Published on Web 02/10/2010
Atomistic Simulation of NO Dioxygenation in Group I
Truncated Hemoglobin
Sabyashachi Mishra and Markus Meuwly*
Department of Chemistry, UniVersity of Basel, Basel, Switzerland
Received September 22, 2009; E-mail: [email protected]
Abstract: NO dioxygenation, i.e., the oxidation of nitric oxide to nitrate by oxygen-bound truncated
hemoglobin (trHbN) is studied using reactive molecular dynamics simulations. This reaction is an important
step in a sequence of events in the overall NO detoxification reaction involving trHbN. The simulations
(≈160 ns in total) reveal that the reaction favors a pathway including (i) NO binding to oxy-trHbN, followed
by (ii) rearrangement of peroxynitrite-trHbN to nitrato-trHbN, and finally (iii) nitrate dissociation from nitratotrHbN. Overall, the reactions occur within tens of picoseconds and the crossing seam of the reactant and
product are found to be broad. The more conventional pathway, where the peroxynitrite-trHbN complex
undergoes peroxide cleavage to form free NO2 and oxo-ferryl trHbN, is found to be too slow due to a
considerable barrier involved in peroxide bond dissociation. The energetics of this step is consistent with
earlier electronic structure calculations and make this pathway less likely. The role of Tyr33 and Gln58 in
the NO dioxygenation has been investigated by studying the reaction in mutants of trHbN. The mutation
study suggests that residues Tyr33 and Gln58 preorient the reactive ligands through a highly dynamical
H-bonding network which facilitates the reaction. In particular, the Y33A mutation leads to a significant
retardation in NO dioxygenation, in agreement with experiments which reveal a strong influence of the
protein environment on the reaction rate.
Introduction
Heme proteins are well-known for their role in ligand
transport.1 With the recent discovery of heme proteins in the
lower strata of the animal and plant kingdoms,2,3 these proteins
have been established to be implicated in a range of functional
roles including neurotransmission, inhibition of mitochondrial
respiration, oxidative phosphorylation, catalytic peroxidation,
and NO scavenging.4-7 NO scavenging, where the toxic NO is
converted to harmless nitrate, has wide-ranging physiological
significance.8 This reaction was first reported in myoglobin (Mb)
by Doyle et al.,9 which has since been extensively studied by
various experimental and computational methods. Recent NMR
studies of the reaction provide concrete evidence of NO
dioxygenation in myoglobin.10 From stopped-flow spectroscopy,
the second-order rate constants for the reaction between NO
and oxy-myoglobin and oxy-hemoglobin, at neutral pH, are
(1) Wittenberg, J. B. Physiol. ReV. 1970, 50, 559–636.
(2) Kundu, S.; Trent, J. T.; Hargrove, M. S. Trends Plant Sci. 2003, 8,
387–393.
(3) Garrocho-Villegas, V.; Gopalasubramaniam, S. K.; Arredondo-Peter,
R. Gene 2007, 398, 78–85.
(4) Wittenberg, J. B.; Wittenberg, B. A. J. Exp. Biol. 2003, 206, 2011–
2020.
(5) Merx, M. W.; Goedecke, A.; Floegel, U.; Schrader, J. FASEB. J. 2005,
19, 1015-1017.
(6) Garry, D. J.; Meeson, A.; Yan, Z.; Williams, R. S. Cell. Mol. Life
Sci. 2000, 57, 896–898.
(7) Marinis, E.; Casella, L.; Ciaccio, C.; Coletta, M.; Visca, P.; Ascenzi,
P. IUBMB Life 2009, 61, 62–73.
(8) Hausladen, A.; Gow, A.; Stamler, J. S. Proc. Natl. Acad. Sci. U.S.A.
2001, 98, 10108–10112.
(9) Doyle, M. P.; Hoekstra, J. W. J. Inorg. Biochem. 1981, 14, 351–358.
(10) Floegel, U.; Merx, M. W.; Goedecke, A.; Decking, U. K. M.; Schrader,
J. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 735–740.
2968
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J. AM. CHEM. SOC. 2010, 132, 2968–2982
determined to be 4.36 × 107 and 8.9 × 107 M-1 s-1,
respectively.11,12 However, the details and sequence of events
that constitute the reaction mechanism and nature of the
intermediates remain elusive.13
With the employment of stopped flow kinetic measurements,
Bourassa et al. proposed a reaction pathway for NO oxidation
in Mb where the peroxynitrite (Fe(III)OONO) intermediate
undergoes O-O homolysis to form free nitrite radicals
(NO2).14 In this model, the free nitrite radical then binds to the
oxo-ferryl (Fe(IV)dO) group to form the nitrato complex
(Fe(III)ONO2), which ultimately leads to free nitrate. This
reaction mechanism proposes heme-bound peroxynitrite, oxoferryl with free NO2, and heme-bound nitrato intermediates for
the NO oxidation reaction.14 A similar pathway is also observed
when peroxynitrite is reacted with metmyoglobin.15 On the other
hand, Herold et al. have provided evidence for a Fe(III)OONO
(high-spin) intermediate in both oxy-Mb and oxy-Hb by rapidscan ultraviolet-visible (UV-vis) spectroscopy,12,16 which was
later corroborated via electron paramagnetic resonance (EPR)
spectroscopy.17 This intermediate is however only observed
(11) Eich, R. F.; Li, T.; Lemon, D. D.; Doherty, D. H.; Curry, S. R.; Aitken,
J. F.; Mathews, A. J.; Johnson, K. A.; Smith, R. D.; Phillips, G. N.,
Jr.; Olson, J. S. Biochemistry 1996, 35, 6976–6983.
(12) Herold, S.; Exner, M.; Nauser, T. Biochemistry 2001, 40, 3385–3395.
(13) Gardner, P. R.; Gardner, A. M.; Brashear, W. T.; Suzuki, T.; Hvitved,
A. N.; Setchell, K. D.; Olson, J. S. J. Inorg. Biochem. 2006, 100,
542–550.
(14) Bourassa, J. L.; Ives, E. L.; Marqueling, A. L.; Shimanovich, R.;
Groves, J. T. J. Am. Chem. Soc. 2001, 123, 5142–5143.
(15) Su, J.; Groves, T. J. Am. Chem. Soc. 2009, 131, 12979–12988.
(16) Herold, S. FEBS Lett. 1999, 443, 81–84.
(17) Olson, J. S.; Foley, E. W.; Rogge, C.; Tsai, A.-L.; Doyle, M. P.;
Lemon, D. D. Free Radical Biol. Med. 2004, 36, 685–697.
10.1021/ja9078144  2010 American Chemical Society
Atomistic Simulation of NO Dioxygenation
under alkaline conditions (pH ) 9.5).12,17 At neutral pH, the
reaction proceeds without any observed intermediates,12 suggesting a rapid rearrangement of the Fe(III)OONO intermediate
to nitrate. The kinetics of the intermediate in NO dioxygenation
is found to be strongly influenced by pH.12 The pH dependence
of the intermediate has been investigated with density functional
theory (DFT) calculations on models that mimic the active site
of the protein at different pH.18 However, the computations did
not provide an unambiguous explanation of the observed pH
dependence of the decay rate of the intermediate. Additionally,
in the experiments of Herold et al., no detectable OONO- or
NO2- are released,12,16 which is at variance with the pathway
proposed by Groves and co-workers.14,15 Herold et al. observed
quantitative nitrate formation and concluded that the peroxynitrite coordinated to heme-Fe rapidly undergoes a rearrangement
to nitrate without nitrating the globin residues.12 Their analysis
is, however, inconclusive so as to decide if the rearrangement
is concerted or not, since the lack of detection of oxo-ferryl
species (obtained from O-O homolysis of the peroxynitrite
species) may either indicate that the intermediate is not formed
at all or it might react too fast to accumulate for experimental
detection.
