitive decomposition pathways to generate bimolecular products.
The reduced moment of inertia is calculated about the axis which includes the twisting
bond. Each hindered rotor’s contribution to the thermodynamic parameters was
determined by generating a rigid potential energy profile of each internal rotor. The
96
profiles were used to generate a hindrance potential as a Fourier series to construct the
Hamiltonian. Using the free internal rotation wave functions as a basis, the hindered rotor
energy levels were calculated by direct diagonalization of the Hamiltonian matrix. The
hindered rotor partition functions were obtained via summation over the energy levels.51
Table 3.7 contains the 298 K enthalpic and free energy barriers for the two 1,4-H transfer
reactions determined using the harmonic-oscillator rigid-rotor approximation,
anharmonic-oscillator, hindered rotor, and a combination of hindered-rotor anharmonic
oscillator treatments. The change in enthalpic barrier due to the refined treatments is very
small, +0.3 kcal/mol between the harmonic and anharmonic oscillator treatments for the
concerted 1,4-H transfer/elimination barriers. The anharmonic treatment yielded no
significant change in the free energy barriers as well. Treatment of internal rotors as
hindered rotors, on the other hand, increased the free energy barriers by ~1.5 kcal/mol.
This increase is attributed to a substantial gain in entropy for n-propylperoxy radical due
to its three internal rotors versus one for each of the transition states.
97
harm. osc.
anharm. osc.
hin. rot./harm.
osc.
hin. rot./anharm.
osc.
ΔH (298 K)
TS (1,4elim)a
TS (1,4)
27.1
31.9
27.4
31.7
27.0
31.9
27.1
31.7
δTSb
4.88
4.31
4.93
4.66
ΔG (298 K)
TS (1,4elim)a
TS (1,4)
27.5
33.1
27.8
32.6
29.1
34.7
29.2
34.5
δTSb
5.54
4.88
5.55
5.27
Table 3.7. Thermodynamic values, ΔH≠ (298 K) and ΔG≠ (298 K) kcal/mol, at the
B3LYP/6-31+G** level relative to n-propylperoxy radical (gG) for the transition states
involving 1,4-H transfer treating internal rotors and frequencies as both harmonic and
anharmonic oscillators.
a
elim distinguishes the concerted TS which includes HO2 elimination from the formal
1,4-H transfer TS. b Energy difference between the two transition states [TS(1,4) –
TS(1,4elim)].
98
3.4. Conclusions
The conformational distribution and unimolecular decomposition pathways for npropylperoxy radical have been generated by high-level theoretical methods. At room
temperature, each of the five unique rotamers of n-propylperoxy radical can be expected
to be present and contribute to the CRDS spectrum. At the CBS-QB3 level, the 298 K
distribution of rotamers is predicted to be 28.1, 26.4, 19.6, 14.0, and 11.9 % for the gG,
tG, gT, gG', and tT conformations, respectively. The B3LYP and mPW1K distributions
vary with respect to the most favorable rotamers. There is a significant deviation between
the CBS-QB3 and two hybrid DFT methods, on the order of ~4–5 kcal/mol, in
calculating the C–OO bond energy. This points to a systematic problem for hybrid DFT
methods causing these bond energies to be underestimated. Aside from underestimating
the C–OO bond energy, the B3LYP/6-31+G** transition state and reaction energies are
in very good agreement with the CBS-QB3 values, suggesting promising utility for
studying unimolecular potential energy surfaces of larger alkylperoxy radical systems.
The mPW1K/6-31+G** method, on the other hand, provided transition state energies
which were significantly larger than the CBS-QB3 values.
The C–O2 bond dissociation energy in n-propylperoxy radical is predicted at the
CBS-QB3 level to be 36.1 kcal/mol. n-Propylperoxy radicals are stable, at temperatures
commensurate with those in the troposphere, to unimolecular decomposition as a result of
formidable barriers (~30 kcal/mol) to formation of bimolecular products. There appears
to be a much greater propensity for bimolecular product formation to dominate reactivity
in oxidizing environments at temperatures above 500 K. The lowest barrier height to
99
produce bimolecular products, from n-propylperoxy radical, occurs through the concerted
1,4-H-atom transfer and elimination transition state which has a ΔH‡(0 K) = +30.9
kcal/mol, relative to n-propylperoxy radical and leads directly to propene and HO2
radical. Furthermore, despite a lower TS energy for the 1,5-isomerization (ΔH‡(0 K) =
+23.9 kcal/mol, relative to n-propylperoxy radical), the subsequent steps for Q(1,5p)OOH
decomposition must proceed through significantly higher energetic barriers, thereby
rendering its unimolecular decomposition products unlikely.
100
References for Chapter 3
1
Finlayson-Pitts, B. J.: Pitts, J. N., Jr. Chemistry of the Upper and Lower Atmosphere:
Theory, Experiments, and Applications, Academic Press, San Diego, California, 2000.
2
Wallington, T. J.; Dagaut, P.; Kurylo, M. Chem. Rev. 1992, 92, 667-710.
3
Compton, R. G.; Hancock, G. Comprehensive Chemical Kinetics, Low-Temperature
Combustion and Autoignition, Vol. 35 Pilling, M. J., Ed., Elsevier, Amsterdam, 1997.
4
Glassman, I. Combustion, Academic Press, San Diego, California, 1996.
5
Bozzelli, J. W.; Pitz, W. J. Twenty-Fifth Symposium (International) on Combustion,
The Combustion Institute: Pittsburgh, PA., 1994; 783-791.
6
Bozzelli, J. W.; Sheng, C. J. Phys. Chem. A 2002, 106, 1113-1121.
7
Wagner, A. F.; Slagle, I. R.; Sarzynski, D.; Gutman, D. J. Phys. Chem. 1990, 94, 1853.
8
Kaiser, E. W.; Wallington, T. J.; Andino, J. M. Chem. Phys. Lett. 1990, 168, 309.
9
Kaiser, E. W.; Rimai, L.; Wallington, T. J. J. Phys. Chem. 1989, 93, 4094.
10
Kaiser, E. W.; Lorkovic, I. M.; Wallington, T. J. J. Phys. Chem. 1990, 94, 3352.
11
Dobis, O.; Benson, S. W. J. Am. Chem. Soc. 1993, 115, 8798.
12
Kaiser, E. W. J. Phys. Chem. A 2002, 106, 1256.
13
Kaiser, E. W. J. Phys. Chem. 1995, 99, 707.
14
Clifford, E. P.; Farrell, J. T.; DeSain, J. D.; Taatjes, C. A. J. Phys. Chem. A 2000, 104,
11549.
15
Bozzelli, J. W.; Dean, A. M. J. Phys. Chem. 1990, 94, 3313.
16
Quelch, G. E.; Gallo, M. M.; Schaefer, H. F., III. J. Am. Chem. Soc. 1992, 114, 8239.
101
17
Quelch, G. E.; Gallo, M. M.; Shen, M.; Xie, Y.; Schaefer, H. F., III.; Moncrief, D. J.
Am. Chem. Soc. 1994, 116, 4953.
18
Ignatyev, I. S.; Xie, Y.; Allen, W. D.; Schaefer, H. F., III. J. Chem. Phys. 1997, 107,
141.
19
Stark, M. S. J. Am. Chem. Soc. 2000, 122, 4162.
20
Chen, C.-J.; Bozzelli, J. W. J. Phys. Chem. A 2000, 104, 4997.
21
Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H. F., III. J. Phys. Chem A 2000, 104,
9823.
22
Miller, J. A.; Klippenstein, S. J.; Robertson, S. H. Proc. Combust. Inst. 2000, 28, 1479.
23
Miller, J. A.; Klippenstein, S. J. Int. J. Chem. Kinet. 2001, 33, 654.
24
Bozzelli, J. W.; Sheng, C. J. Phys. Chem. A 2002, 106, 1113.
25
Sheng, C. Y.; Bozzelli, J. W.; Dean, A. M.; Chang, A. Y. J. Phys. Chem A 2002, 106,
7276.
26
Ruiz, R. P.; Bayes, K. D. J. Phys. Chem. 1984, 88, 2592-2595.
27
Slagle, I. R.; Park, J.; Gutman, D. Twentieth Symposium (International) on
Combustion, The Combustion Institute: Pittsburgh, PA., 1984, 733-741.
28
Kaiser, E. W.; Wallington, T. J. J. Phys. Chem. 1996, 100, 18770-18774
29
DeSain, J. D.; Clifford, E. P.; Taatjes, C. A. J. Phys. Chem. A 2001, 105, 3205-3213.
30
(a)DeSain, J. D.; Klippenstein, S. J.; Miller, J. A.; Taatjes, C. A. J. Phys. Chem. A
2003, 107, 4415-4427. (b) DeSain, J. D.; Klippenstein, S. J.; Miller, J. A.; Taatjes, C. A.
J. Phys. Chem. A 2004, 108, 7127-7128.
102
31
DeSain, J. D.; Taatjes, C. A.; Miller, J. A.; Klippenstein, S. J.; Hahn, D. K. Faraday
Discuss. 2001, 119, 101-120.
32
Naik, C.; Carstensen, H. -H.; Dean, A. M. Proceedings of the Third Joint Meeting of
the U. S. Sections of the Combustion Institute, Chicago, Illinois, 2003.
33
Chan, C. -J.; Hamilton, I. P.; Pritchard, H. O. Faraday Trans. 1998, 94, 2303-2306.
34
Chan, C. -J.; Hamilton, I. P.; Pritchard, H. O. Phys. Chem. Chem. Phys. 1999, 1, 3715-
3719.
35
Zalyubovsky, S. J.; Glover, B. G.; Miller, T. A.; Hayes, C. J.; Merle, J. K.; Hadad, C.
M. J. Phys. Chem. A 2005, 109, 1308–1315.
36
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.;
Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani,
G.; Rega, N.; Pettersson, G. A.; Nakatsuji, H; Hada, M.; Ehara, M.; Toyota, K.; Fukuda,
R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.;
Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.;
Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.;
Ayala, P. Y.; Morokuma, K.; Voth, g. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V.
G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.;
Cioslowski, J.; Stefanov, B. B.; Lui, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;
Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
103
Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.;
Pople, J. A. Gaussian 03, Revision B.04, Gaussian, Inc.; Pittsburgh, PA, 2003.
37
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
38
Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1998, 37, 785-789.
39
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 4811.
40
Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem. Phys.
1999, 110, 2822-2827.
41
(a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.;
Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523.
42
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502_16513.
43
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936-2941.
44
Knyazev, V. D.; Slagle, I. R. J. Phys. Chem. A 1998, 102, 1770-1778.
45
Please note that the collaborating authors use a naming convention utilizing all upper
case letters as opposed to alternating upper and lower case letters. Furthermore, in
reference 35 the naming order started at the terminal methyl carbon as opposed to the
terminal peroxy oxygen.
46
Tarczay, G.; Zalyubovsky, S. J.; Miller, T. A. Chem. Phys. Lett. 2005, 406, 81.
47
Viskolcz, B.; Lendvay, G.; Körtvélyesi, T.; Seres, L. J. Am. Chem. Soc. 1996, 118,
3006-3009.
48
Lendvzy, G.; Viskolcz, B. J. Phys. Chem. A 1998, 102, 10777-10786.
104
49
The <S2> values for the Hartree-Fock wavefunctions are ~0.91, ~0.82, and ~0.80 for
the ab initio components for the transition state structures TS (1,4elim), TS(1,4), and
TS(1,5), respectively.
50
Green, W. H.; Wijaya, C. D.; Yelvington, P. E.; Sumathi, R. Mol. Phys. 2004, 102,
371-380.
51
The calculations were performed using software provided via personal communication
by Dr. Timothy A. Barckholtz, ExxonMobil Research and Engineering Company,
Annandale, New Jersey.
105
CHAPTER 4
STUDY OF SUBSTITUENT EFFECTS ON THE BOND DISSOCIATION
ENTHALPIES AND HYDROXYL RADICAL REACTIONS OF ETHENES AND
BENZENES
4.1. Introduction
Aromatic moieties are ubiquitous in the structure of coal and gasoline fuel blends
which are burned to yield energy. Various aromatics and unsaturated molecules resulting
from the partial oxidation of these aromatic compounds are emitted into the troposphere
as a result of incomplete combustion.1,2 Combustion processes are difficult to study in
totality, due to the complexity in coal structure and diverse constituency of gasoline
formulations, creating a vast number of chemical reactions occurring in non-uniform
environments. These complexities can make predicting emissions to be demanding as
well. Combustion emissions can contribute to environmental problems via formation of
particulate matter (PM), acid rain (NOx and SOx), and ozone formation. 3 Furthermore,
many aromatic compounds have been shown to be human carcinogens.4 In order to
reduce the amount of potentially carcinogenic pollutants generated and to increase the
efficiency of the combustion process (thereby conserving natural resources), a thorough
understanding of the oxidation processes for aromatic compounds is imperative.
106
The decomposition of combustion and atmospheric organic compounds is
initiated by reaction with free radicals. To advance our knowledge of aromatic oxidation
processes, many experimental5,6,7,8,9,10,11,12 and theoretical13,14,15 studies have examined the
.
reaction of hydroxyl radical with benzene. Hydroxyl radical ( OH) is a highly reactive
oxidant responsible for the initiation of decomposition for volatile organic compounds
(VOCs) in the troposphere during daylight hours and is prominent in combustion’s
radical pool (i.e. OH, H, and O).3,16,17,18,19 The initiation of benzene oxidation by OH
radical is believed to proceed through either an abstraction or addition mechanism as
shown in equation 4.1.
+ H2O
+ OH
(4.1a)
OH
+ OH
(4.1b)
At lower temperatures (T< 400 K), relevant to atmospheric reactions and lowtemperature combustion, the addition mechanism (eqn. 4.1b) predominates with the rate
coefficients showing negative temperature dependence. This temperature dependence is
attributed to a shift in equilibrium favoring regeneration of reactants at increasing
107
temperatures.5,3,16 When the temperature becomes greater than 600 K, the equilibrium
between reactants and forming the addition adduct (i.e., the hydroxycyclohexadienyl
radical, eqn. 4.1b) significantly shifts toward reactants, and the abstraction channel (eqn.
4.1a) begins to predominate, exhibiting a normal temperature dependence.3 The
temperature profile of the rate coefficients for the OH radical reaction with benzene is
dependent on the reaction energy for adduct formation at low temperatures, as well as the
C–H bond dissociation energies, which typically determine abstraction barrier heights.
Due to a decrease in vapor pressure typically seen when a benzene’s hydrogen atom is
replaced by a substituent (caused by an increase in polarity and molecular weight), many
studies of hydroxyl radical with mono-substituted benzenes have been performed in the
condensed phase.20,21,22,23 However, the reactivity of a system in the gas phase can be
significantly different from the solution phase. In fact, we have noted an unexpected
solvation effect for hydroxyl radical reaction with benzene between aqueous and organic
solvents whereby OH radical reacts faster in water due to a differential stabilization of the
transition state due to partial electron transfer. 24,25
In previous efforts, we have shown that the C–H BDE values for polycyclic
aromatic hydrocarbons, including N, O, and S ring atoms, can be effectively modeled as
the monocyclic analog. 13,26,27 However, coal also has functional groups attached as
substituents adjacent to the aromatic ring. As a result, we sought to explore the effect of
substituents on the sp2 C–H BDE values via a computational study. We have, therefore,
investigated substituted ethenes and benzenes as a function of substituent X.
108
X
X
H
H
H
H
The purpose of this study is to use density functional theory (DFT) 28 to determine
the gas-phase reaction and barrier height energies for the addition channel for the reaction
of OH radical with a series of ethenes and benzenes which are mono-substituted with the
F, Cl, CF3, CH3, OCH3, OH, CHO, SH, SCH3, CN, NH2, and NO2 substituent groups.
Furthermore, C–H bond dissociation enthalpies (BDEs, ΔH(298 K)) for the substituted
ethenes and benzenes will be calculated. Several thorough works examining the C–X (X
= substituent) BDEs for many of these substituents have already been reported for the
ethenes and benzenes.29,30 Comparisons will be made concerning the reactivity of ethenes
vis-à-vis benzenes and the effect of H-substitution in regards to reactions 4.1a and 4.1b.
This work also serves as a continuation of our previous studies exploring the phenomena
responsible for regulating the reactivity of hydroxyl radical towards aromatic rings24,25
and aromatic bond dissociation energies.26
4.2. Method
All geometry optimizations, single-point energy and vibrational frequency
calculations were performed using Gaussian9831 at the Ohio Supercomputer Center or on
our IBM RS/6000 workstations. All stationary points were optimized using the B3LYP
and BH&HLYP hybrid density functional theory (DFT)28 functionals. B3LYP32,33
geometries were optimized with the 6-31G* basis set and BH&HLYP geometries with
109
the 6-31+G** basis set.34 The B3LYP functional has been shown to evaluate aromatic
C−H and other homolytic bond dissociation enthalpies accurately, relative to more
expensive high-level ab initio methods, with both reduced cost and spin contamination in
the calculated wavefunction.26,35 In general, 〈S2〉 values for all B3LYP and BH&HLYP
wavefunctions were as expected, typically 0.75 ≤ 〈S2〉 ≤ 0.88. Vibrational frequency
calculations were performed on all stationary points to confirm the nature of the
geometry. Minima were confirmed to have all real vibrational frequencies. All transition
state geometries were confirmed to have a single imaginary vibrational frequency
corresponding to motion along the reaction coordinate, and these were further shown to
connect to the proper reactant and product by displacement along the transition vector
(typically 10%) for the imaginary vibrational frequency in both the positive and negative
direction, followed by careful optimization using either opt=calcfc or calcall. Single-point
energy calculations on all B3LYP stationary points were determined at the B3LYP/6311++G** level with the scf = tight option. All basis sets for these B3LYP calculations
used six Cartesian d functions.
The thermal contributions were calculated using unscaled harmonic vibrational
frequencies and rotational constants derived from the B3LYP/6-31G* and BH&HLYP/631+G** geometries and assuming an ideal gas at 1 atm. The B3LYP zero-point
vibrational energies (ZPE) were scaled by a factor of 0.9806,36 while the BH&HLYP
ZPEs were used unscaled.
The B3LYP/6-311++ G**//B3LYP/6-31G* wavefunctions were utilized to
estimate the atomic charges and spin densities via the atoms in molecules (AIM) method
provided via the AIMPAC software.37
110
4.3. Bond Dissociation Enthalpies
4.3.1. Substituted Ethenes
Table 4.1 summarizes the bond dissociation enthalpies (BDEs, ΔH(298 K)
kcal/mol) for the cis C–H bonds and substituent R–H bonds (R = C, N, O, S) for the
substituted ethenes calculated at the B3LYP/6-311++G**//B3LYP/6-31G* level, along
with available experimental values. For the purpose of comparison with the BDEs of both
ortho C–H bonds on the benzenes, both the anti and syn substituent orientations were
examined for the ethenes. Also provided in Table 4.1 are charges and cis radical-center
spin densities (populations) derived from the AIM analysis for the combined substituent
(i.e., F, CH3, etc). The calculated B3LYP/6-311++ G**//B3LYP/6-31G* C–H BDE for
ethene is 109.5 kcal/mol, which is in good agreement with the recommended
experimental value of 110.7±0.6 kcal/mol.38 The largest calculated BDE was that of
fluoroethene with a value of 114.0 kcal/mol. Zhang39 has calculated a comparable value
of 115.2 kcal/mol at the CBS-4 level. Furthermore, Zhang showed for the fluoro and
trifluoromethyl mono-substituted ethenes that the substituent affected both vicinal C–H
bonds similarly.
We have also calculated the BDE values for the X–H bonds on the substituents,
and those values at the B3LYP method are in reasonable agreement with experiment.
These values will not be discussed further, however, since this study’s primary focus is
on the effect of the substituents on the sp2 C–H BDEs.
Generally, replacing one of ethene’s hydrogens by a substituent increases the
BDE for the C–H bond cis to the substituent (Figure 4.1). The range of BDE values,
111
however, is very small. For the 18 BDEs calculated, the energies differ no more than 4.5
kcal/mol from the value for ethene. Figure 4.1 shows two plots of the calculated B3LYP
BDE values for the cis C–H bonds against the total AIM charge localized on the
substituent for the mono-substituted ethenes. Both inductive/field and steric effects are
found to influence the magnitude of the cis C–H BDE. Overall, BDE values correlate
reasonably well with the total AIM charge of the substituent (R2 = 0.78). However, when
the values for syn-oriented substituents are removed from the BDE set, the correlation is
significantly improved (R2 = 0.92). Given the small range of the BDE values, steric
interactions can play nearly as significant a role as field effects. Structural relaxation of
the syn-oriented mono-substituted ethenes after removal of the cis H-atom opposes, and
nearly negates, the inductive effect of the substituent on the BDE. The fluoro and nitro
substituents have AIM charges of –0.62 and –0.54 e, respectively, and yield the largest
BDEs (114.0 and 113.9 kcal/mol, respectively), reflecting the importance of inductive
effects. Interestingly, the AIM charge for hydrogen on the parent benzene is 0.02 e, and is
not predicted to be the most positively charged substituent (0.10 e for SCH3 syn);
however, it still provides the lowest BDE value.
112
cis C–H
substituent
ΔH(298 K)
NH2
SCH3 syn
OCH3 anti
SCH3 anti
OH syn
OCH3 syn
SH syn
OH anti
SH anti
CHO syn
CH3
CHO anti
CN
Cl
H
F
NO2
CF3
112.1
110.8
113.7
110.8
112.2
111.9
110.4
113.6
110.9
112.1
110.2
110.8
112.6
112.1
109.5
114.0
113.9
112.0
subst. (C, N, O, S)–H
Expt.
ΔH(298 K)
Expt.
87.8 (87.0)a
93.6
95.2
81.0
96.9
85.7
81.0
88.5
85.2
89.4
110.7±0.638
113c
88.8±0.438
87.1±1.0b
AIM
substituent
charge
–0.34
0.10
–0.51
0.09
–0.52
–0.50
0.08
–0.52
0.06
–0.09
0.04
–0.08
–0.26
–0.21
0.02
–0.62
–0.54
–0.18
β–C spin
density
0.92
0.92
0.93
0.90
0.92
0.91
0.91
0.93
0.91
0.94
0.91
0.93
0.95
0.92
0.92
0.93
0.94
0.92
Table 4.1. Summary of Bond Dissociation enthalpies (BDEs, ΔH(298 K) kcal/mol), Spin
Densities, (Populations) and AIM Substituent Charges for mono-Substituted Ethenes.
a
Corresponds to N–H bond with syn orientation. b McMillan, D. F.; Golden, D. M. Ann.
Rev. Phys. Chem. 1982, 33, 493. c Steinkruger, F. J.; Rowland, F. S. J. Phys. Chem. 1981,
85, 136.
113
BDE vs subst. charge
115
y = -4.72x + 110.79
114
R2 = 0.78
BDE (kcal/mol)
113
112
111
110
109
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
BDE vs
subst.
charge
substituent charge
-0.1
0.0
0.1
0.2
0.1
0.2
115
y = -5.90x + 110.58
114
R2 = 0.92
BDE (kcal/mol)
113
112
111
110
109
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0.0
substituent charge
Figure 4.1. Correlation plots for cis C–H BDEs of mono-substituted ethenes versus AIM
charge on the substituent of the parent ethene. All conformations are considered (top) and
with syn orientations omitted (bottom).
114
4.3.2. Substituted Benzenes
Table 4.2 summarizes the bond dissociation enthalpies (BDEs, ΔH(298 K)
kcal/mol) for the ortho, meta, and para C–H bonds as well as substituent X–H bonds (X =
C, N, O, S) of the substituted benzenes calculated at the B3LYP/6-311++G**//B3LYP/631G* level, along with some experimental values. Also provided in Table 4.2 are the
total substituent charges and radical-center spin densities (populations) derived from the
AIM analysis. The B3LYP C–H BDE for benzene is 110.6 kcal/mol, in reasonable
agreement with the recommended experimental value of 112.9 ± 0.5 kcal/mol.38,40 While
the calculated value is in reasonably good agreement with experiment, the discrepancy of
~2 kcal/mol may signify a need to shift all of the values upward ~2 kcal/mol. We do
anticipate, however, that qualitative trends will be adequately treated. The fluoro- and
nitro- substituted benzenes yield the largest ortho C–H BDEs, both with values of 113.2
kcal/mol.
The B3LYP X–H BDEs for the actual substituents’ bond cleavages are in fair
agreement with the experimental values. Estimation of the gas-phase S–H and O–H bond
strengths, however, are underestimated by ~7.5 kcal/mol based on the limited
experimental values in aqueous solution.
Figure 4.2 shows correlation plots for cis C–H BDEs of mono-substituted
benzenes verses the AIM charge localized on the substituent. The calculated ortho C–H
BDE values for substituted benzenes are similar to the analogous cis C–H BDEs for
substituted ethenes. For larger substituents, there are significant steric interactions. The
OH, OCH3, SH, and SCH3 substituents have an asymmetric orientation with respect to the
115
ortho positions on the benzene ring, and the lone pair electrons have a destabilizing
interaction with the benzene π orbital. Therefore, the substituted benzenes have
destabilizing interactions on both sides of the substituent, which are being relieved by
abstraction of a syn ortho hydrogen, unlike the substituted ethenes. This extra strain
release relative to the ethenes may be responsible for the poor correlation seen in the plot
including all BDE values (Figure 4.2, top). However, when the syn ortho BDE values are
removed from the plot, a good correlation between BDE and AIM substituent charge is
seen (R2 = 0.90).
The spread of the calculated ortho C–H bond dissociation enthalpies of 3.7
kcal/mol is slightly smaller than that of the ethenes. This may be due to an increased
ability to distribute the spin density of the unpaired electron in the substituted benzene
radicals. Typical values for the AIM derived radical-center spin densities are 0.86 – 0.89
e for phenyl radicals and 0.91 – 0.95 e for the ethenyl radicals. The BDEs for the meta
and para C–H bonds in the substituted benzenes are highly invariant, ranging from ~110
to ~112 kcal/mol. In general, the meta C–H BDEs tend to be closer to 110 kcal/mol,
while the para C–H BDE lie nearer to 112 kcal/mol.
116
ortho C–H
meta C–H
para C–H
substituent (C, N, O, S)–H
substituent
ΔH(298 K)
ΔH(298 K)
ΔH(298 K)
ΔH(298 K)
CH3S syn
CH3O syn
CH3
OH syn
SH syn
H
CH3S anti
NH2
SH anti
CHO anti
CF3
Cl
CH3O anti
CN
CHO syn
OH anti
F
NO2
109.5
110.1
110.1
110.5
110.6
110.6
110.8
110.9
111.0
111.2
111.9
112.1
112.3
112.4
112.7
112.8
113.2
113.2
110.2
110.2
110.3
111.0
111.0
111.4
111.7
110.9
111.8
111.5
92.2
94.6
86.6
82.6
75.5
110.5
110.2
110.6
111.0
111.3
110.8
110.5
111.4
110.8
110.6
111.0
111.6
111.4
111.8
111.5
110.8
111.1
111.5
111.7
111.2
110.8
111.8
111.7
111.4
92.2
88.1
75.5
88.5
Expt.
89.7±0.638
90±338
83.3±2a
112.9±0.538
88.0±2a
83.3±2a
86.9±1a
94.6
88.5
82.6
86.9±1a
90±338
AIM
substituent
charge
0.08
–0.51
0.03
–0.52
0.05
0.02
0.08
–0.32
0.05
–0.10
–0.19
–0.22
–0.51
–0.28
–0.10
–0.52
–0.63
–0.53
radical
center spin
density
0.86
0.86
b
0.88
0.88
0.88
0.88
b
0.88
0.88
b
0.89
0.89
0.88
0.89
0.89
0.89
0.89
Table 4.2. Summary of Bond Dissociation Enthalpies (BDEs, ΔH(298 K) kcal/mol), Spin
Densities (Populations), and AIM Substituent Charges for mono-Substituted Benzenes.
a
McMillan, D. F.; Golden, D. M. Ann. Rev. Phys. Chem. 1982, 33, 493. b The AIM
integration routine for this atom failed to converge.
117
114
y = -2.60x + 110.86
R2 = 0.32
BDE (kcal/mol)
113
112
111
110
109
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
substituent charge
-0.1
0.0
0.1
0.2
114
y = -3.89x + 110.92
R2 = 0.90
BDE (kcal/mol)
113
112
111
110
109
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
substituent charge
-0.1
0.0
0.1
0.2
Figure 4.2. Correlation plots for the ortho B3LYP/6-311++G**//B3LYP/6-31G* C–H
BDEs of the mono-substituted benzenes verses AIM charge on the substituent of the
parent benzene. All conformations are considered (top) and with syn orientations omitted
(bottom).
118
4.4. Hydroxyl Radical Addition Reactions
4.4.1. Substituted Ethenes
The barrier heights (ΔΗ‡298) and reaction energies (ΔΗ298) for the addition of
hydroxyl radical to the double bond carbons of the mono-substituted ethenes have been
calculated at the BH&HLYP/6-31+G** level and are summarized in Table 4.3. Figure
4.3 shows several representative OH radical addition transition-state structures. Attempts
were made to calculate the OH radical + mono-substituted ethene addition transition
states at the B3LYP/6-31G* level. However, due to low barriers for the OH-radical
addition to unsaturated molecules (OH radical + ethene, Ea = –0.87 kcal/mol),41 the
B3LYP method predicted a transition-state structure with a long C---O distance, as a
result of attractive forces between the OH hydrogen and the polar substituent in several
instances. We are not judging these transition states; however, they are not ideal for
examining qualitative trends in substituent effects. On the other hand, the BH&HLYP/631+G** transition state geometries are free of these interactions (Figure 4.3).
