The self-reaction of hydroperoxyl radicals: ab initio characterization
of dimer structures and reaction mechanisms
Rongshun Zhu and M. C. Lin*
Paper
Department of Chemistry, Emory University, Atlanta, GA 30322, USA.
E-mail: [email protected]
Received 21st August 2001, Accepted 15th October 2001
Published on the Web 31st October 2001
The global potential energy surfaces of singlet and triplet H2O4 systems have been searched at the B3LYP/
6-311G(d, p) level of theory; their relative energies have been calculated at the G2M(CC5)// B3LYP/6-311G
(d, p) level. The results show that the most stable intermediate out of the 11 open-chain and cyclic dimers of
HO2 is the singlet HO4H chain-structure with C1 symmetry which lies 19.1 kcal mol21 below the reactants. The
transition states for the production of H2O2 z O2 (singlet and triplet), H2O z O3 and H2 z 2O2 have been
calculated at the same level of theory. The results show that the most favored product channel, producing
H2O2 z 3O2, occurs by the formation of a triplet six-member-ring intermediate through head-to-tail association
with a dual hydrogen-bonding energy of 9.5 kcal mol21. The intermediate fragments to give H2O2 z 3O2 via a
transition state, which lies below the reactants by about 0.5 kcal mol21. There are four channels over the singlet
surface which can produce 1O2; all the transition states associated with these channels lie above the reactants by
2.8–5.6 kcal mol21 at the G2M level. Similarly, the O3 and H2 formation channels also occur over the singlet
surface with high energy barriers, 5.2 and 74.2 kcal mol21, respectively; their formation is kinetically
unimportant.
1. Introduction
The hydroperoxyl radical, HO2, plays a pivotal role in the
chemistry of Earth’s atmosphere, from troposphere to mesosphere. It is one of the key oxidizers, which can react with
volatile organic compounds and efficiently convert NO to NO2
while regenerating OH.1–2 There have been numerous kinetic
studies on the self-reaction of HO2 because of the significant
role it plays in the atmosphere and combustion chemistry.3–54
The existing kinetic data vary widely; for example, at room
temperature where most data have been determined, the values
of the rate constant reported to date for the major product
channel,
HO2 z HO2 A H2O2 z O2
(1)
are scattered by more than an order of magnitude. Part of the
reason for the scatter was concluded to result from the effect of
pressure,4,5,6,10,28,34,36,38,40,48 which had not been recognized
earlier. The origin and the extent of the pressure effect on the
reaction rate are still not clearly understood.
Another interesting aspect of the reaction is the mechanism
responsible for reaction (1) as well as the minor product
channel,
HO2 z HO2 A H2 z 2O2,
(2)
which has been shown to occur by as much as 9%.11 There has
been a report of the chemiluminescence from the excited O2
(1D) state in an electrochemical reaction involving H2O2; the
emission was assumed to result from the decomposition of an
excited H2O4 intermediate.55 In addition, the high exothermicity of the spin-allowed O3 producing reaction channel via an
open chain HO4H intermediate,
HO2 z HO2 A H2O z O3,
(3)
may potentially drive the process to occur, although it has not
yet been observed experimentally to date.
Theoretically, one of the most interesting aspects of the
reaction lies perhaps in the mechanisms responsible for the
formation of these products and the pronounced effect of H2O
on the overall rate constant.50,51 Do these products share a
common precursor, which is long-lived and responsible for the
observed pressure dependence? If there are many possible longlived intermediates, four of which have been predicted to be
stable in a series of papers by Schaefer and co-workers,56–58
how are they connected in the potential energy surface (PES),
which predisposes the observed product branching ratios?
In this work, we investigate the reaction system by systematically characterizing its PES with high-level molecular orbital
calculations. Hopefully the predicted energetics for the lowenergy paths will be employed in the future for prediction of
their rate constants under varying experimental conditions so
as to reconcile the observed widely scattered data.