In a reaction of NO2 with oxo-ferryl myoglobin, a rate of
1.2 × 107 M-1 s-1 for the oxidation of NO2 to nitrate via the
Fe(III)ONO2 intermediate was found.19 The assignment of the
intermediate was based on thermo-kinetic arguments, and it was
suggested that the intermediates observed in both, the Fe(IV)dO
+ NO2 reaction (ref 19) and the Fe(II)sO2 + NO reaction (ref
12) are the same, i.e., Fe(III)ONO2, which is in contrast to the
peroxynitrite intermediate reported in oxy-myoglobin12 (see
previous paragraph). The Fe(III)ONO2 intermediate has a similar
decay constant (190 ( 20 s-1) as the Fe(III)OONO intermediate
(205 ( 5 s-1) reported earlier.12 It should be noted that the
evidence for the peroxynitrite intermediate obtained from EPR
spectroscopy in ref 17 cannot unambiguously distinguish
between Fe(III)ONO2 and Fe(III)OONO.20 In a recent resonance
Raman study, the intermediate in myoglobin has been assigned
to the Fe(III)ONO2 complex,21 although the temporal resolution
of the experiment does not allow one to determine whether the
peroxynitrite intermediate is formed during the reaction.21
DFT calculations for model heme systems have suggested
that the reaction progresses via the peroxynitrite (Fe(III)OONO)
intermediate which rapidly undergoes homolytic O-O bond
fission, and the resulting NO2 recombines with oxo-ferryl
(Fe(IV)dO) species even faster.18 Each of the steps are found
to have moderate to large (2-10 kcal/mol) activation barriers.
From electronic structure calculations, it was concluded that
the peroxynitrite intermediate is too short-lived to have been
experimentally detected. It should be noted that the DFT
calculation finds a low-spin peroxynitrite instead of a high-spin
Fe(III)OONO as suggested from EPR experiments.17
In plant hemoglobin (leghemoglobin or Lb), even under
alkaline conditions, no intermediate in the NO oxidation reaction
was reported,22 whereas a reactive intermediate (Fe(III)OONO
or Fe(III)ONO2) was detected for the reaction in Hb and Mb at
(18) Blomberg, L. M.; Blomberg, M. R. A.; Siegbahn, P. E. M. J. Biol.
Inorg. Chem. 2004, 9, 923–935.
(19) Goldstein, S.; Merenyi, G.; Samuni, A. J. Am. Chem. Soc. 2004, 126,
15694–15701.
(20) Hvitved, A.; Foley, E.; Rogge, C.; Tsai, A.-L.; Olson, J. Free Radical
Biol. Med. 2005, 39, S101–S101.
(21) Yukl, E. T.; de Vries, S.; Moenne-Loccoz, P. J. Am. Chem. Soc. 2009,
131, 7234–7235.
(22) Herold, S.; Puppo, A. J. Biol. Inorg. Chem. 2005, 10, 935–945.
ARTICLES
alkaline pH.12 The observation that the intermediate decays
considerably faster in Lb than in Hb/Mb suggests that the protein
environment is important for details of the reaction. A major
difference between the structures of Hb/Mb and Lb is the
presence of a wider and more flexible heme pocket in Lb.23
The mechanistic details of NO dioxygenation is likely to be
influenced by the distal site residues of the particular globin
chain, and hence, intermediates found in one type of globin do
not necessarily occur in other globins.
The role of flavohemoglobins (FHb, a group of hemoglobins
found in bacteria and yeasts) in protecting against nitrosative
stress is now well established.8,24,25 While under aerobic
conditions, O2 is the preferred ligand for binding to heme, it
has been shown that under physiological NO/O2 concentrations,
FHbs bind NO at the heme iron and catalyze the reaction of
heme-bound NO with O2 to produce nitrate.8 The reaction where
the heme-bound O2 oxidizes free NO has the advantage of high
reactivity of both, the free NO radical as well as the superoxide
nature of heme-bound O2. The reaction of bound NO and free
O2 in FHbs, on the other hand, is assisted by the presence of a
flavoreductase domain together with Hb.26 For human Hb, the
reaction of heme-bound NO with free O2 has been shown to
proceed in three steps, where the first step involves the
dissociation of NO radical from heme, which then binds to O2,
and finally the bound O2 oxidizes free NO.27,28
In truncated hemoglobin N (trHbN) of Mycobacterium
tuberculosis, the rate for NO dioxygenation is faster compared
to that in vertebrate Mbs and Hbs. It was suggested that this is
due to a tunnel system in the protein matrix and ligand
stabilizing residues in the heme active site.29 Irrespective of the
reaction mechanism, it is commonly agreed that the diffusion
controlled migration of the ligand to the heme active site is the
slowest process in NO detoxification and, hence, it is the rate
determining step.11,30 The second order rate constant of NO
reaction with oxy-trHbN is determined to be 7.5 × 108 M-1
s-1, which is about an order of magnitude faster than in vertebrate Hb.29 The in vitro kinetics for NO dioxygenation in oxytrHbN is studied under aerobic conditions,29 although in vivo
trHbN operates at microaerobic conditions. Under such circumstances, which ligand binds to the heme is determined by the
relative abundance of NO and O2 as well as the ligand affinity
of the protein. In group II truncated hemoglobin (trHbO) of
Mycobacterium tuberculosis, the rate constant for NO binding
to deoxygenated trHbO (0.18 µM-1 s-1 (80%) and 0.95 µM-1
s-1 (20%)) is only marginally larger than the corresponding rate
constant for O2 binding (0.11 µM-1 s-1 (80%) and 0.85 µM-1
s-1 (20%)).31,32 For trHbN of Mycobacterium tuberculosis,
(23) Hargrove, M. S.; Barry, J. K.; Brucker, E. A.; Berry, M. B.; Phillips,
G. N., Jr.; Olson, J. S.; Arredondo-Peter, R.; Dean, J. M.; Klucas,
R. V.; Sarath, G. J. Mol. Biol. 2007, 266, 1032–1042.
(24) Gardner, P. R.; Gardner, A. M.; Martin, L. A.; Salzman, A. L. Proc.
Natl. Acad. Sci. U.S.A. 1998, 95, 10378–10383.
(25) Hausladen, A.; Gow, A. J.; Stamler, J. S. Proc. Natl. Acad. Sci. U.S.A.
1998, 95, 14100–14105.
(26) Ermler, U.; Siddiqui, R. A.; Cramm, R.; Friedrich, B. EMBO J. 1995,
14, 6067–6077.
(27) Herold, S.; Rock, G. Biochemistry 2005, 16, 6223–6231.
(28) Moller, J. K. S.; Skibsted, L. H. Chem.sEur. J. 2004, 10, 2291–2300.
(29) Ouellet, H.; Ouellet, Y.; Richard, C.; Labarre, M.; Wittenberg, B.;
Wittenberg, J.; Guertin, M. Proc. Natl. Acad. Sci. U.S.A. 2002, 99,
5902–5907.
(30) Angelo, M.; Hausladen, A.; Singel, D.; Stamler, J. S. Methods Enzymol.
2008, 436, 131–168.
(31) Ouellet, H.; Juszczak, L.; Dantsker, D.; Samuni, U.; Ouellet, Y. H.;
Savard, P.-Y.; Wittenberg, J. B.; Wittenberg, B. A.; Friedman, J. M.;
Guertin, M. Biochemistry 2003, 42, 5764–5774.
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Mishra and Meuwly
ARTICLES
which is the protein investigated here, the corresponding rate
constant was only determined for O2 binding (25 µM-1 s-1).32,33
In Mycobacterium leprae, the O2-mediated oxidation of trHbONO occurs with a reaction mechanism in which the heme-bound
NO is displaced by the O2 ligand in the first step followed by
the reaction of NO with the oxy-trHbO to give rise to nitrate.34
Given this sequence of events and the typically higher affinity
of Fe(II) toward NO than to O2, it is likely that under
physiological conditions NO dioxygenation of O2-bound heme
is one step, probably the last one, in a sequence of events in
NO detoxification. As far as possible intermediates of NO
dioxygenation are concerned, there has been no experimental
kinetics studies for trHbN. For oxy-trHbN, where the reaction
is 20 times faster at physiological conditions, no pH dependence
of the NO dioxygenation is known,29 contrary to oxy-Mb.