Furthermore, a comparison of the BH&HLYP addition barrier heights to the available
experimental ambient temperature activation energies (Ea) shows good agreement. In
each of the cases in which an experimental Ea is listed, the calculated barrier height for βaddition is within ~1 kcal/mol.
Table 4.3 also provides calculated and experimental ionization energy (IE) values
for the mono-substituted ethenes at the BH&HLYP/6-31+G** level, along with several
experimental values. The BH&HLYP IE values are calculated as the difference in ZPE
corrected energies (SCF + ZPE) between the closed-shell mono-substituted ethene and
119
the corresponding lowest energy radical cation. The calculated IEs tend to underestimate
the experimental values by ~10 kcal/mol or less, and once again, qualitative trends are
being pursued in this investigation. Figure 4.4 shows a comparison of the theoretical IEs
with the barrier heights for addition of hydroxyl radical to the β-carbon of the substituted
ethenes. It can be seen that there is good correlation (R2 = 0.87) for the barrier heights
and the adiabatic ionization energy of the parent ethene. A similar correlation was not
observed for the α-addition barrier heights. Furthermore, the thermodynamic reaction
energies for α-additions appear to have no correlation with either barrier heights or IE
values (Figure 4.4). This analysis shows that the reaction rates and product distributions
for the electrophilic attack of alkenes by hydroxyl radical in the gas phase are regulated
primarily by the propensity of the alkene to transfer electron density to hydroxyl radical.
Such a trend has recently been noted in resonance Raman spectroscopy21 as well as in
laser flash photolysis experiments.24,25
120
substituent
NH2
SCH3 syn
OCH3 anti
SCH3 anti
OH syn
OCH3 syn
SH syn
OH anti
SH anti
CHO syn
CH3
CHO anti
CN
Cl
H
F
NO2
CF3
Ea
Expt.
–1.0041
–1.05a
–0.8741
–0.78a
β–addition
TS
adduct
–3.4
–27.6
–2.3
–29.1
–1.9
–26.5
–1.8
–29.7
–1.7
–26.6
–1.7
–24.0
–1.6
–29.6
–1.6
–27.3
–1.4
–29.4
–1.0
–35.2
–0.5
–25.6
–0.4
–31.3
–0.3
–32.5
–0.1
–27.4
0.0
–25.7
0.4
–24.2
0.4
–30.1
1.1
–25.2
α–addition
TS
adduct
–3.2
–26.1
2.9
–23.9
–3.4
–31.5
–0.5
–25.1
–0.1
–27.5
–0.1
–28.0
2.5
–25.6
–3.0
–31.9
0.4
–27.2
–4.0
–23.7
–0.4
–25.9
0.2
–22.0
3.5
–20.9
2.4
–30.1
0.0
–25.7
0.4
–34.5
2.5
–29.4
2.6
–26.3
ionization energy
BH&&HLYP
Expt.b
178.3
186.8
187.3
194.9
191.2
c
184.2
c
205.5
215.2
196.6
206.4
198.1
d
201.8
c
197.0
d
223.7
c
212.4
224.4
224.3
233.1
239.5
251.6
222.4
230.4
229.8
242.4
229.3
238.9
245.7
250.2
247.4
252.5
Table 4.3. Summary of Hydroxyl Radical Addition to mono-Substituted Ethenes
Reaction Barrier Heights, Reaction Energies (ΔH(298 K), kcal/mol), and Ionization
Energies (ΔH(0 K), kcal/mol) at the BH&HLYP/6-31+G** level.
a
Atkinson, R. Chem. Rev. 1986, 86, 69. b NIST Chemistry WebBook,
http://webbook.nist.gov/chemistry, 69, June 2005. c See the IE value for the other
substituent orientation. d Ionization energy not available.
121
2.67
2.15
2.77
2.29
2.15
2.22
methoxyethene
2.27
2.20
propenal
thiomethoxyethene
2.32
2.17
2.21
aminoethene
2.14
2.19
ethenol
2.21
ethenthiol
propene
Figure 4.3. BH&HLYP/6-31+G** transition state structures for OH radical addition to
the β-carbons of some mono-substituted ethenes. When applicable, the syn-oriented
substituent is on top. Distances are given in angstroms.
122
BH&HLYP beta addition
barrier height ΔH(298 K) (kcal/mol)
2
1
y = 0.05x - 11.41
R2 = 0.87
0
-1
-2
-3
-4
170
180
190
200
210
220
IE alpha
(kcal/mol)
BH&HLYP
addition
230
240
250
230
240
250
4
barrier height ΔH(298 K) (kcal/mol)
3
y = 0.05x - 9.58
R2 = 0.19
2
1
0
-1
-2
-3
-4
-5
170
180
190
200
210
220
IE (kcal/mol)
Figure 4.4. Plot correlating the BH&HLYP/6-31+G** barrier heights for OH radical
addition to the β-carbon (top) and α-carbon (bottom) of the mono-substituted ethenes
with the calculated ionization energies of the ethene precursor.
123
4.4.2. Substituted Benzenes
Table 4.4 lists the transition state barrier heights and reaction energies (ΔH(298
K), kcal/mol) at the BH&HLYP/6-31+G** level for the addition of hydroxyl radical to
the ipso, ortho, meta, and para ring positions of the mono-substituted benzenes. The
recommended gas-phase ambient temperature Ea for the reaction of OH radical with
benzene is 0.60 kcal/mol.2 The barrier height calculated via the BH&HLYP method is 4.7
kcal/mol, which appears to be overestimated. The discrepancy is not, however,
significant enough to prevent extraction of qualitative trends regarding substituent
effects.
Table 4.4 also contains the BH&HLYP/6-31+G** ionization energies for the
mono-substituted benzenes, along with the experimental values. The IE values are
calculated as the difference in ZPE-corrected energies (SCF + ZPE) between the closedshell substituted benzene and the corresponding radical cation. Comparison of the
calculated BH&HLYP barrier heights (ΔH≠(298 K) and IE values reveal trends similar to
those seen for the substituted ethenes. For OH radical addition to the ortho ring position
with a syn oriented substituent, the substituent’s hydrogen can interact with the incoming
OH oxygen via hydrogen bonding and reduce the barrier height relative to addition at the
anti ortho position. Figure 4.5 shows the structure for the syn and anti ortho transition
state geometries where hydrogen bonding is prominent. For benzaldehyde, on the other
hand, the anti ortho addition transition state is favored via interaction with the carbonyl
carbon’s large positive (+0.96 e) AIM charge. This interaction is manifested as a shorter
C---O distance and shift toward the carbonyl carbon relative to the syn ortho addition
124
transition state, as can be seen in Figure 4.5. Since in the TS structure for OH radical
addition to a phenyl ring, the hydrogen resides over the ring, the oxygen atom of the OH
unit can interact with a large substituent, resulting in poor correlation with IEs. In the
case of the OH radical addition to the ethenes, the OH radical’s hydrogen typically was
directed toward the substituent, and energetically favorable H-bonding type interactions
are minimal.
When these barrier heights for syn ortho addition are removed from the set, a
good correlation (R2 = 0.96, Figure 4.6 (top)) with IE values is observed. However, the
correlation for addition meta and ipso to the substituent is very low (Figure 4.7). The
analogous α and β barrier heights for OH radical addition to the substituted ethenes had a
similar correlation with the IE values. A good correlation is also seen in the comparison
of all para addition barrier heights (R2 = 0.89, Figure 4.6 (bottom)). The barrier heights or
IE values showed no correlation with reaction energies, however. The data show that, in
the gas phase, the ability of an aromatic functional group to transfer electron density to an
electrophilic hydroxyl radical can activate the ring toward radical addition. 42 This
activation is most significantly attenuated at ring positions ortho to a substituent.
125
substituent
NH2
OCH3 anti
OCH3 syn
H
CHO anti
CHO syn
CF3
Cl
CN
F
NO2
OH anti
OH syn
SCH3 anti
SCH3 syn
SH anti
SH syn
CH3
ipso addition
ortho addition
meta addition
para addition
TS
3.4
4.8
adduct
–13.0
–14.5
adduct
–14.6
–13.3
BH&HLYP
169.3
181.5
Expt.a
178.0
189.1
–12.9
–7.9
4.7
4.8
–12.9
–15.8
203.3
214.3
213.2
219.1
6.9
9.0
10.3
6.5
9.1
3.7
–12.5
–14.9
–6.3
–18.8
–14.8
–16.0
5.5
4.7
5.1
4.8
5.8
3.6
–12.3
–13.6
–15.2
–12.4
–14.3
–13.3
215.1
201.9
215.2
204.3
221.6
187.7
223.3
209.2
224.4
212.2
229.2
195.8
6.9
–13.2
3.4
–14.9
176.2
183.1
6.6
–13.4
3.7
–14.8
185.3
191.4
3.9
–14.4
TS
4.9
5.6
4.5
4.7
5.1
5.8
5.4
5.4
5.9
5.5
6.2
5.5
4.8
5.3
4.6
5.0
4.9
4.5
TS
2.3
3.5
4.7
7.1
TS
0.1
3.4
2.4
4.7
4.7
5.6
6.0
5.1
5.7
5.2
6.4
4.0
1.0
3.6
2.2
3.8
2.2
2.9
4.9
–13.6
193.7
203.6
adduct
–17.6
–14.3
–13.1
–12.9
–14.0
–13.3
–12.7
–13.3
–14.1
–12.3
–12.2
–13.5
–16.8
–15.3
–15.3
–14.9
–16.8
–14.4
adduct
–12.5
–13.1
–13.6
–12.9
–12.7
–11.5
–13.0
–12.8
–12.0
–12.8
–11.7
–12.0
–13.2
–12.8
–13.4
–12.9
–13.0
–13.3
ionization energy
Table 4.4. Summary of Hydroxyl Radical Addition to mono-Substituted Benzenes:
Reaction Barrier Heights, Reaction Energies (ΔH(298 K), kcal/mol), and Ionization
Energies (ΔH(0 K), kcal/mol) at the BH&HLYP/6-31+G** level.
a
NIST Chemistry WebBook, 69, http://webbook.nist.gov/chemistry, June 2005.
126
2.44
2.43
1.95
1.96
1.97
1.98
1.95
anisole
2.67
1.97
benzaldehyde
thiomethoxybenzene
2.60
2.00
2.38
1.98
1.98
H–O–C–C = 28.8
1.96
aniline
phenol
H–S–C–C = 35.8
1.97
thiophenol
2.77
1.96
toluene
Figure 4.5. BH&HLYP/6-31+G** transition state structures for OH radical addition to
the ortho positions of some mono-substituted benzenes. When applicable syn-oriented
substituent is on top. Distances are given in angstroms and dihedral angles given in
degrees.
127
ortho addition
barrier height ΔH(298 K) (kcal/mol)
7
y = 0.07x - 8.18
R2 = 0.96
6
5
4
3
2
160
170
180
190
200
IE (kcal/mol)
BH&HLYP
para addition
210
220
230
210
220
230
barrier height ΔH (298 K) (kcal/mol)
6
y = 0.06x - 6.69
R2 = 0.89
5
4
3
2
160
170
180
190
200
IE (kcal/mol)
Figure 4.6. Plots correlating the barrier heights for OH radical addition to monosubstituted benzenes with the calculated ionization energy. Ortho addition (top) and para
addition (bottom).
128
meta addition
barrier height ΔH (298 K) (kcal/mol)
6.5
y = 0.02x + 0.28
R2 = 0.56
6.0
5.5
5.0
4.5
4.0
160
barrier height ΔH (298 K) (kcal/mol)
12
10
170
180
190
200
IE (kcal/mol)
ipso addition
210
220
230
180
190
200
IE (kcal/mol)
210
220
230
y = 0.09x - 10.74
R2 = 0.43
8
6
4
2
0
160
170
Figure 4.7. Plots correlating the barrier heights for OH radical addition to monosubstituted benzenes with the calculated ionization energy. Meta addition (top) and ipso
addition (bottom).
129
4.5. Conclusions
The C–H bond dissociation enthalpies have been calculated for a series of monosubstituted ethenes and benzenes at the B3LYP/6-311++G**//B3LYP/6-31G* level.
Comparison has been made between the cis C–H BDEs of the mono-substituted ethenes
and ortho C–H BDEs for mono-substituted benzenes. In general, the magnitude of the
BDE values follows a similar ordering. Steric effects are more prominent in the benzenes
due to added destabilizing interactions with the phenyl ring on both sides of the
substituent. When BDE values influenced by steric interactions are removed from the
series, good correlation of both the cis C–H and the ortho C–H are found with the AIM
charge localized on the substituent. The meta and para C–H BDEs appear to be
minimally influenced by the substituent. Overall, the B3LYP method predicts that all
substituents increase the BDE for an sp2 C–H bond β to the substituent for both monosubstituted ethenes and benzenes.
The barrier heights and reaction energies for hydroxyl radical addition to monosubstituted ethenes and benzenes have been calculated at the BH&HLYP/6-31+G**
level. A good correlation is found between the ionization energies and barrier heights for
hydroxyl radical addition to the β-carbons (ethenes) and ortho and para addition
(benzenes). This finding is consistent with previous works in which the aromatic ring was
found to have radical cation character in the transition state for electrophilic radical
attack. 24,25 Furthermore, solution-phase reaction rates were correlated with ionization
potentials of the parent aromatic.21 In general, this study verifies that the gas-phase
130
addition of hydroxyl radical to the substituted benzenes proceeds according to the
established rules for electrophilic aromatic substitution.43
131
References for Chapter 4
1
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Mandronich, S.; Moortgat, G. K.; Wallington,
T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the Alkenes, Oxford
University Press, New York, 2000.
2
Calvert, J. G.; Atkinson, R.; Becker, K. H.; Kamens R. M.; Seinfeld, J. H.; Wallington,
T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of Aromatic
Hydrocarbons, Oxford University Press, New York, 2000.
3
Finlayson-Pitts, B. J.; Pitts, J. N., Jr. Chemistry of the Upper and Lower Atmosphere;
Academic Press: San Diego, 2000.
4
Dabestani, R.; Ivanov, I. N. Photochem. Photobiol. 1999, 70.10.
5
Atkinson, R. J. Phys. Chem. Ref. Data 1989, 1, 1–246.
6
Atkinson, R. Chem. Rev. 1985, 85, 69.
7
Davis, D. D.; Bollinger, W.; Fischer, S. J. Phys. Chem. 1975, 79, 293.
8
Perry, R. A.; Atkinson, R.; Pitts, J. N., Jr. J. Phys. Chem. 1977, 81, 296.
9
Tully, F. P.; Ravishankara, A. R.; Thompson, R. L.; Nicovich, J. M.; Shah, R. C.;
Kreutter, N. M.; Wine, P. H. J. Phys. Chem. 1981, 85, 2262.
10
Wahner, A.; Zetsch, C. J. Phys. Chem. 1983, 87, 4945.
11
Madronich, S.; Felder, W. J. Phys. Chem. 1985, 89, 3556.
12
Lin, C. Y.; Lin, M. C. J. Phys. Chem. 1986, 90, 425.
13
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
14
Lay, T. H.; Bozzelli, J. W.; Seinfeld, J. H. J. Phys. Chem. 1996, 100, 6543.
15
Tokmakov, I. V.; Lin, M. C. J. Phys. Chem. A 2002, 106, 11309.
132
16
Atkinson, R. Reactions of Oxygen Species in the Atmosphere. In Active Oxygen in
Chemistry; Foote, C. S., Valentine, J. S., Greenberg, A., Liebman, J. F., Eds.; Blackie
Academic and Professional; New York, 1995; Vol. 2, pp 249–279.
17
Glassman, I. Combustion 3rd Ed.; Academic Press: San Diego, 1996.
18
Compton, R. G.; Hancock, G. Comprehensive Chemical Kinetics, Low-Temperature
Combustion and Autoignition, Vol. 35 Pilling, M. J., Ed., Elsevier, Amsterdam, 1997.
19
Thompson, A. M. Science 1992, 256, 1157.
20
Raghavan, N. V.; Steenken, S. J. Am. Chem. Soc. 1980, 102, 3495.
21
Tripathi, G. N. R. J. Am. Chem. Soc. 1998, 120, 4161.
22
Albarrán, G.; Schuler, R. H. Rad. Phys. Chem. 2002. 63, 661.
23
Albarrán, G.; Bentley, J.; Schuler, R. H. J. Phys. Chem. A 2003, 107, 7770.
24
Poole, J. S.; Shi, X.; Hadad, C. M.; Platz, M. S. J. Phys. Chem. A. 2005, 109, 2547.
25
DeMatteo, M. P.; Poole, J. S.; Shi, X.; Sachdeva, R.; Hatcher, P. G.; Hadad, C. M.;
Platz, M. S. J. Am. Chem. Soc. 2005, 127, 7094.
26
27
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Am. Chem. Soc. 1999, 121, 491.
(a) Fadden, M. J.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 6088. (b) Fadden, M. J.;
Hadad, C. M. J. Phys. Chem. A 2000, 104, 6324.
28
(a) Parr, R. G.; Yang, W. Density Functional Theory in Atoms and Molecules; Oxford
University Press: New York, 1989. (b) Labanowski, J. W.; Andzelm, J. Density
Functional Methods in Chemistry; Springer: New York, 1991.
29
Wiberg, K. B.; Rablen, P. R. J. Am. Chem. Soc. 1993, 115, 9234.
30
Wiberg, K. B.; Rablen, P. R. J. Org, Chem. 1998, 63, 3722.
133
31
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J.
C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.;
Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.;
Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.;
Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J.
V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;
Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98,
Revision A.11, Gaussian, Inc.; Pittsburgh, PA, 1998.
32
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
33
Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1998, 37, 785-789.
34
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital
Theory; John Wiley & Sons: New York, 1986.
35
Bauschlichter, C. W., Jr.; Langhoff, S. R. Mol. Phys. 1999, 96, 471.
36
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502-16513.
37
AIMPAC 95. Bader, R. F. W., and associates. McMaster University, Hamilton, Ont.,
1995.
38
Blanksby, J. S.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255.
39
Zhang, X.-M. J. Org. Chem. 1998, 63. 3590.
40
Ervin, K. M.; DeTuri, V. F. J. Phys. Chem. A 2002, 106, 9947.
134
41
Atkinson, R. J. Phys. Chem. Ref. Data 1997, 26, 235.
42
(a) Minisci, F.; Galli, R. Tetr. Lett. 1962, 533 – 538. (b) Norman, R. O. C.; Radda, G.
K. Proc. Chem. Soc. 1962, 138. (c) Cadet, J.; Douki, T.; Gasparutto, D.; Ravanat, J.-L.
Mutation Res. 2003, 531, 5 – 23.
43
Solomons, T. W. G. Organic Chemistry; John Wiley & Sons, Inc.: New York, 1996.
135
CHAPTER 5
DFT STUDY OF THE REACTIONS OF H AND OH RADICALS WITH
POLYCYCLIC AROMATIC HYDROCARBONS
5.1. Introduction
Polycyclic aromatic hydrocarbons (PAHs) are seemingly ubiquitous in our
environment. Fossil fuels including coal and crude petroleum are constituted of various
forms of the PAH functionality.1 When fossil fuels or their derivatives are burned for heat
and energy generation, incomplete combustion or non-optimal combustion conditions
results in the emission of PAHs into the atmosphere. Some sources of PAH emission
include coal-fired power plants, waste incinerators, auto exhaust, burning vegetation, and
even cooking oil.2,3 Once emitted into the atmosphere PAHs can be distributed downwind of the point source and deposited onto vegetation and soil.1,4
PAH are also known to be the building blocks for soot generation. Past studies
have concluded that 85% of airborne PAH are in the form of particles that are less than
5µm.5 Particles of this size can readily be inhaled into the respiratory airways and enter
the lungs.1 Many PAHs have been found to be human carcinogens after activation by
transforming enzymes, such as the cytochrome P450 family. 6,7,8
136
A topic of strong debate is the reaction mechanism responsible for yielding the
first benzene molecule as a seed in a pyrolytic environment to allow larger PAH
formation.9,10,11,12,13 Once the first aromatic ring is formed, however, subsequent reactions
with acetylene is thought to be responsible for continued PAH growth.9,14 Furthermore,
several intermediates have been isolated in studies of benzene oxidation, including
phenylacetylene, vinylbenzene, and naphthalene.15 Frenklach and Wang have delineated
a mechanism for this growth termed the HACA (H-abstraction-C2H2-addition)
mechanism.9,16 Figure 5.1 shows the successive acetylene addition steps that occur after
H-atom abstraction from benzene.
HC
CH
CH
C2H2
+ H
CH
Figure 5.1. Reaction scheme for the successive addition of acetylene to phenyl radical to
yield a PAH (naphthalene).
137
Once emitted into the atmosphere, the major sink for PAH compounds in the
gaseous and condensed phases is the subsequent reaction with hydroxyl radical.17 Under
daytime tropospheric conditions, hydroxyl-radical addition to an sp2 carbon of the
aromatic ring to form a [PAH-OH]• radical adduct is the dominant mechanism.
Subsequent to [PAH-OH]• adduct formation, reactions with O2 and NO2 result in
quinones, hydroxy-substituted PAHs, ring-scission products, and nitro-substituted
PAHs.18,19 Reactions with NO3 radical during night-time hours can form analogous
adducts, and eventually yield hydroxy-PAH, and nitro-PAH products.18 Nitro-PAHs, in
particular, are significant since they are thought to be highly mutagenic.20
In this study, we have utilized the B3LYP and mPW1K hybrid-DFT methods to
calculate C–H BDEs as well as the addition and abstraction reactions for a series of
PAHs, as initiated by hydrogen atom and hydroxyl radical (OH). Important factors that
moderate the growth rate and direction of a PAH are C–H bond strengths; furthermore,
the reactivity of the PAH toward hydrogen atoms is considered to be a major promoter of
PAH growth.9 The B3LYP density functional theory (DFT) method has been used to
successfully estimate bond dissociation energies (BDEs) for aromatic molecules.21,22,23,24
Furthermore, we have expanded upon the original mPW1K DFT functional report by
Truhlar and co-workers25,26 and shown that this method provides H-atom abstraction and
radical addition reaction barrier heights which are superior to high level ab initio
methods.27 It is hoped that further insight can be gained regarding the preferable growth
characteristics for PAHs that lead to soot formation as well as the most probable products
resulting from atmospheric reactivity.
138
5.2. Methods
All geometry optimizations, single-point energy and vibrational frequency
calculations were performed using Gaussian9828 at the Ohio Supercomputer Center or on
our IBM RS/6000 workstations. All stationary points were optimized using the
B3LYP29,30 and mPW1K31 hybrid density functional theory (DFT)32 methods. B3LYP
geometries were optimized with the 6-31G* basis set and mPW1K geometries with the 631+G** basis set.33 In general, 〈S2〉 values for all B3LYP and mPW1K wavefunctions
were as expected, typically 0.75 ≤ 〈S2〉 ≤ 0.88. Vibrational frequency calculations were
performed on all stationary points to confirm the nature of the geometry. Minima were
confirmed to have all real vibrational frequencies. All transition state geometries were
confirmed to have a single imaginary vibrational frequency corresponding to motion
along the reaction coordinate and were further shown to connect to the proper reactant
and product by displacement along the transition vector (typically 10%) for the imaginary
vibrational frequency in both the positive and negative direction, followed by careful
optimization using either opt=calcfc or calcall. Single-point energy calculations on all
B3LYP/6-31G* stationary points were determined at the B3LYP/6-311+G** level with
the scf=tight option. All basis sets for these B3LYP calculations used six Cartesian d
functions.
The thermal contributions were calculated using unscaled harmonic vibrational
frequencies and rotational constants derived from the B3LYP/6-31G* and mPW1K/631+G** geometries and assuming an ideal gas at 1 atm. The B3LYP zero-point
vibrational energies (ZPEs) were scaled by a factor of 0.9806,34 and the mPW1K ZPEs
were scaled by a factor of 0.9515.35
139
8a
7
6
4a
2
7
3
6
8a
9a
10a
4a
naphthalene
9
10a
7
4b
2
3
4
3
phenanthrene
8
2
4a
1
9a
12
6
3a
4
12b
6
12a
11
2
4a
5
12c
1
9b
9c
5
4
9
7a
7
4
1
4a
5
6
6a
10
3
C
H2
7
8
9
benzo[c]phenanthrene (BcP)
4H-cylopenta[d,e,f]phenanthrene (4H-CP)
10
10
1
1
10a
10a
9
9
2
2
10b
8a
10d
10c
3
10c
2a
8a
2a
10b
8
3
anthracene
10
8a
8
2
10
5
4
5
1
9
8
1
8
10d
3
8
10e 10f
7
5b
6
7
4
5a
4
4a
6a
5
6
5
corannulene
benzo[g,h,i]fluoranthene (BF)
Figure 5.2. Structures and relevant carbon labels for the polycyclic aromatic
hydrocarbons.
140
5.3.Results and Discussion
The molecular structures for naphthalene, anthracene, phenanthrene, 4Hcyclopenta[d,e,f]-phenanthrene (4H-CP), benzo[c]phenanthrene (BcP),
benzo[g,h,i]fluoranthene (BF), and corannulene are shown in Figure 5.2 as well as the
carbon numbering used in this study.1,36 Unlike the other PAHs in Figure 5.2, the
structures of 4H-CP, BcP, and corannulene are non-planar. 4H-CP is non-planar due to a
methylene group which forms the five-membered ring. The ground-state structure for
BcP is non-planar, and its 4 angular (peri) fused six-membered ring structure resembles a
helical fragment. This uneven structure results in an increased number of structures for
the radical addition and H-atom abstractions transition states and addition adducts. For
the purpose of labeling the BcP carbon atoms, when relevant, the 1-carbon is designated
to be above the 12-carbon. Furthermore, corannulene is bowl-shaped, and radical addition
can occur on either the concave or convex sides of the molecule. To indicate which side
the reaction takes place, the carbon number is appended by concave or convex, when
relevant.
5.3.1. Bond Dissociation Energies
In previous studies, we have examined the C–H bond dissociation energies for a
variety of monocyclic aromatic compounds, including benzene, using density functional
theory at the B3LYP/6-311+G**//B3LYP/6-31G* level.22 It has been shown, by us and
others, that the B3LYP method provides reliable C–H BDEs for a variety of monocyclic
aromatic systems with minimal spin contamination of the wavefunction.21,22 At the
141
B3LYP/6-311+G**//B3LYP/6-31G* level, the calculated C–H BDE (ΔH298) is 109.5
kcal/mol, and compares well with the recommended experimental value of 112.9 ± 0.5
kcal/mol determined via a thermodynamic cycle. 37,38 This chapter will extend the study
of monocyclic aromatic molecules to polycyclic aromatic hydrocarbons.
Table 5.1 lists the C–H BDEs (ΔH298) for each of the unique C–H bonds on the
seven PAHs shown in Figure 5.2 at the B3LYP/6-31G*, B3LYP6-311+G**//B3LYP/631G*, and mPW1K/6-31+G** levels of theory. In addition to the benzene C–H BDEs,
the experimental bond dissociation energies for the C1–H and C2–H bonds of naphthalene
have been reported. Kass et al.24 reported C1–H and C2–H BDE values of 112.3 ± 1.3 and
111.9 ± 1.4 kcal/mol, respectively, as calculated via a thermodynamic cycle from gasphase acidities and electron affinities determined via mass spectrometric methods.
Furthermore, they employed DFT calculations, and at the B3LYP/6-31+G* level, they
calculated BDE values of 110.7 and 110.6 kcal/mol for the C1–H and C2–H bonds,
respectively. We have obtained C1–H BDEs (ΔH298) of 111.1, 110.7 and 110.5 kcal/mol
and C2–H values of 111.0, 110.7 and 110.3 kcal/mol at the B3LYP/6-31G*, B3LYP/6311+G**//B3LYP/6-31G*, and mPW1K/6-31+G** levels, respectively. The C–H BDEs
determined via the B3LYP and mPW1K methods are both in very good agreement with
experiment.
An examination of the C–H BDE values listed in Table 5.1 shows very little
variability over the range of PAHs studied. Two values, however, stand out from the
others. The C4–H BDE for 4H-CP is approximately 80 kcal/mol at all three theoretical
levels. The radical produced by homolytic scission of the C4–H bond is stabilized as a
result of planarization of the resultant radical to allow delocalization throughout the π
142
network of the phenanthrene as a result of the p character of the unpaired electron’s
orbital. This is in contrast to the remaining C–H bonds which yield sp2 radicals, thereby
minimizing delocalization interactions with the PAH π network.
The second unusual C–H BDE is that of C1–H for benzo[c]phenanthrene (BcP).
Due to steric interactions between the hydrogens on the 1 and 12 carbons, the structure
for BcP is non-planar. The non-planarity results in a C2–C6–C7–C11 dihedral angle which
is –20.5˚ and –21.0˚ at the B3LYP/6-31G* and mPW1K/6-31+G** levels, respectively.