2. Computational methods
Ab initio calculations
The geometry of the reactants, intermediates, transition states,
and products of the HO2 z HO2 reaction were optimized by
the B3LYP method (Becke’s three-parameter nonlocal
exchange functional59–61 with nonlocal correlation functional
of Lee et al.62) using the standard Gaussian 6-311G(d,p) basis
set. Vibrational frequencies and zero-point energies for all
species were calculated at the same B3LYP/6-311G(d, p) level
of theory. The energies of all species were calculated by the
G2M method,63 which uses a series of calculations with the
B3LYP/6-311G(d,p) optimized geometry to approximate the
CCSD(T)/6-311zG(3df,2p) level of theory including a ‘‘higher
level correction (HLC)’’ based on the number of paired and
DOI: 10.1039/b107602g
PhysChemComm, 2001, 23, 1–6
This journal is # The Royal Society of Chemistry 2001
1
unpaired electrons. The total G2M energy given in units of Eh
(hartrees) with zero-point energy (ZPE) correction is calculated
as follows:
E[G2M(CC5)] ~ E[CCSD(T)/6-311G(d, p)]
z DE(z3df, 2p) z DE(HLC)
z ZPE[B3LYP/6-311G(d, p)].
DE(z3df, 2p) ~ E[MP2/6-311zG(3df, 2p)]
2 E[MP2/6-311G(d, p)].
DE(HLC) ~ 20.00530nb 2 0.00019na;
where na and nb are the numbers of valence electrons, na ¢ nb.
All calculations were carried out with Gaussian 98.64
3. Results and discussion
The optimized geometries of the reactants and long-lived
intermediates are shown in Fig. 1 and those of transition states
are shown in Fig. 2. The potential energy diagrams of singlet
and triplet species are presented separately for clarity in Figs. 3
and 4, respectively. The total and relative energies are compiled
in Table 1. As shown in Figs. 3 and 4 the HO2 z HO2 reaction
can occur by both singlet and triplet potential surfaces
involving different intermediates shown in Fig. 1 to form
different products. The detailed mechanisms for these processes
are discussed in the following sections.
A. Stable isomers of HO4H
Singlet. Due to the rotation of OH and HO2 groups in the
HO4H chain molecules, there are several isomers with similar
stabilities. In the present calculation, six chemically bonded
chain-structures have been identified. They are LM1a, LM1b,
LM2a, LM2b, LM3a and LM3b as shown in Fig. 1. These
isomers, LM1a and LM1b, LM2a and LM2b, and LM3a and
LM3b, are mirror isomers of each other. LM1a, LM2a and
their mirror-isomers have C2 symmetry, the apparent structure
differences are that the bridging O–O bonds in LM2a and
LM2b are 0.024 Å shorter than those in LM1a and LM1b;
however, the O–O bonds in the HO2 groups of LM2a and
LM2b are 0.016 Å longer than those in LM1a and LM1b. In
addition, in LM2a and LM2b, there are intra-molecular
hydrogen bonds (2.824 Å) which LM1a and LM1b lack.
LM3a and LM3b have C1 symmetry with slightly stronger
intra-molecular hydrogen bonds (2.661 Å) compared with
those in LM2a and LM2b. From Fig. 1 and Table 1, one can
see that the most stable chain structure intermediates are LM3a
and LM3b. The predicted HO2 dimerization energies (see
Table 1) in LM1, LM2 and LM3 are 218.2, 218.5 and
219.1 kcal mol21 at the G2M//B3LYP/6-311G (d, p) level. The
Fig. 1 The optimized geometries of the reactants, singlet and triplet intermediates, in the HO2 z HO2 reaction at the B3LYP/6-311G(d, p) level.
2
PhysChemComm, 2001, 23, 1–6
Fig. 2 The optimized geometries of the singlet and triplet transition states for HO2 z HO2 at the B3LYP/6-311G(d, p) level.
most stable isomer is LM3 because of its relatively stronger
intra-molecular hydrogen bond. Schaefer and co-workers57
also observed a similar result for two of these isomers, LM1
and LM3.