Furthermore, unlike that of flavohemoglobins,8 no steady state
turnover of NO or mass balance accounting of product has been
reported so far for trHb.30
Over the years, mixed quantum mechanics/molecular mechanics (QM/MM) has been used to study chemical reactions
in biological systems. In QM/MM, the reacting atoms are
described by quantum mechanics which are then embedded in
the classical force field of the surrounding atoms.35-37 The
computationally demanding QM part is the bottleneck of the
method that dictates the accessible time scale of the simulations.
Except for cases where the QM part is treated with semiempirical methods, the nuclear dynamics and conformational
sampling are typically not included in such studies. This is also
the case for the QM/MM work carried out so far on the reactions
of interest in the present work (see below).38,39 An alternative
approach to study chemical reactions in condensed phases is to
use empirical force fields with provisions to form and break
bonds. One such approach is empirical valence bond (EVB)40
which has been extensively used to investigate catalytic reactions
in biological systems. An alternative to EVB is adiabatic reactive
molecular dynamics (ARMD) which has been recently proposed.41-43 In ARMD, the reactant and product are treated with
individually parametrized force fields which differ in a small
number of terms. The algorithm employs an energy criterion
to decide when a crossing should occur. After a crossing is
detected, the two states are mixed over a short period of time,
and the simulation continues on the second surface.42,43 Such
an approach allows one to efficiently treat bond breaking and
bond formation reactions in the framework of classical MD
(32) Milani, M.; Pesce, A.; Nardini, M.; Ouellet, H.; Ouellet, Y.; Dewilde,
S.; Bocedi, A.; Ascenzi, P.; Guertin, M.; Moens, L.; Friedman, J. M.;
Wittenberg, J. B.; Bolognesi, M. J. Inorg. Biochem. 2005, 99, 97–
109.
(33) Couture, A.; Yeh, S.-R.; Wittenberg, B. A.; Wittenberg, J. B.; Ouellet,
Y.; Rousseau, D. L.; Guertin, M. Proc. Natl. Acad. Sci. U.S.A. 1999,
96, 11223–11228.
(34) Ascenzi, P.; Bolognesi, M.; Visca, P. Biochem. Biophys. Res. Commun.
2007, 357, 809–814.
(35) Warshel, A.; Levitt, M. J. Mol. Biol. 1976, 103, 227–249.
(36) Singh, U. C.; Kollman, P. A. J. Comput. Chem. 1986, 7, 718–730.
(37) Field, M. J.; Bash, P. A.; Karplus, M. J. Comput. Chem. 1990, 11,
700–733.
(38) Crespo, A.; Martı́, M. A.; Kalko, S. G.; Morreale, A.; Orozco, M.;
Gelpi, J. L.; Luque, F. J.; Estrin, D. A. J. Am. Chem. Soc. 2005, 127,
4433–4444.
(39) Martı́, M. A.; Bidon-Chanal, A.; Crespo, A.; Yeh, S.-R.; Guallar, V.;
Luque, F. J.; Estrin, D. A. J. Am. Chem. Soc. 2008, 130, 1688–1693.
(40) Warshel, A.; Weiss, R. M. J. Am. Chem. Soc. 1980, 102, 6218–6226.
(41) Meuwly, M.; Becker, O. M.; Stone, R.; Karplus, M. Biophys. Chem.
2002, 98, 183–207.
(42) Nutt, D.; Meuwly, M. Biophys. J. 2006, 90, 1191–1201.
(43) Danielsson, J.; Meuwly, M. J. Chem. Theory Comput. 2008, 4, 1083–
1093.
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simulations. With the use of ARMD, the nonexponential rebinding of NO in myoglobin42 and the conformational equilibrium in neuroglobin43 have been previously studied and provide
quantitative and novel insight into mechanistic aspects of the
reactions.
The fact that detailed experimental studies on NO dioxygenation in trHbN is rather scarce and the corresponding studies
in Mb and Hb provide conflicting and inconclusive views on
the mechanism of the reaction12,14,19,21 provides a strong
motivation to use state-of-the art computational techniques to
investigate the energetics and dynamics of this interesting and
challenging reactive system. In the present work, we have
studied the mechanistic details of the oxidation of nitric oxide
to nitrate by oxy-trHbN which recently has received considerable
experimental and computational attention.18,29,38 The reaction
between oxy-trHbN and NO is one of the steps in a sequence
of events during overall NO detoxification involving trHbN
under physiological conditions.
The NO dioxygenation in trHbN is about an order of
magnitude faster than in human Hb, which makes it an ideal
target for atomistic simulations. For this, ARMD is used together
with force fields for the reactive intermediates determined from
ab initio electronic structure calculations. The entire reaction is
divided into the following four steps:
Fe(II)-O2 + NO f Fe(III)[-OONO] O2-N distance
(I)
Fe(III)[-OONO] f Fe(IV)dO + NO2 O1-O2 distance
(II)
Fe(IV)dO + NO2 f Fe(III)[-ONO2] O1-N distance
(III)
Fe(III)[-ONO2] f Fe+(III) + [NO3]- Fe-O1 distance
(IV)
The right-hand side column of the above reaction steps
indicates the bond broken/formed in the reaction step. In step
I, the oxy-trHbN reacts with free NO to form a peroxynitrite
intermediate complex which then undergoes homolytic fission.
Step II involves production of the oxo-ferryl species and the
free NO2 radical. The free NO2 radical then attacks the oxoferryl species to form the heme-bound nitrato complex (step
III). Finally, the dissociation of the Fe-O bond results in free
NO3- and pentacoordinated heme (step IV). We have studied
each of the above reaction steps by analyzing the structural and
energetic requirement for the reaction, by characterizing the
reaction seam, and by estimating the kinetics of these steps.
Furthermore, we have explored the role of the protein in the
NO dioxygenation by studying the above steps in different
trHbN mutants. Finally, an alternative pathway which involves
a peroxynitrite to nitrato rearrangement is investigated because
a number of key intermediates postulated by steps I-IV were
not observed experimentally.
Computational Methods
Molecular Dynamics Simulations. The initial structure of the
protein is monomer A of the X-ray structure, protein data bank
entry 1IDR. The protein contains 131 amino acid residues, a
prosthetic heme group to which O2 is bound, and an NO ligand.
All MD simulations are carried out with the CHARMM22 force
field44 and the CHARMM program.45 Nonbonded interactions are
truncated at a distance of 14 Å by using a shift function for the
electrostatic terms and a switch algorithm for the van der Waals
Atomistic Simulation of NO Dioxygenation
(vdW) terms.46 All bonds involving hydrogen atoms are kept fixed
by using SHAKE.47 Initially, missing H atoms are added and
histidine residues are treated as δ-protonated. The heme group is
covalently bound to the Nε of residue His81, and the dioxygen
molecule is ligated to the Fe(II) atom of the heme group, while the
NO ligand is initially unbound. Since the aim of the simulations is
to study the redox reaction occurring in the active site surrounding
the heme group, the stochastic boundary method was used to
increase computational efficiency.48 The heme active site was
solvated by a water sphere of radius 25 Å, and the reaction region,
where Newtonian dynamics is used, had a radius of 20 Å. Water
molecules that overlap protein atoms are removed and a short
minimization was done. Then Langevin dynamics was performed
for heating and equilibration during 500 ps (at 300 K). The water
molecules are represented with the modified TIP3P potential.49 The
entire solvated system contains 6867 atoms.