Removal of either the C1–H or C12–H hydrogen allows the molecule to regain planarity
and maximize overlap of the π network. By comparison of the C1–H BDE value with the
others, it can be determined that the combination of steric strain and reduced aromaticity,
resulting from the non-planarity of BcP, is ~7 kcal/mol. The C4–H BDE of ~109 kcal/mol
for phenanthrene also reflects a small degree of steric strain (~ 1–2 kcal/mol) between
C4–H and C5–H hydrogens. This steric interaction, however, is not strong enough to
result in a non-planar structure.
The effect of increasing the basis set size for the B3LYP/6-31G* geometries is
negligible for the BDEs for the seven PAHs in Figure 5.2. Furthermore, the mPW1K
values compare very well with the B3LYP values.
143
site
B3LYP/6-31G*
B3LYP/6-31G*
B3LYP/6-311+G**
mPW1K
6-31+G**
naphthalene
1
2
111.1
111.0
110.7
110.7
110.5
110.3
anthracene
1
2
9
110.9
111.0
111.4
110.8
110.8
111.1
110.2
110.1
110.5
phenanthrene
1
2
3
4
10
111.1
111.2
110.9
109.1
111.0
110.8
111.0
110.8
109.0
110.7
110.5
110.6
110.3
108.6
110.4
4H-CPx
1
2
3
4
9
111.4
110.5
111.1
80.1
110.8
111.2
110.3
110.8
79.7
110.5
110.8
109.7
110.5
80.7
110.1
BcP
1
2
3
4
5
6
104.0
110.7
111.2
111.0
111.2
111.0
104.1
110.5
111.0
110.6
110.9
110.7
104.2
110.2
110.7
110.4
110.8
110.6
BF
1
2
3
4
5
110.8
110.7
111.3
110.5
110.8
110.5
110.5
111.1
110.4
110.7
110.2
110.1
110.7
109.8
110.3
corannulene
1
110.3
110.2
109.9
Table 5.1. List of homolytic C–H bond dissociation energies (ΔH298, kcal/mol) for the
PAHs shown in Figure 5.2. See text for the limited experimental values.
144
5.3.2. Reactions with H and OH Radicals
5.3.2.1. Radical Additions
Each of the PAHs in Figure 5.2 can react with hydrogen atom and hydroxyl
radical by either a radical-addition mechanism to an sp2-hybridized carbon or by
abstraction of a hydrogen atom. Tables 5.2–5.8 provide the barrier height and reaction
energies (ΔH298, relative to reactants at infinite separation) for each radical addition and
H-atom abstraction reaction of the seven PAHs with both hydrogen atom and hydroxyl
radical. Five of the PAHs have complete data at the B3LYP/6-31G*, B3LYP/6311+G**//B3LYP/6-31G*, and mPW1K/6-31+G** levels, while BF and BcP have only
B3LYP/6-31G* and B3LYP/6-311+G**//B3LYP/6-31G* results at this time.
Several general observations can be made via examination of Tables 5.2–5.8. For
each PAH, the radical addition with either hydrogen atom or hydroxyl radical to a nonring-fusing sp2 carbon atom is more facile than H-atom abstraction at 298 K, based on the
barrier heights and reaction energies. In the case of the H-atom reactions, addition is
always preferred to abstraction. Also, while the barrier heights for OH-radical addition
are more favorable than H-atom addition, the reaction energies for H-atom addition are
more exothermic than those for OH-radical addition by ~11 kcal/mol. This may be a
result of steric interactions for the multiple [PAH-OH]• adducts. The barrier heights for
the H-atom addition reactions at the B3LYP and mPW1K levels are typically in good
agreement. In general, the mPW1K barrier heights are ~1 kcal/mol larger than the
B3LYP values. On the other hand, the OH radical addition barriers heights show larger
discrepancies between the two methods. The mPW1K OH-radical addition barrier heights
145
are typically 4–8 kcal/mol greater than the B3LYP values. For the H-atom abstraction
barrier heights, the B3LYP method predicts values ~ 4 kcal/mol greater than for
abstraction reactions by hydrogen atoms, and ~ 5 kcal/mol greater for abstractions by OH
radicals.
sitea
B3LYPb
1
2
8a
1.4
2.0
8.7
1
2
8a
–31.5
–26.8
–5.5
1
2
10.6
10.4
1
2
6.7
6.5
B3LYP-SPc
mPW1Kd
H addition TS
1.5
2.3
2.1
3.0
7.5
8.2
H addition adduct
–31.2
–35.2
–26.4
–30.1
–7.2
–9.5
H abstraction TS
10.4
14.4
10.2
14.2
H abstraction reaction
6.1
9.6
6.1
9.4
B3LYPb
B3LYP-SPc
mPW1Kd
OH addition TS
–4.7
–4.7
–0.5
–3.7
–3.5
0.6
7.0
7.0
9.8
OH addition adduct
–24.9
–21.8
–25.9
–20.1
–17.4
–20.9
2.4
3.4
2.0
OH abstraction TS
0.1
–0.4
5.2
1.1
–0.5
5.4
OH abstraction reaction
1.2
–4.6
–1.6
1.1
–4.6
–1.7
Table 5.2. List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to
reactants at infinite separation) for the addition and H-atom abstraction reactions for
naphthalene with hydrogen atom and hydroxyl radical.
a
See Figure 5.2 for PAH structure and site locations. b Derived at the B3LYP/6-31G*
level. c Derived at the B3LYP/6-311+G**//B3LYP/6-31G* level. d Derived at the
mPW1K/6-31+G** level.
146
sitea
1
2
9
9a
1
2
9
9a
1
2
9
1
2
9
B3LYPb
B3LYP-SPc
mPW1Kd
H addition TS
1.0
1.2
1.6
1.4
1.7
2.0
0.3
0.5
0.7
8.3
7.4
7.2
H addition adduct
–35.5
–35.0
–39.7
–31.3
–30.7
–35.3
–42.1
–41.6
–46.9
–7.6
–9.0
–12.4
H abstraction TS
10.6
10.6
14.2
10.3
10.3
14.1
11.1
11.1
14.6
H abstraction reaction
6.6
6.2
9.3
6.5
6.1
9.2
7.0
6.5
9.6
B3LYPb
B3LYP-SPc
mPW1Kd
OH addition TS
–6.1
–6.3
–1.9
–4.9
–4.9
–1.1
e
e
e
5.4
5.5
7.7
OH addition adduct
–28.9
–25.6
–30.3
–24.4
–21.6
–25.9
–35.8
–31.8
–37.5
–1.8
–0.5
–3.1
OH abstraction TS
–0.5
–0.3
5.1
0.0
–0.3
5.5
1.1
–0.3
5.1
OH abstraction reaction
1.2
–4.5
–1.8
1.1
–4.5
–2.0
1.6
–4.2
–1.6
Table 5.3. List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to
reactants at infinite separation) for the addition and H-atom abstraction reactions for
anthracene with hydrogen atom and hydroxyl radical.
a
See Figure 5.2 for PAH structure and site locations. b Derived at the B3LYP/6-31G*
level. c Derived at the B3LYP/6-311+G**//B3LYP/6-31G* level. d Derived at the
mPW1K/6-31+G** level. e A transition state structure for this reaction was not found.
147
sitea
1
2
3
4
10
4a
10a
1
2
3
4
10
4a
10a
1
2
3
4
10
1
2
3
4
10
B3LYPb
B3LYP-SPc mPW1Kd
H addition TS
1.6
1.8
2.6
2.2
2.4
3.2
2.0
2.2
3.1
1.5
1.7
2.3
1.4
1.6
2.3
6.9
5.9
6.5
7.9
6.9
7.5
H addition adduct
–29.4
–29.2
–32.8
–25.4
–25.1
–28.6
–26.7
–26.2
–29.8
–30.1
–29.8
–33.7
–31.0
–30.5
–34.8
–12.1
–13.6
–16.2
–8.7
–10.2
–12.8
H abstraction TS
10.7
10.6
14.4
10.5
10.4
14.4
10.3
10.3
14.2
11.0
10.8
14.4
10.6
10.6
14.4
H abstraction reaction
6.7
6.2
9.6
6.8
6.4
9.7
6.5
6.1
9.4
4.7
4.4
7.7
6.6
6.1
9.5
B3LYPb
B3LYP-SPc
mPW1Kd
OH addition TS
–4.3
–4.2
–0.1
–3.2
–3.0
1.1
–3.7
–3.5
0.8
–4.6
–4.3
–0.3
–5.1
–5.2
–0.9
2.5
2.5
6.5
4.0
4.0
8.0
OH addition adduct
–22.9
–20.0
–23.6
–18.7
–16.1
–19.3
–20.1
–17.5
–20.8
–23.1
–19.8
–23.7
–24.5
–21.2
–25.6
–3.2
–1.8
–6.3
–5.8
–4.2
–3.9
OH abstraction TS
0.1
–0.3
5.2
1.2
–0.3
5.7
1.0
–0.5
5.5
–0.1
0.2
5.5
0.0
–0.3
5.1
OH abstraction reaction
1.3
–4.5
–1.6
1.3
–4.3
–1.5
1.1
–4.5
–1.7
–0.8
–6.3
–3.4
1.2
–4.5
–1.6
Table 5.4. List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to
reactants at infinite separation) for the addition and H-atom abstraction reactions for
phenanthrene with hydrogen atom and hydroxyl radical.
a
See Figure 5.2 for PAH structure and site locations. b Derived at the B3LYP/6-31G*
level. c Derived at the B3LYP/6-311+G**//B3LYP/6-31G* level. d Derived at the
mPW1K/6-31+G** level.
148
sitea
1
2
3
9
3a
9b
9a
1
2
3
9
3a
9b
9a
1
2
3
4
9
1
2
3
4
9
B3LYPb
B3LYP-SPc mPW1Kd
H addition TS
1.3
1.5
2.4
1.9
2.1
3.0
1.4
1.5
2.5
1.1
1.3
2.0
3.7
3.4
4.0
6.6
5.4
6.1
7.9
6.8
7.6
H addition adduct
–30.8
–30.4
–33.9
–25.9
–25.5
–28.7
–28.2
–27.8
–31.2
–33.4
–32.9
–37.1
–24.1
–24.8
–28.1
–13.4
–14.9
–17.6
–8.4
–9.9
–12.2
H abstraction TS
10.7
10.7
14.6
10.0
9.8
13.7
10.4
10.3
14.3
0.9
0.6
3.8
10.3
10.2
14.1
H abstraction reaction
7.0
6.5
9.9
6.1
5.6
8.8
6.6
6.1
9.6
–24.3
–24.9
–20.2
6.3
5.8
9.2
B3LYPb
B3LYP-SPc
mPW1Kd
OH addition TS
–4.6
–4.8
–0.3
–3.7
–3.6
0.8
–4.8
–4.6
–0.3
–5.2
–5.4
–1.0
–3.7
–3.8
0.5
1.7
1.4
5.7
4.0
3.7
8.0
OH addition adduct
–24.2
–21.2
–24.7
–19.4
–16.8
–19.7
–21.4
–18.8
–21.8
–26.4
–23.3
–27.4
–16.6
–14.8
–8.0
–6.8
–2.5
–1.5
OH abstraction TS
0.4
–0.2
5.4
0.8
–0.7
5.1
0.7
–0.6
5.3
–3.9
–4.3
0.2
0.2
–0.4
5.1
OH abstraction reaction
1.6
–4.1
–1.2
0.6
–5.0
–2.3
1.2
–4.5
–1.6
–29.7
–35.6
–31.4
0.9
–4.8
–2.0
Table 5.5. List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to
reactants at infinite separation) for the addition and H-atom abstraction reactions for 4Hcyclopenta[d,e,f]phenanthrene with hydrogen atom and hydroxyl radical.
a
See Figure 5.2 for PAH structure and site locations. b Derived at the B3LYP/6-31G*
level. c Derived at the B3LYP/6-311+G**//B3LYP/6-31G* level. d Derived at the
mPW1K/6-31+G** level.
149
sitea
1
2
2a
3
4
5
5a
10a
10b
10c
1
2
2a
3
4
5
5a
10a
10b
10c
1
2
3
4
5
1
2
3
4
5
B3LYPb
B3LYP-SPc
H addition TS
1.2
1.4
1.0
1.2
8.0
6.9
0.9
1.3
1.8
2.2
1.4
1.5
3.8
3.3
6.5
5.7
4.6
3.6
5.2
4.5
H addition adduct
–33.4
–32.9
–34.9
–34.3
–8.2
–9.8
–36.5
–36.1
–28.3
–27.9
–32.1
–31.8
–25.6
–26.8
–13.3
–14.9
–22.7
–24.4
–17.9
–19.4
H abstraction TS
10.3
10.2
10.3
10.1
10.7
10.6
10.1
9.9
10.4
10.4
H abstraction reaction energy
6.4
5.9
6.3
5.9
6.8
6.4
6.1
5.7
6.4
6.1
B3LYPb
B3LYP-SPc
OH addition TS
–5.0
–5.1
–5.1
–5.2
4.3
4.2
–4.9
–4.8
–2.5
–2.7
–3.8
–3.8
–1.6
–1.8
3.0
2.8
0.5
–0.2
0.5
-0.2
OH addition adduct
–26.1
–23.1
–27.4
–24.3
–2.1
–1.2
–28.7
–25.8
–21.1
–18.4
–24.2
–21.4
–17.2
–15.7
–5.8
–4.8
–14.0
–13.0
–11.3
–10.3
OH abstraction TS
0.4
–0.4
0.3
–0.4
0.6
–0.1
0.9
–0.6
0.1
–0.3
OH abstraction reaction energy
0.9
–4.7
0.9
–4.8
1.4
–4.2
0.7
–4.9
1.0
–4.6
Table 5.6. List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to
reactants at infinite separation) for the addition and H-atom abstraction reactions for
benzo[g,h,i]fluoranthene with hydrogen atom and hydroxyl radical.
a
See Figure 5.2 for PAH structure and site locations. b Derived at the B3LYP/6-31G*
level. c Derived at the B3LYP/6-311+G**//B3LYP/6-31G* level.
150
sitea
1/12
2/11
3/10
4/9
4a/8a
5/8
6/7
6a
12a/12c
12b
1/12
2/11
3/10
4/9
4a/8a
5/8
6/7
6a
12a/12c
12b
1/12
2/11
3/10
4/9
5/8
6/7
1
2
3
4
5
6
B3LYPb
B3LYP-SPc
H addition TS
2.3/1.8
2.0/2.0
2.1/1.6
2.1/1.8
2.4/1.7
2.5/1.8
1.9/1.3
1.8/1.4
8.9/6.8
7.6/5.8
2.0/0.9
2.0/0.9
1.3/1.8
1.3/1.9
6.8
5.8
8.2/5.7
7.0/4.7
4.4
3.6
H addition adduct
–29.6
–29.4
–27.3
–26.8
–26.7
–26.3
–30.3
–30.0
–6.7/–11.5
–8.4/–12.8
–32.7
–32.5
–30.3
–30.0
–13.9
–15.2
–10.1/–14.3
–11.3/–15.7
–23.7
–24.7
H abstraction TS
10.7
10.4
10.2
9.9
10.5
10.3
10.6
10.3
10.8
10.5
10.7
10.4
H abstraction reaction
–0.4
–0.5
6.3
5.8
6.8
6.3
6.5
6.0
6.8
6.3
6.6
6.1
B3LYPb
B3LYP-SPc
OH addition TS
–3.0/–6.9
–3.1/–5.6
–3.5/–5.3
–3.4/–4.2
–3.4/–3.7
–3.1/–3.5
–4.3/–4.6
–4.3/–4.6
6.1/2.4
6.2/2.4
–5.0/–5.3
–5.1/–5.2
–5.0/–4.6
–5.1/–4.8
2.6/2.2
2.4/2.1
4.6/1.1
5.0/1.8
–1.0/–0.7
–1.2/–1.1
OH addition adduct
–23.1
–19.8
–20.5/–20.7
–17.8/–18.0
–20.0/–19.4
–17.4/–17.0
–24.0/–23.7
–20.7/–20.9
0.0/–6.1
1.4/–4.8
–26.4/–25.2
–23.0/–22.7
–23.5/–24.0
–20.7/–20.7
–8.0/–8.2
–6.8/–6.8
–7.4/–2.5
–5.0/–0.5
–16.4/–16.3
–14.0/–14.3
OH abstraction TS
1.5
0.7
0.8/1.0
–0.9/–0.6
1.2/1.2
–0.4/–0.5
–0.1/0.0
–0.5//–0.5
0.2/0.2
–0.3/–0.3
0.1/0.1
–0.3//–0.3
OH abstraction reaction
–5.9
–11.1
0.9
–4.8
1.4
–4.3
1.1
–4.7
1.4
–4.4
1.2
–4.6
Table 5.7. List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to
reactants at infinite separation) for the addition and H-atom abstraction reactions for
benzo[c]phenanthrene with hydrogen atom and hydroxyl radical.
a
See Figure 5.2 for PAH structure and site locations Some sites may not have a unique
structure at both sites as a result of symmetry, and will have only one energy value.
b
Derived at the B3LYP/6-31G* level. c Derived at the B3LYP/6-311+G**//B3LYP/631G* level.
151
sitea
B3LYPb
1
10a
10b
0.5
3.7
0.8
1
(concave)
10a
(concave)
10b
–35.6
–19.3
(–3.6)
–30.9
1
(concave)
10.0
1
7.9
B3LYP-SPc
H addition TS
0.8
3.5
0.7
H addition adduct
–35.0
–20.2
(–4.8)
–31.4
H abstraction TS
9.9
H abstraction reaction
7.6
mPW1Kd
1.6
4.4
1.4
–38.7
–22.2
(–6.9)
–34.4
13.8
9.0
B3LYPb
B3LYP-SPc
OH addition TS
e
e
–1.2
–1.0
e
e
OH addition adduct
–27.3
–24.5
(–28.8)
(–25.5)
–12.5
–10.7
(5.6)
(7.6)
–23.3
–21.2
OH abstraction TS
0.1
–0.5
(0.2)
(–0.6)
OH abstraction reaction
2.8
–2.8
mPW1Kd
–1.1
3.6
0.3
–28.1
(–29.2)
–12.2
(f)
–23.7
5.2
(5.0)
–2.2
Table 5.8. List of reaction energies and barrier heights (ΔH298, kcal/mol, relative to
reactants at infinite separation) for the addition and H-atom abstraction reactions for
corannulene with hydrogen atom and hydroxyl radical.
a
See Figure 5.2 for PAH structure and site locations. Values in parentheses correspond to
OH radical reactions on the concave side of corannulene. b Derived at the B3LYP/6-31G*
level. c Derived at the B3LYP/6-311+G**//B3LYP/6-31G* level. d Derived at the
mPW1K/6-31+G** level. e A transition state structure was not found at the B3LYP/631G* level for this reaction. f Structure not found.
The H-atom addition reactions of the PAHs with hydrogen atoms typically
involve only one orientation due to the spherical symmetry of the hydrogen atom. Any
complexity in orientation is derived from the non-planarity in the structure of the parent
PAH. At the B3LYP levels of theory reported here, the barrier heights for H-atom
addition to the non-ring-fusing carbons range from ~1 to 2 kcal/mol, and at the mPW1K
152
level are ~2 to 3 kcal/mol. The reaction energies for these H-atom addition reactions
range from about –25 to –36 kcal/mol at the B3LYP levels and about –30 to –40 kcal/mol
at the mPW1K level. One particular exception is H-atom addition at the 9-carbon of
anthracene, for which the barrier height is calculated to be 0.3, 0.5, and 0.7 kcal/mol
(Table 5.3) at the B3LYP/6-31G*, B3LYP/6-311+G**//B3LYP/6-31G*, and mPW1K/631+G** levels, respectively. Furthermore, the reaction energies range from about –42
kcal/mol at the B3LYP levels and –46.9 kcal/mol at the mPW1K level (Table 5.3). The
increased kinetic and thermodynamic favorability can be attributed to an increase in the
number of benzenoid rings, and is in accord with Clar’s postulate which assigns increased
stability to resonance structures and reactions that have an increased number of
benzenoid rings.39 In anthracene, only one of the terminal rings is benzenoid, with the
remaining π electrons linked together in a linear chain. For the linearly (kata) annealed
PAHs, the internal non-ring-fusing carbons will have more favorable radical addition
pathways relative to those on the terminal rings.
For hydrogen-atom addition to the ring-fusing carbons, the typical barrier heights
range from ~ 4 to 8 kcal/mol, which is several kcal/mol greater than for addition to a nonring-fused carbon. The reaction energies for these H-atom addition reactions are typically
exothermic by ~ 5 to 15 kcal/mol, significantly less exothermic than H-atom additions to
the non-ring-fusing carbons. There are several exceptions to these typical H-atom
addition barrier heights and reaction energies. Hydrogen-atom addition to ring-fused
carbons in bay regions (e.g. C4–C4a–C4b–C5 segment of phenanthrene, Figure 5.2) are
more kinetically and thermodynamically favorable than at the non-bay regions (e.g.
C10–C10a–C1 segment of phenanthrene, Figure 5.2). H-atom additions to the 3a-carbon of
153
level are ~2 to 3 kcal/mol. The reaction energies for these H-atom addition reactions
range from about –25 to –36 kcal/mol at the B3LYP levels and about –30 to –40 kcal/mol
at the mPW1K level. One particular exception is H-atom addition at the 9-carbon of
anthracene, for which the barrier height is calculated to be 0.3, 0.5, and 0.7 kcal/mol
(Table 5.3) at the B3LYP/6-31G*, B3LYP/6-311+G**//B3LYP/6-31G*, and mPW1K/631+G** levels, respectively. Furthermore, the reaction energies range from about –42
kcal/mol at the B3LYP levels and –46.9 kcal/mol at the mPW1K level (Table 5.3). The
increased kinetic and thermodynamic favorability can be attributed to an increase in the
number of benzenoid rings, and is in accord with Clar’s postulate which assigns increased
stability to resonance structures and reactions that have an increased number of
benzenoid rings.39 In anthracene, only one of the terminal rings is benzenoid, with the
remaining π electrons linked together in a linear chain. For the linearly (kata) annealed
PAHs, the internal non-ring-fusing carbons will have more favorable radical addition
pathways relative to those on the terminal rings.
For hydrogen-atom addition to the ring-fusing carbons, the typical barrier heights
range from ~ 4 to 8 kcal/mol, which is several kcal/mol greater than for addition to a nonring-fused carbon. The reaction energies for these H-atom addition reactions are typically
exothermic by ~ 5 to 15 kcal/mol, significantly less exothermic than H-atom additions to
the non-ring-fused carbons. There are several exceptions to these typical H-atom addition
barrier heights and reaction energies. Hydrogen-atom addition to ring-fused carbons in
bay regions (e.g. C4–C4a–C4b–C5 segment of phenanthrene, Figure 5.2) are more
kinetically and thermodynamically favorable than at the non-bay regions (e.g.
C10–C10a–C1 segment of phenanthrene, Figure 5.2). H-atom additions to the 3a-carbon of
153
4H-CP, 10b- and 5a-carbons of BF, 12b-carbon of BcP, and 10b-carbon of corannulene
all show significant increases in thermodynamic stability, having H-atom reaction
exothermicities ranging from –23 to –31 kcal/mol. Many of these addition sites are on
carbon atoms that fuse together five- and six-membered rings. For these sites, H-atom
addition, leading to pyramidalization of the attacked carbon, may relieve strain due to the
tighter structure of the five-membered ring. This relief is particularly significant for the
bowl-shaped corannulene (Table 5.10) in which the reaction for H-atom addition at
carbon 10b, on the convex side, is >10 kcal/mol more exothermic than at carbon 10a.
Interestingly, for radical additions to carbon 10b on the concave side of corannulene,
pyramidalization causes the ring to invert, resulting in the convex side adduct. We have
calculated the barrier to ring inversion for corannulene to be 8.1, 10.0, and 9.4 kcal/mol at
the B3LYP/6-31G*, B3LYP/6-311+G**//B3LYP/6-31G*, and mPW1K/6-31+G**
levels, respectively.
The barrier heights for hydroxyl-radical addition to the non-ring-fused carbons
ranges from about –3 to –6 kcal/mol at the B3LYP levels of theory and about –2 to 1
kcal/mol at the mPW1K level. The mPW1K barrier heights are in good agreement with
experimental studies which have found the OH-radical addition to PAHs to be
barrierless.40 Reaction exothermicities for these hydroxyl radical addition reactions range
from about –16 to –26 kcal/mol at the B3LYP levels and about –20 to –30 kcal/mol at the
mPW1K level. The increased reactivity at the internal non-ring-fusing carbon of
anthracene is also evident for the OH radical addition reactions. In fact, we were not able
to isolate a transition-state structure for OH-radical addition at C9 of anthracene at either
level of theory, and this process is very exothermic. Furthermore, transition-state
154
contain a fjord region (e.g. C12–C12a–C12b–C12c–C1 segment of BcP, Figure 5.2) in which
steric interaction results in non-planarity.
5.3.2.2. H-atom Abstractions
The barrier heights and reaction energies of H-atom abstraction of the PAH
hydrogens by hydrogen atom are greater than those for the radical-addition reactions. The
barrier heights are typically ~10 kcal/mol at the B3LYP levels and ~14 kcal/mol at the
mPW1K level. The sp3 4-carbon C–H’s of 4H-CP have abstraction barrier heights which
are more favorable as a result of the lower C–H BDE (Table 5.2). The typical reaction
energies for H-atom abstraction by hydrogen atoms are endothermic by about 6–7
kcal/mol at the B3LYP levels and about 9–10 kcal/mol at the mPW1K level. There are
several exceptions, one being the C4–H hydrogen of 4H-CP, which is exothermic by
about –20 to –25 kcal/mol as a result of delocalization of the resultant unpaired electron.
Also the C4–H hydrogen of phenanthrene and C1–H (and C12–H) hydrogen of BcP, both
of which benefit from the release of steric strain between the terminal bay and fjord
hydrogens, respectively.
The H-atom abstraction reaction for the PAHs with hydroxyl radical have barrier
heights of ~0 kcal/mol at the B3LYP levels and ~5 kcal/mol at the mPW1K level. The
exception of the sp3 C4–H bond of 4H-CP, found for the H-atom abstractions with
hydrogen atom, is also evident for the hydroxyl-radical reaction. In the OH-radical
mediated H-atom abstraction transition states, the OH radical’s O–H bond is oriented
approximately perpendicular to the PAH ring plane. This orientation of the hydroxyl
radical’s O–H bond in the transition state structures for the non-planar BcP and
156
corannulene has a negligible effect of the abstraction barrier height (see Tables 5.7 and
5.8).
The reaction energies for the H-atom abstraction reaction for the PAHs with
hydroxyl radical are predicted to be slightly endothermic by ~1 kcal/mol at the B3LYP/631G* level. However, a significant basis set effect is evident from the B3LYP/6311+G**//B3LYP/6-31G* energies which predict the hydroxyl radical H-atom
abstraction reactions to be almost –5 kcal/mol exothermic. The mPW1K/6-31+G** level
also predicts a reaction exothermicity of about –2 kcal/mol. We have shown in a previous
study on the reactions of hydroxyl radical with benzene that the HO–H bond dissociation
energy of water exhibits a basis set effect of ~5 kcal/mol between the 6-31G* and 6311+G** basis sets (97.9 and 102.7 kcal/mol, respectively) of the B3LYP/6-31G*
structures.41 Furthermore, Barckholtz et al.41 showed that the B3LYP/6-31G*, B3LYP/6311+G**//B3LYP/6-31G*, and mPW1K/6-31+G** levels underestimate the HO–H BDE
from experiment (119 kcal/mol)42 by 9.5, 4.1, and 7.2 kcal/mol, respectively.
5.4. Conclusions
The C–H bond dissociation energies and H-atom abstraction and radical addition
reactions of hydrogen atom and hydroxyl radical with naphthalene, anthracene,
phenanthrene, 4H-cyclopenta[d,e,f]phenanthrene, benzo[c]phenanthrene,
benzo[g,h,i]fluoranthene, and corannulene have been studied using density functional
theory. Minima and transition states for the H-atom abstraction and radical-addition
reactions of hydrogen atom and hydroxyl radical with the series of PAHs have been
calculated at the B3LYP/6-31G* and mPW1K/6-31+G** levels of theory. Furthermore,
157
the B3LYP/6-31G* energies were refined by B3LYP/6-311+G** single-point energies.
At 298 K, the barrier heights for radical addition are generally more favorable than for Hatom abstraction. For H-atom reactions, radical addition is kinetically preferred to Hatom abstraction at all times. For the hydroxyl-radical reactions, the trend is similar;
however, radical addition to ring-fusing carbons is kinetically less favorable than H-atom
abstraction. Thermodynamically, hydrogen-atom and hydroxyl-radical addition reactions
with PAHs are more favorable than H-atom abstraction reactions. The bond dissociation
energies for the PAHs studied here are typical for aromatic C–H bonds (~111 kcal/mol).
The bond dissociation energies for terminal C–H’s of bay regions are slightly more
favorable due to release of steric strain, while terminal C–H’s for fjord regions are even
more favorable as a result of released steric strain and relaxation to a planar structure.
158
References for Chapter 5
1
Harvey, R. G. Polycyclic Aromatic Hydrocarbons: Chemistry and Carcinogenicity;
Cambridge University Press, New York, NY, 1991.
2
Li, K.; Christensen, E. R.; Van Camp, R. P.; Imamoglu, I. Environ. Sci. Technol. 2001,
35, 2896.