Besides these chain isomers, we also found two fourmember-ring minima, LM4 and LM5. In these two loose
intermediates, the O4-ring was formed by the anti-parallel
association of the two HO2 radicals with the O–H bonds
oriented differently. The head-to-tail connected O–O bond
lengths are 2.140 and 2.149 Å in LM4 and LM5, respectively;
other structural parameters are close to those in the HO2
monomer (see Fig. 1). These two minima are sensitive to the
methods employed; they are found to be endothermic with
respect to the reactants. They lie above the reactants by 10.1
and 12.0 kcal mol21 (without ZPE corrections) at the B3LYP/
6-311G (d, p) level. However, at the G2M level, which includes
Fig. 3 Schematic energy diagram of the singlet HO2–HO2 system
computed at the G2M level.
Fig. 4 Schematic energy diagram of the triplet HO2–HO2 system
computed at the G2M level.
PhysChemComm, 2001, 23, 1–6
3
Table 1 Total and relative energies of reactants, intermediates, transition states and products for the self-reaction of HO2 calculated at different
levels of theory with B3LYP/6-311G(d, p) optimized geometries
Energiesb
Species
ZPEa
B3LYP/6-311G (d, p)
MP2/6-311G(d, p)
MP2/6-311zG(3df, 2p)
CCSD(T)/6-311G (d, p)
G2M
HO2 z HO2
LM1a
LM1b
LM2a
LM2b
LM3a
LM3b
LM4
LM5
LM6
LM7
LM8
TS1
TS2
TS3
TS4
TS5
TS6
TS7
TS8
TS9
TS10
TS11
TS12
H2O2 z 3O2
H2O z O3
H2O2 z 1O2
H2 z 2O2
17.7
21.0
21.0
21.0
21.0
21.1
21.1
21.4
21.3
20.5
19.6
20.5
19.2
19.4
18.4
19.3
14.8
18.2
21.1
20.5
21.2
17.7
18.9
17.4
18.9
17.9
18.9
11.0
2301.900816
210.9
210.9
210.5
210.5
211.4
211.4
10.1
12.0
214.8
27.4
214.6
27.0
23.7
32.8
13.7
75.4
15.6
21.7
27.3
25.2
25.5
26.7
27.8
235.0
210.9
3.9
25.2
2301.1704524
220.7
220.7
221.5
221.5
221.5
221.5
223.9
222.1
211.5
26.4
211.4
21.1
24.3
6.5
210.1
68.8
5.9
211.1
217.1
214.7
2.5
23.3
2.3
252.9
244.2
220.9
223.1
2301.353157
226.9
226.9
227.9
227.9
227.9
227.9
231.9
230.6
211.3
25.9
211.3
24.9
27.9
6.3
215.0
67.4
20.2
217.2
223.4
220.3
2.6
23.1
2.1
252.6
252.1
222.5
216.0
2301.229014
212.1
212.1
212.2
212.2
212.9
212.9
3.5
5.3
212.5
26.6
212.4
11.2
9.1
5.7
9.3
81.7
13.9
22.7
28.8
26.0
1.6
23.9
20.06
239.7
221.9
29.1
29.2
2301.44973
218.2
218.2
218.5
218.5
219.1
219.1
24.1
22.8
29.49
24.3
29.5
5.6
3.9
2.9
2.8
74.2
5.2
28.6
215.3
211.4
1.7
22.6
20.5
238.2
232.8
212.6
25.6
a
Values are in units of kcal mol21. bThe total energies of the reactants (2 6 HO2) at different level are given in au (Eh) and the relative energies
(relative to the reactants) of other species at the corresponding levels are given in units of kcal mol21, ZPE corrections are included only in the
G2M energies.
basis set expansion and high-level correlation, they lie below
the reactants by 4.1 and 2.8 kcal mol21 (with ZPE corrections),
respectively. It is apparent that the use of larger basis sets with
high-level treatment of electronic correlation corrections is
necessary to properly describe these minima.