Reactions I-IV are studied by employing the recently developed
ARMD algorithm.42,43 In this method, the potential energy surfaces
of the reactants VR and products VP are described with empirical
force fields that correctly describe geometric, energetic, and other
physical properties of the reactant and product states. Since VR and
VP are parametrized individually, they differ by a constant ∆ which
corresponds to the asymptotic energy difference between the two
states40,42,43 and which is the only free parameter in ARMD. In
other words, ∆ ensures that VR and VP share a common zero of
energy. The system is propagated on the lower of the two surfaces
by solving Newton’s equations of motion and the energy difference
∆E ) VR - VP is monitored. A surface crossing occurs whenever
∆E changes sign, and the system is promoted from one state to the
next by mixing the two potential energy surfaces (PESs) over a
short time window (typically a few femtoseconds).42,43
The asymptotic energy difference ∆ is determined as follows. If
sufficient experimental data is available (e.g., interconversion
rates),43 ∆ is chosen to reproduce such quantities. In the absence
of suitable reference quantities, an initial ∆0 is used from ab initio
calculations. In a next step, the sensitivity of the computed
observables (here reaction rates and the reaction seam) is assessed
through variation of ∆ around ∆0. This procedure is reminiscent
of ab initio parametrizations of EVB40,50 or of approximate valence
bond (AVB)51 although the parametrization of an off-diagonal
matrix element as a function of a configurational coordinate is not
necessary in ARMD, since the only progression coordinate in
ARMD is time. ∆ is expected to be influenced by structural changes
and the solvent environment which differentially stabilizes/
destabilizes the reactants or products. Therefore, microscopically
∆ should be viewed as an averaged quantity. In comparing EVB
with ARMD it is interesting to note that in the former a similar
quantity arises as the gas-phase formation energy of X-Y+ from
XY at infinite separation.40 When a bond-breaking/bond-formation
reaction is studied in a protein environment with ARMD, ∆ cannot
be calculated from electronic structure calculations because its value
depends on the instantaneous configuration of the system and
therefore it is only meaningful to view ∆ as a conformationally
averaged quantity. To sample configurational space, six snapshots
of the reactants in each of the reaction steps (reactions I-IV) were
considered and multiple ARMD trajectories from each of the initial
snapshots were initiated. This is done for a range of ∆ values for
each of the reaction steps studied in this work.
(44) MacKerell, A. D., Jr.; et al. J. Phys. Chem. B 1998, 102, 3586–3616.
(45) Brooks, B.; Bruccoleri, R.; Olafson, B.; States, D.; Swaminathan, S.;
Karplus, M. J. Comput. Chem. 1983, 4, 18–217.
(46) Steinbach, P. J.; Brooks, B. R. J. Comput. Chem. 1994, 15, 667–683.
(47) van Gunsteren, W.; Berendsen, H. Mol. Phys. 1977, 34, 1311–1327.
(48) Brooks, B.; Karplus, M. J. Chem. Phys. 1983, 79, 6312–6325.
(49) Jorgensen, W. L.; Chandrasekhar, J.; Madura, J. D.; Impey, R. W.;
Klein, M. L. J. Chem. Phys. 1983, 79, 926–935.
(50) Chang, Y.-T.; Miller, W. H. J. Phys. Chem. 1990, 94, 5884–5888.
(51) Grochowski, P.; Lesyng, B.; Bala, P.; McCammon, J. A. Int. J.
Quantum Chem. 1996, 60, 1143–1164.
ARTICLES
Ab Initio Determination of Force Field. The necessary force
fields for the different states in reactions I-IV were derived from
electronic structure calculations at the DFT/B3LYP level with the
6-31G** basis set that were carried out with Gaussian.52 The model
system contains the porphyrin ring, Fe atom, and an imidazole ring
representing the proximal histidine and the O2 and NO ligands.
The geometries of all five states in reactions I-IV were optimized
in each of their lowest three spin multiplicities (doublet, quartet,
and sextet), and the most stable spin multiplet is considered for
further investigation. All calculations were carried out with the
polarized continuum model (PCM), with ε ) 4, which corresponds
to a dielectric constant of protein and water medium surrounding
the protein.53 The present ab initio calculations are validated by
comparing them with previous work18,38 (see also the Supporting
Information). In particular, it was found that bound OONO is more
stable than free NO by 17.6 and 19.3 kcal/mol, in the gas and
solvent phases, respectively, which compares well with values
obtained previously, which are 13 and 15 kcal/mol, respectively.18,38
The remaining energetics are very similar to the results from
Blomberg et al. but they differ substantially from those by Crespo
et al., which employs, unlike the present work or the work of
Blomberg et al., a pseudopotential-based DFT method.18,38 Further
details are given in the Supporting Information. Mulliken charges
were calculated at the optimized geometries. Compared to the
charges used in the CHARMM force field, Mulliken charges are
often found to be too large. Therefore, they were rescaled in the
following way:54 First, the charges of the Fe and N-porphyrin atoms
were scaled to reproduce CHARMM charges for the heme system
(Table S1 in the Supporting Information), which leads to a net
charge of the heme group that differs from its usual value of -2.
The residual charge is then redistributed over the C atoms of the
porphyrin ring of the heme. An overview of all charges is given in
Table S2 in the Supporting Information. As can be seen, the residual
charges are often negligibly small.
Harmonic force constants for internal coordinates were determined from five energies calculated along the respective coordinate
around its equilibrium value. For bond lengths, the grid spacing is
0.01 Å whereas for bond angles and dihedrals it is 5°. The harmonic
force constants are determined from the second derivative of the
energy using the five-point rule55
f''(x) ≈
-f(x - 2h) + 16f(x - h) - 30f(x) + 16f(x + h) - f(x - 2h)
12h2
(1)
where h is the grid spacing. Since the bonds undergoing breaking
and formation in steps I-IV exhibit large fluctuations, the potential
energy curves are calculated over a wide range for bond distances
between 1 and 4 Å and the resulting energy profiles are fit to Morse
functions
VM ) De[1 - exp(-β(r - r0))]2
(2)
where De is the bond dissociation energy, β is the width of the
potential, and r0 is the equilibrium bond distance.
To validate the interaction potentials, total energies for snapshots
corresponding to the reactant, product, and the crossing points
obtained from five arbitrarily chosen ARMD trajectories for step I
were determined from DFT/6-31G** single point calculations, see
Figure 9 for energy differences between the reactant, product, and
transition state (TS) structures. The system which was used for these
(52) Frisch, M. J.; et al. Gaussian 03, revision C.02; Gaussian, Inc.:
Wallingford, CT, 2004.
(53) Blomberg, M. R. A.; Siegbahn, P. E. M.; Babcock, G. T. J. Am. Chem.
Soc. 1998, 120, 8812–8824.
(54) Nutt, D.; Meuwly, M. ChemPhysChem 2004, 5, 1710–1718.
(55) Abramowitz, M.; Stegun, I. A. Handbook of Mathematical Functions
with Formulas, Graphs, and Mathematical Tables; Dover: New York,
1970.
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Table 1. Differential Force Fields between Two Given Atoms in
ARMD Simulation for Reaction Steps I-IVa
atom1-atom2
trHbN-O2 + NO
trHbN-O2NO
O2-N
O1-N
O2-O
O1-O
Fe-N
nonbonded
nonbonded
nonbonded
nonbonded
nonbonded
Morse potential
bond angle via O2
bond angle via N
dihedral via O2-N
dihedral via O1-O2
atom1-atom2
trHbN-O2NO
trHbNdO + NO2
O1-O2
O1-N
Fe-O2
O1-O
Fe-N
O2-Nε of H81
Morse potential
bond angle via O2
bond angle via O1
dihedral via O2-N
dihedral via O1-O2
dihedral via O1-Fe
Nonbonded
Nonbonded
Nonbonded
Nonbonded
Nonbonded
Nonbonded
atom1-atom2
trHbNdO + NO2
trHbN-ONO2
O1-N
Fe-N
Fe-O2/O
O1-O2/O
N-Nε of H81
nonbonded
nonbonded
nonbonded
nonbonded
nonbonded
Morse potential
bond angle via O1
dihedral via O1-N
bond angle via N
dihedral via O1-Fe
atom1-atom2
trHbN-ONO2
trHbN + NO3-
Fe-O1
Np-O1
Fe-N
Fe-O2/O
N-Nε2 of H81
Morse potential
angle via Fe
bond angle via O1
dihedral via O1-N
dihedral via O1-Fe
nonbonded
nonbonded
nonbonded
nonbonded
nonbonded
a
Nonbonded interactions include electrostatic and van der Waals
terms. H81 is the proximal histidine attached to Fe atom of heme.
calculations (see Figure S1 in the Supporting Information) is
identical to the one for which the parametrization was carried out.