3
Li, C.-T.; Lin, Y.-C.; Lee, W.-J.; Tsai, P.-J. Environ. Health Perspectives 2003, 111,
483.
4
Reisen, F.; Wheeler, S.; Arey, J. Atmos. Environ. 2003, 37, 3653.
5
Albagli, A.; Oja, H.; Dubois, L. Environ. Lett. 1974, 6, 241.
6
Pavanello, S.; Simioli, P.; Lupi, S.; Gregorio, P.; Clinfero, E. Cancer Epidemiology,
Biomarkers & Prevention 2002, 11, 998-1003.
7
Williams, J. A.; Martin, F. L.; Muir, G. H.; Hewer, A.; Grover, P. L.; Phillips, D. H.
Carcinogenesis 2000, 21, 1683-1689.
8
WHO (1997) The World Health Report. World Health Organization, Geneva,
Switzerland.
9
Frenklach, M. Phys. Chem. Chem. Phys. 2002, 4, 2028.
10
Bittner, J. D.; Howard, J. B. Proc. Combust. Inst. 1981, 18, 1105.
11
Westmoreland, P. R.; Dean, A. M.; Howard, J. B.; Longwell, J. P. J. Phys. Chem.
1989, 93, 8171.
12
Miller, J. A.; Melius, C. F. Combust. Flame 1992, 91, 21.
13
Melius, C. F.; Colvin, M. E.; Marinov, N. M.; Pitz, W. J.; Senkin, S. M. Proc.
Combust. Inst. 1996, 26, 685.
159
14
Glassman, I. Combustion, 3rd Ed.; Academic Press, San Diego, CA, 1996.
15
Chai, Y.; Pfefferle, L. D. Fuel 1998, 77, 313.
16
Frenklach, M.; Wang. H. Proc. Combust. Inst. 1991, 23, 1559.
17
Vione, D.; Barra, S.; De Gennaro, G.; De Rienzo, M.; Gilardoni, S.; Perrone, M. G.;
Pozzoli, L. Ann. Chim. 2004, 94, 257.
18
Bunce, N. J.; Liu, L.; Zhu, J.; Lane, D. A. Environ. Sci. Technol. 1997, 31, 2252.
19
Sasaki, J.; Aschmann, S. M.; Kwok, E. S.; Atkinson, R.; Arey, J. Environ. Sci. Technol.
1997, 31, 3173.
20
Ohe, T.; Watanabe, T.; Wakabayashi, K. Mutat.Res. 2004, 567, 109.
21
Bauschlichter, C. W., Jr.; Langhoff, S. R. Mol. Phys. 1999, 96, 471.
22
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Am. Chem. Soc. 1999, 121, 491.
23
Cioslowski, J.; Liu, G.; Martinov, M.; Piskorz, P.; Moncrieff, D. J. Am. Chem. Soc.
1996, 118, 5261.
24
Reed, D. R.; Kass, S. R. J. Mass Spectrom. 2000, 35, 534.
25
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 4811.
26
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.
27
See Chapters 6 and 7 of this dissertation.
28
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J.
C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.;
Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.;
Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.;
160
Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J.
V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;
Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98,
Revision A.11, Gaussian, Inc.; Pittsburgh, PA, 1998.
29
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
30
Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1998, 37, 785-789.
31
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 4811.
32
(a) Parr, R. G.; Yang, W. Density Functional Theory in Atoms and Molecules; Oxford
University Press: New York, 1989. (b) Labanowski, J. W.; Andzelm, J. Density
Functional Methods in Chemistry; Springer: New York, 1991.
33
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital
Theory; John Wiley & Sons: New York, 1986.
34
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502.
35
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.
36
Dabestani, R.; Ivanov, I. N. Photochem. Photobiol. 1999, 70, 10.
37
Ervin, K. M.; DeTuri, V. F. J. Phys. Chem. A 2002, 106, 9947.
38
Blanksby, J. S.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255.
39
Clar, E. The Aromatic Sextet, Wiley, New York, 1972.
40
Brubaker, W. W., Jr.; Hites, R. A. J. Phys. Chem. A 1998, 102, 915.
41
Barkholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
161
42
CRC Handbook of Chemistry and Physics; 69th Ed.; Weast, R. C.; Astle, M. J.; Beyer,
W. H., Eds.; CRC Press: Boca Raton FL, 1988–1989.
162
CHAPTER 6
AB INITIO AND DFT STUDY OF THE ATMOSPHERIC REACTIONS OF
ACROLEIN WITH HYDROXYL RADICAL
6.1. Introduction
Volatile organic compounds (VOCs) are emitted into the atmosphere via
anthropogenic and biogenic sources. The fate of a VOC is largely determined by its
reactivity with a group of reactive radicals present in the troposphere (OH, O(3P), O3, and
NO3). Hydroxyl radical (OH) is the most significant tropospheric oxidizer of VOCs
during daylight hours.1 Primary sources for atmospheric aldehydes include incomplete
combustion of fuel and vegetation; in addition, a variety of α,β–unsaturated aldehydes
are introduced into the troposphere as secondary VOCs resulting from the oxidative
decomposition of primary VOCs with terminal allylic hydrogens, such as 1,3–butadiene
(CH2=CHCH=CH2).1,2,3 Acrolein (2–propenal, CH2=CHCHO) is the simplest
α,β–unsaturated aldehyde. Acrolein has been reported to constitute approximately
55–58% of the atmospheric–initiated oxidation products of 1,3–butadiene.4,5 Acrolein is
also a lung irritant and has mutagenic properties.6,7
Reliable thermochemical and kinetic data for processes such as hydrogen-atom
abstractions and radical addition by hydroxyl radical to unsaturated bonds (i.e. C=C, and
C≡C) over a wide temperature range is desirable as an aid in understanding the
163
decomposition and reactions of important VOCs so as to provide information toward
improving atmospheric and combustion models. Since acrolein is the simplest of the
unsaturated aldehydes, it provides a good reference for studying the competition between
the H-atom abstraction and radical addition mechanisms by hydroxyl radical for the
variety of atmospherically relevant α,β–unsaturated aldehyde analogs. Furthermore,
acrolein provides a good test case for judging the ability of theoretical methods to provide
reliable data for these two important gas-phase reaction mechanisms.
The pathways for the tropospheric oxidation of acrolein by hydroxyl radical can
proceed via either an abstraction or addition mechanism.
CH2=CHCH(=O) + •OH → CH2=CHC•(=O) + H2O
6.1a
→ •CH2CH(OH)CH(=O)
6.1b
→ HOCH2C•HCH(=O)
6.1c
Mechanism 6.1a corresponds to hydrogen-atom abstraction of the aldehydic hydrogen to
yield 1–oxo–but–2–en–1–yl radical and water. Abstraction of the vinylic hydrogens are
expected to be insignificant under tropospheric conditions, given that the bond
dissociation energies for a typical vinylic hydrogen is 111 kcal/mol compared to 87
kcal/mol for the aldehydic hydrogen in acrolein.8 We should note that the abstraction of
the vinylic hydrogens may become important at higher temperatures and may require
consideration in combustion scenarios. The addition of hydroxyl radical to the carbonyl
carbon of an aldehyde has also been shown computationally to be uncompetitive with
abstraction of the aldehydic hydrogen.9 Mechanisms 6.1b and 6.1c correspond to OH
164
addition to the C=C bond, either α or β to the carbonyl carbon, resulting in either
2–hydroxy–1–oxo–butan–3–yl or 3–hydroxy–1–oxo–butan–2–yl, respectively.
Mechanism 6.1c might be expected to be thermodynamically favored vis-à-vis 6.1b
because the unpaired electron may delocalize into the π bond of the adjacent carbonyl
group. This, of course, assumes that the addition reactions obey an Evans–Polanyi
relationship. Experimental and computational studies which have examined rate
coefficients for the reaction of hydroxyl radical with benzene show that at T ≤ 500 K, the
addition channel is favored, whereas at T ≥ 500 K, the hydrogen-atom abstraction
channel is favored.10,11 Therefore, it may be beneficial to analyze the mechanistic
competition of the abstraction and addition mechanisms over a broad temperature range.
The absolute rate of reaction for acrolein with hydroxyl radical in the gas phase
has been measured experimentally. Recently, Magneron et al.12 used pulsed laser
photolysis-laser induced fluorescence (PLP–LIF) to measure the rate of hydroxyl radical
loss under pseudo-first order conditions ([acrolein] >> [OH]0) to determine the absolute
rate coefficients between 20–300 Torr and 243–372 K. Prior to these experiments, kinetic
studies of the reaction of acrolein with hydroxyl radical had been limited to relative rate
determinations at ambient temperature and atmospheric pressure.13,14,15,16 While the
various experimentally–determined overall rate coefficients for the reaction of acrolein
with hydroxyl radical are within fair agreement ((1.83–2.66) x 10–11 cm3 molecule–1 s–1 at
298 K), the experimental techniques utilized were incapable of determining precise
branching ratios for the possible oxidative pathways. By analyzing the acrolein/OH
reaction products via Fourier–transform infrared spectroscopy (FTIR) analysis,
Magneron et al.12 were able to estimate that at least 20% of the reaction products resulted
165
from pathways for addition of OH to the C=C bond at 298 K, the remaining 80% of
products from abstraction of the aldehydic hydrogen. More recently, Orlando and
Tyndall17 utilizing an environmental chamber at 298 K determined, via FTIR analysis of
the reaction products, that 32% of the reaction proceeds by an OH-addition pathway.
Magneron et al.12 experimentally observed that the rate coefficients exhibit a
negative temperature dependence over the 243–372 K temperature range. The two
prominent mechanistic explanations for negative temperature dependence are a direct
hydrogen-atom abstraction and an addition–elimination mechanism with formation of a
long-lived intermediate.18 Reactions with negative temperature dependences have
recently been characterized by a two-step mechanism in which a pre–reactive complex
forms in the first and the barrier height to form products is lower than that of the reactant
species.9,19,20 In these studies, this mechanism has been successfully applied to the
reactions of simple aldehydes and olefins with hydroxyl radical. This complex then
proceeds over the transition state barrier height that has a lower total energy than the
reactants at infinite separation. This model lends support to the long-lived intermediate
explanation. Based on our general interest in the reactions of hydroxyl radicals,10,21,22,23
we have performed and extensive theoretical evaluation of the reaction of OH radical
with acrolein. Detailed computational analysis of these proposed mechanisms can help to
determine whether these pre–reactive complexes play an important role in determining
rate coefficients for the reaction of acrolein with OH radical.
166
6.2. Computational and Theoretical Methods
All calculations were performed using the Gaussian 0324 or Gaussian 9825 suite of
programs at the Ohio Supercomputer Center. Geometries for all stationary points were
optimized at the mPW1K/6–311G**,26 BH&HLYP/6–311G**,27,28
MP2/6–311++G**,29,30 QCISD/6–31G**, and QCISD/6–311G**31 levels of theory.
CCSD(T)31,32,33,34,35 single–point energies for the MP2 and QCISD geometries were
determined using an aug–cc–pVDZ basis set; additionally, the 6–311++G(3df,3pd) basis
set was also used for the MP2 geometries. All Pople-style basis sets used six Cartesian d
functions. All mPW1K calculations were performed using Gaussian 98. Each stationary
point was characterized by an analysis of the harmonic vibrational frequencies calculated
at the same theoretical level for the optimized geometry. Minima were confirmed to have
adequate convergence and zero imaginary vibrational frequencies. Transition state (TS)
structures were confirmed to have one imaginary vibrational frequency and furthermore
shown to be connected to the attributed reactant and product by displacement along the
normal mode coordinate (typically 10%) for the imaginary vibrational frequency in the
positive and negative directions, followed by careful minimization using either opt =
calcfc or opt = calcall. For reaction coordinates requiring a more accurate treatment, an
intrinsic reaction coordinate (IRC)36 calculation was performed. In general, 〈S2〉 values
for the optimized geometries were typically 0.75 ≤ 〈S2〉 ≤ 0.79, except where noted in the
text.
In order to account for potential errors in the thermodynamic values associated
with the harmonic-oscillator rigid-rotor approximation, low-energy torsions were treated
as hindered rotors when applicable. The reduced moment of inertia for each internal
167
rotation was calculated about the axis that includes the torsional bond using the code
provided by Multiwell 1.4.1.37 The contribution of each internal rotor to the
thermodynamic parameters, H(T) and S(T), was determined by generating a rigid
potential energy profile for a complete rotation of each internal rotor. The profiles were
then modeled via a Fourier series to construct a hindrance potential to be used in the
Hamiltonian. Using the free internal rotation wave functions as a basis, the hindered rotor
energy levels were calculated by direct diagonalization of the Hamiltonian matrix. The
hindered rotor partition functions were obtained via summation over the energy levels
and the thermodynamic values obtained using standard methods.38 All other vibrational
frequencies were treated as harmonic. Zero–point vibrational energy scaling factors of
0.9515, 0.9748, and 0.9776 were used for the mPW1K, MP2, and QCISD geometries,
respectively.39,40 While none of the method/basis set combinations we have used have
calibrated ZPE scaling factors, we utilized the closest available value. The BH&HLYP
method currently has no reported ZPE scaling factor; therefore, those vibrational
frequencies and ZPE corrections were left unscaled.
Conventional transition state theory (TST) was utilized to estimate the aldehydic
hydrogen-atom abstraction and hydroxyl radical addition high-pressure limit rate
coefficients over the 200–2000 K temperature range.41 The conventional TST rate
equation in the thermodynamic formulation as a function of temperature is as follows:
k(T)TST
=
Γ(T)
kB T
exp( − ΔG0≠ /kB T)
h
€
168
6.2
In Equation 6.2, T is the absolute temperature, h is Planck’s constant, kB is Boltzmann
constant, and ΔG≠0 is the free energy barrier height relative to reactants at infinite
separation. The temperature dependent factor Γ(T) represents quantum mechanical
tunneling and is accounted for via the Wigner approximation:42
Γ(T) = 1+
1  hv i 


24  kB T 
6.3
where νi is the imaginary vibrational frequency representing the TS barrier’s curvature.
€
The first low lying electronic state due to spin-orbit coupling in the 2Π hydroxyl radical
was accounted for in calculating its electronic partition function. An energy splitting
value of 139.21 cm–1, obtained by Maillard et al.,43 was used with both ground and
excited states having a degeneracy of 2.
6.3. Results and Discussion
The reaction energy profiles for the aldehydic and vinylic H–atom abstraction and
C=C addition reactions of E–acrolein and OH radical, based on the mPW1K/6–311G**
ΔH0 energies are shown in Figure 6.1. Furthermore, Table 6.1 lists the ΔH0 values for
each of the stationary points shown in Figure 6.1 at all levels of theory utilized here,
relative to E–acrolein and OH radical at infinite separation which was defined as zero in
energy. Figures 6.2 and 6.3 show the structures for each of the stationary points in Figure
6.1 along with select geometric parameters. Self-consistent field (SCF) energies,
geometrical parameters, 〈S2〉 values, Cartesian coordinates, and harmonic vibrational
frequencies for all species at each level of theory are provided in the Appendix. All
169
energies referred to in the remainder of this paper correspond to enthalpies at 0 K (H0, i.e.
SCF energy + zero–point vibrational energy (ZPVE)), unless otherwise indicated. In
order to maintain space constraints, in some instances the aug–cc–pVDZ and
6–311++G(3df,3pd) basis sets have been represented with the D and P labels,
respectively. Potential energy surfaces calculated via the mPW1K method with its
prescribed basis set (6-31+G**)26 resulted in rate coefficients that were inconsistent with
experiment. Particularly, difficulty in obtaining a transition state structure for addition of
OH radical β to the carbonyl, resulted in an over-prediction of the OH-radical addition
branching ratio. Supporting material in the appendix has been provided for the
mPW1K/6-31+G** energy surfaces, but they will not be discussed.
170
10
TSβ–trans– vinyl
TSβ–cis–vinyl
5
0
ΔH0K kcal/mol
-5
TSα–add
E–CH2CHCHO
+ OH
TSabst
RC2
-10
TSα–vinyl
TSβ–add
trans–.CHCHCHO
CH2C.CHO
cis–.CHCHCHO
RC1
-15
-20
CH2CHC.O +H2O
-25
PC
-30
.CH2CHOHCHO
-35
CH2OHC.HCHO
-40
Figure 6.1. Potential energy diagram (ΔH0, kcal/mol) for the aldehydic and vinyl H–atom
abstraction and C=C addition reactions of E–acrolein and OH radical based on the
mPW1K/6–311G** energies. See Figures 6.2 and 6.3 for the structures.
171
QCISD/
QCISD/
6–31G**
6–311G**
CCSD(T) CCSD(T) QCISDe CCSD(T) QCISDa CCSD(T)
/Dc
/Pd
/Dc
/Dc
MP2/6–311++G**
mPW1Ka BH&HLYPa
MP2b
abstraction
acrolein + OH
RC1 2A” (2A’)
RC2 2A” (2A’)
TSabst
0.0
–6.6
(–5.0)
–6.0
(–5.2)
–1.5
0.0
0.0
0.0
0.0
–6.9 (–5.4)
(–4.1)
(–4.9)
(–4.6)
–0.5
–4.3
(–4.1)
3.1
–5.0
(–4.9)
–3.5
–3.2
–5.9 (–5.3)
0.0
0.0
0.0
0.0
1.1
–2.9
0.6
–2.0
PC
–26.4
–24.4
–30.2
–26.2
–27.5
CH2CHC.O + OH
–26.0e
–22.5e
–28.4
–24.2
–25.9e
–20.4
–25.0
–23.2
–25.5
4.5
0.1
4.4
0.0
2.9
–0.8
3.0
–0.9
α–addition
TSα–add
1.1
3.1
13.3
3.7
3.7
C.H2CHOHCHO
–29.3
–23.3
–26.7
–24.4
–26.0
β–addition
TSβ–add
–1.0
0.5
13.4
2.8
2.5
CH2OHC.HCHO
–35.2
–29.9
–23.2
–25.6
–28.1
vinyl–abstraction
TSα–vinyl
4.5
CH2C.CHO
–1.4
TSβ–cis–vinyl
6.5
cis–C.HCHCHO
–2.0
TSβ–trans–vinyl
7.2
trans–C.HCHCHO
–1.5
Table 6.1. Relative energies (ΔH0, kcal/mol) for the stationary points on the energy
surface for aldehydic H–atom abstraction and C=C addition reactions of E–acrolein and
OH radical.
a
6–311G** basis set. b 6–311++G** basis set. c D represents the aug–cc–pVDZ basis
set. d P represents the 6–311++G(3df,3pd) basis set. e Energy corresponds to the
CH2=CHC•(=O) conformation with a linear C–C–O moiety.
172
0.972
0.971
0.976
1.142
1.181
1.175
1.177
1.166
1.901
1.917
1.974
2.517
2.533
2.929
RC1 (2A")
MP2 = (2A')
E–CH2CHCHO
+ OH
1.896
1.911
1.945
0.972
0.970
0.976
2.734
2.738
3.243
H–O---C–O
54.32
52.54
24.31
56.36
55.11
O–C–C–C
180
180
157.31
180
180
1.619
1.434
1.452
1.457
1.508
TSabst C–C–C---OH
1.58
4.17
3.16
1.49
2.75
2.430
2.471
2.466
PC
H–O---C–C
42.54
39.57
35.21
44.94
47.67
0.956
0.954
0.964
CH2CHC.O + H2O
2.306
2.321
2.392
2.254
2.111
2.033
2.143
2.127
CH2OHC.HCHO
TSβ–add
2.107
2.015
2.040
2.069
2.060
RC2 (2A")
TSα–add
2.015
2.048
2.063
H–O---C–CH2
5.58
4.96
9.69
1.50
15.35
.CH2CHOHCHO
Figure 6.2. Structures for each of the stationary points in Figure 6.1 along with select
geometric parameters. The parameters are listed according to mPW1K/6–311G** (top),
BH&HLYP/6–311G** (second), MP2/6–311++G** (third), QCISD/6–31G** (fourth),
and QCISD/6–311G** (fifth). Distances are provided in angstrom (Å) and torsion angles
in degrees.
173
6.3.1. Potential Energy Surfaces
Due to the strong dipolar nature of both acrolein and hydroxyl radical, their
interactions can form pre–reactive complexes, RC1 and RC2 (Figures 6.1 and 6.2).
Complexes RC1 and RC2 both have Cs symmetry and involve coordination of the
hydroxyl radical’s hydrogen to the carbonyl oxygen on acrolein. They differ by the
coordination of the hydroxyl radical oxygen, with RC1 coordinating with the hydrogen
on the carbon adjacent to the carbonyl and RC2 with the aldehydic hydrogen. Both
reactant complexes have a small preference for the 2A" electronic state, over the 2A'
electronic state (Table 6.1). A stable wavefunction for the 2A" state at the
MP2/6–311++G** level could not be isolated. Complex RC1 is predicted to have a
binding energy ranging from 6.9 kcal/mol at the BH&HLYP/6–311G** level to 4.1
kcal/mol at the MP2/6–311++G** level (Table 6.1). The binding energy of RC1 is
roughly 1 kcal/mol more favorable than that of RC2, with binding energies ranging from
6.0 kcal/mol at the mPW1K/6–311G** level to 4.3 kcal/mol at the MP2/6–311++G**
level. Nevertheless, the orientation of the hydroxyl radical in RC2 appears to have less
constrained access to the pathway for abstraction of the aldehydic hydrogen, giving it a
greater role in the overall reactivity of acrolein with OH radical. The interaction distances
within complexes RC1 and RC2 are in excellent agreement among the DFT structures,
differing at most by 0.016 Å (Figure 6.2). The MP2 distances are as much as 0.5 Å longer
than the DFT values, with the largest discrepancy corresponding to the O---H distance
between the hydroxyl radical’s oxygen and acrolein’s hydrogen.
The pathway with the overall lowest barrier height at all levels of theory reported
here is the aldehydic H–abstraction pathway (TSabst, Figures 6.1 and 6.2). The barriers
174
for OH to abstract the aldehydic hydrogen (ΔH≠0) at most levels of theory are below the
energy of the reactants at infinite separation. The exceptions are the MP2/6–311++G**,
QCISD/6–31G**, and QCISD/6–311G** barrier heights of 3.1, 1.1, and 0.6 kcal/mol,
respectively. Barrier heights derived from CCSD(T)/aug–cc–pVDZ and
CCSD(T)/6–311++G(3df,3pd) single–point energies on the MP2 and QCISD geometries
resulted in significant downward corrections. In the most extreme case, the MP2 barrier
height was reduced more than 6.0 kcal/mol to >3.0 kcal/mol lower than the energy of
infinitely separated reactants. The poor agreement between the MP2 and CCSD(T)
energies suggest that, despite the use of a fairly large basis set for the MP2 optimization,
a higher degree of correlation may be necessary to accurately describe the H-atom
abstraction transition-state geometries. In each transition-state structure for aldehydic
hydrogen transfer (TSabst) the hydrogen atom has made little progress toward transfer,
and thus the TS should be considered an early one. The mPW1K/6–311G** level predicts
the earliest transition state with an aldehydic C–H distance of 1.142 Å and an H---O
distance of 1.619 Å. The BH&HLYP/6–311G** level predicts the latest transition state
with C–H and H---O distances of 1.181 and 1.434 Å, respectively. Another interesting
feature regarding TSabst is that it lacks Cs symmetry at the levels of theory reported here.
The hydroxyl radical’s oxygen sits out of the molecular plane of acrolein by several
degrees, and the H–O---C–O dihedral angle ranges from ~56 to ~24˚. The combination of
a pre-reactive complex at the entrance channel for abstraction (RC2) and an early
transition state due to the exothermicity of the abstraction reaction allows the activation
barrier to be lower in energy than reactants.
175
Following aldehydic H-abstraction, a complex of the resultant acroleinyl radical
(CH2=CHC•(=O)) and the resulting water molecule is formed (PC). In complex PC, the
abstracted hydrogen is coordinated to the unpaired electron on the carbonyl carbon of the
acroleinyl radical, and a lone electron pair on the water molecule’s oxygen is coordinated
to the cis methylene hydrogen of acroleinyl radical (Figure 6.2). The exothermicity of PC
is predicted to be between 24.4 and 30.2 kcal/mol. Complex PC is ~2–4 kcal/mol more
stable than acroleinyl radical and water at infinite separation.
The reaction energy for the aldehydic H-abstraction pathway is particularly
exothermic due to the O–H bond strength of water. The abstraction reaction energies are
all within reasonable agreement predicting values from ~20 to ~28 kcal/mol.
Interestingly, there is a lack of consensus regarding the most favorable conformation of
the acroleinyl radical. The mPW1K, BH&HLYP, and CCSD(T)/aug-cc-pVDZ//MP2/6311++G** levels predict that the acroleinyl radical conformation with a linear C–C–O
bond angle is favored over the bent conformation (Figure 6.2). The remaining levels of
theory favor the bent conformation.
Addition of the hydroxyl radical at the carbon β to the carbonyl on acrolein
provides the next lowest energy reaction pathway. The calculated barrier heights (ΔH≠0)
for the β–addition reaction cover a considerable range from –1.0 kcal/mol at the
mPW1K/6–311G** level to 13.4 kcal/mol at the MP2/6–311++G** level. Single-point
energies on the MP2 geometries via the CCSD(T) method reduce the barrier height by as
much as ~11 kcal/mol. Similar to the case for the TSabst geometric parameters, the
mPW1K method predicts a significantly earlier TSβ–add structure than the other methods
with a C---O distance of 2.254 Å. The MP2 TSβ–add predicts the shortest C---O distance
176
at 2.033 Å. In TSβ–add, the hydroxyl OH is situated nearly parallel over the C=C acrolein
bond with the O–H bond displaced from the C=C plane by typically ~40˚. The 〈S2〉 values
for the MP2 and QCISD wavefunctions for TSβ–add signify considerable spin
contamination with values of ~1. The DFT wavefunctions provide lower 〈S2〉 values of
~0.80, closer to the proper value of 0.75 for a radical.
The reaction energy for the β–addition pathway, yielding HOCH2C•HCH(=O), is
very exothermic. However, a significant range of reaction energies is obtained from the
methods reported here. The mPW1K level gives a reaction energy of –35.0 kcal/mol, and
the MP2 level gives a reaction energy of –23.1 kcal/mol. The CCSD(T) method singlepoint energies on the MP2 geometries increase the reaction exothermicity to –28.0
kcal/mol, more in accord with the DFT values.
The pathway for addition of hydroxyl radical to the carbon α to the carbonyl
group of acrolein has the next highest barrier. The barrier heights for α–addition range
from 1.1 kcal/mol at the mPW1K/6–311G** level to 13.3 kcal/mol at the
MP2/6–311++G** level. Single–point energies on the MP2 geometries at the CCSD(T)
level reduce the barrier height by as much as ~10.0 kcal/mol. The mPW1K method again
predicts a significantly earlier transition state geometry than the other theoretical levels
with a C---O distance at 2.107 Å. The BH&HLYP method predicts the shortest C---O
distance of 2.015 Å. Similar to TSβ–add, the OH in TSα–add is situated over the acrolein
C=C bond with the O–H displaced via torsion from the C=C plane by several degrees.
The 〈S2〉 values for the TSα–add wavefunctions are similar to those for TSβ–add: the MP2
and QCISD wavefunctions have 〈S2〉 values of ~1, and the DFT wavefunctions have
values of ~0.80.
177
Unlike the β–addition adduct, the α–adduct (•CH2CH(OH)CH(=O)) is not
capable of delocalizing the unpaired electron. The reaction energy for the α–addition
pathway, however, is still very exothermic. At the mPW1K level, the reaction has a 0 K
enthalpy of –29.3 kcal/mol, while the BH&HLYP level gives a reaction enthalpy of –23.3
kcal/mol, providing reasonable agreement among the levels of theory. Hydrogen bonding
between the hydroxyl hydrogen and carbonyl oxygen stabilizes the α–adduct by ~2.5
kcal/mol, relative to the next most stable conformer.
For comparison with the more favorable aldehydic H-atom abstraction
mechanism, the transition states and reaction energies for abstraction of the vinylic
hydrogens of acrolein have been calculated at the mPW1K/6-311G** level (Figures 6.1
and 6.3). The vinylic H-atom abstraction barriers are significantly greater than the
aldehydic H-atom abstraction and OH radical addition reactions with nearly
thermoneutral reaction energies. Abstraction of the β–vinylic hydrogens follow an
Evans–Polanyi relationship with barrier heights of 6.5 and 7.2 kcal/mol and reaction
energies of –2.0 and –1.5 kcal/mol for the β–cis– and β–trans–vinyl C–H bonds,
respectively. On the other hand, the α–vinylic H-atom abstraction barrier height is 4.5
kcal/mol and slightly exothermic at 1.4 kcal/mol. The reduced barrier height relative to
the β–vinylic hydrogens can be attributed to the existence of a favorable reactant
complex (RC1) at the entrance channel.
178
1.280
1.175
CH2C.CHO
TSα–vinyl
1.260
1.208
cis–.CHCHCHO
TSβ–cis–vinyl
1.261
TSβ–trans– vinyl
trans–.CHCHCHO
1.195
Figure 6.3. Structures for the transition states and radical products of the vinylic H–atom
abstraction reactions of E–acrolein and hydroxyl radical at the mPW1K/6–311G** level.