As alluded to above, Schaefer and co-workers56–58 have
reported two singlet chain-structure minima with C1 and C2
symmetry; they estimated the dissociation energies D0 for the
lowest minima with chain structures to be y11 kcal mol21
(DZ z P CI).55 These two structures are similar to our
structures LM1a and LM3a as aforementioned. One sixmember-ring singlet minimum was also located in their work
using the two-configuration DZ (TC) SCF method56 and found
to be only 0.01 kcal mol21 above the analogous triplet minima
located with singlet DZ SCF method.56 In our calculation, the
six-member-ring singlet minimum LM6 was located only when
the UHF wavefunctions were used. At the G2M level, the
energy is 0.1 kcal mol21 lower than that of the corresponding
triplet state to be described below.
Triplet intermediates. As depicted in Fig. 4, the products
H2O2 z 3O2 can be formed via two triplet channels which
involve different intermediates. First, HO2 and HO2 can form a
one-hydrogen-bond chain intermediate, LM7 (see Fig. 1) by
head-to-tail association. The hydrogen bond length (O…H) in
this molecule is 1.861 Å which is shorter than the experimental
O…H distance, 2.02 Å, of a water dimer.65 The OHO bond
angle is 173.8u. It can be seen that the structures of the two
HO2 fragments in LM7 are almost the same as that of the
HO2 monomer; the O–O bond length changes are
20.004 yz 0.001 Å and HOO bond angle changes are
20.8u yz 0.2u. The bonding energy D0 is predicted to be
4.3 kcal mol21 at the G2M level, which is close to the
dimerization energy about 5 kcal mol21 found for water.66–68
The two HO2 radicals can also form a planar six-member-ring
4
PhysChemComm, 2001, 23, 1–6
intermediate LM8 with two hydrogen bonds. The two equal
O–H bond lengths are 1.809 Å at the B3LYP/6-311G (d, p)
level; they are shorter than those of 2.192, 2.242 and 1.967 Å
predicted at the HF/DZP, HF/DZ and TZ2P z diff-CISD
levels, respectively, by Schaefer et al.56–58 We also examined
this structure at the B3LYP/6-311zzG (d, p) and MP2/
6-311G (d, p) levels; the corresponding O–H bond lengths are
1.844 and 1.855 Å, respectively. From this comparison, we see
that the hydrogen bond length is sensitive to the methods
employed. The O–O bond lengths also vary with different
methods; they are 1.309, 1.367 and 1.305 Å at the HF/DZP,
HF/DZ and TZ2P z diff-CISD levels, respectively, in
Schaefer’s calculations.56–58 The values obtained in our
calculation are 1.324, 1.324 and 1.298 Å at the B3LYP/
6-311G (d, p), B3LYP/6-311zzG (d, p) and MP2/6-311G
(d, p) levels, respectively (Fig. 1 only shows the structures
obtained at the B3LYP/6-311G (d, p) level). These values can
be compared with the predicted (1.328 Å) and experimental
(1.314 Å) O–O bond length in HOO.69 In LM8, the HOO bond
angle of 103.9u predicted in our calculation can be compared
with 105.6, 107.3 and 104.6u predicted by HF/DZ z P,56 HF/
DZ56 and CISD/TZ2P z diff58 level calculations, respectively.
The O–H bond length has relatively minor changes by different
methods. The bonding energy D0 of LM8 is 9.5 kcal mol21 at
the G2M level; this is slightly larger than that of y7 kcal mol21
estimated by Schaefer and co-workers.57
B. Product formation
Although some of stable minima were discussed in the
literature as cited above,56–58 to our knowledge, the full
potential energy surfaces for the formation of different
products have not been reported. In this section, we will
discuss the mechanisms for product formation.
(a) Singlet product channels. H2O2 z O2 (1D). O2 (1D) can
only be produced through a singlet surface, as shown in Fig. 3.