It is found that the energetic ordering between reactant, product,
and TS from both types of calculations (compare Figures S2 in the
Supporting Information and Figure 9) agree and therefore we expect
that the force field gives realistic energetics for investigating the
reactions. It can also be seen that conformational sampling
influences and modulates the relative energies of transition state
and product relative to the reactant. Further validations are provided
in the Discussion and Conclusions.
Results
Dynamics of NO Dioxygenation in trHbN. Step I: NO
Binding to oxy-trHbN. In step I, the free NO ligand attacks the
heme-bound O2 to form a bound peroxynitrite complex. In the
product, a bond between the O2 atom of O2 and the N atom of
NO is formed which also gives rise to additional angles (Table
1). In a first approximation, ∆0 ) 25.6 kcal/mol, which
corresponds to the dissociation energy of the O2-N Morse
potential. As the potential energy surfaces describing the two
states are multidimensional, ∆ will differ somewhat from ∆0
and the grid for ∆ included ∆ ) 60, 30, 26, 15, and 5 kcal/
mol. From six snapshots of oxy-trHbN with free NO (see Figure
1 for the relative positions of ligands and heme plane), multiple
50 ps trajectories were started with different initial velocities.
The geometric characterization of the crossing seam is
presented in parts A and B of Figure 2. While Fe-O1, O1-O2,
and N-O distances during the crossing events are more or less
centered around their respective equilibrium values for all values
of ∆, the rebinding takes place over a broad range of O2-N
distances, see Figure 2A. For ∆ ) 60, 30, and 26 kcal/mol, the
crossing seam along the O2-N coordinate ranges from 2.7 to
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VOL. 132, NO. 9, 2010
Figure 1. Ribbon representation of trHbN showing the heme plane, the
reactive ligands (O2 and NO), and the active site residues Y33 and Q58.
The H81 residue is shown in the proximal side of the heme plane. The Fe
atom of the heme is shown as a green sphere.
5.0 Å and centers around 3.2 Å. Concomitantly, a wide range
of angles Fe-O1-O2, O1-O2-N, and O2-N-O (Figure 2A)
are found at the crossing geometries. The distribution of
dihedrals in Figure 2A suggests that both cis and trans OONO
are possible during crossing whereas an exclusive trans geometry
for the Fe-O1-O2-N dihedral is favored. Figure 2B shows a
two-dimensional plot of O2-N distance versus O1-O2-N
angle at the crossings for ∆ ) 60, 30, 26, and 15 kcal/mol. It
is evident that the crossing geometries only weakly depend on
the precise value of ∆ and that the crossing seam is rather broad.
Figure 2C analyzes the time dependence of crossing events
where the survival probability p(t) of free NO is shown as a function
of simulation time (t) for ∆ ) 60, 30, 26, and 15 kcal/mol. p(t)
can be fit to an exponential function, p(t) ) exp(-t/τ), to describe
the underlying kinetics, where τ is the associated time constant.
Table 2 summarizes the fitted time constants. For ∆ ) 60 kcal/
mol, the reaction is essentially monophasic with τ ) 1.5 ps
and increases to 11 and 16 ps for ∆ ) 30 and 26 kcal/mol,
respectively. The fastest crossings occur within 70-100 fs. This
suggests that an exclusive geminate recombination between
bound O2 and free NO occurs. For ∆ ) 15 kcal/mol, only 25%
of the trajectories showed rebinding, which leads to a longer
time constant of about 200 ps.
It is also of interest to analyze the H-bonding network
(between Tyr33, Gln58, O2, and NO) during the crossing events.
Figure 2D reports the probability distribution of the distance
between some of the H-bonding partners. During most of the
crossing events, H-bonding between the amide group of Gln58
and the phenol group of Tyr33 is observed (upper panel of
Figure 2D) where TyrO acts as a H-bond acceptor of amide N
of Gln58 and Tyr33 remains close to the reacting ligands. While
for many crossings Tyr33 is a H-bond donor to the O2 atom of
O2, in some of the cases it participates in H-bonding with the
O atom of NO. Nevertheless, crossings also take place even
when Tyr33 is at a non-hydrogen-bonding distance from the
ligand, see Figure 2D. A H-bond between Tyr33 and NO or O2
suggests that the amino acid influences the movement of the
ligands (NO/O2), thus making it available for reaction I. Thus,
Atomistic Simulation of NO Dioxygenation
ARTICLES
Figure 2. (A) Probability distribution of (i) bond distances [Fe-O (black), O1-O2 (red), O2-N (green), and N-O (blue)]; (ii) bond angles [Fe-O1-O2
(black), O1-O2-N (red), and O2-N-O (green)]; and (iii) dihedrals [O1-O2-N-O (black), Fe-O1-O2-N (red)] at the crossing points for NO rebinding
oxy-trHbN with ∆ ) (a) 30, (b) 26, and (c) 15 kcal/mol, respectively. (B) Two-dimensional plot showing the correlated distribution of crossing points along
the O2-N distance and O1-O2-N angle. The circles in black, red, green, and blue represent the crossings obtained with ∆ ) 60, 30, 26, and 15 kcal/mol,
respectively. The corresponding one-dimensional distribution along O2-N and O1-O2-N coordinates are also shown. (C) Time distribution of fraction of
trajectories without crossing for ∆ ) 60, 30, and 26 kcal/mol, shown in black, red, and green, respectively. (D) Probability distribution of the H-bonding
network between Q58, Y33, bound O2, and NO during the rebinding of NO. The distribution is shown for distances between (i) O atom of Y33 (OY33) and
OQ58 (black); OY33 and NQ58 (red); (ii) O2O2 and NQ58 (black); O2O2 and OY33 (red); (iii) ONO and NQ58 (black); ONO and OY33 (red).
Tyr33 would also determine whether the N atom or the O atom
of NO will react with O2. In the present force field, based on
ab initio calculations, the ONO carries negative charge and hence
is the H-bond acceptor. Consequently, it is the NNO atom which
reacts with O2.
In summary, for the recombination of NO with oxy-trHbN,
rate constants are of the order of several 10 ps over a wide
range of ∆ values. With decreasing ∆, the time constant for
reaction I increases. It is found that the crossing geometry is
little affected by varying ∆ whereas the kinetics of the reaction
depends somewhat on ∆. Analysis of the intermolecular
interactions around the active site reveals that residues Tyr33
and Gln58 facilitate and guide the reaction to some extent.
Step II: NO2 Dissociation. From six snapshots of trHbNOONO, 10 ARMD trajectories of 50 ps each are started to study
the homolytic cleavage of the peroxide bond with ∆ ) 50 kcal/
mol, which is close to the dissociation energy of O1-O2 bond
(∆0 ) 47.6 kcal/mol). In none of these trajectories a reaction
was observed. Analysis of the trajectories revealed that at the
equilibrium geometry of bound O2NO, where the bond distance
of the peroxide oxygens is about 1.4 Å, the dissociated state is
energetically unfavorable due to large vdW repulsion between
the two oxygen atoms of the peroxide bond. Figure 3A shows
a one-dimensional potential energy curve of the bound and
dissociated states along the O1-O2 bond distance. The bound
state is a Morse potential associated with the O1-O2 bond,
and the dissociated state is represented by the vdW and
electrostatic interaction of O1 and O2 in the dissociated state.
As the Figure suggests, the crossing of the two states with the
present force field is at an O1-O2 distance of 2.25 Å and has
an activation barrier of about 40 kcal/mol.