179
CCSD(T)/P//
CCSD(T)/D//
ΒΗ&ΗLYP MP2/6–311++G** QCISD/6–311G**
4.50E–12
1.08E–08
2.39E–10
Temperature (K)
200
243
253
273
298
mPW1K
3.99E–11
1.36E–11
2.42E–12
5.24E–10
4.38E–11
300
323
348
372
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
1.34E–11
2.41E–12
5.05E–10
4.30E–11
9.38E–12
8.60E–12
8.90E–12
9.77E–12
1.10E–11
1.26E–11
1.45E–11
1.67E–11
1.91E–11
2.18E–11
2.47E–11
2.79E–11
3.14E–11
3.51E–11
3.91E–11
4.34E–11
4.78E–11
2.12E–12
2.26E–12
2.61E–12
3.11E–12
3.76E–12
4.55E–12
5.48E–12
6.55E–12
7.77E–12
9.13E–12
1.06E–11
1.23E–11
1.41E–11
1.61E–11
1.82E–11
2.05E–11
2.30E–11
1.26E–10
6.22E–11
4.26E–11
3.49E–11
3.18E–11
3.09E–11
3.12E–11
3.24E–11
3.42E–11
3.65E–11
3.91E–11
4.21E–11
4.55E–11
4.91E–11
5.31E–11
5.73E–11
6.18E–11
2.19E–11
1.65E–11
1.48E–11
1.46E–11
1.52E–11
1.62E–11
1.76E–11
1.94E–11
2.13E–11
2.35E–11
2.59E–11
2.86E–11
3.14E–11
3.45E–11
3.78E–11
4.12E–11
4.49E–11
Experiment
2.66E–11a
2.53E–11 a
2.26E–11 a
2.01E–11 a
2.66E–11 b
1.90E–11 c
1.83E–11 d
2.04E–11 e
1.84E–11 a
1.80E–11 a
1.68E–11 a
Table 6.2. The total rate coefficients for the reaction of acrolein with hydroxyl radical at
each level of theory and for experiment.
a
Mangeron et al. values are averages when multiple measurements were provided at that
temperature.b Ref. 7: Maldotti, A.; Chiorboli, C.; Bignozzi, C. A.; Bartocci, C.; Carassiti,
V. Int. J. Chem. Kinet. 1980, 12, 905. c Ref. 8: Kerr, J. A.; Sheppard, D. W. Environ. Sci.
Technol. 1981, 15, 960. d Ref. 9: Atkinson, R.; Aschmann, S. M.; Pitts, J. N. Int. J. Chem.
Kinet. 1983, 15, 75. e Ref. 10: Edney, E. O.; Kleindienst, T. E.; Corse, E. W. Int. J. Chem.
Kinet. 1986, 18, 1355.
180
-7
mPW1K/6-311G**
BH&HLYP/6-311G**
log k (cm3/molecule
-8
CCSD(T)/P//MP2/6-311++G**
CCSD(T)/D//QCISD/6-311G**
-9
Mangeron et al.
-10
-11
-12
0
1
2
1000/T(K)
3
4
5
Figure 6.4. Arrhenius plots of the total theoretical TST rate coefficients for the
reaction of E–acrolein with OH radical.
6.3.2. Rate Coefficients
Table 6.2 contains the total rate coefficients for the reaction of acrolein with
hydroxyl radical from 200–2000 K at the mPW1K/6–311G**, BH&HLYP/6–311G**,
CCSD(T)/6–311++G(3df,3pd)//MP2/6–311++G**, and CCSD(T)/aug–cc–pVDZ
//QCISD/6–311G** theoretical levels, and for comparison, the available experimental
values from Mangeron et al. Figure 6.4 shows the data in Table 6.2 in the form of
Arrhenius plots along with the variable temperature values of Mangeron et al.12
Furthermore, the rate coefficients for mechanisms 6.1a–6.1c at each level of theory as
181
well as extensive information relevant to the treatment of low energy harmonic vibrations
as internal rotors can be found in the Appendix.
The TST rate coefficients at the high-pressure limit generated at the mPW1K
level of theory are in very good agreement with the experimentally determined values
over the temperature 243–372 K range of Mangeron et al.12 (Table 6.2 and Figure 6.4).
These values are well within a factor of 2 of the experimental values, which is
exceptional for theoretically determined TST rate coefficients. The other levels of theory
do not provide the same agreement. The BH&HLYP method yielded rate coefficients that
underestimate the experimental values by approximately an order of magnitude. On the
other hand, both of the ab initio methods produced rate coefficients that are much greater
than the experimental values.
The Arrhenius profiles in Figure 6.4 show that the rate coefficients at low
temperatures exhibit an inverse temperature dependence. It is also in this low-temperature
regime where the theoretically derived rate coefficients are in the greatest disagreement
and with significantly diverging values. Comparison of the rate coefficients at the lower
temperatures can provide a good means for evaluating the theoretical H-atom abstraction
barrier heights (ΔH≠0, Table 6.1) since the aldehydic H-atom abstraction reaction is
predicted to dictate the Arrhenius profile in this regime (Figure 6.5 and Supporting
Information). The mPW1K barrier of –1.5 kcal/mol (relative to infinitely separated
reactants) appears to provide the best estimate, given the excellent agreement with the
experimental values. With respect to the other levels of theory, the BH&HLYP level is
one extreme relative to the mPW1K level, overestimating the abstraction barrier by ~1
kcal/mol, while the CCSD(T)//MP2 level is the other extreme and appears to significantly
182
underestimate the barrier by ~2 kcal/mol relative to the mPW1K value. Re–optimizing
the MP2 geometries at the QCISD/6–31G** and QCISD/6–311G** levels, to provide a
greater degree of electron correlation for the UHF reference wavefunction, yielded
CCSD(T)//QCISD single–point barrier heights that provide a significant energy
correction, from the CCSD(T)//MP2 values and aim toward the mPW1K values. Clearly,
the hydrogen-atom abstraction mechanism requires that the TS geometry be derived from
a highly correlated ab initio method. The electron correlation provided by the MP2
method is insufficient for quantitative results for these open-shell systems, and other
researchers have observed similar trends.44
The rate coefficients for the gas-phase reaction of hydroxyl radical with aldehydes
such as formaldehyde, acetaldehyde, and longer aliphatic chain aldehydes exhibit an
inverse temperature dependence in the 243–425 K temperature regime.9,18,45,46 The
prevalent explanation involves the existence of a meta–stable intermediate which
stabilizes the barrier for abstracting the aldehydic hydrogen.18 An inverse dependence of
the rate coefficients at low temperatures is also observed for the reaction of hydroxyl
radical with acrolein and other α,β–unsaturated aldehydes over a similar temperature
range.12,47 Reaction rates for some of the same aldehyde substrates with Cl atoms,
however, exhibit normal temperature dependence for low temperature rate coefficients,
supporting the significant role of pre-reactive complexes in decreasing the reaction
barrier heights.46,48,49
The quality of the barrier heights (ΔH≠0, Table 6.1) for the addition mechanisms is
much harder to extract from the total rate coefficients and Arrhenius profiles. The
contribution from the β–addition mechanism becomes significant at ~400–800 K and
183
affects the total rate coefficient and Arrhenius behavior. The poor agreement among the
low-temperature TST rate coefficients is minimized at high temperatures as both the
aldehydic H-atom abstraction and β–addition mechanisms contribute significantly. Figure
6.5 shows plots of the branching ratios derived from each of the theoretical levels over
the 200–2000 K temperature range as well as the 298 K experimentally determined ratios.
The mPW1K level predicts a branching ratio profile with values that run between the 298
K experimentally predicted ratios of Mangeron et al. (0.80 abstraction, 0.20 addition)12
and Orlando et al. (0.68 abstraction, 0.32 addition)17 and predicts a theoretical 298 K
abstraction branching ratio of 0.71. As the temperature approaches 2000 K, the
abstraction branching ratio is reduced to ~0.60. The other levels of theory predict a
significantly more dominant contribution from aldehydic H-atom abstraction.
184
mPW1K
CCSD(T)/P//MP2/6-311++G**
Mangeron et al.
1.00
BH&HLYP
CCSD(T)/D//QCISD/6-311G**
Orlando et al.
0.90
0.80
branching ratio
0.70
0.60
abstraction
addition
0.50
0.40
0.30
0.20
0.10
0.00
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Temperature (K)
Figure 6.5. Plot of the branching ratios for the aldehydic H–abstraction and OH addition
mechanisms contribution to the total rate coefficients for the reaction of E–acrolein with
OH radical.
Using the previously derived information regarding the quality of the aldehydic
H-atom abstraction barrier heights and experimental branching ratios, we can try to
utilize the difference between the abstraction and addition barrier heights to evaluate the
quality of each. Since the contribution of α–addition to the total rate coefficient is
negligible at most temperatures (~4% at 2000 K, see Appendix), we can expect useful
information from the differences between H-atom abstraction and β–addition barrier
heights. These barrier height differences are 0.5, 1.0, 5.7, and 1.1 kcal/mol, all in favor of
185
abstraction, for the mPW1K/6–311G**, BH&HLYP/6–311G**,
CCSD(T)/6–311++G(3df,3pd)//MP2/6–311++G**, and CCSD(T)/aug–cc–pVDZ//
QCISD/6–311G** levels of theory, respectively. Given that Mangeron et al. were
capable of more complete product analysis and near 100% carbon balance, we shall also
judge their 298 K branching ratio to be the more accurate of the two experimental values.
In order for the mPW1K branching ratio to better agree with experiment, a small increase
in the β–addition barrier height, to just above its –1.0 kcal/mol value, or a small decrease
in the abstraction barrier height, to just below its –1.5 kcal/mol value, would need to be
made. Alternatively, each could be simultaneously corrected, but by no more than a total
of 0.4 kcal/mol, which would result in a branching ratio similar to that at the BH&HLYP
level, which overestimates the abstraction branching ratio relative to experiment. Given
the small change in the β–addition barrier height required at the mPW1K level, we could
use the mPW1K barrier height values to judge the β–addition barrier heights obtained at
the other levels of theory. The quality of the mPW1K barrier heights should also be
validated by the convergence of the higher level ab initio values toward the mPW1K
values. The BH&HLYP barrier heights for abstraction and β–addition both appear to be
too high, but the overestimation of each barrier is at least consistent with respect to the
mPW1K barrier heights. On the other hand, the ab initio methods underestimate the
abstraction barrier height and overestimate the addition barrier heights. The CCSD(T)
derived barrier height from the QCISD TSβ–add geometry of –0.9 kcal/mol, however, is in
very good agreement with the mPW1K value of –1.0 kcal/mol. These results highlight
the potential of DFT methods in the prediction of reaction barrier heights for open-shell
reactions of larger chemical systems.
186
The contribution from the pathways for vinylic H-abstraction to the total rate
coefficients is expected to be negligible due to significant barrier heights. Even the
α–addition mechanism is only predicted to contribute ~4% at 2000 K. This conclusion is
supported by the large difference in C–H bond dissociation energies for E–acrolein. We
have determined the bond dissociation energies (ΔH(298 K)) for each of the E–acrolein
C–H bonds at the CBS-QB3 level. The bond dissociation energies are 90.6, 112.4, 111.8,
and 111.9 kcal/mol for the aldehydic, α–, β–cis-, and β–trans–vinylic C–H bonds,
respectively. These values are in good agreement with the experimental values for
acrolein’s aldehydic C–H bond of 87.1±1.0 kcal/mol and that for ethene’s sp2 C–H bond
at 111.2±0.8 kcal/mol.8
The correction due to quantum mechanical tunneling for the hydrogen-atom
abstraction reaction is predicted to cover a large range of values based on the range of
barrier heights and imaginary vibrational frequencies obtained from the different levels of
theory utilized in this study. At low temperatures, the Wigner correction (eqn. 6.3) to
tunneling is dominated by the magnitude of the imaginary frequency. The values for
imaginary vibrational frequencies of TSabst vary from 182i cm–1 at the mPW1K level to
1171i cm–1 at the MP2/6–311++G** level to give tunneling correction factors of 1.07 and
3.96 at 200 K, respectively. At the QCISD/6–311G** level, TSabst has an imaginary
vibrational frequency (425i cm–1) which is greatly reduced relative to the MP2 value,
providing a 200 K tunneling correction of 1.44. The reduction in the tunneling
corrections via the higher correlated QCISD method indicates that tunneling in the
aldehydic H-atom abstraction reaction of acrolein and hydroxyl radical is not nearly as
significant as predicted by the MP2 method’s imaginary vibrational frequency. Therefore,
187
we believe the Wigner tunneling approximation is sufficient for this reaction. Further
evidence for the minimized contribution to the low temperature rate coefficients from
tunneling is provided by the estimated CCSD(T)/aug–cc–pVDZ minimum-energy
pathway (MEP) based on a spline fitting to the MP2/6–31+G** MEP for the aldehydic
H-abstraction reaction in Figure 6.6.50,51 These calculations were performed utilizing the
ISPE–752 method provided in the Polyrate 9.1 program.53 Figure 6.6 shows that the
estimated CCSD(T)/aug–cc–pVDZ MEP results in a flattened and broad barrier for the
H-atom abstraction reaction. Both of these features result in reduced tunneling.
188
10
MP2/6-31+G**
5
CCSD(T)/aug-cc-pVDZ
ISPE
Energy (kcal/mol)
0
-5
-10
-15
-20
-25
-30
-2.5
-1.5
-0.5
0.5
Reaction Coordinate (bohr)
1.5
2.5
Figure 6.6. Minimum energy pathways (MEPs) for the aldehydic H–abstraction reaction
of E–acrolein and OH radical.
189
6.4. Conclusions
We have generated detailed DFT and ab initio potential energy surfaces for the
gas-phase reaction of E–acrolein with hydroxyl radical. From these potential energy
surfaces, transition state theory rate coefficients at the high–pressure limit were
calculated over the 200–2000 K temperature range. The rate coefficients derived from the
mPW1K DFT energies were superior to the other methods, including those of highly
correlated ab initio methods, when compared to the experimental values12 measured from
243–372 K. Furthermore, the mPW1K method yielded branching ratios for the H-atom
abstraction and addition mechanisms which are in good agreement with the
experimentally determined values.12,17 Throughout the 200–2000 K temperature range,
the H-atom abstraction reaction is predicted to be dominant.
An inverse temperature dependence for the rate coefficients at low temperatures
was shown to result from the existence of strong pre–reactive complexes, between the
polar acrolein and OH radical substrates, and allow the energy of the transition state for
the H-atom abstraction and β–addition mechanisms to be lower than the energy for the
reactants at infinite separation. Moreover, tunneling, at the lowest temperatures, for the
H-atom abstraction mechanism was shown to have a small effect on the rate coefficients.
Our best estimate of the rate coefficients at the high–pressure limit for the reaction of
acrolein with hydroxyl radical based on the mPW1K PES over the 200–2000 K
temperature range, in 3–parameter Arrhenius form, is k(T) = 4.00 x 10–20 T 2.66
exp(1322/T) cm3 molecule–1 s–1.
190
References for Chapter 6
1
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Madronich, S.; Moortgat, G. K.; Wallington, T.
J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the Alkenes, Oxford
University Press, New York, 2000.
2
Atkinson, R. Reactions of Oxygen Species in the Atmosphere in Active Oxygen in
Chemistry, Foote, C. S., Valentine, J. S., Greenberg, A., Liebman, J. F., Eds., Blackie
Academic & Professional, New York, 1995, pp. 249.
3
Agency for Toxic Substatnces and Disease Registry (ATSDR), ToxFAQs for Acrolein,
July 1999. Available on-line at http://www.atsdr.cdc.gov/tfacts124.html (12/17/02)
4
Liu, X.; Jeffries, H. E.; Sexton, K. G. Atmos. Environ. 1999, 33, 3005.
5
Tuazon, E. C.; Alvarado, A.; Aschmann, S. M.; Atkinson, R.; Arey, J. Environ. Sci.
Technol. 1999, 33, 3586.
6
Destaillates, H.; Spaulding, R. S.; Charles, M. J. Environ. Sci. Technol. 2002, 36, 2227.
7
Kozekov, I. D.; Nechev, L. V.; Moseley, M. S.; Harris, C. M.; Rizzo, C. J.; Stone, M.
P.; Harris, T. M. J. Am. Chem. Soc. 2003, 125, 50.
8
McMillan, D. F.; Golden, D. M. Ann. Rev. Phys. Chem. 1982, 33, 493.
9
Raul Alvarez-Idaboy, J.; Mora-Diez, N.; Boyd, R. J.; Vivier-Bunge, A. J. Am. Chem.
Soc. 2001, 123, 2018.
10
Barckholtz, C.; Barckholtz, T.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
11
Tulley, F. P.; Ravishankara, A. R.; Thompson, R. L.; Nicovich, J. M.; Shah, R. C.;
Kreutter, N. M.; Wine, P. H. J. Phys. Chem. 1982, 85, 2262.
191
12
Magneron, I.; Thévenet, R.; Mellouki, A.; LeBras, G.; Moortgat, G. K.; Wirtz, K. J.
Phys. Chem. A 2002, 106, 2526.
13
Maldotti, A.; Chiorboli, C.; Bignozzi, C. A.; Bartocci, C.; Carassiti, V. Int. J. Chem.
Kinet. 1980, 12, 905.
14
Kerr, J. A.; Sheppard, D. W. Environ. Sci. Technol. 1981, 15, 960.
15
Atkinson, R.; Aschmann, S. M.; Pitts, J. N., Jr. Int. J. Chem. Kinet. 1983, 15, 75.
16
Edney, E. O.; Kleindienst, T. E.; Corse, E. W. Int. J. Chem. Kinet. 1986, 18, 1355.
17
Orlando, J. J.; Tyndall, G. S. J. Phys. Chem. A 2002, 106, 12252.
18
Semmes, D. H.; Ravishankara, A. R.; Gump-Perkins, C. A.; Wine, P. H. Int. J. Chem.
Kinet. 1985, 17, 303.
19
Raul Alvarez-Idaboy, J.; Mora-Diez, N.; Boyd, R. J.; Vivier-Bunge, A. J. Am. Chem.
Soc. 2001, 123, 2018.
20
Raul Alvarez-Idaboy, J.; Mora-Diez, N.; Vivier-Bunge, A. J. Am. Chem. Soc. 2000,
122, 3715.
21
Villamena, F. A.; Hadad, C. M.; Zweier, J. L. J. Am. Chem. Soc. 2004, 126, 1816.
22
Villamena, F. A.; Rockenbaur, A.; Gallucci, J.; Velayutham, M.; Hadad, C. M.;
Zweier, J. L. J. Org. Chem. 2004, 69, 7994.
23
(a) Poole, J. S.; Shi, X.; Hadad, C. M.; Platz, M. S. J. Phys. Chem. A. 2005, 109, 2547.
(b) DeMatteo, M. P.; Poole, J. S.; Shi, X.; Sachdeva, R.; Hatcher, P. G.; Hadad, C. M.;
Platz, M. S. J. Am. Chem. Soc. 2005, 127, 7094.
24
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.;
192
Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani,
G.; Rega, N.; Pettersson, G. A.; Nakatsuji, H; Hada, M.; Ehara, M.; Toyota, K.; Fukuda,
R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.;
Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.;
Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.;
Ayala, P. Y.; Morokuma, K.; Voth, g. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V.
G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;
Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.;
Cioslowski, J.; Stefanov, B. B.; Lui, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.;
Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.;
Pople, J. A. Gaussian 03 (Revision B.04), Gaussian, Inc.; Pittsburgh, PA, 2003.
25
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J.
C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.;
Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.;
Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.;
Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J.
V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;
193
Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98,
Revision A.11, Gaussian, Inc.; Pittsburgh, PA, 2001.
26
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 4811.
27
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
28
Lee, C.; Yang, W.; Parr, R.G. Phys. Rev. B 1998, 37, 785.
29
Moller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618.
30
Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett. 166, 275 (1990).
31
Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968.
32
Cizek, J. Adv. Chem. Phys. 1969, 14, 35.
33
Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910.
34
Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F., III J. Chem. Phys. 1988, 89, 7382.
35
Scuseria, G. E.; Schaefer, H. F., III J. Chem. Phys. 1989, 90, 3700.
36
(a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.;
Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523.
37
a) Barker, J. R.; Ortiz, N. F.; Preses, J. M.; Lohr, L. L. MultiWell-1.4.1 software,
http://aoss.engin.umich.edu/multiwell/, (2004). b) Barker, J. R. Int. J. Chem. Kinet. 2001,
33, 232.
38
The calculations were performed using software provided via personal communication
by Dr. Timothy A. Barckholtz, ExxonMobil Research and Engineering Company,
Annandale, New Jersey.
39
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.
40
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502.
194
41
Laidler, K. J. Chemical Kinetics, Harper & Row, Publishers, Inc., New York, 1987.
42
Wigner, E. P. Z. Phys. Chem. Abt. B 1932, 19, 203.
43
Maillard, J. P.; Chauville, J.; Mantz, A. W. J. Mol. Spectrosc. 1976, 63, 120.
44
Chuang, Y.-Y.; Coitiño, E. L.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 446.
45
Smith, I. W. M.; Ravishankara, A. R. J. Phys. Chem. A 2002, 106, 4798.
46
Thévenet, R.; Mellouki, A.; Le Bras, G. Int. J. Chem. Kinet. 2000, 32, 676.
47
Chuong, B.; Stevens, P. S. J. Phys. Chem. A 2003, 107, 2185.
48
Aranda, A.; Díaz de Mera, Y.; Rodríguez, A.; Rodríguez, D.; Martínez, E. J. Phys.
Chem. A 2003, 107, 5717.
49
50
Hansen, J. C.; Francisco, J. S. ChemPhysChem 2002, 3, 833.
Truhlar, D. G.; Isaacson, A. D.; Garrett, B. C. Theory of Chemical Reaction Dynamics,
Vol. 4, edited by Baer, M. CRC Press, Boca Raton, FL, 1985, pp 65–137.
51
Truhlar, D. G.; Garrett, B. C. Annual Review of Physical Chemistry, Vol. 35, edited by
Rabinovitch, B. S.; Schurr, J. M.; and Strauss, H. L., Annual Reviews, Inc., Palo Alto,
California, 1984, pp 159-189.
52
Chuang, Y. Y.; Corchado, J. C.; Truhlar, D. G. J. Phys. Chem. A 1999, 103, 1140.
53
Corchado, J. C.; Chuang, Y.-Y.; Fast, P. L.; Villa, J.; Hu, W.-P.; Liu, Y.-P.; Lynch, G.
C.; Nguyen, K. A.; Jackels, C. F.; Melissas, V. S.; Lynch, B. J.; Rossi, I.; Coitiño, E. L.;
Fernandez-Ramos, A.; Pu, J.; Albu, T. V.; Steckler, R.; Garrett, B. C.; Isaacson, A. D.;
Truhlar, D. G., Polyrate 9.1, University of Minnesota, Minneapolis, MN, 2003.
195
CHAPTER 7
COMPUTATIONAL STUDY OF THE HYDROGEN-ATOM ABSTRACTION
REACTIONS OF ETHERS BY HYDROXYL RADICAL
7.1. Introduction
As a result of the 1990 amendments to the Clean Air Act, oxygenated compounds
have been utilized as additives to gasoline to increase oxygen content within the internal
combustion process in automobiles, so as to help attain national ambient air quality
standards (NAAQSs) for carbon monoxide (CO) and ozone. In addition to reducing CO
emissions, oxygenated fuel additives reduce the carbon:hydrogen ratio and minimize soot
and particulate matter (PM) formation, as well as increase a fuel’s octane level.1 Many
states now require oxygen-enriching fuel additives to be used during the winter months
due to inefficient combustion as a result of slower reaction kinetics and decomposition
shunting on cold engine surfaces.1 Several of the more widely used oxygenated additives
are methyl tertiary-butyl ether (MTBE), ethyl tertiary-butyl ether (ETBE), tertiary-amyl
methyl ether (TAME), diisopropyl ether (DIPE), and ethanol.1 Incomplete fuel
combustion results in the emission of volatile organic compounds (VOCs) and
combustion intermediates which can act as precursors to ozone and smog, contributing
significantly to poor regional air quality. Furthermore, ether compounds are extensively
196
used as precursors and solvents in large-scale processes such as polymer and fine
chemical syntheses. Tetrahydrofuran (THF), for example, has an annual consumption of
68.1 million kilograms for use mainly as a resin solvent, reaction solvent, and
intermediate in the synthesis of plastics.
Subsequent to emission into the atmosphere, initiation of decomposition for most
VOCs is dominated by their reactivity with hydroxyl radical (•OH). 2 Hydrogen-atom
abstraction, as opposed to addition due to lack of unsaturation, by hydroxyl radical
initiates decomposition for alkanes and saturated ethers as shown in equations 7.1 and
7.2.
R–H + •OH → R• + H2O
(7.1)
ROCH2–H + •OH → ROCH2• + H2O
(7.2)
Accurate rate coefficients for the abstraction of hydrogen atoms from ethers by hydroxyl
radical over a temperature range commensurate to both combustion and tropospheric
conditions is therefore desirable to aid in combustion and atmospheric modeling studies.
In order to calculate accurate transition state theory (TST) rate coefficients from
electronic structure data, it is typically necessary to use very expensive post-Hartree-Fock
(HF) ab initio3 methods to obtain reliable energetics. 4,5,6 Density functional theory
(DFT) 7 methods have become very popular due to their ability to provide reasonably
accurate energies with the implicit inclusion of electron correlation using much fewer
computational resources. However, it has been demonstrated, that DFT methods, both
pure and hybrid, underestimate reaction barriers heights.8,9,10,11 A popular DFT functional
197
is the hybrid B3LYP12 method, which is capable of calculating reliable molecular
geometries and energies for equilibrium stationary points. However, while it is
significantly more capable than pure DFT functionals for calculating transition state
geometries and energies, it still too often falls short of the accuracy required for
calculating accurate rate coefficients.13,14
Recently, a new hybrid DFT functional has been developed with the goal of
calculating accurate transition state geometries and reaction barrier heights. This
functional is designated the modified Perdew and Wang 1-parameter functional for
kinetics (mPW1K),15 which is a re-parameterization of the mPW1PW9116 hybrid
functional. The mPW1K functional has an increased amount of exact Hartree-Fock
exchange included to minimize deviation against a database of theoretically derived
barrier heights and reaction energies for small hydrogen-atom transfer reactions. Fast et
al.8 determined the optimal percentage of exact HF exchange to be 42.8% for the best
overall agreement with their data set of calibration reactions. This component of HartreeFock exchange is significantly greater than both the original mPW1PW91 functional
value of 25% and the value of 20% used in the B3LYP functional. For the 40 barrier
heights evaluated for H-atom transfers, the mPW1K functional coupled with the
6-31+G** basis set resulted in mean signed errors of –1.3 kcal/mol, far superior to
current DFT methods. Of the 20 overall thermodynamic reaction energies evaluated, the
mPW1K values were competitive with B3LYP values.
In this study, electronic structure methods are utilized to generate the stationary
points on the hydrogen-atom abstraction potential energy surfaces (PES) for the reactions
of dimethyl ether (DME) and tetrahydrofuran (THF) with OH radical. These PESs will
198
be utilized to calculate theoretical (TST) rate coefficients over the 200–2000 K
temperature range. Experimental studies of THF with hydroxyl radical are limited and
have not been modeled theoretically to our knowledge.17,18,19,20 The rate determinations
for the reaction of THF with hydroxyl radical are primarily limited to single nearambient temperature values. However, recently Moriarty et al.20 studied the atmospheric
reactivity of a series of ethers, including THF, with hydroxyl radical. In their study,
absolute rate coefficients for the reaction of THF with OH radical were determined over
the 263–372 K range by monitoring OH radical via pulsed laser photolysis–laser induced
fluorescence at 100 Torr pressure. Absolute rate coefficients for the THF (and THF-d8) +
OH radical reaction for ~3 Torr pressure have also been determined in our laboratory
over the 243–359 K temperature range using chemical ionization techniques with a
variable temperature flowing afterglow (VTFA) quadrupole mass spectrometer.21 The
rate coefficients as a function of temperature, from our group and those of Moriarty et
al.,20 are in disagreement. The Moriarty et al.20 rate coefficients are inversely dependent
on temperature, while our values for the THF + OH radical reaction are directly related to
temperature and furthermore they exhibit an inverse kinetic isotope effect. Theoretical
rates will be compared with the available experimental values in order to highlight the
reaction features responsible for the temperature dependence for the THF + OH radical
reaction. Many experimental rate determinations have been performed for the DME
reaction with hydroxyl radical22,23,24,25,26,27,28,29,30 over a large temperature range, and
several theoretical evaluations for the PES and rate coefficients have also been reported.
Atadinc et al.31 have determined TST rate coefficients at 298 K based on MP2/6-31G**
geometries and MP2, MP4, and CCSD(T) single-point energies. Bottoni et al.32 have
199
calculated activation energies (Ea) at 298 K based on ab initio and DFT methods.