There are four possible channels. Channels a and b are
direct abstraction reactions via transition states TS1 and
TS2, respectively, corresponding to the trans–cis–trans and
trans–trans–trans structures as shown in Fig. 2. They lie 5.6 and
3.9 kcal mol21 above the reactants, respectively. The third
channel, c, occurring by the singlet chain intermediate LM1a,
can produce H2O2 z O2 (1D) via TS3 with a barrier of
3.0 kcal mol21 above the reactants. The structure of TS3 seems
to be looser with an imaginary frequency of 489 cm21. IRC
results with a smaller step size (0.01 u21/2 a0) along the reaction
path indicate that the TS3 directly connects with the
H2O2 z O2 (1D) products and the intermediate LM1a. The
fourth channel occurs by LM4 producing H2O2 z O2 (1D) via
TS4 with a 2.8 kcal mol21 barrier relative to the reactants.
H2 z 2O2. There have been reports8–11 that H2 z 2O2
products were formed in experiments, but the product ratios
are uncertain, varying from 0 to 9%. In this calculation, the
barrier for formation of H2 z 2O2 also predicted to be rather
high, 74.2 kcal mol21 at the G2M level, and an IRC calculation
showed that the products are produced from LM2a via TS5.
The transition state TS5 (Fig. 2) has a six-member ring
structure with C2v symmetry. This channel is exothermic
with an exothermicity of 5.6 kcal mol21. Apparently, this
channel is kinetically unimportant because of its higher barrier.
H2O z O3. In the intermediate LM3a, one of the terminal
H atom moves forward to the O atom attached to the other H
atom to form a five-member-ring transition state TS6, followed
by H2O elimination to form H2O and O3. The breaking O–O
and O–H bonds are 1.970 and 1.157 Å, which are 0.534 and
0.187 Å longer than those of in LM3a, respectively. The
relative energy of TS6 is 5.2 kcal mol21 above the reactants and
the exothermicity for the production of O3 z H2O is
32.8 kcal mol21 at the G2M level. The relatively high barrier
for the formation O3 implies that this channel is unimportant at
low temperatures. Our result is qualitatively consistent with
experimental result of Niki et al.70 in which 2HO2 A
O3 z H2O channel was determined to be less than 0.1% of the
total reaction.
Isomerization of the HO4H chain intermediates. The HO4H
chain intermediates can isomerize to each other through the
rotation of the HO2 group along the newly formed O–O bond.
TS7 is the isomerization transition state with Cs symmetry
between LM1a and LM2a; the barrier of this process lies
8.6 kcal mol21 below the reactants. In TS7, the noticeable
changes are that the bridging O–O bond increases by about
0.2 Å and the O–O bond in the HO2 group decreases by about
0.08 Å compared with those in LM1a and LM2b. TS8
corresponds to the transition state for the isomerization of
LM2a and LM3a with C1 symmetry; it has only 3.2 kcal mol21
isomerization barrier. The final rotational transition state is
TS9 which connects LM1a and LM3a with an isomerization
barrier of 6.8 kcal mol21; the structure change is similar to that
of TS7.
(b) Triplet product channels. H2O2 z O2 (3Sg2). As shown
in Fig. 4, the ground state O2 can be produced via two triplet
channels. First, the two HO2 molecules form a one-hydrogenbonded chain-structure intermediate LM7 barrierlessly, following by dissociation via TS10 with a similar structure to
produce H2O2 and the ground state O2. In TS10, the forming
H–O and breaking O–H bond lengths are 0.414 Å shorter and
0.059 Å longer than those of in LM7, respectively. The relative
energy of TS10 is 1.7 kcal mol21 above the reactants at the
G2M level. Second, the two HO2 form a double-hydrogenbonded complex LM7 or LM8 with no barrier; either
intermediate can also be formed via a rotational transition
state (TS11) with only 1.7 kcal mol21 barrier. LM8 can
dissociate via TS12 to produce H2O2 z O2 (3Sg2) with a
barrier of 9.0 kcal mol21. We should mention that TS12 has a
mirror structure TS12’ (see Fig. 1) with the same energy. This
process is apparently the major channel for H2O2 z 3O2
formation.