Blomberg et al. found a transition state for this step at an
O1-O2 distance of 1.94 Å with an estimated barrier of 6.7
kcal/mol, which corresponds to simulation time scales of
submicro- to microseconds, assuming an entirely diffusionlimited reaction to be occurring in the picoseconds time
scale.56,57 To assess the sensitivity of this observation on the
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Table 2. Brief Summary of ARMD Simulations of NO Dioxygenation in trHbNa
a
∆ (kcal/mol)
no. of crossings (no. of trajectories)
duration of trajectories (ps)
total simulation time (ns)
60
30*
26
15
5
60 (60)
179 (180)
58 (60)
18 (60)
0 (60)
trHbN-O2 + NO f trHbN-OONO (Step I)
50
50
50
50
50
3
9
3
3
3
1.3 (1.0)
11 (1.0)
16 (1.0)
68
59*
55
50
40
60 (60)
176 (180)
44 (60)
12 (60)
0 (60)
trHbNdO + NO2 f trHbN-ONO2 (Step III)
50
50
100
100
100
3
9
6
6
6
3 (1.0)
18 (1.0)
66 (1.0)
60*
50
30
173 (180)
37 (60)
3 (60)
trHbN-ONO2 f trHbN+ + NO3- (Step IV)
100
100
100
18
6
6
30 (1.0)
80 (1.0)
80*
75
70
60
171 (180)
41 (60)
12 (60)
0 (60)
trHbN-OONO f trHbN-ONOO (Rearrangement)
100
18
100
6
100
6
100
6
time constant (ps) (coefficient)
10 (0.6), 46 (0.4)
80 (1.0)
The asterisks indicate the most probable ∆ for a particular reaction.
parametrization, the vdW radius (σO) of the O1 and O2 atoms
are varied between 1.0 e σ e 1.75 Å on a grid with a separation
of 0.05 Å. Five trajectories of 50 ps length were started from
each of the six snapshots. For small values of σ, the reaction
occurs rapidly since the vdW minimum is close to the
equilibrium O1-O2 distance in the bound state. The O1-O2
distance at the crossing increases with increasing σ. Figure 3B
shows the relationship between the O1-O2 distance at the
crossings and σO. A geometry with an O1-O2 distance of
1.94 Å (DFT value) at the transition state corresponds to σO )
1.55 Å (see Figure 3B). Additional aspects of step II are
addressed in the Discussion and Conclusions.
Step III: Rebinding of NO2. In this step, the free NO2 radical
combines with the oxo-ferryl species (trHbNdO + NO2) to give
rise to a heme-bound nitrato complex. The reaction involves
the formation of an O1-N bond which requires angular (O1N-O2, O1-N-O, and Fe-O1-N), dihedral (Fe-O1-N-O2/
O, N-O1-F-N(His)), and improper (N-O1-O2-O) terms
to be included in the force field of the product state (Table 1).
Following the discussion of step I, the dissociation energy of
the O1-N Morse bond provides a first estimate of ∆0 ) 50.5
kcal/mol for the asymptotic separation.
Six snapshots with dissociated NO2 in trHbN were chosen
to study reaction III for which multiple ARMD trajectories were
run and the rebinding of NO2 with trHbN-oxo species was
followed with ∆ between 40 and 68 kcal/mol. All results
obtained are summarized in Table 2. For ∆ ) 68 and 59 kcal/
mol, most of the trajectories rebind, whereas for ∆ ) 55 kcal/
mol, 44 out of 60 trajectories showed crossing. On the other
hand, for ∆ ) 50 kcal/mol, 12 out of 60 trajectories showed
crossing during 100 ps of simulation, while for ∆ ) 40 kcal/
mol, none of the 60 trajectories were found reactive.
The analysis reveals that the Fe-O1, O2-N, and O3-N
distances during the crossing events are predominantly centered
around their respective equilibrium values, whereas rebinding
takes place over a broad range of O1-N distances (Figure S3
(56) Nauser, T.; Koppenol, W. H. J. Phys. Chem. A 2002, 106, 4084–
4086.
(57) van Holde, K. E. Biophys. Chem. 2002, 101, 249–254.
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in the Supporting Information). The bound ONO2 moiety
remains planar during the crossing. Figure 4A shows that
crossing occurs with a Fe-O1 distance varying between 1.6
and 1.7 Å. For ∆ ) 68, 59, and 55 kcal/mol, the crossings occur
more toward the oxo-ferryl (reactant) side, whereas crossing
geometries are rather more shifted toward the product side
(heme-ONO2) for ∆ ) 50 kcal/mol (blue circles in Figure 4A).
Figure 4A shows the two-dimensional view of the Fe-O1-N
angle versus O1-N distance for ∆ ) 68, 59, 55, and 50 kcal/
mol. For all values of ∆, the reaction occurs with a O1-N
distance between 2.7 and 4 Å with a maximum around 3.2 Å,
i.e., changing ∆ by 20 kcal/mol leaves the crossing seam largely
unaffected.
The time dependence of the crossing events is analyzed by
calculating the survival probability of free NO2 as a function
of simulation time which was then fitted to an exponential
function for ∆ ) 68, 59, and 55 kcal/mol. Table 2 reports the
corresponding time constants and shows that the reaction is best
described by a single exponential decay with τ in the range of
a few tens of picoseconds. The time constants change by 1 order
of magnitude for the different values of ∆: for ∆ ) 55 kcal/
mol τ ) 66 ps, which decreases to 18 and 3 ps for ∆ ) 59 and
68 kcal/mol, respectively.
The H-bonding network between Tyr33, Gln58, and the
ligands (Figure 4B) shows that for most of the crossing events
the amide group of Gln58 and phenol group of Tyr33 are
hydrogen bonded (Figure 4B). Here, TyrO acts as the H-bond
acceptor of amide N. Similar to NO rebinding to heme-O2, in
the present case, Tyr33 remains close to the reacting ligands
during the crossing (Figure 4B). In the majority of cases, Tyr33
is a H-bond donor to one of the O atoms of NO2 (blue curve).
Again, the H-bond between Tyr33 and NO2 indicates the
importance of Tyr33 residue, which arrests the movement of
the ligand (NO2), thus positioning it suitably for reaction III.
In summary, recombination of NO2 to oxo-ferryl suggests a
weak dependence of the crossing seam on ∆ values. On the
other hand, the rebinding dynamics is found to vary between
66 and 3 ps depending on the value of ∆, see Table 2. The fact
that only 20% of the trajectories showed crossing for ∆0 ) 50
Atomistic Simulation of NO Dioxygenation
Figure 3. (A) One dimensional potential energy curve for heme-bound
O2NO (solid line) and NO2 dissociated oxo-ferryl species (dashed line) along
the O1-O2 distance. The bound state is given by the Morse potential of
the O1-O2 bond in heme-bound O2NO, and the dissociated state is given
by the nonbonding interaction between the O atom of oxo-ferryl and the O
atom of NO2. (B) Average value of the O1-O2 distance during NO2
dissociation against vdW radius of O atoms. A vdW radius of 1.55 Å is
expected to provide NO2 dissociation at 1.94 Å O1-O2 separation (the
DFT value).
kcal/mol and no crossings were observed for ∆ ) 40 kcal/mol
suggest that τ ≈ 100 ps is rather a lower limit for this step.
From the analysis of the interaction between the reactive ligands
and active site amino acids Tyr33 and Gln58 appear to assist
the reaction by interacting with the NO2 radical and prepositioning it.
Step IV: Dissociation of NO3-. Dissociation of nitrate involves
breaking the Fe-O1 bond in the heme-bound nitrato complex.
During step IV, the heme changes from hexa- to pentacoordinated. For this step, the dissociation energy of the Fe-O1 Morse
bond provides a first estimate of ∆0 ) 50.7 kcal/mol for the
asymptotic separation. Therefore, we have studied the reaction
for a range of ∆ around this value.
From the six snapshots of trHbN-ONO2, 10 ARMD trajectories of 100 ps each are started and dissociation of NO3- is
followed with ∆ ) 60, 50, and 30 kcal/mol. Table 2 shows
that with decreasing ∆, the number of crossing events decreases.
For ∆ ) 30 kcal/mol, only 3 of 60 trajectories dissociate within
100 ps while dissociation is more frequent for ∆ ) 50 and 60
kcal/mol, see Table 2.