Francisco et al.33 and Jursic34 have published decomposition pathway studies for dimethyl
ether. Wu et al. performed dual-level direct dynamics calculations over the 230–2000 K
range at the G3//MP2/6-311G** level and obtained excellent agreement with
experimental rate coefficients.35
Herein, we report a detailed theoretical study of the reactions of hydroxyl radical
with DME and THF to support our recent experimental study and to continue our general
interest in the reactions of hydroxyl radical with organic compounds. 36,37,38,39
7.2. Methods
All calculations were performed using the Gaussian 9840 suite of programs either
on our RS/6000 workstations or at the Ohio Supercomputer Center. Geometries for all
stationary points were obtained at the MP2/6-31G* (using the frozen core
approximation),41,42 B3LYP/6-31G*,43,44 and mPW1K/6-31+G**45 hybrid density
functional theory (DFT)7 levels. All stationary points were characterized via vibrational
frequency analysis using the same level of theory from which the geometries were
generated. Minima were confirmed to have adequate convergence and all real vibrational
frequencies. Transition state structures were confirmed to have one imaginary vibrational
frequency and, in addition, shown to connect to the implied reactant and product by
displacement along the transition vector for the imaginary vibrational frequency
(typically 10%) in the positive and negative directions, followed by careful minimization
using opt=calcfc or calcall when necessary.
200
CCSD(T) single-point energy calculations were carried out using the 6-31+G**
and aug-cc-pVDZ basis sets on the MP2 and B3LYP geometries. To gauge the accuracy
of the DFT and ab initio reaction energies, G246 calculations were carried out on the
reactant and product minima. Hybrid DFT generated open-shell wave functions resulted
in 〈S2〉 values of 0.76 or less for all open-shell species. In most cases the unrestricted MP2
wave functions gave 〈S2〉 values of 0.78 or less, and all were below 0.79.
Conventional transition state theory (TST) was utilized to estimate all hydrogenatom abstraction and hydroxyl-radical addition reaction rate coefficients over the
200–2000 K temperature range at the high-pressure limit.47 The conventional TST rate
equation in the thermodynamic formulation as a function of temperature is as follows:
k(T)TST
=
Γ(T)
kB T
exp( − ΔG ≠ (T)/kB T)
h
(7.3)
€
In equation 7.3, T is the absolute temperature, h is Planck’s constant, kB is Boltzmann
constant, and ΔG‡ (T) is the free energy barrier height relative to reactants at infinite
separation. The first low lying electronic state due to spin-orbit coupling in the 2Π
hydroxyl radical was accounted for in calculating its electronic partition function. An
energy splitting value of 139.21 cm-1, obtained by Maillard et al.,48 was used with both
ground and excited states having a degeneracy of 2. The temperature-dependent factor
Γ(T) represents quantum mechanical tunneling and is accounted for via an unsymmetrical
Eckart potential. The Eckart potentials were constructed using the ΔH0 values from the
reactant complex, transition state, and product complex. Solving the time-independent
201
Schrödinger equation allows for the determination of the wavefunction for a particle
subject to an Eckart potential. Subsequently, the transmission (tunneling) probability is
calculated as the ratio of the transmitted flux density to the incident flux density at a
given energy. The tunneling correction is the ratio of the quantum mechanical rate and
the classical mechanical rate over a Boltzmann distribution of energies.49
In order to account for potential errors in the thermodynamic values associated
with the harmonic-oscillator rigid-rotor approximation, low-energy torsions were treated
as hindered rotors when applicable. The reduced moment of inertia for each internal
rotation was calculated about the axis that includes the torsional bond using the code
provided by Multiwell 1.4.1.50 The contribution of each internal rotor to the
thermodynamic parameters, H(T) and S(T), was determined by generating a rigid
potential energy profile for a complete rotation of each internal rotor. The profiles were
then modeled via a Fourier series to construct a hindrance potential to be used in the
Hamiltonian. Using the free internal rotation wave functions as a basis, the hindered rotor
energy levels were calculated by direct diagonalization of the Hamiltonian matrix. The
hindered rotor partition functions were obtained via summation over the energy levels
and the thermodynamic values obtained using standard methods.51 All other vibrational
frequencies were treated as harmonic. Scaling factors of 0.967652, 0.980653 and 0.951554
were applied, respectively, to the MP2(fc), B3LYP and mPW1K zero-point energies for
the determination of thermodynamic values.
202
1.097
1.095
1.090
1.410
1.416
1.394
1.093
1.090
1.086
112.30
111.05
112.67
1.103
1.094
1.094
1.092
1.089
1.084
1.100
1.096
1.092
1.420
1.426
1.402
1.360
1.365
1.343
114.90
113.44
115.15
1.098
1.094
1.090
1.432
1.437
1.414
1.096
1.094
1.088
1.544
1.536
1.529
1.423
1.427
1.405
THF (C2, 3T2)
1.094
1.094
1.088
1.094
1.093
1.087
1.094
1.092
1.086
THF (Cs, Eo)
1.084
1.082
1.076
1.090
1.088
1.082
MMR
1.096
1.094
1.088
1.085
1.085
1.078
0.969
0.969
0.953
0.983
0.979
0.966
1.539
1.525
1.519
1.101
1.099
1.093
DME (C2v)
1.104
1.101
1.096
1.094
1.094
1.087
103.58
103.90
106.15
1.109
1.104
1.099
1.105
1.102
1.097
1.099
1.097
1.092
1.378
1.381
1.360
1.441
1.445
1.421
THFR C1
1.094
1.092
1.087
1.100
1.097
1.092
1.429
1.434
1.410
1.496
1.496
1.487
1.083
1.082
1.077
1.427
1.430
1.408 1.094
1.092
1.086
1.098
1.095
1.090
1.104
1.100
1.095
THFR C2
Figure 7.1. Structures and parameters (bond lengths in angstrom and bond angles in
degrees) for reactants and products involved in the hydrogen-atom abstraction of
dimethyl ether (DME) and tetrahydrofuran (THF) by hydroxyl radical at the B3LYP/631G* (top), MP2/6-31G* (middle), and mPW1K/6-31+G** (bottom) levels.
203
7.3. Potential Energy Surfaces
7.3.1. DME + OH Radical
Figure 7.1 shows the structures for dimethyl ether (DME), methoxy methyl
radical (MMR), hydroxyl radical, and water as well as select geometric parameters at the
B3LYP/6-31G*, MP2/6-31G*, and mPW1K/6-31+G** levels of theory. Furthermore,
Figure 7.2 shows the intermediate structures on the DME + OH abstraction reaction
surface, and Table 7.1 includes a detailed listing of the energies (ΔH0, kcal/mol) relative
to the reactants at infinite separation. Cartesian coordinates, vibrational frequencies, SCF
energies, and rotational constants are provided in the Appendix. All energies discussed
refer to ΔH0 (kcal/mol), unless otherwise specified.
Dimethyl ether (CH2OCH2, DME) has C2v symmetry with two unique C–H
bonds. Four C–H bonds point out of the C–O–C backbone plane and the other two remain
in the C−O−C plane. The C–H bonds extending out of the C–O–C plane are slightly
longer than those that are in the plane. Hydrogen-atom abstraction from DME results in
methoxy methyl radical (CH3OCH2•, MMR). At the G2 level, the DME + OH radical Hatom abstraction reaction is exothermic by –21.9 kcal/mol. The CCSD(T)/aug-cc-pVDZ
single-point energies on both the B3LYP/6-31G* and MP2/6-31G* geometries provide
good agreement with the G2 value, both at –20.2 kcal/mol. There appears to be a small
basis set limitation with the CCSD(T) energies using the 6-31+G** basis set.
Furthermore, the mPW1K/6-31+G** level provides reasonable reaction energies,
compared to G2 values, with a reaction energy of –18.5 kcal/mol. The G3//MP2/6311G** value of Wu et al. is –21.8 kcal/mol.
204
Each of the DME + OH radical energy surfaces includes pre-reactive reactant
complex (RC), in which the hydroxyl radical’s hydrogen is coordinated to the DME
oxygen atom. There is also a product complex (PC), in which a water molecule’s
hydrogen is coordinated to the MMR oxygen atom (Figure 7.2). Two first-order saddle
points correspond to transfer of an out-of-plane DME hydrogen to the hydroxyl radical
oxygen. These structures are designated TS1 and TS2, as shown in Figure 7.2. In TS1,
the hydrogen on the O–H moiety is directed toward the DME oxygen atom, while in
TS2, the hydroxyl hydrogen is directed away from the DME oxygen atom. TS1 is
slightly lower in energy at all levels of theory with δΔH0‡, relative to reactants, ranging
from 0.12 kcal/mol at the CCSD(T)/aug-cc-pVDZ//MP2/6-31G* level to 0.97 kcal/mol at
the MP2/6-31G* level.
205
0.980
0.979
0.964
1.098
1.095
1.091
1.173
1.203
1.163
1.491
1.349
1.454
183i
1988i
475i
TS1
1.092
1.090
1.085
1.855
1.882
1.802
0.969
0.968
0.952
0.979
0.979
0.964
0.990
0.986
0.977
1.092
1.089
1.085
1.098
1.095
1.091
RC
mPW1K = C2v
1.485
1.358
1.460
2.577
2.633
3.159
189i
1948i
438i
1.176
1.201
1.163
0.973
0.974
0.960
1.996
1.992
1.922
1.362
1.368
1.348
TS2
PC
0.978
0.979
0.963
1.092
1.090
1.085
1.248
1.266
1.209
1.271
1.266
1.293
1316i, 77i
2328i
1395i
TS3
Figure 7.2. Structures and parameters (bond lengths in angstrom and imaginary
vibrational frequencies in cm–1) for intermediates involved in the hydrogen-atom
abstraction of dimethyl ether by hydroxyl radical at the B3LYP/6-31G* (top), MP2/631G* (middle), and mPW1K/6-31+G** (bottom) levels.
206
DMEb
RC
TS1
TS2
TS3
PC
MMRc
mPW1K/6-31+G** geometries
mPW1K/6-31+G**
0.00
–5.82
0.84
1.51
3.02
–21.91
–18.52
B3LYP/6–31G*
0.00
B3LYP/6–31G* geometries
–6.01
–4.19
–3.51
d
–18.82
–14.64
CCSD(T))/6–31+G**
0.00
–5.32
3.47
4.30
d
–21.39
–18.09
CCSD(T)/aug–cc–pVDZ
0.00
–4.65
1.01
1.41
d
–23.09
–20.17
MP2/6–31G* geometries
MP2/6–31G*
0.00
–6.37
6.94
7.91
9.37
–20.81
–16.09
CCSD(T))/6–31+G**
CCSD(T)/aug–cc–pVDZ
0.00
0.00
–5.57
–4.99
2.10
–0.83
2.63
–0.75
5.57
2.68
–21.62
–23.31
–18.09
–20.18
G2
0.00
e
0.00
G3
–21.87
–7.59
0.78
3.62
–21.81
Table 7.1. Relative Energies (ΔH0‡, kcal/mol) of Stationary Points for the Reaction of
Dimethyl Ether and Hydroxyl Radical.a
a
See Figures 7.2–7.3 for dimethyl ether + OH radical structures. b Energy includes OH
radical. c Energy includes H2O. d The stationary point for abstraction of the in-plane
hydrogen is a 2nd order saddle point at the B3LYP/6-31G* level. e Energies are from
reference 35.
207
A third H-atom abstraction transition state (TS3) exists at the MP2 and mPW1K
levels of theory. TS3 corresponds to abstraction of in-plane hydrogens with Cs symmetry.
The barrier height for abstraction of the in-plane hydrogen is significantly greater than
either TS1 or TS2 with values ranging from 2.68 to 9.37 kcal/mol at the MP2/6-31G*
and CCSD(T)/aug-cc-pVDZ//MP2/6-31G* levels, respectively. Attempts to isolate an inplane transition state at the B3LYP/6-31G* level resulted in a second-order saddle point.
One of the imaginary modes corresponds to movement of the abstracted hydrogen along
an abstraction vector and the other to rotation of the C–O ether bond. Upon displacement
and careful minimization, the out-of-plane transition state geometry TS1 was obtained.
The relative order of ΔH0‡ for the enthalpic activation barriers derived from the singlepoint energies is TS1 < TS2 < TS3 at all levels. The barrier heights ΔH0‡ calculated by
Wu et al. at the G3//MP2/6-311G** level of theory for TS1 and TS3, 0.78 and 3.62
kcal/mol, agree very well with the values calculated at the mPW1K/6-31+G** level of
theory (Table 7.1).
7.3.2. THF + OH Radical
The B3LYP/6-31G*, MP2/6-31G* and mPW1K/6-31+G** pathways for C1 and
C2 hydrogen-atom abstraction of tetrahydrofuran (THF) by hydroxyl radical are shown in
Figures 7.1 and 7.3. Table 7.2 shows the (ΔH0)energies of each stationary point shown in
Figures 7.1 and 7.3 relative to the energies of the reactants at infinite separation at the
mPW1K/6-31+G**, B3LYP/6-31G*, MP2/6-31G* levels as well as the values derived
from CCSD(T) single-point energies with the 6-31+G** and aug-cc-pVDZ basis sets on
208
the B3LYP and MP2 structures. Cartesian coordinates, vibrational frequencies, SCF
energies, and rotational constants are provided in the Supporting Information.
The conformational space for THF can be represented by the pseudorotational
itinerary of Sundaralingam shown in Figure 7.4.24 We have found four equilibrium
structures on the itinerary; these are the enanteomeric twist geometries (3T2 and 2T3), and
the homomeric envelope geometries (EO and OE). THF was found to have twist and an
envelope minima at the mPW1K/6-31+G** and B3LYP/6-31G* levels. However, at the
MP2/6-31G* level, only the twist form corresponded to a minimum. The envelope
geometry corresponded to a first-order saddle point connecting the 3T2 and 2T3 twist
conformations. The energies for the 3T2 and EO conformations are similar and slightly
favor the twist conformation, with ΔH0 ranging from 0.21 to 0.30 kcal/mol. The
pseudorotational conformations of THF have been studied experimentally55,56,57,58 and
theoretically58,59,60,61,62,63 by several researchers and a conclusive view of the
pseudorotational PES has yet to be obtained. We feel the microwave studies of Melnik et
al.58 provide the best view, which consists of the twist and envelope conformations as the
only minima, with the twist form favored by 11 cm–1. Our DFT-based results are in good
agreement with this view.
209
1.723
1.370
1.551
0.981
0.979
0.965
2.461
2.605
3.009
0.969
0.969
0.952
176i
1809i
278i
1.128
1.194
1.140
0.974
0.974
0.962
2.019
2.018
1.890
TS1 C1
2.719
0.994
1.098
1.832
1.093
1.099
1.095
B3LYP
0.989
1.093
1.745
1.369
1.542
1.095
1.098
2.490
2.635
3.043
TS2 C1
2.478
2.205
2.578
0.980
0.982
0.965
1.094
MP2
1.091
1.087
1.088
1.794
THFR C1
136i
1810i
277i
1.126
1.192
1.140
2.812
1.851
0.981
0.979
0.965
1.310
1.291
1.336
1.231
1.222 1126i
1.196 2179i
1120i
TS1 C2
0.977
0.979
0.964
0.979
1.201
1.195
1.174
1.091
mPW1K
1.366
1.331
1.386
0.978
0.978
0.964
0.968
0.968
0.952
1.928
1.902
1.838
538i
1852i
631i
RC THF
THFR C2
TS2 C2
0.978
0.979
0.963
1.358
1.325
1.378
1.202
1.196
1.175
571i
1883i
672i
TS3 C2
Figure 7.3. Structures and parameters (bond lengths in angstrom and imaginary
vibrational frequencies in cm-1) for intermediates involved in the hydrogen atom
abstraction of THF by hydroxyl radical at the B3LYP/6-31G* (top), MP2/6-31G*
(middle), and mPW1K/6-31+G** (bottom) levels.
210
3T
2
3
E2
O
4
O
3E
1
2
O
0°
1E
E4
O
O
O
O
270°
EO
90 °
OE
Planar
O
O
4E
O
O
E3
E1
180°
O
2
4
O
1
2E
3
2T
3
Figure 7.4. Pseudorotational itinerary for tetrahydrofuran (THF).
211
212
Both C1 H-atom abstraction transition states appear to involve coordination of the
hydroxyl radical’s hydrogen with a lone electron pair on the THF oxygen atom. This
coordinating interaction is weakest at the mPW1K level of theory with H---O distances of
~ 3.0 Å in both structures. Instead, TS1 C1 and TS2 C1 differ primarily by the
conformation of the THF ring, being a twist form in TS1 C1 and a 4E conformation in
TS2 C1 (Figures 7.3 and 7.4). At all levels of theory utilized in this study, TS1 C1 has the
lowest barrier height for H-atom abstraction in the THF + OH radical reaction. The
barrier heights (ΔH0‡) provided by TS1 C1 cover a significant range, from –4.48 kcal/mol
at the B3LYP/6-31G* level to 4.08 kcal/mol at the MP2/6-31G* level, relative to the
energy of infinitely separated reactants. The TS2 C1 barrier height is typically ~0.5
kcal/mol greater than that for TS1 C1. Single-point energies at the CCSD(T) level on the
B3LYP and MP2 geometries provide significant corrections to these outermost lying
barrier heights.
Three transition-state geometries have been isolated for the abstraction of the C2
hydrogen atoms (TS1 C2, TS2 C2, and TS3 C2, Figure 7.3). TS1 C2, like TS1 C1 and
TS2 C1, includes coordination of the hydroxyl radical’s hydrogen to the THF oxygen
atom. TS1 C2 also has the lowest C2 H-atom abstraction barrier of the three obtained. In
the TS2 C2 and TS3 C2 structures, the hydroxyl radical’s hydrogen is pointing away from
the THF ring with no coordination involved. Each of the three C2 transition states
geometries differs by the THF ring conformation. The approximate THF ring
conformation of each are E4, 1E, and OE for TS1 C2, TS2 C2, and TS3 C2, respectively,
from the perspective of the OH radical above the THF ring and the ring oxygen atom in
213
front (Figures 7.3 and 7.4). The barrier heights for C2 H-atom abstraction vary
significantly, with the B3LYP/6-31G* activation barriers at the low extreme and the
MP2/6-31G* values at the high extreme. CCSD(T) single-point energy calculations
provide significant corrections to the MP2 and B3LYP barrier heights in most cases. The
order of barrier heights for C2 H-atom abstraction is TS1 C2 < TS2 C2 < TS3 C2.
However, for each of the CCSD(T)//MP2/6-31G* barrier heights, TS2 C2 is slightly
lower in energy than TS1 C2. This may be an indication that a larger basis set or greater
degree of election correlation is required for the geometry optimization of an H-atom
abstraction transition state.
Descending down to the product side of the TS1 C1, TS2 C1, and TS1 C2 barriers
leads to product complexes in which the newly-formed water molecule coordinates with
the THF radical’s oxygen atom (THFR C1 and THFR C2, Figure 7.3). The product
complex THFR C1 is typically ~4 kcal/mol lower in energy than the products at infinite
separation, while THFR C2 is typically ~ 5 kcal/mol lower than products. At the G2
level, the reaction energies for C1 and C2 abstraction are –24.53 and –19.89 kcal/mol,
respectively. The reaction energies are in good agreement with the G2 values, with the
exception of the B3LYP/6-31G* and MP2/6-31G* reaction energies, which
underestimate the G2 values by ~6 kcal/mol.
214
7.4. Rate Calculations
7.4.1. DME +OH Radical
Table 7.3 lists the TST/Eckart tunneling rate coefficients for the DME + OH
radical reaction from 200–2000 K at the mPW1K/6-31+G**, CCSD(T)/aug-ccpVDZ//B3LYP/6-31G*, and CCSD(T) /aug-cc-pVDZ //MP2/6-31G* levels of theory.
Available experimental rate coefficients are also listed in Table 7.3. Figure 7.5 shows an
Arrhenius plot of the rate coefficients listed in Table 7.3, including the variable
temperature rate coefficients of Moriarty et al.20 The temperature-dependent Eckert
tunneling corrections and data relevant to the treatment of hindered rotors are provided in
the Appendix.
The DME + OH rate coefficients reflect only the rate coefficient provided by
TS1. The contributions from TS2 and TS3 are accounted for in the entropy term of TS1
via the hindered rotor analysis. In DME, normal mode vibrations corresponding to
rotation about both C–O ether bonds were treated as hindered rotors. In TS1, normal
mode vibrations corresponding to rotation about each C–O ether bond and rotation of the
abstracting OH moiety about the C---O axis were treated as hindered rotors. The external
symmetry number of 2 for C2v DME and the presence of an enantiomer of TS1 have been
accounted for with the appropriate subtraction and addition of Rln2 to the entropy terms,
respectively.
The rate coefficients generated from the mPW1K/6-31+G** DME +OH radical
H-atom abstraction energy surface are in very good agreement (well within a factor of 2)
with the available experimental measurements. On the other hand, rate coefficients
215
produced using the CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G* and CCSD(T)aug-ccpVDZ//MP2/6-31G* energy surfaces yielded drastically varying results. The
CCSD(T)//B3LYP rate coefficients significantly underestimate the experimental values
over the whole 200–2000 K range. The CCSD(T)//MP2 rate coefficients on the other
hand drastically overestimate the experimental values at the lower temperatures and
converge near the mPW1K values at ~700 K. Given the general reliability of the
CCSD(T) method, the barrier height inaccuracies are likely a result of deficiencies in the
MP2/6-31G* and B3LYP/6-31G* levels of theory in describing the transition state
structures and the corresponding vibrational frequencies. Particularly, we and others have
shown that even with large basis sets the MP2 method is insufficient in describing
transition state structures hydrogen-atom transfer.64,65 Typically, methods which include a
greater degree of election correlation are required for these TS geometry optimizations.
Recently, Wu et al. have reported variational TST rate coefficients for the DME +
OH radical H-abstraction reaction at the G3//MP2/6-311G** level using dual-level direct
dynamic methods.35 With the TS1 transition state, they obtained a barrier height (ΔH0‡)
of 0.78 kcal/mol, which is very close to the mPW1K value of 0.87 kcal/mol.
Furthermore, the variational TST method utilized by Wu et al. yielded a variational
effect, thereby minimizing the rate coefficients relative to the conventional TST values.
This effect involves an adjustment in the final barrier height toward the mPWIK value.
Both barrier heights appear slightly high when compared with experiment, but
nevertheless both are in excellent agreement with the experimentally-determined
activation energies ranging from 0.6–0.8 kcal/mol.18,22,23,24
216
Temp (K)
200
298
mPW1Ka
8.06E–13
1.51E–12
CCSD(T)//B3LYPb
6.70E–14
1.47E–13
CCSD(T)//MP2c
2.23E–09
9.14E–11
300
400
1.53E–12
2.61E–12
1.48E–13
2.71E–13
8.82E–11
2.73E–11
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
4.15E–12
6.27E–12
9.11E–12
1.28E–11
1.74E–11
2.30E–11
2.97E–11
3.75E–11
4.66E–11
5.70E–11
6.87E–11
8.17E–11
9.62E–11
1.12E–10
1.29E–10
1.48E–10
4.57E–13
7.33E–13
1.13E–12
1.67E–12
2.41E–12
3.36E–12
4.57E–12
6.06E–12
7.87E–12
1.00E–11
1.25E–11
1.55E–11
1.88E–11
2.25E–11
2.68E–11
3.14E–11
1.77E–11
1.58E–11
1.64E–11
1.83E–11
2.12E–11
2.49E–11
2.95E–11
3.50E–11
4.12E–11
4.84E–11
5.64E–11
6.54E–11
7.54E–11
8.63E–11
9.82E–11
1.11E–10
Expt.
2.32 E–12d
2.35 E–12e
2.86 E–12h
2.67 E–12i
3.50 E–12f
3.73 E–12g
3.02 E–12j
4.62 E–12g
7.12 E–12g
Table 7.3. Total TST/Eckart rate coefficients (cm3 molecule–1 s–1) for the DME + OH
reaction.
a
Corresponds to 6–31+G** basis set. b Corresponds to CCSD(T)/aug–cc–pVDZ//
B3LYP/6–31G*. c Corresponds to CCSD(T)/aug–cc–pVDZ//MP2/6–31G*. d RR,
Wallington et al.23 e PR–KS, Nelson, et al.25 f FP–RF, Perry et al.24 g LP–LIF at 299 K,
Arif et al.,28 at 396, 490, and 601 K. h RR, DeMore and Bayes.29 i PLP–LIF, Bonard et al.
J. Phys. Chem. A 2002, 106, 4384.
j
FP–RF, Wallington et al.18 Pulsed laser
photolysis–laser induced fluorescence = PLP–LIF. Flash photolysis–resonance
fluorescence = FP–RF. Relative rate = RR. Pulse radiolysis–kinetic spectroscopy =
PR–KS.
217
Dimethyl Ether + OH radical H abstraction rates
mPW1K
CCSD(T)//MP2
CCSD(T)//B3LYP
Wu et al.
Bonard et al.
Arif et al.
Wallington et al.
Tranter and Walker
-7
log k (cm3/molecule s)
-8
-9
-10
-11
-12
-13
-14
0
1
2
3
1000/T(K)
4
5
6
Figure 7.5. Arrhenius plots of the TST/Eckart and literature rate coefficients between 200
and 2000 K for the H-atom abstraction reaction of DME + OH radical.
218
Tunneling for the H-atom abstraction reaction of DME+ OH radical is predicted
to have only a moderate effect on the rate coefficients. At 200 K, the tunneling
corrections derived from the mPW1K, CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G*, and
CCSD(T)/aug-cc-pVDZ//MP2/6-31G* energy surfaces are 1.66, 1.07, and 172.34,
respectively. The imaginary vibrational frequencies for TS1 are 475i, 183i, and 1988i
cm–1 for the mPW1K, B3LYP, and MP2 TS1 transition state geometries, respectively.
There is a considerable overestimation of the barrier curvature associated with the large
MP2 imaginary vibrational frequency. The lower tunneling corrections of the mPW1K
and CCSD(T)//B3LYP levels yield an Arrhenius profile in good agreement with the
experimental profile. Wu et al. predicted a slightly larger tunneling correction of 2.47 for
the TS1 barrier with a more sophisticated multi-dimensional tunneling approximation
using a G3//MP2/6-311G** minimum energy reaction path.35
7.4.2. THF + OH Radical
Table 7.4 lists the TST/Eckart tunneling rate coefficients for the THF + OH
radical reaction from 200–2000 K at the mPW1K, CCSD(T)/aug-cc-pVDZ//B3LYP/631G*, and CCSD(T)/aug-cc-pVDZ//MP2/6-31G* levels of theory. Also listed in Table
7.4 are the rate coefficients for THF-d8 + OH radical H-atom abstraction reaction at the
mPW1K level of theory. Figure 7.6 shows plots of the rate coefficients listed in Table 7.4
as an Arrhenius plot that includes the variable temperature rate coefficients from our
group and Moriarty et al.20 The temperature-dependent Eckert tunneling correction values
are provided in the Appendix. Furthermore, the contributions to the total rate coefficient
219
for each reaction from each transition state are provided in the Appendix. The total rate
coefficients from the reactions of THF and THF-d8 with hydroxyl radical were
calculated to be the sum of the TST rates for each of the five transition states (TS1 C1,
TS2 C2, TS1 C2, TS2 C2, and TS3 C2). Each of the five THF + OH H-atom abstraction
transition states exists as an enantiomer and a value of Rln2 was added to the entropy
term for each transition state. Furthermore, the harmonic vibrational frequency
corresponding to rotation of the OH radical in each of the five transition states was
treated as a hindered rotor. The contribution of symmetry to the entropy for C2v THF was
accounted for by subtracting Rln2. Data relevant to the treatment of OH hindered rotors is
provided in the Appendix.
220
Temp. (K)
mPW1K
200
298
1.94E–11
1.31E–11
CCSD(T)//
B3LYPb
7.81E–11
1.72E–11
300
400
500
600
700
800
900
1000
1100
1200
1300
1400
1500
1600
1700
1800
1900
2000
1.31E–11
1.36E–11
1.61E–11
1.98E–11
2.47E–11
3.07E–11
3.79E–11
4.61E–11
5.56E–11
6.62E–11
7.81E–11
9.13E–11
1.06E–10
1.21E–10
1.39E–10
1.57E–10
1.77E–10
1.98E–10
1.70E–11
1.27E–11
1.31E–11
1.50E–11
1.78E–11
2.15E–11
2.59E–11
3.11E–11
3.70E–11
4.37E–11
5.12E–11
5.96E–11
6.87E–11
7.87E–11
8.94E–11
1.01E–10
1.14E–10
1.27E–10
a
THF
CCSD(T)//
MP2c
3.76E–08
8.36E–10
8.00E–10
1.63E–10
7.94E–11
5.81E–11
5.23E–11
5.25E–11
5.59E–11
6.15E–11
6.87E–11
7.73E–11
8.74E–11
9.86E–11
1.11E–10
1.25E–10
1.40E–10
1.56E–10
1.74E–10
1.92E–10
THF–d8
Expt.
h
Expt.
1.67 E–11d
1.78 E–11e
1.46 E–11f
1.62 E–11g
1.20 E–11
mPW1Ka
Expt.h
6.67E–12
6.54E–12
8.50 E–12
6.56E–12
8.09E–12
1.06E–11
1.41E–11
1.86E–11
2.41E–11
3.07E–11
3.85E–11
4.74E–11
5.75E–11
6.88E–11
8.14E–11
9.53E–11
1.10E–10
1.27E–10
1.45E–10
1.64E–10
1.84E–10
Table 7.4. Total TST/Eckart and experimental rate coefficients (molecules cm–3 s–1) for
the THF + OH reaction.
a
Corresponds to 6–31+G** basis set. b Corresponds to CSD(T)/aug–cc–pVDZ//
B3LYP/6–31G*. c Corresponds to CCSD(T)/aug–cc–pVDZ//MP2/6–31G*. d PLP–LIF,
Moriarty et al.20 e FP–RF, Wallington et al.18 f RR, Winer et al.19 g FP–RF, Ravishankara,
et al.17 h Experimental rates from this lab. Pulsed laser photolysis–laser induced
fluorescence = PLP–LIF. Flash photolysis–resonance fluorescence = FP–RF. Relative
rate = RR.