4. Conclusion
Several singlet and triplet intermediates can be formed in the
dimerization of HO2 radicals. They are: six singlet chainstructure intermediates with the dissociation energies
D0 ~ 18.2–19.1 kcal mol21, two loose singlet four-memberring intermediates with D0 ~ 2.8 and 4.1 kcal mol21, two
hydrogen-bonded six-member-ring intermediates (singlet and
triplet) with D0 # 9.5 kcal mol21 and one hydrogen-bonded
triplet open-structure intermediate with D0 # 4.3 kcal mol21.
The chain-structure with C1 symmetry is the most stable one
due to its intra-molecular hydrogen bonding.
Those intermediates can dissociate to produce different
products via several transition states. The transition states
corresponding to the production of H2 z 2O2 and H2O z O3
lie above the reactants at 74.2 and 5.2 kcal mol21 respectively.
The formation of the H2O2 z 3O2 products is found to be the
most favorable channel in the self-reaction of HO2 with the
transition state lying below the reactants by 0.5 kcal mol21.
The rate constants for all the channels will be calculated and
reported in the near future.
Acknowledgements
The authors are grateful for the support of this work by the
Office of Naval Research, the US Navy, under the contract No.
N00014-89-J-1494.
References
1 M. E. Jenkin, Proc. EUROTRAC Symp. 98: Transp. Chem.
Transform. Troposphere, ed. P. M. Borrell and P. Borrell, WIT
Press, Southampton, 1999, vol. 1, pp. 33–42.
2 A. Roger, Atmos. Environ., 2000, 34, 2063.
3 C. A. Taatjes and D. B. Oh, Appl. Opt., 1997, 36, 5817.
4 M. J. Kurylo, P. A. Ouellette and A. H. Laufer, J. Phys. Chem.,
1986, 90, 437.
5 R. Simonaitis and J. Heicklen, J. Phys. Chem., 1982, 86, 3416.
6 S. P. Sander, M. Peterson and R. T. Watson, J. Phys. Chem., 1982,
86, 1236.
7 H. Niki, P. D. Maker, C. M. Savage and L. P. Breitenbach, Chem.
Phys. Lett., 1980, 73, 43.
8 S. L. Stephens, J. W. Birks and R. J. Glinski, J. Phys. Chem., 1989,
93, 8384.
9 R. J. Glinski and J. W. Birks, J. Phys. Chem., 1985, 89, 3449.
10 R. R. Baldwin, C. E. Dean, M. R. Honeyman and R. W. Walker,
J. Chem. Soc., Faraday Trans., 1984, 80, 3187.
11 K. A. Sahetchian, A. Heiss and R. Rigny, J. Phys. Chem., 1987, 91,
2382.
12 J. Sehested, J. T. Mogelberg, K. Fagerstrom, G. Mahmoud and
T. J. Wallington, Int. J. Chem. Kinet., 1997, 29, 673.
13 W. B. DeMore, S. P. Sander, D. M. Golden, R. F. Hampson,
M. J. Kurylo, C. J. Howard, A. R. Ravishankara, C. E. Kolb and
M. J. Molina, JPL Publ., 1997, 97.
14 R. Atkinson, D. L. Baulch, R. A. Cox, R. F. Jr. Hampson,
J. A. Kerr, M. J. Rossi and J. Troe, J. Phys. Chem. Ref. Data,
1997, 26, 1329.
15 M. M. Maricq and J. J. Szente, J. Phys. Chem., 1994, 98, 2078.
16 D. L. Baulch, C. J. Cobos, R. A. Cox, P. Frank, G. Hayman,
Th. Just, J. A. Kerr, T. Murrells, M. J. Pilling, J. Troe,
R. W. Walker and J. Warnatz, J. Phys. Chem. Ref. Data, 1994,
23, 847.