ARTICLES
For ∆ ) 60 and 50 kcal/mol, the distribution of crossing
points along several coordinates is given in Figure S4 in the
Supporting Information and Figure 5A shows two-dimensional
plots of Fe-O1 distance against O1-N distance and Fe-O1-N
angle together with the corresponding one-dimensional probability distributions. For both values of ∆, the reaction occurs
with an Fe-O1 distance between 2 and 2.2 Å. Compared to
the previous reaction steps, the dissociation of NO3- occurs in
a relatively constrained geometric space. The fraction of
undissociated NO3- as a function of simulation time is fitted to
an exponential function, and the reaction is found monophasic
with time constants varying between τ ) 30 ps for ∆ ) 60
kcal/mol and τ ) 80 ps for ∆ ) 50 kcal/mol (see Table 2). The
H-bonding network between Tyr33, Gln58, and the nitrate ligand
during the crossing events is shown in Figure 5B. During most
of the crossing events, the amide group of Gln58 is H-bonded
to the phenol group of Tyr33 (Figure 5B), where TyrO acts as
a H-bond acceptor of amide N. During nitrate dissociation, both
Tyr33 and Gln58 form H-bonds with the dissociating NO3-,
see Figure 5B.
In summary, reaction IV occurs over a wide phase space and
the reaction seam does not strongly depend on ∆. The dynamics
of the reaction are characterized by a single exponential decay
with time constants on the order of a few tens of picoseconds.
Similar to step III, the time constant τ ) 80 ps for ∆ ≈ ∆0
suggests that the actual rate for this step is probably slower.
The surrounding residues Tyr33 and Gln58 are found to
participate in H-bonding with the dissociating ligand.
Tyr33Ala and Gln58Ala Mutation. For the four elementary
steps investigated so far, residues Tyr33 and Gln58 are found
to play more or less prominent roles as hydrogen-bond donors
and acceptors. To further explore their role, we have studied
each reaction step for three mutants: (i) Y33A, (ii) Q58A, and
(iii) the double mutant Y33A/Q58A. For this, one of the starting
structures was arbitrarily chosen and the three mutations were
performed. The structures were optimized and equilibrated for
200 ps. For ARMD simulations, 40 trajectories were started
from each of the three mutants for reactions steps I-IV with
∆ ) 30, 50, 59, and 60 kcal/mol, respectively, which are close
to ∆0 from the ab initio calculations. In addition, since the
dependence of the crossing seam and the rate constants on the
choice of ∆ was found to be rather weak for all the reactions
studied so far, the choice of ∆ is not expected to greatly affect
the results discussed in the following.
Step I. Recombination of NO with oxy-trHbN occurred in
each of the 40 trajectories for all three mutants, and the observed
crossing seam is wide as was the case for the wild-type protein.
Figure 6 compares the crossing seam for the wild-type protein
and its three mutants. The crossing occurs at a similar O2-N
distance and O1-O2-N angle. Similar results are obtained for
other internal coordinates (not shown). The fraction of unbound
trajectories as a function of simulation time shows that for all
mutants the rebinding is single exponential similar to the wildtype protein with similar time constants, see Table 3.
Step II. Similar to the wild-type protein, in none of the three
mutants is NO2 dissociation from peroxynitrite-trHbN observed.
Step III. For the wild-type protein with ∆ ) 59 kcal/mol, 59
of the 60 trajectories showed NO2 rebinding. On the other hand,
for Y33A, Q58A, and Y33A + Q58A mutants, 10, 39, and 28
of the 40 trajectories, respectively, were reactive during 50 ps
of simulations. The above results suggest that Q58A mutation
has little effect on NO2 rebinding. On the contrary, the Y33A
mutation considerably reduces the number of crossing events.
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Figure 4. (A) Two-dimensional plot showing the correlated distribution of crossing points along (i) O1-N distance and Fe-O1 distance and (ii) Fe-O1-N
angle and O1-N distance. The circles in black, red, green, and blue represent the crossings obtained for NO2 rebinding with ∆ ) 68, 59, 55, and 50
kcal/mol, respectively. (B) Probability distribution of the H-bonding network between Q58, Y33, and NO2 during the rebinding of NO2. The distribution is
shown for distances between (i) O atom of Y33 (OY33) and OQ58 (black); OY33 and NQ58 (red); (ii) O1NO2 and NQ58 (black); O1NO2 and OY33 (red); O2NO2 and
NQ58 (green); O2NO2 and OY33 (blue).
However, when both Y33 and Q58 are mutated to alanine, the
number of crossing events increases compared to the Y33A
mutant. The fraction of nonreactive trajectories as a function
of simulation time are fitted to exponential functions. The time
constants associated with the mutants are 201, 18, and 42 ps
for Y33A, Q58A, and Y33A + Q58A, respectively. A detailed
analysis of the crossing geometries shows that the NO2 rebinding
is largely controlled by Tyr33 and Gln58. The dynamic
H-bonding network between the residues and the ligands is
responsible for an efficient NO2 rebinding in the wild-type
protein. The large value of the time constant for Y33A mutant
arises from the fact that only a small fraction of the trajectories
exhibit crossings. Strictly speaking, the trajectories of 50 ps
simulation time are inadequate to describe the dynamics
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VOL. 132, NO. 9, 2010
occurring at a time scale of 200 ps, despite the fact that we
have run multiple trajectories with a cumulative simulation time
of 2 ns.58 However, for the present purpose, it suffices to say
that the time constants associated with the Y33A mutant is
significantly larger than that of the wild-type trHbN.
Step IV. During 50 ps of simulations, most of the trajectories
in each of the three mutants exhibited nitrate dissociation. The
crossing seam along the Fe-O1 distance and O1-N distance
and Fe-O1 distance and Fe-O1-N angle are shown in Figure
7A for the three mutants as well as for the wild-type protein.
The figure suggests a reduction of the Fe-O1 distance during
crossing for the single mutants, i.e., Y33A and Q58A, whereas
(58) Fersht, A. R. Proc. Natl. Acad. Sci. U.S.A. 2002, 99, 14122–14125.
Atomistic Simulation of NO Dioxygenation
ARTICLES
Figure 5. (A) Two-dimensional plot showing the correlated distribution of crossing points along the (i) O1-N distance and Fe-O1 distance and the (ii)
Fe-O1-N angle and Fe-O1 distance. The circles in black and red represent the crossings obtained for NO3- dissociation with ∆ ) 60 and 50 kcal/mol,
respectively. (B) Probability distribution of the H-bonding network between Q58, Y33, and NO2 during NO3- dissociation. The distribution is shown for
distances between the (i) O atom of Y33 (OY33) and OQ58 (black); OY33 and NQ58 (red); (ii) O1, O2, and O3 atoms of NO3- and NQ58 (black); O1, O2, and
O3 atoms of NO3- and OY33 (red), shown in solid, dashed, and dotted lines, respectively.
for the double mutant it is indistinguishable from that of the
wild-type protein. Figure 7B shows the kinetics of nitrate
dissociation for the three mutants and the wild-type protein.
While the wild-type protein and the double mutant show similar
dissociation rates (with time constants about 30 ps), both single
mutants show a faster nitrate dissociation compared to the wildtype protein. The kinetics of the single mutants are found to be
best described by a double exponential function with time
constants of 2 ps (coefficient 0.7) and 35 ps (coefficient 0.3)
for the Y33A mutant and 8 ps (coefficient 0.9) and 35 ps
(coefficient 0.1) for the Q58A mutant, see Figure 7B.
Similar to NO2 rebinding (step III), the NO3- dissociation
also shows a complicated protein dependence. While absence
of one of the two H-bonding residues triggers a faster dissociation of the Fe-O1 bond at a shorter Fe-O1 distance, simul-
taneous mutation of the two bulky and H-bonding residues
shows a similar crossing seam and kinetic pattern as that of the
wild-type protein.
In summary, studies of the four reaction steps involved in
NO dioxygenation have shown that (A) All steps but one (step
II) can be investigated and analyzed in a meaningful way by
ARMD. Step II is elusive and is also the one that has not been
found in experiments.12,16 (B) Investigations of single and
double mutants establish that for specific elementary steps (steps
III and IV in particular) the protein plays an active role through
H-bond formation to the reacting species. The fact that step II
could not be followed and no direct experimental evidence for
formation of NO2 is available prompts us to study an alternative
pathway.