221
Arrhenius Plot for THF + OH H Abstraction Reaction
-7
mPW1K
CCSD(T)//B3LYP
CCSD(T)//MP2
Moriarty et al.
Group THF
mPW1K THF-d8
Group THF-d8
log k (cm3/molecule s)
-8
-9
-10
-11
-12
0
1
2
3
1000/T (K)
4
5
6
Figure 7.6. Arrhenius plots of the TST/Eckart and experimental rate coefficients between
200 and 2000 K for the H-atom abstraction reaction of THF (THF-d8) + OH radical.
The THF + OH rate coefficients generated from the mPW1K//6-31+G ** energy
surfaces are in excellent agreement with the experimental values of Moriarty et al.20
Furthermore, the mPW1K and Moriarty et al. Arrhenius profiles agree very well (Figure
7.6). The CCSD(T)/aug-cc-pVDZ//B3LYP/6-31G* rate coefficients also provide
excellent agreement within the experimental range of 263–372 K and are even within
experimental error at 298 K. However the Arrhenius profile is too steep in this region
and cuts through the Arrhenius data of Moriarty et al.20 The CCSD(T)/aug-ccpVDZ//MP2/6-31G* rate coefficients are severely over-predicted at lower temperatures
222
by several orders of magnitude and eventually converge with the mPW1K values at T >
1300 K.
To our knowledge, this is the first theoretical study for the H-atom abstraction
reaction of THF + OH radical; therefore, no other theoretical barrier height data exist for
comparison. Moriarty et al.20 obtained an Ea of –0.35 kcal/mol via a 2-parameter
Arrhenius fitting from their data. This value agrees well with the mPW1K barrier heights
(ΔH≠0) of –0.78 and –0.34 for TS1 C1 and TS2 C1, respectively. The mPW1K rate
coefficients for C2 H-atom abstraction make only a very small contribution to the total
rate coefficient. The analogous TS1 C1 and TS2 C1, barrier heights at the CCSD(T)/augcc-pVDZ//B3LYP/6-31G* and CCSD(T)/aug-cc-pVDZ//MP2/6-31G* levels are –1.60
and –1.29 kcal/mol and –3.30 and –2.91 kcal/mol, respectively; both of the CCSD(T)
derived TS1 C1 and TS2 C1 barrier heights are too low and result in accentuated
curvature in their Arrhenius profiles.
Tunneling plays a minimal role in the total rate coefficient from the THF + OH
reaction (see Appendix). At the mPW1K and CCSD(T)//B3LYP levels, the Eckart
tunneling correction for transition states TS1 C1 and TS2 C1 range from 1.04 to 1.18 at
200 K. As was the case in the DME + OH reaction, the value of the MP2/6-31G*
imaginary vibrational frequencies (Figure 7.3) predict excessive barrier curvature and
drastically overestimate tunneling values. The CCSD(T)//MP2 TS1 C1 and TS2 C1
Eckart tunneling corrections are 25.41 and 39.33, respectively. At all levels of theory
reported here, the 200 K tunneling correction from TS1 C2 was the largest, with values
ranging from 17.43 at the CCDS(T)//B3LYP level to 1580.23 at the CCSD(T)//MP2
level.
223
The mPW1K rate coefficients for the THF-d8 + OH radical 2H-atom abstraction
reaction are included in Table 7.4 and in Arrhenius form in Figure 7.6. The theoretical
high-pressure rate coefficients for the protiated and deuterated THF + OH radical
reactions predict a normal primary isotope effect from 200–2000 K; that is, the
abstraction of deuterium being slower than the abstraction of hydrogen. These theoretical
results are not in support of the experimental results for these same reactions using a
chemical ionization mass spectrometer at ~3 Torr in our laboratory. At low temperatures,
data (Figure 7.6) from our group show an inverse kinetic isotope effect and the transition
to a normal isotope effect at ~ 300K. Furthermore, the experimental results from our
group shows that THF-h8 rate coefficients have normal temperature dependence, while
the THF-d8 rate coefficients are inversely dependent on temperature at this low pressure.
These results are in disagreement with the (high-pressure limit) theoretical results
obtained in this study and the experimental results of Moriarty et al.20 using the pulsed
laser photolysis–laser induced fluorescence technique at 100 Torr. Currently, our best
explanation for this disagreement is the possibility of a pressure dependence of the
reaction rate. The pressure in our neutral flow reactor (NFR) experiments is 2.6 ± 1 Torr.
The viability of this explanation is also supported by the predicted strength of the reactant
complex (RC THF) which has a binding energy of about –6 kcal/mol.
7.5. Conclusions
We have calculated the potential energy surfaces for the H-atom abstraction
reactions of dimethyl ether and tetrahydrofuran by hydroxyl radical for the determination
of transition state theory derived rate coefficients from 200 to 2000 K. The recently224
parameterized mPW1K hybrid density functional theory functional, coupled with the 631+G** basis set, can calculate H-atom abstraction barrier heights which yield rate
coefficients within a factor of 2 from experiment. The mPW1K DFT functional can be a
valuable tool for the determination of open-shell bimolecular reaction rate data of
importance to atmospheric and combustion chemistry. On the other hand, ab initio
methods require either very large basis sets or electron correlation greater than that
provided by the MP2 method to obtain reliable barrier height and barrier curvature
information.
The potential energy surfaces provided here indicate that the reactions of OH
radical with ethers involve the initial formation of a reactant complex. There is structural
evidence that the ether/OH radical complexes involve a small degree of coordination
between a hydrogen on a carbon adjacent to oxygen and the OH radical’s oxygen. In the
case of an acyclic ether (DME), for abstraction of H-atom on carbon adjacent to the ether
oxygen, transition state coordination between the OH radical’s hydrogen and the ether’s
oxygen atom is negligible, and the H-atom abstraction barrier height is greater than that
of reactants at infinite separation, yielding a normal temperature dependence of the rate
coefficients. For the cyclic ethers, coordination of the OH radical’s hydrogen and ether
ring’s oxygen in the transition state is more pronounced, and the barrier heights are
reduced to values below that of reactants, allowing for inversely-temperature-dependent
rate coefficients. Such differential coordination effects between reactant and transition
state has recently been elucidated to yield an unexpected solvation effect for OH
reactions with aromatic hydrocarbons.39b This ability to coordinate with the ether oxygen
may be simply due to a more facile access of the abstractable hydrogens in the cyclic
225
structures. Given to the excellent agreement between the mPW1K/6-31+G** rate
coefficients and experimental values, we have fit the rates over the 200 to 2000 K
temperature range to provide the following 3-parameter Arrhenius expression: k(T) =
1.29 x 10–19 T2.73 exp(868.9/T) cm3 molecule–1 s–1.
226
References for Chapter 7
1
National Science and Technology Council (NTSC), Committee on Environment and
Natural Resources, ‘Interagency Assessment of Oxygenated Fuels’, June 1997.
2
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Mandronich, S.; Moortgat, G. K.; Wallington,
T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the Alkenes, Oxford
University Press, New York, 2000.
3
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular Orbital
Theory; John Wiley & Sons, New York, NY, 1986.
4
Isaacson, A. D. The Reaction Path in Chemistry: Current Approaches and Perspectives,
edited by Heidrich, D., Kluwer Academic Publishers, Dordrecht, The Netherlands, 1995,
pp 191–228.
5
Truhlar, D. G.; Isaacson, A. D.; Garrett, B. C. Theory of Chemical Reaction Dynamics,
Vol. 4, edited by Baer, M. CRC Press, Boca Raton, FL, 1985, pp 65–137.
6
Truhlar, D. G.; Garrett, B. C. Annual Review of Physical Chemistry, Vol. 35, edited by
Rabinovitch, B. S.; Schurr, J. M.; and Strauss, H. L., Annual Reviews, Inc., Palo Alto,
California, 1984, pp 159-189.
7
(a) Parr, R. G.; Yang, W. Density Functional Theory in Atoms and Molecules, Oxford
University Press, New York, NY, 1989. (b) Labanowski, J. W.; Andzelm, J. Density
Functional Methods in Chemistry, Springer, New York, NY, 1991.
8
Truhlar, D. G. Faraday Discuss. 1998, 110, 362.
9
Durant, J. L. Chem. Phys. Lett. 1996, 256, 595.
10
Kobayashi, Y.; Kamiya, M.; Hirao, K. Chem. Phys. Lett. 2000, 319, 695.
227
11
Skokov, S.; Wheeler, R. A. Chem. Phys. Lett. 1997, 271, 251.
12
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
13
Rice, B. M.; Pai, S. V.; Chabalowski, C. F. J. Phys. Chem. A 1998, 102, 6950.
14
Bach, R. D.; Glukhovstev, M. N.; Gonzalez, C.; Marquez, M.; Estevez, C. M.; Baboul,
A. G.; Schlegel, H. B. J. Phys. Chem. A 1997, 101, 6092.
15
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 4811.
16
Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664.
17
Ravishankara, A. R.; Davis, D. D. J. Phys. Chem. 1978, 82, 2852.
18
Wallington, T. J.; Liu, R.; Dagaout, P.; Kurylo, M. J. Int. J. Chem. Kinet. 1988, 20, 41.
19
Winer, A. M.; Lloyd, A. C.; Darnall, K. R.; Atkinson, R.; Pitts, J. N., Jr. Chem. Phys.
Lett. 1977, 51, 221.
20
Moriarty, J.; Sidebottom, H.; Wenger, J.; Mellouki, A.; Le Bras, G. J. Phys. Chem. A
2003, 107, 1499.
21
(a) Frink, B. T.; Hadad, C. M. J. Chem. Soc.-Perkin Trans. 2 1999. 11, 2397. (b) Bond,
J. J., MS Thesis, The Ohio State University, 1999. (c) Sokolov, O. V.; Bond, J. J.; Geise,
C. M.; Frink, B. T.; Cohen, M. H.; Hadad, C. M., to be submitted.
22
Tully, F. P.; Droege, A. T. Int. J. Chem. Kinet. 1987, 19, 251.
23
Wallington, T. J.; Andino, J. M.; Skewes, L. M.; Siegl, W. O.; Japar, S. M. Int. J.
Chem. Kinet. 1989, 21, 993.
24
Perry, R. A.; Atkinson, R.; Pitts, J. N., Jr. J. Chem. Phys. 1977, 67, 611.
25
Nelson, L.; Pattagan, O.; Neavyn, R.; Sidebottom, H.; Treacy, J.; Nielsen, O. J. Int. J.
Chem. Kinet. 1990, 22, 1111.
228
26
Japar, S. M.; Wallington, T. J.; Richert, J. F. O.; Ball, J. C. Int. J. Chem. Kinet. 1990,
22, 1257.
27
Mellouki, A.; Teton, S.; Le Bras, G. Int. J. Chem. Kinet. 1995, 27, 791.
28
Arif, M.; Dellinger, B; Taylor, P. H. J. Phys. Chem. 1997, 101, 2436.
29
DeMore, W.B.; Bayes, K. D. J. Phys. Chem. 1999, 103, 2649.
30
Tranter, R. S.; Walker, R. W. Phys. Chem. Chem. Phys. 2001, 3, 4722.
31
Atadinc, F.; Selcuki, C.; Sari, L.; Aviyente, V. Phys. Chem. Chem. Phys. 2002, 4,
1797.
32
Bottoni, A.; Della Casa, P.; Poggi, G. J. Mol. Struct. (Theo.) 2001, 542, 123.
33
(a) Nash, J. J.; Francisco, J. S. J. Phys. Chem. A 1998, 102, 236. (b) Good, D. A.;
Francisco, J. S. J. Phys, Chem. A 2000, 104, 1171.
34
Jursic, B. S. Chem. Phys. Lett. 1998, 295, 447.
35
Wu, J.; Liu, J.; Li, Z.; Sun, C. J. Chem. Phys. 2003, 118, 10986.
36
Barckholtz, C.; Barckholtz, T.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
37
Villamena, F. A.; Hadad, C. M.; Zweier, J. L. J. Am. Chem. Soc. 2004, 126, 1816.
38
Villamena, F. A.; Rockenbaur, A.; Gallucci, J.; Velayutham, M.; Hadad, C. M.;
Zweier, J. L. J. Org. Chem. 2004, 69, 7994.
39
(a) Poole, J. S.; Shi, X.; Hadad, C. M.; Platz, M. S. J. Phys. Chem. A. 2005, 109, 2547.
(b) DeMatteo, M. P.; Poole, J. S.; Shi, X.; Sachdeva, R.; Hatcher, P. G.; Hadad, C. M.;
Platz, M. S. J. Am. Chem. Soc. 2005, 127, 7094.
40
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J.
229
C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.;
Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.;
Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.;
Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J.
V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.;
Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;
Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98,
Revision A.11, Gaussian, Inc.; Pittsburgh, PA, 2001.
41
Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618.
42
Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett. 1990, 166, 275.
43
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
44
Lee, C.; Yang, W.; Parr, R.G. Phys. Rev. B 1998, 37, 785.
45
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 4811.
46
Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys. 1991, 94,
7221.
47
Laidler, K. J. Chemical Kinetics Harper & Row, Publishers, Inc., New York, 1987.
48
Maillard, J. P.; Chauville, J.; Mantz, A. W. J. Mol. Spectrosc. 1976, 63, 120.
49
(a) Eckart, C. Phys. Rev. 1930, 35, 1303. (b) Johnston, H. S.; Heicklen, J. J. Phys.
Chem. 1962, 66, 532.
230
50
(a) Barker, J. R.; Ortiz, N. F.; Preses, J. M.; Lohr, L. L. MultiWell-1.4.1 software,
http://aoss.engin.umich.edu/multiwell/, (2004). (b) Barker, J. R. Int. J. Chem. Kinet.
2001, 33, 232.
51
The calculations were performed using software provided via personal communication
by Dr. Timothy A. Barckholtz, ExxonMobil Research and Engineering Company,
Annandale, New Jersey.
52
Foresman, J. B.; Frisch, A. Exploring Chemistry with Electronic Structure Methods, 2nd
Ed., Gaussian, Inc., Pittsburgh, PA, 1996, pg. 64.
53
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502.
54
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.
55
Engerholm, G. G.; Luntz, A. C.; Gwinn, W. D.; Harris, D. O. J. Chem. Phys. 1969, 50,
2446.
56
Meyer, R.; Lopez, J. C.; Alonso, J. L.; Melandri, S.; Favero, P. G.; Caminati, W. J.
Chem. Phys. 1999, 111, 7871.
57
Mamleev, A. H.; Gunderova, L. N.; Gallev, R. V. J. Struct. Chem. 2001, 42, 365.
58
Melnik, D. G.; Gopalakrishnan, S.; Miller, T. A.; De Lucia, F. C. J. Chem. Phys. 2003,
118, 3589.
59
Cadioli, B.; Gallinella, E.; Coulombeau, C.; Jobic, H.; Berthier, G. J. Phys. Chem.
1993, 97, 7844.
60
Han, S. J.; Kang, Y. K. J. Mol. Struct. (Theo.) 1996, 369, 157.
61
Strajbl, M.; Florian, J. Theor. Chem. Acc. 1998, 99, 166.
62
Wu, A.; Cremer, D. Int. J. Mol. Sci. 2003, 4, 158.
231
63
Rayon, V. M.; Sordo, J. A. J. Chem. Phys. 2005, 122, 204303.
64
Merle, J. K.; Hadad, C. M. J. Phys. Chem. A, submitted.
65
Chuang, Y. –Y.; Coitiño, E. L.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 446.
232
LIST OF REFERENCES
Chapter 1
1.
Gorches, R.; Olivella, M. A.; de las Heras, F. X. M. Org. Geochem. 2003, 34,
1627.
2.
Pankow, J. F.; Luo, W.; Bender, D. A.; Isabelle, L. I.; Hollingsworth, J. S.; Chen,
C.; Asher, W. E.; Zogorski, J. S. Atmos. Environ. 2003, 37, 5023.
3.
Heeb, N. V.; Forss, A.-M.; Saxer, C. J.; Wilhelm, P. Atmos. Environ. 2003, 37,
5185.
4.
Semenov, N. N. Some Problems in Chemical Kinetics and Reactivity, Chap. 7.
Princeton Univ. Press, Princeton, New Jersey, 1958.
5.
Glassman, I. Combustion, Academic Press, San Diego, California, 1996.
6.
Benson, S. W. J. Am. Chem. Soc. 1965, 87, 972.
7.
Compton, R. G.; Hancock, G. Comprehensive Chemical Kinetics, LowTemperature Combustion and Autoignition, Vol. 35 Pilling, M. J., Ed., Elsevier,
Amsterdam, 1997.
8.
Fujii, N.; Asaba, T. Proc. Combust. Inst. 1973, 14, 433.
9.
Venkat, C.; Brezinsky, K.; Glassman, I. Proc. Combust. Inst. 1982, 19, 143.
233
10.
Smith, G. P.; Golden, D. M.; Frenklach, M.; Moriarty, N. W.; Eiteneer, B.;
Goldenberg, M.; Bowman, C. T.; Hanson, R. K.; Song, S.; Gardiner, W. C., Jr.;
Lissianski, V. V.; Qin, Z. http://www.me.berkeley.edu/gri_mech/.
11.
Albagli, A.; Oja, H.; Dubois, L. Environ. Lett. 1974, 6, 241.
12.
Pavanello, S.; Simioli, P.; Lupi, S.; Gregorio, P.; Clinfero, E. Cancer
Epidemiology, Biomarkers & Prevention 2002, 11, 998.
13.
Williams, J. A., Martin, F. L.; Muir, G. H.; Hewer, A.; Grover, P.L.; Phillips, D.
H. Carcinogenesis 2000, 21, 1683-1689.
14.
WHO (1997) The World Health Report. World Health Organization, Geneva,
Switzerland.
15.
Frenklach, M. Phys. Chem. Chem. Phys. 2002, 4, 2028.
16.
Bittner, J. D.; Howard, J. B. Proc. Combust. Inst. 1981, 18, 1105.
17.
Westmoreland, P. R.; Dean, A. M.; Howard, J. B.; Longwell, J. P. J. Phys. Chem.
1989, 93, 8171.
18.
Miller, J. A.; Melius, C. F. Combust. Flame 1992, 91, 21.
19.
Melius, C. F.; Colvin, M. E.; Marinov, N. M.; Pitz, W. J.; Senkin, S. M. Proc.
Combust. Inst. 1996, 26, 685.
20.
Glassman, I. Combustion, 3rd Ed.; Academic Press, San Diego, CA, 1996.
21.
Chai, Y.; Pfefferle, L. D. Fuel, 1998, 77, 313.
22.
Frenklach, M.; Wang. H. Proc. Combust. Inst. 1991, 23, 1559.
23.
Richter, H.; Howard, J. B. Prog. Energy Combust. Sci. 2000, 26, 565.
234
24.
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Madronich, S.; Moortgat, G. K.;
Wallington, T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the
Alkenes, Oxford University Press, New York, 2000.
25.
Finlayson-Pitts, B. J.; Pitts, J. N., Jr. Chemistry of the Upper and Lower
Atmosphere: Theory, Experiments, and Applications; Academic Press, San Diego,
California, 2000.
26.
Atkinson, R.; Arey, J. Atmos. Environ. 2003, 37 (Supp. 2), S197.
27.
George, L. A.; Hard, T. M.; O’Brien, R. J. J. Geophys. Res. 1999, 104, 11643.
28.
Wallington, T. J.; Dagaut, P.; Kurylo, M. Chem. Rev. 1992, 92, 667-710.
29.
Andrew, L. S.; Snyder, R. Casarett and Doull’s Toxicology: The Basic Science of
Poisons; Amdur, O. A.; Doull, J.; Klaassen, D. K. (Eds.), Pergamon Press, New
York, 1991.
Chapter 2
1
Santos, C. Y. M.; Almeida Azevedo, D.; Aquino Neto, F. R. Atmos. Environ.
2004, 38, 1247-1257.
2
Burri, J.; Crockett, R.; Hany, R.; Rentsch, D. Fuel 2004, 83, 187-193.
3
Yamada, E.; Hosokawa, Y.; Furuya, Y.; Matsushita, K.; Fuse, Y. Analytical
Sciences 2004, 20, 107-112.
4
Schuetzle, D.; Siegl, W. O.; Jensen, T. E.; Dearth, M. A.; Kaiser, E. W.; Gorse,
R.; Kreucher, W.; Kulik, E. Environ. Health Persp. 1994, 102(S4), 3-12.
5
Richter, H.; Howard, J. B. Prog. Energy and Combust. Sci. 2000, 26, 565-608.
6
Marsh, N. D.; Ledesma, E. B.; Sandrowitz, A. K.; Wornat, M. J. Energy and
Fuels 2004, 18, 209-217.
235
7
Venkat, C.; Brezinsky, K.; Glassman, I. Symp. (Int.) Combust., 19th 1982, 143152.
8
Rotzoll, G. Int. J. Chem. Kinet. 1985, 17, 637-653.
9
Frank, P.; Herzler, J.; Just T.; Wahl, C. Symp. (Int.) Combust., 25th 1994, 833840.
10
Bermudez, G.; Pfefferle, L. Combustion and Flame 1995, 100, 41-51.
11
Chai, Y.; Pfefferle, L. D. Fuel 1998, 77, 313-320.
12
Yu, T.; Lin, M. C. J. Am. Chem. Soc. 1994, 116, 9571-9576.
13
Norrish, R. G. W.; Taylor, G. W. Proc. R. Soc. 1965, A234, 160-177.
14
Carpenter, B. K. J. Am. Chem. Soc. 1993, 113, 9806-9807.
15
Barckholtz, C.; Fadden, M. J.; Hadad, C. M. J. Phys. Chem. A 1999, 103, 81088117.
16
Fadden, M. J.; Barckholtz, C.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 30043011.
17
Ruifeng, L.; Morokuma, K.; Mebel, A. M.; Lin, M. C. J. Phys. Chem. 1996, 100,
9314-9322.
18
Mebel, A. M.; Lin, M. C. J. Am. Chem. Soc. 1994, 116, 9577-9584.
19
Cioslowski, J.; Liu, G.; Martinov, M.; Piskorz, P.; Moncrieff, D. J. Am. Chem.
Soc. 1996, 118, 5261-5264.
20
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Am. Chem. Soc. 1999, 121,
491-500.
21
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.;
236
Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain,
M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.;
Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.;
Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko,
A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.;
Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;
Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.7,
Gaussian, Inc.; Pittsburgh, PA, 1998.
22
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
23
Lee, C.; Yang, W.; Parr, R.G. Phys. Rev. B 1998, 37, 785-789.
24
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular
Orbital Theory; John Wiley & Sons; New York, 1986.
25
Bauschlichter, C. W., Jr.; Langhoff, S. R. Mol. Phys. 1999, 96, 471.
26
Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.;
Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523.
27
Rablen, P. R. Thermo94, Yale University: New Haven, CT, 1994.
28
Reference 29 recommends that B3LYP/6-31G(d) vibrational frequencies used for
the determination of ΔHvib(T) and ΔSvib(T) be scaled by 0.9989 and 1.0015,
respectively. However, considering how close those values are to 1, we have
chosen to leave the frequencies unscaled for simplicity.
29
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502-16513.
237
30
Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem.
Phys. 1999, 110, 2822-2827.
31
Fadden, M. J.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 8121-8130.
Chapter 3
1
Finlayson-Pitts, B. J.: Pitts, J. N., Jr. Chemistry of the Upper and Lower
Atmosphere: Theory, Experiments, and Applications, Academic Press, San Diego,
California, 2000.
2
Wallington, T. J.; Dagaut, P.; Kurylo, M. Chem. Rev. 1992, 92, 667-710.
3
Compton, R. G.; Hancock, G. Comprehensive Chemical Kinetics, LowTemperature Combustion and Autoignition, Vol. 35 Pilling, M. J., Ed., Elsevier,
Amsterdam, 1997.
4
Glassman, I. Combustion, Academic Press, San Diego, California, 1996.
5
Bozzelli, J. W.; Pitz, W. J. Twenty-Fifth Symposium (International) on
Combustion, The Combustion Institute: Pittsburgh, PA., 1994; 783-791.
6
Bozzelli, J. W.; Sheng, C. J. Phys. Chem. A 2002, 106, 1113-1121.
7
Wagner, A. F.; Slagle, I. R.; Sarzynski, D.; Gutman, D. J. Phys. Chem. 1990, 94,
1853.
8
Kaiser, E. W.; Wallington, T. J.; Andino, J. M. Chem. Phys. Lett. 1990, 168, 309.
9
Kaiser, E. W.; Rimai, L.; Wallington, T. J. J. Phys. Chem. 1989, 93, 4094.
10
Kaiser, E. W.; Lorkovic, I. M.; Wallington, T. J. J. Phys. Chem. 1990, 94, 3352.
11
Dobis, O.; Benson, S. W. J. Am. Chem. Soc. 1993, 115, 8798.
12
Kaiser, E. W. J. Phys. Chem. A 2002, 106, 1256.
13
Kaiser, E. W. J. Phys. Chem. 1995, 99, 707.
238
14
Clifford, E. P.; Farrell, J. T.; DeSain, J. D.; Taatjes, C. A. J. Phys. Chem. A 2000,
104, 11549.
15
Bozzelli, J. W.; Dean, A. M. J. Phys. Chem. 1990, 94, 3313.
16
Quelch, G. E.; Gallo, M. M.; Schaefer, H. F., III. J. Am. Chem. Soc. 1992, 114,
8239.
17
Quelch, G. E.; Gallo, M. M.; Shen, M.; Xie, Y.; Schaefer, H. F., III.; Moncrief, D.
J. Am. Chem. Soc. 1994, 116, 4953.
18
Ignatyev, I. S.; Xie, Y.; Allen, W. D.; Schaefer, H. F., III. J. Chem. Phys. 1997,
107, 141.
19
Stark, M. S. J. Am. Chem. Soc. 2000, 122, 4162.
20
Chen, C.-J.; Bozzelli, J. W. J. Phys. Chem. A 2000, 104, 4997.
21
Rienstra-Kiracofe, J. C.; Allen, W. D.; Schaefer, H. F., III. J. Phys. Chem A 2000,
104, 9823.
22
Miller, J. A.; Klippenstein, S. J.; Robertson, S. H. Proc. Combust. Inst. 2000, 28,
1479.
23
Miller, J. A.; Klippenstein, S. J. Int. J. Chem. Kinet. 2001, 33, 654.
24
Bozzelli, J. W.; Sheng, C. J. Phys. Chem. A 2002, 106, 1113.
25
Sheng, C. Y.; Bozzelli, J. W.; Dean, A. M.; Chang, A. Y. J. Phys. Chem A 2002,
106, 7276.
26
Ruiz, R. P.; Bayes, K. D. J. Phys. Chem. 1984, 88, 2592-2595.
27
Slagle, I. R.; Park, J.; Gutman, D. Twentieth Symposium (International) on
Combustion, The Combustion Institute: Pittsburgh, PA., 1984, 733-741.
28
Kaiser, E. W.; Wallington, T. J. J. Phys. Chem. 1996, 100, 18770-18774
239
29
DeSain, J. D.; Clifford, E. P.; Taatjes, C. A. J. Phys. Chem. A 2001, 105, 32053213.
30
(a) DeSain, J. D.; Klippenstein, S. J.; Miller, J. A.; Taatjes, C. A. J. Phys. Chem.
A 2003, 107, 4415-4427. (b) DeSain, J. D.; Klippenstein, S. J.; Miller, J. A.;
Taatjes, C. A. J. Phys. Chem. A 2004, 108, 7127-7128.
31
DeSain, J. D.; Taatjes, C. A.; Miller, J. A.; Klippenstein, S. J.; Hahn, D. K.
Faraday Discuss. 2001, 119, 101-120.
32
Naik, C.; Carstensen, H. -H.; Dean, A. M. Proceedings of the Third Joint Meeting
of the U. S. Sections of the Combustion Institute, Chicago, Illinois, 2003.
33
Chan, C. -J.; Hamilton, I. P.; Pritchard, H. O. Faraday Trans. 1998, 94, 23032306.
34
Chan, C. -J.; Hamilton, I. P.; Pritchard, H. O. Phys. Chem. Chem. Phys. 1999, 1,
3715-3719.
35
Zalyubovsky, S. J.; Glover, B. G.; Miller, T. A.; Hayes, C. J.; Merle, J. K.; Hadad,
C. M. J. Phys. Chem. A 2005, 109, 1308–1315.
36
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.;
Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.;
Scalmani, G.; Rega, N.; Pettersson, G. A.; Nakatsuji, H; Hada, M.; Ehara, M.;
Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.;
Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.;
Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A.
J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth,
240
g. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels,
A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.;
Stefanov, B. B.; Lui, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.;
Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;
Gonzalez, C.; Pople, J. A. Gaussian 03, Revision B.04, Gaussian, Inc.; Pittsburgh,
PA, 2003.
37
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
38
Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1998, 37, 785-789.
39
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104,
4811.
40
Montgomery, J. A., Jr.; Frisch, M. J.; Ochterski, J. W.; Petersson, G. A. J. Chem.