17 O. Dobis and S. W. Benson, J. Am. Chem. Soc., 1993, 115, 8798.
18 J. N. Crowley, F. G. Simon, J. P. Burrows, G. K. Moortgat,
M. E. Jenkin and R. A. Cox, J. Photochem. Photobiol., A, 1991, 60,
1.
PhysChemComm, 2001, 23, 1–6
5
19 V. P. Bulatov, Y. V. Matyagin, O. M. Sarkisov and
E. A. Sviridenkov, Khim. Fiz., 1991, 10, 1224.
20 P. D. Lightfoot, B. Veyret and R. Lesclaux, J. Phys. Chem., 1990,
94, 708.
21 H. Hippler, J. Troe and J. Willner, J. Chem. Phys., 1990, 93, 1755.
22 P. D. Lightfoot, B. Veyret and R. Lesclaux, Chem. Phys. Lett.,
1988, 120, 150.
23 B. Y. Andersson, R. A. Cox and M. E. Jenkin, Int. J. Chem. Kinet.,
1988, 20, 283.
24 K. McAdam, B. Veyret and R. Lesclaux, Chem. Phys. Lett., 1987,
39, 133.
25 W. Tsang and R. F. Hampson, J. Phys. Chem. Ref. Data, 1986, 15,
1087.
26 G. A. Takacs and C. J. Howard, J. Phys. Chem., 1986, 90, 687.
27 W. J. Pitz and C. K. Westbrook, Combust. Flame, 1986, 63, 113.
28 M. J. Kurylo, P. A. Ouellette and A. H. Laufer, J. Phys. Chem.,
1986, 90, 437.
29 F. C. Cattell, J. Cavanagh, R. A. Cox and M. E. Jenkin, J. Chem.
Soc., Faraday Trans. 2, 1986, 82, 1999.
30 M. Mozurkewich and S. W. Benson, Int. J. Chem. Kinet., 1985, 17,
787.
31 J. Warnatz, Combustion Chemistry, ed. W. C. Gardiner, Jr.,
Springer-Verlag, New York, 1984.
32 G. A. Takacs and C. J. Howard, J. Phys. Chem., 1984, 88, 2110.
33 S. P. Sander, J. Phys. Chem., 1984, 88, 6018.
34 V. B. Rozenshtein, Yu. M. Gershenzon, S. D. Il’in and
O. P. Kishkovitch, Chem. Phys. Lett., 1984, 112, 473.
35 C. C. Kircher and S. P. Sander, J. Phys. Chem., 1984, 88, 2082.
36 B. A. Thrush and G. S. Tyndall, Chem. Phys. Lett., 1982, 92, 232.
37 B. A. Thrush and G. S. Tyndall, J. Chem. Soc., Faraday Trans. 2,
1982, 78, 1469.
38 S. P. Sander, M. Peterson and R. T. Watson, J. Phys. Chem., 1982,
86, 1236.
39 R. Patrick and M. J. Pilling, Chem. Phys. Lett., 1982, 91, 343.
40 R.-R. Lii, M. C. Sauer and S. Gordon, J. Phys. Chem., 1981, 85,
2833.
41 J. P. Burrows, R. A. Cox and R. G. Derwent, J. Photochem., 1981,
16, 147.
42 R.-R. Lii, R. A. Gorse, M. C. Sauer and S. Gordon, J. Phys.
Chem., 1980, 84, 813.
43 C. J. Hochanadel, T. J. Sworski and P. J. Ogren, J. Phys. Chem.,
1980, 84, 3274.
44 J. P. Burrows, D. I. Cliff, G. W. Harris, B. A. Thrush and
J. P. T. Wilkinson, Proc. R. Soc. London, Ser. A, 1980, 368, 463.
45 B. A. Thrush and J. P. T. Wilkson, Chem. Phys. Lett., 1979, 66,
441.