Phys. 1999, 110, 2822-2827.
41
(a) Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez,
C.; Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523.
42
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502_16513.
43
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936-2941.
44
Knyazev, V. D.; Slagle, I. R. J. Phys. Chem. A 1998, 102, 1770-1778.
45
Please note that the collaborating authors use a naming convention utilizing all
upper case letters as opposed to alternating upper and lower case letters.
Furthermore, in reference 35 the naming order started at the terminal methyl
carbon as opposed to the terminal peroxy oxygen.
241
46
Tarczay, G.; Zalyubovsky, S. J.; Miller, T. A. Chem. Phys. Lett. 2005, 406, 81.
47
Viskolcz, B.; Lendvay, G.; Körtvélyesi, T.; Seres, L. J. Am. Chem. Soc. 1996,
118, 3006-3009.
48
Lendvzy, G.; Viskolcz, B. J. Phys. Chem. A 1998, 102, 10777-10786.
49
The <S2> values for the Hartree-Fock wavefunctions are ~0.91, ~0.82, and ~0.80
for the ab initio components for the transition state structures TS (1,4elim), TS(1,4),
and TS(1,5), respectively.
50
Green, W. H.; Wijaya, C. D.; Yelvington, P. E.; Sumathi, R. Mol. Phys. 2004,
102, 371-380.
51
The calculations were performed using software provided via personal
communication by Dr. Timothy A. Barckholtz, ExxonMobil Research and
Engineering Company, Annandale, New Jersey.
Chapter 4
1
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Mandronich, S.; Moortgat, G. K.;
Wallington, T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the
Alkenes, Oxford University Press, New York, 2000.
2
Calvert, J. G.; Atkinson, R.; Becker, K. H.; Kamens R. M.; Seinfeld, J. H.;
Wallington, T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of
Aromatic Hydrocarbons, Oxford University Press, New York, 2000.
3
Finlayson-Pitts, B. J.; Pitts, J. N., Jr. Chemistry of the Upper and Lower
Atmosphere; Academic Press: San Diego, 2000.
4
Dabestani, R.; Ivanov, I. N. Photochem. Photobiol. 1999, 70.10.
5
Atkinson, R. J. Phys. Chem. Ref. Data 1989, 1, 1–246.
242
6
Atkinson, R. Chem. Rev. 1985, 85, 69.
7
Davis, D. D.; Bollinger, W.; Fischer, S. J. Phys. Chem. 1975, 79, 293.
8
Perry, R. A.; Atkinson, R.; Pitts, J. N., Jr. J. Phys. Chem. 1977, 81, 296.
9
Tully, F. P.; Ravishankara, A. R.; Thompson, R. L.; Nicovich, J. M.; Shah, R. C.;
Kreutter, N. M.; Wine, P. H. J. Phys. Chem. 1981, 85, 2262.
10
Wahner, A.; Zetsch, C. J. Phys. Chem. 1983, 87, 4945.
11
Madronich, S.; Felder, W. J. Phys. Chem. 1985, 89, 3556.
12
Lin, C. Y.; Lin, M. C. J. Phys. Chem. 1986, 90, 425.
13
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
14
Lay, T. H.; Bozzelli, J. W.; Seinfeld, J. H. J. Phys. Chem. 1996, 100, 6543.
15
Tokmakov, I. V.; Lin, M. C. J. Phys. Chem. A 2002, 106, 11309.
16
Atkinson, R. Reactions of Oxygen Species in the Atmosphere. In Active Oxygen
in Chemistry; Foote, C. S., Valentine, J. S., Greenberg, A., Liebman, J. F., Eds.;
Blackie Academic and Professional; New York, 1995; Vol. 2, pp 249–279.
17
Glassman, I. Combustion 3rd Ed.; Academic Press: San Diego, 1996.
18
Compton, R. G.; Hancock, G. Comprehensive Chemical Kinetics, LowTemperature Combustion and Autoignition, Vol. 35 Pilling, M. J., Ed., Elsevier,
Amsterdam, 1997.
19
Thompson, A. M. Science 1992, 256, 1157.
20
Raghavan, N. V.; Steenken, S. J. Am. Chem. Soc. 1980, 102, 3495.
21
Tripathi, G. N. R. J. Am. Chem. Soc. 1998, 120, 4161.
22
Albarrán, G.; Schuler, R. H. Rad. Phys. Chem. 2002. 63, 661.
23
Albarrán, G.; Bentley, J.; Schuler, R. H. J. Phys. Chem. A 2003, 107, 7770.
243
24
Poole, J. S.; Shi, X.; Hadad, C. M.; Platz, M. S. J. Phys. Chem. A. 2005, 109,
2547.
25
DeMatteo, M. P.; Poole, J. S.; Shi, X.; Sachdeva, R.; Hatcher, P. G.; Hadad, C.
M.; Platz, M. S. J. Am. Chem. Soc. 2005, 127, 7094.
26
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Am. Chem. Soc. 1999, 121,
491.
27
(a) Fadden, M. J.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 6088. (b) Fadden,
M. J.; Hadad, C. M. J. Phys. Chem. A 2000, 104, 6324.
28
(a) Parr, R. G.; Yang, W. Density Functional Theory in Atoms and Molecules;
Oxford University Press: New York, 1989. (b) Labanowski, J. W.; Andzelm, J.
Density Functional Methods in Chemistry; Springer: New York, 1991.
29
Wiberg, K. B.; Rablen, P. R. J. Am. Chem. Soc. 1993, 115, 9234.
30
Wiberg, K. B.; Rablen, P. R. J. Org, Chem. 1998, 63, 3722.
31
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.;
Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain,
M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.;
Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.;
Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko,
A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.;
Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;
244
Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.11,
Gaussian, Inc.; Pittsburgh, PA, 1998.
32
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
33
Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1998, 37, 785-789.
34
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular
Orbital Theory; John Wiley & Sons: New York, 1986.
35
Bauschlichter, C. W., Jr.; Langhoff, S. R. Mol. Phys. 1999, 96, 471.
36
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502-16513.
37
AIMPAC 95. Bader, R. F. W., and associates. McMaster University, Hamilton,
Ont., 1995.
38
Blanksby, J. S.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255.
39
Zhang, X.-M. J. Org. Chem. 1998, 63. 3590.
40
Ervin, K. M.; DeTuri, V. F. J. Phys. Chem. A 2002, 106, 9947.
41
Atkinson, R. J. Phys. Chem. Ref. Data 1997, 26, 235.
42
(a) Minisci, F.; Galli, R. Tetr. Lett. 1962, 533 – 538. (b) Norman, R. O. C.;
Radda, G. K. Proc. Chem. Soc. 1962, 138. (c) Cadet, J.; Douki, T.; Gasparutto,
D.; Ravanat, J.-L. Mutation Res. 2003, 531, 5 – 23.
43
Solomons, T. W. G. Organic Chemistry; John Wiley & Sons, Inc.: New York,
1996.
Chapter 5
1
Harvey, R. G. Polycyclic Aromatic Hydrocarbons: Chemistry and
Carcinogenicity; Cambridge University Press, New York, NY, 1991.
245
2
Li, K.; Christensen, E. R.; Van Camp, R. P.; Imamoglu, I. Environ. Sci. Technol.
2001, 35, 2896.
3
Li, C.-T.; Lin, Y.-C.; Lee, W.-J.; Tsai, P.-J. Environ. Health Perspectives 2003,
111, 483.
4
Reisen, F.; Wheeler, S.; Arey, J. Atmos. Environ. 2003, 37, 3653.
5
Albagli, A.; Oja, H.; Dubois, L. Environ. Lett. 1974, 6, 241.
6
Pavanello, S.; Simioli, P.; Lupi, S.; Gregorio, P.; Clinfero, E. Cancer
Epidemiology, Biomarkers & Prevention 2002, 11, 998-1003.
7
Williams, J. A.; Martin, F. L.; Muir, G. H.; Hewer, A.; Grover, P. L.; Phillips, D.
H. Carcinogenesis 2000, 21, 1683-1689.
8
WHO (1997) The World Health Report. World Health Organization, Geneva,
Switzerland.
9
Frenklach, M. Phys. Chem. Chem. Phys. 2002, 4, 2028.
10
Bittner, J. D.; Howard, J. B. Proc. Combust. Inst. 1981, 18, 1105.
11
Westmoreland, P. R.; Dean, A. M.; Howard, J. B.; Longwell, J. P. J. Phys. Chem.
1989, 93, 8171.
12
Miller, J. A.; Melius, C. F. Combust. Flame 1992, 91, 21.
13
Melius, C. F.; Colvin, M. E.; Marinov, N. M.; Pitz, W. J.; Senkin, S. M. Proc.
Combust. Inst. 1996, 26, 685.
14
Glassman, I. Combustion, 3rd Ed.; Academic Press, San Diego, CA, 1996.
15
Chai, Y.; Pfefferle, L. D. Fuel 1998, 77, 313.
16
Frenklach, M.; Wang. H. Proc. Combust. Inst. 1991, 23, 1559.
246
17
Vione, D.; Barra, S.; De Gennaro, G.; De Rienzo, M.; Gilardoni, S.; Perrone, M.
G.; Pozzoli, L. Ann. Chim. 2004, 94, 257.
18
Bunce, N. J.; Liu, L.; Zhu, J.; Lane, D. A. Environ. Sci. Technol. 1997, 31, 2252.
19
Sasaki, J.; Aschmann, S. M.; Kwok, E. S.; Atkinson, R.; Arey, J. Environ. Sci.
Technol. 1997, 31, 3173.
20
Ohe, T.; Watanabe, T.; Wakabayashi, K. Mutat.Res. 2004, 567, 109.
21
Bauschlichter, C. W., Jr.; Langhoff, S. R. Mol. Phys. 1999, 96, 471.
22
Barckholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Am. Chem. Soc. 1999, 121,
491.
23
Cioslowski, J.; Liu, G.; Martinov, M.; Piskorz, P.; Moncrieff, D. J. Am. Chem.
Soc. 1996, 118, 5261.
24
Reed, D. R.; Kass, S. R. J. Mass Spectrom. 2000, 35, 534.
25
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104,
4811.
26
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.
27
See Chapters 6 and 7 of this dissertation.
28
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.;
Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain,
M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.;
Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.;
Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko,
247
A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.;
Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;
Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.11,
Gaussian, Inc.; Pittsburgh, PA, 1998.
29
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
30
Lee, C.; Yang, W.; Parr, R. G. Phys. Rev. B 1998, 37, 785-789.
31
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104,
4811.
32
(a) Parr, R. G.; Yang, W. Density Functional Theory in Atoms and Molecules;
Oxford University Press: New York, 1989. (b) Labanowski, J. W.; Andzelm, J.
Density Functional Methods in Chemistry; Springer: New York, 1991.
33
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular
Orbital Theory; John Wiley & Sons: New York, 1986.
34
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502.
35
Dabestani, R.; Ivanov, I. N. Photochem. Photobiol. 1999, 70, 10.
36
Ervin, K. M.; DeTuri, V. F. J. Phys. Chem. A 2002, 106, 9947.
37
Blanksby, J. S.; Ellison, G. B. Acc. Chem. Res. 2003, 36, 255.
38
Clar, E. The Aromatic Sextet, Wiley, New York, 1972.
39
Brubaker, W. W., Jr.; Hites, R. A. J. Phys. Chem. A 1998, 102, 915.
40
Barkholtz, C.; Barckholtz, T. A.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
41
CRC Handbook of Chemistry and Physics; 69th Ed.; Weast, R. C.; Astle, M. J.;
Beyer, W. H., Eds.; CRC Press: Boca Raton FL, 1988–1989.
248
Chapter 6
1
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Madronich, S.; Moortgat, G. K.;
Wallington, T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the
Alkenes, Oxford University Press, New York, 2000.
2
Atkinson, R. Reactions of Oxygen Species in the Atmosphere in Active Oxygen in
Chemistry, Foote, C. S., Valentine, J. S., Greenberg, A., Liebman, J. F., Eds.,
Blackie Academic & Professional, New York, 1995, pp. 249.
3
Agency for Toxic Substatnces and Disease Registry (ATSDR), ToxFAQs for
Acrolein, July 1999. Available on-line at http://www.atsdr.cdc.gov/tfacts124.html
(12/17/02)
4
Liu, X.; Jeffries, H. E.; Sexton, K. G. Atmos. Environ. 1999, 33, 3005.
5
Tuazon, E. C.; Alvarado, A.; Aschmann, S. M.; Atkinson, R.; Arey, J. Environ.
Sci. Technol. 1999, 33, 3586.
6
Destaillates, H.; Spaulding, R. S.; Charles, M. J. Environ. Sci. Technol. 2002, 36,
2227.
7
Kozekov, I. D.; Nechev, L. V.; Moseley, M. S.; Harris, C. M.; Rizzo, C. J.; Stone,
M. P.; Harris, T. M. J. Am. Chem. Soc. 2003, 125, 50.
8
McMillan, D. F.; Golden, D. M. Ann. Rev. Phys. Chem. 1982, 33, 493.
9
Raul Alvarez-Idaboy, J.; Mora-Diez, N.; Boyd, R. J.; Vivier-Bunge, A. J. Am.
Chem. Soc. 2001, 123, 2018.
10
Barckholtz, C.; Barckholtz, T.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
11
Tulley, F. P.; Ravishankara, A. R.; Thompson, R. L.; Nicovich, J. M.; Shah, R.
C.; Kreutter, N. M.; Wine, P. H. J. Phys. Chem. 1982, 85, 2262.
249
12
Magneron, I.; Thévenet, R.; Mellouki, A.; LeBras, G.; Moortgat, G. K.; Wirtz, K.
J. Phys. Chem. A 2002, 106, 2526.
13
Maldotti, A.; Chiorboli, C.; Bignozzi, C. A.; Bartocci, C.; Carassiti, V. Int. J.
Chem. Kinet. 1980, 12, 905.
14
Kerr, J. A.; Sheppard, D. W. Environ. Sci. Technol. 1981, 15, 960.
15
Atkinson, R.; Aschmann, S. M.; Pitts, J. N., Jr. Int. J. Chem. Kinet. 1983, 15, 75.
16
Edney, E. O.; Kleindienst, T. E.; Corse, E. W. Int. J. Chem. Kinet. 1986, 18, 1355.
17
Orlando, J. J.; Tyndall, G. S. J. Phys. Chem. A 2002, 106, 12252.
18
Semmes, D. H.; Ravishankara, A. R.; Gump-Perkins, C. A.; Wine, P. H. Int. J.
Chem. Kinet. 1985, 17, 303.
19
Raul Alvarez-Idaboy, J.; Mora-Diez, N.; Boyd, R. J.; Vivier-Bunge, A. J. Am.
Chem. Soc. 2001, 123, 2018.
20
Raul Alvarez-Idaboy, J.; Mora-Diez, N.; Vivier-Bunge, A. J. Am. Chem. Soc.
2000, 122, 3715.
21
Villamena, F. A.; Hadad, C. M.; Zweier, J. L. J. Am. Chem. Soc. 2004, 126, 1816.
22
Villamena, F. A.; Rockenbaur, A.; Gallucci, J.; Velayutham, M.; Hadad, C. M.;
Zweier, J. L. J. Org. Chem. 2004, 69, 7994.
23
(a) Poole, J. S.; Shi, X.; Hadad, C. M.; Platz, M. S. J. Phys. Chem. A. 2005, 109,
2547. (b) DeMatteo, M. P.; Poole, J. S.; Shi, X.; Sachdeva, R.; Hatcher, P. G.;
Hadad, C. M.; Platz, M. S. J. Am. Chem. Soc. 2005, 127, 7094.
24
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.;
Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.;
250
Scalmani, G.; Rega, N.; Pettersson, G. A.; Nakatsuji, H; Hada, M.; Ehara, M.;
Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.;
Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.;
Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A.
J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth,
g. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels,
A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.;
Stefanov, B. B.; Lui, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.;
Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.;
Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.;
Gonzalez, C.; Pople, J. A. Gaussian 03 (Revision B.04), Gaussian, Inc.;
Pittsburgh, PA, 2003.
25
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.;
Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain,
M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.;
Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.;
Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko,
A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.;
Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;
251
Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.11,
Gaussian, Inc.; Pittsburgh, PA, 2001.
26
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104,
4811.
27
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
28
Lee, C.; Yang, W.; Parr, R.G. Phys. Rev. B 1998, 37, 785.
29
Moller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618.
30
Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett. 166, 275 (1990).
31
Pople, J. A.; Head-Gordon, M.; Raghavachari, K. J. Chem. Phys. 1987, 87, 5968.
32
Cizek, J. Adv. Chem. Phys. 1969, 14, 35.
33
Purvis, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910.
34
Scuseria, G. E.; Janssen, C. L.; Schaefer, H. F., III J. Chem. Phys. 1988, 89, 7382.
35
Scuseria, G. E.; Schaefer, H. F., III J. Chem. Phys. 1989, 90, 3700.
36
Gonzalez, C.; Schlegel, H. B. J. Chem. Phys. 1989, 90, 2154. (b) Gonzalez, C.;
Schlegel, H. B. J. Phys. Chem. 1990, 94, 5523.
37
(a) Barker, J. R.; Ortiz, N. F.; Preses, J. M.; Lohr, L. L. MultiWell-1.4.1 software,
http://aoss.engin.umich.edu/multiwell/, (2004). (b) Barker, J. R. Int. J. Chem.
Kinet. 2001, 33, 232.
38
The calculations were performed using software provided via personal
communication by Dr. Timothy A. Barckholtz, ExxonMobil Research and
Engineering Company, Annandale, New Jersey.
39
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.
40
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502.
252
41
Laidler, K. J. Chemical Kinetics, Harper & Row, Publishers, Inc., New York,
1987.
42
Wigner, E. P. Z. Phys. Chem. Abt. B 1932, 19, 203.
43
Maillard, J. P.; Chauville, J.; Mantz, A. W. J. Mol. Spectrosc. 1976, 63, 120.
44
Chuang, Y.-Y.; Coitiño, E. L.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 446.
45
Smith, I. W. M.; Ravishankara, A. R. J. Phys. Chem. A 2002, 106, 4798.
46
Thévenet, R.; Mellouki, A.; Le Bras, G. Int. J. Chem. Kinet. 2000, 32, 676.
47
Chuong, B.; Stevens, P. S. J. Phys. Chem. A 2003, 107, 2185.
48
Aranda, A.; Díaz de Mera, Y.; Rodríguez, A.; Rodríguez, D.; Martínez, E. J.
Phys. Chem. A 2003, 107, 5717.
49
Hansen, J. C.; Francisco, J. S. ChemPhysChem 2002, 3, 833.
50
Truhlar, D. G.; Isaacson, A. D.; Garrett, B. C. Theory of Chemical Reaction
Dynamics, Vol. 4, edited by Baer, M. CRC Press, Boca Raton, FL, 1985, pp
65–137.
51
Truhlar, D. G.; Garrett, B. C. Annual Review of Physical Chemistry, Vol. 35,
edited by Rabinovitch, B. S.; Schurr, J. M.; and Strauss, H. L., Annual Reviews,
Inc., Palo Alto, California, 1984, pp 159-189.
52
Chuang, Y. Y.; Corchado, J. C.; Truhlar, D. G. J. Phys. Chem. A 1999, 103, 1140.
53
Corchado, J. C.; Chuang, Y.-Y.; Fast, P. L.; Villa, J.; Hu, W.-P.; Liu, Y.-P.;
Lynch, G. C.; Nguyen, K. A.; Jackels, C. F.; Melissas, V. S.; Lynch, B. J.; Rossi,
I.; Coitiño, E. L.; Fernandez-Ramos, A.; Pu, J.; Albu, T. V.; Steckler, R.; Garrett,
B. C.; Isaacson, A. D.; Truhlar, D. G., Polyrate 9.1, University of Minnesota,
Minneapolis, MN, 2003.
253
Chapter 7
1
National Science and Technology Council (NTSC), Committee on Environment
and Natural Resources, ‘Interagency Assessment of Oxygenated Fuels’, June
1997.
2
Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Mandronich, S.; Moortgat, G. K.;
Wallington, T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of the
Alkenes, Oxford University Press, New York, 2000.
3
Hehre, W. J.; Radom, L.; Schleyer, P. v. R.; Pople, J. A. Ab Initio Molecular
Orbital Theory; John Wiley & Sons, New York, NY, 1986.
4
Isaacson, A. D. The Reaction Path in Chemistry: Current Approaches and
Perspectives, edited by Heidrich, D., Kluwer Academic Publishers, Dordrecht,
The Netherlands, 1995, pp 191–228.
5
Truhlar, D. G.; Isaacson, A. D.; Garrett, B. C. Theory of Chemical Reaction
Dynamics, Vol. 4, edited by Baer, M. CRC Press, Boca Raton, FL, 1985, pp
65–137.
6
Truhlar, D. G.; Garrett, B. C. Annual Review of Physical Chemistry, Vol. 35,
edited by Rabinovitch, B. S.; Schurr, J. M.; and Strauss, H. L., Annual Reviews,
Inc., Palo Alto, California, 1984, pp 159-189.
7
(a) Parr, R. G.; Yang, W. Density Functional Theory in Atoms and Molecules,
Oxford University Press, New York, NY, 1989. (b) Labanowski, J. W.; Andzelm,
J. Density Functional Methods in Chemistry, Springer, New York, NY, 1991.
8
Truhlar, D. G. Faraday Discuss. 1998, 110, 362.
9
Durant, J. L. Chem. Phys. Lett. 1996, 256, 595.
254
10
Kobayashi, Y.; Kamiya, M.; Hirao, K. Chem. Phys. Lett. 2000, 319, 695.
11
Skokov, S.; Wheeler, R. A. Chem. Phys. Lett. 1997, 271, 251.
12
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
13
Rice, B. M.; Pai, S. V.; Chabalowski, C. F. J. Phys. Chem. A 1998, 102, 6950.
14
Bach, R. D.; Glukhovstev, M. N.; Gonzalez, C.; Marquez, M.; Estevez, C. M.;
Baboul, A. G.; Schlegel, H. B. J. Phys. Chem. A 1997, 101, 6092.
15
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104,
4811.
16
Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664.
17
Ravishankara, A. R.; Davis, D. D. J. Phys. Chem. 1978, 82, 2852.
18
Wallington, T. J.; Liu, R.; Dagaout, P.; Kurylo, M. J. Int. J. Chem. Kinet. 1988,
20, 41.
19
Winer, A. M.; Lloyd, A. C.; Darnall, K. R.; Atkinson, R.; Pitts, J. N., Jr. Chem.
Phys. Lett. 1977, 51, 221.
20
Moriarty, J.; Sidebottom, H.; Wenger, J.; Mellouki, A.; Le Bras, G. J. Phys.
Chem. A 2003, 107, 1499.
21
(a) Frink, B. T.; Hadad, C. M. J. Chem. Soc.-Perkin Trans. 2 1999. 11, 2397. (b)
Bond, J. J., MS Thesis, The Ohio State University, 1999. (c) Sokolov, O. V.;
Bond, J. J.; Geise, C. M.; Frink, B. T.; Cohen, M. H.; Hadad, C. M., to be
submitted.
22
Tully, F. P.; Droege, A. T. Int. J. Chem. Kinet. 1987, 19, 251.
23
Wallington, T. J.; Andino, J. M.; Skewes, L. M.; Siegl, W. O.; Japar, S. M. Int. J.
Chem. Kinet. 1989, 21, 993.
255
24
Perry, R. A.; Atkinson, R.; Pitts, J. N., Jr. J. Chem. Phys. 1977, 67, 611.
25
Nelson, L.; Pattagan, O.; Neavyn, R.; Sidebottom, H.; Treacy, J.; Nielsen, O. J.
Int. J. Chem. Kinet. 1990, 22, 1111.
26
Japar, S. M.; Wallington, T. J.; Richert, J. F. O.; Ball, J. C. Int. J. Chem. Kinet.
1990, 22, 1257.
27
Mellouki, A.; Teton, S.; Le Bras, G. Int. J. Chem. Kinet. 1995, 27, 791.
28
Arif, M.; Dellinger, B; Taylor, P. H. J. Phys. Chem. 1997, 101, 2436.
29
DeMore, W.B.; Bayes, K. D. J. Phys. Chem. 1999, 103, 2649.
30
Tranter, R. S.; Walker, R. W. Phys. Chem. Chem. Phys. 2001, 3, 4722.
31
Atadinc, F.; Selcuki, C.; Sari, L.; Aviyente, V. Phys. Chem. Chem. Phys. 2002, 4,
1797.
32
Bottoni, A.; Della Casa, P.; Poggi, G. J. Mol. Struct. (Theo.) 2001, 542, 123.
33
(a) Nash, J. J.; Francisco, J. S. J. Phys. Chem. A 1998, 102, 236. (b) Good, D. A.;
Francisco, J. S. J. Phys, Chem. A 2000, 104, 1171.
34
Jursic, B. S. Chem. Phys. Lett. 1998, 295, 447.
35
Wu, J.; Liu, J.; Li, Z.; Sun, C. J. Chem. Phys. 2003, 118, 10986.
36
Barckholtz, C.; Barckholtz, T.; Hadad, C. M. J. Phys. Chem. A 2001, 105, 140.
37
Villamena, F. A.; Hadad, C. M.; Zweier, J. L. J. Am. Chem. Soc. 2004, 126, 1816.
38
Villamena, F. A.; Rockenbaur, A.; Gallucci, J.; Velayutham, M.; Hadad, C. M.;
Zweier, J. L. J. Org. Chem. 2004, 69, 7994.
39
(a) Poole, J. S.; Shi, X.; Hadad, C. M.; Platz, M. S. J. Phys. Chem. A. 2005, 109,
2547. (b) DeMatteo, M. P.; Poole, J. S.; Shi, X.; Sachdeva, R.; Hatcher, P. G.;
Hadad, C. M.; Platz, M. S. J. Am. Chem. Soc. 2005, 127, 7094.
256
40
Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.;
Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.;
Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain,
M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.;
Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.;
Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.;
Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko,
A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.;
Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.;
Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98, Revision A.11,
Gaussian, Inc.; Pittsburgh, PA, 2001.
41
Møller, C.; Plesset, M. S. Phys. Rev. 1934, 46, 618.
42
Frisch, M. J.; Head-Gordon, M.; Pople, J. A. Chem. Phys. Lett. 1990, 166, 275.
43
Becke, A. D. J. Chem. Phys. 1993, 98, 5648.
44
Lee, C.; Yang, W.; Parr, R.G. Phys. Rev. B 1998, 37, 785.
45
Lynch, B. J.; Fast, P. L.; Harris, M.; Truhlar, D. G. J. Phys. Chem. A 2000, 104,
4811.
46
Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A. J. Chem. Phys.
1991, 94, 7221.
47
Laidler, K. J. Chemical Kinetics Harper & Row, Publishers, Inc., New York,
1987.
48
Maillard, J. P.; Chauville, J.; Mantz, A. W. J. Mol. Spectrosc. 1976, 63, 120.
257
49
(a) Eckart, C. Phys. Rev. 1930, 35, 1303. (b) Johnston, H. S.; Heicklen, J. J. Phys.
Chem. 1962, 66, 532.
50
(a) Barker, J. R.; Ortiz, N. F.; Preses, J. M.; Lohr, L. L. MultiWell-1.4.1 software,
http://aoss.engin.umich.edu/multiwell/, (2004). (b) Barker, J. R. Int. J. Chem.
Kinet. 2001, 33, 232.
51
The calculations were performed using software provided via personal
communication by Dr. Timothy A. Barckholtz, ExxonMobil Research and
Engineering Company, Annandale, New Jersey.
52
Foresman, J. B.; Frisch, A. Exploring Chemistry with Electronic Structure
Methods, 2nd Ed., Gaussian, Inc., Pittsburgh, PA, 1996, pg. 64.
53
Scott, A. P.; Radom, L. J. Phys. Chem. 1996, 100, 16502.
54
Lynch, B. J.; Truhlar, D. G. J. Phys. Chem. A 2001, 105, 2936.
55
Engerholm, G. G.; Luntz, A. C.; Gwinn, W. D.; Harris, D. O. J. Chem. Phys.
1969, 50, 2446.
56
Meyer, R.; Lopez, J. C.; Alonso, J. L.; Melandri, S.; Favero, P. G.; Caminati, W.
J. Chem. Phys. 1999, 111, 7871.
57
Mamleev, A. H.; Gunderova, L. N.; Gallev, R. V. J. Struct. Chem. 2001, 42, 365.
58
Melnik, D. G.; Gopalakrishnan, S.; Miller, T. A.; De Lucia, F. C. J. Chem. Phys.
2003, 118, 3589.
59
Cadioli, B.; Gallinella, E.; Coulombeau, C.; Jobic, H.; Berthier, G. J. Phys. Chem.
1993, 97, 7844.
60
Han, S. J.; Kang, Y. K. J. Mol. Struct. (Theo.) 1996, 369, 157.
61
Strajbl, M.; Florian, J. Theor. Chem. Acc. 1998, 99, 166.
258
62
Wu, A.; Cremer, D. Int. J. Mol. Sci. 2003, 4, 158.
63
Rayon, V. M.; Sordo, J. A. J. Chem. Phys. 2005, 122, 204303.
64
Merle, J. K.; Hadad, C. M. J. Phys. Chem. A, submitted.
65
Chuang, Y. –Y.; Coitiño, E. L.; Truhlar, D. G. J. Phys. Chem. A 2000, 104, 446.
259