46 R.-R. Lii, R. A. Gorse, Jr., M. C. Sauer, Jr. and S. Gordon,
J. Phys. Chem., 1979, 83, 1803.
6
PhysChemComm, 2001, 23, 1–6
47 R. A. Graham, A. M. Winer, R. Atkinson and J. N. Pitts, Jr.,
J. Phys. Chem., 1979, 83, 1563.
48 R. A. Cox and J. P. Burrows, J. Phys. Chem., 1979, 83, 2560.
49 J. P. Burrows, D. I. Cliff, G. W. Harris, B. A. Thrush and
J. P. T. Wilkinson, Proc. R. Soc. London, Ser. A, 1979, 368, 463.
50 E. J. Hamilton, Jr. and R.-R. Lii, Int. J. Chem. Kinet., 1977, 9, 875.
51 E. J. Hamilton, Jr., J. Chem. Phys., 1975, 63, 3682.
52 A. C. Lloyd, Int. J. Chem. Kinet., 1974, 6, 169.
53 T. T. Paukert and H. S. Johnston, J. Chem. Phys., 1972, 56, 2824.
54 C. J. Hochanadel, J. A. Ghormley and P. J. Ogren, J. Chem. Phys.,
1972, 56, 4426.
55 H. Sugimoto, D. T. Sawyer and J. R. Kanofsky, J. Am. Chem.
Soc., 1988, 110, 8707.
56 G. Fitzgerald and H. F. Schaefer III, J. Chem. Phys., 1984, 81, 362.
57 G. Fitzgerald, T. J. Lee, R. J. Bartlett and H. F. Schaefer III,
J. Chem. Phys, 1985, 83, 6275.
58 J. T. Fermann, B. C. Hoffman, G. S. Tschumper and H. F. Schaefer
III, J. Chem. Phys., 1997, 106, 5102.
59 A. D. Becke, J. Chem. Phys., 1993, 98, 5648.
60 A. D. Becke, J. Chem. Phys., 1992, 96, 2155.
61 A. D. Becke, J. Chem. Phys., 1992, 97, 9173.
62 C. Lee, W. Yang and R. G. Parr, Phys. Rev., 1988, 37B, 785.
63 A. M. Mebel, K. Morokuma and M. C. Lin, J. Chem. Phys., 1995,
103, 7414.
64 M. J. Frisch, G. W. Trucks, H. B. Schlegel, P. M. W. Gill,
B. G. Johnson, M. A. Robb, J. R. Cheeseman, T. Keith,
G. A. Petersson, J. A. Montgomery, K. Raghavachari, M. A.
Al-Laham, V. G. Zakrzewski, J. V. Ortiz, J. B. Foresman,
J. Cioslowski, B. B. Stefanov, A. Nanayakkara, M. Challacombe,
C. Y. Peng, P. Y. Ayala, W. Chen, M. W. Wong, J. L. Andres,
E. S. Replogle, R. Gomperts, R. L. Martin, D. J. Fox, J. S. Binkley,
D. J. Defrees, J. Baker, J. P. Stewart, M. Head-Gordon,
C. Gonzalez and J. A. Pople, Gaussian 98, Revision A.1, Gaussian,
Inc., Pittsburgh, PA, 1998.
65 J. A. Odutola and T. R. Dyke, J. Chem. Phys., 1980, 72, 5062.
66 G. H. F. Diercksen, W. P. Kraemer and B. O. Roos, Theor. Chim.
Acta, 1975, 36, 249.
67 O. Matsuoka, E. Clementi and M. Yoshimine, J. Chem. Phys.,
1976, 64, 1351.
68 H. A. Gebbie, W. J. Borroughs, J. Chamberlain, J. E. Harris and
R. G. Jones, Nature, 1969, 221, 143.
69 C. E. Barnes, J. M. Brown and H. E. Radford, J. Mol. Spectrosc.,
1980, 84, 179.
70 H. Niki, P. D. Maker, C. M. Savage and L. P. Breitenbach, Chem.
Phys. Lett., 1980, 73, 43.