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and simultaneous formation of an O1-N bond in trHbN-ONO2,
see the inset in Figure 8B. Rearrangement then leads to a large
change in the O1-O2-N angle of the peroxynitrite complex
and O1-N-O2 angle of the nitrato complex. To study such a
process, we used a topology in which OONO and the nitrato
(ONO2) ligands are described by bonds instead of bonds, angles,
and dihedrals. For example, the force field for OONO is given
by
VOONO ) VO1-O2 + VO2-N + VO1-N + VO1-O +
VO2-O + VN-O (3)
Figure 6. Two-dimensional plot showing the correlated distribution of
crossing points, during the NO recombination reaction, along the O2-N
distance and O1-O2-N angle for the wild-type protein (black), Y33A (red),
Q58A (green), and Y33A + Q58A (blue) mutants with ∆ ) 30 kcal/mol.
Table 3. Summary of Time Constants (in Picoseconds) for the
wt-trHbN and Its Three Mutants during NO Dioxygenation
step I
∆ ) 30
kcal/mol
step III
∆ ) 59
kcal/mol
11
18
Y33A
4
201
Q58A
6
18
Y33A + Q58A
6
42
wt-trHbN
step IV
∆ ) 60
kcal/mol
30 (1.0)
2 (0.7),
35 (0.3)
8 (0.9),
35 (0.1)
27
rearrangement
∆ ) 80
kcal/mol
10 (0.6),
46 (0.4)
193
20
262
Alternative Pathway. Previously, the barrier associated with
step II has been estimated to be 6.7 kcal/mol by Blomberg et
al.18 Such a large barrier suggests that the reaction occurs on a
submicro- to microsecond time scale, which is too slow to be
observed in the present simulations. Furthermore, with an overall
rate of NO dioxygenation of 7.5 × 108 M-1 s-1, it raises doubts
if the reaction indeed occurs via this step. Under normal
physiological conditions, Herold et al. were unable to observe
any dissociated NO2.12,16 The lack of experimental detection
of free NO2 during NO dioxygenation has led to the suggestion
of an alternative mechanism. It was postulated that, after NO
rebinding with oxy-Hb, the peroxynitrite (-OONO) complex
undergoes a rearrangement to a nitrato (-ONO2) complex.12,59
The rearrangement of peroxynitrite to nitrate catalyzed by
metallo-porphyrins are well-known for 5,10,15,20-tetrakis(Nmethyl-4′-pyridyl) porphinatoiron(III) [FeIII(TMPyP)] or 5,10,
15,20-tetrakis(2,4,6-trimethyl-3,5-sulfonatophenyl) porphinatoiron(III) [FeIII(TMPS)]60,61 and for mutated myoglobin (H64A
and H64D),62 where it was shown that the reactivity of
metMb(III) toward peroxynitrite depends on the presence of the
distal histidine (H64).
The peroxynitrite to nitrato rearrangement reaction involves
breaking of the O1-O2 and O2-N bonds in trHbN-OONO
(59) Gardner, P. R. J. Inorg. Biochem. 2005, 99, 247–266.
(60) Stern, M. K.; Jensen, M. P.; Kramer, K. J. Am. Chem. Soc. 1996,
118, 8735–8736.
(61) Lee, J.; Hunt, J. A.; Groves, J. T. J. Am. Chem. Soc. 1998, 120, 7493–
7501.
(62) Herold, S.; Matsui, T.; Watanabe, Y. J. Am. Chem. Soc. 2001, 123,
4085–4086.
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where, except for the last term on the right-hand side (the N-O
bond), all other bonds are described by the Morse potentials.
Since the N-O bond undergoes little change in conformation
from reactant to product, a harmonic potential is sufficient.
To study trHbN-OONO to trHbN-ONO2 rearrangement, we
considered six snapshots of heme-bound peroxynitrite and
carried out several ARMD trajectories for a range of ∆ values.
The initial estimate of ∆0 for this reaction is obtained from the
sum of the dissociation energies of O1-O2 and O2-N Morse
potentials, which amounts to 72 kcal/mol. Therefore, we have
carried out simulations with ∆ ) 60, 70, 75, and 80 kcal/mol,
see Table 2. For ∆ ) 80 kcal/mol, 171 of 180 trajectories
crossed while for ∆ ) 75 and 70 kcal/mol, 41 and 12 of 60
trajectories reacted. For ∆ ) 60 kcal/mol, none of the trajectories are found reactive on the time scale of the simulations
(100 ps).
A time series of the energy associated with the rearrangement
of the peroxynitrite to the nitrato complex for both the reactant
and the product states is shown in Figure 8A. In this trajectory,
crossing occurs after 38 ps and the energy of the product state
after crossing is lower by about 25 kcal/mol compared to the
energy of the reactant before crossing. Figure 8A also shows
the time evolution of the O1-O2 and O1-N bonds and the
O1-N-O2 and O1-O2-N angles where rearrangement is
accompanied by substantial changes of the bonds and angles
involved in the reaction. During the crossing, the O1-O2 bond
of trHbN-OONO breaks and the O1-N bond of trHbN-ONO2
is formed. The breaking and formation of these bonds also lead
to changes in the corresponding valence angles, see Figure 8A.
The distribution of Fe-O1, O1-O2, O2-N, O-N, O1-N
distances as well as for O1-O2-N and O1-N-O2 angles
along the crossing seam for ∆ ) 80, 75, and 70 kcal/mol are
shown in Figure S5 in the Supporting Information. The analysis
reveals that crossings occur over a range of O1-N distances
between 2.3 and 2.7 Å, with a peak at 2.47 Å, which is close
to the equilibrium O1-N distance in the reactant. Figure 8C
shows two-dimensional plots of the crossing seam along (i)
O1-N and O1-O2 and (ii) O1-N and O1-O2-N coordinates
for ∆ ) 80, 75, and 70 kcal/mol together with the corresponding
one-dimensional distributions. The crossing seam is broad in
these coordinates. A smaller value of ∆ results in crossings with
a comparatively longer O1-O2 distance, see the probability
distribution along O1-O2 coordinate for ∆ ) 70 kcal/mol.
Similar to other reaction steps, the crossing seam moderately
depends on ∆.
The fraction of trajectories without rearrangement as a
function of simulation time p(t) is analyzed for ∆ ) 80 and 75
kcal/mol. p(t) for ∆ ) 80 kcal/mol can be fit to a double exponential with two time constants: τ1 ) 10 ps and τ2 ) 46 ps
with coefficients 0.6 and 0.4, respectively. On the other hand,
for ∆ ) 75 kcal/mol, the underlying kinetics can be described
Atomistic Simulation of NO Dioxygenation
ARTICLES
Figure 7. (A) Two-dimensional plot showing the correlated distribution of crossing points along the (i) O1-N distance and Fe-O1 distance and the (ii)
Fe-O1-N angle and O1-N distance during the nitrate dissociation reaction for ∆ ) 60 kcal/mol. The circles in black, red, green, and blue represent the
crossings obtained for the wild-type protein (black), Y33A (red), Q58A (green), and Y33A + Q58A (blue) mutants. (B) Time distribution of the fraction of
trajectories without nitrate dissociation in the case of the wild-type protein (black), Y33A (red), Q58A (green), and the Y33A + Q58A (blue) mutants for
∆ ) 60 kcal/mol.
with a single exponential with time constant 80 ps. These results
suggest that ∆ has a substantial effect on the kinetics of the
reaction, and with decreasing ∆, the reaction slows down.
However, for a detailed understanding of the slow processes,
longer simulations are required.
To study the role of protein in the rearrangement of
peroxynitrite to nitrato complex, we started 40 trajectories of
100 ps duration each, with ∆ ) 80 kcal/mol, from each of the
three mutants studied in this work. Out of 40 trajectories, 19,
39, and 16 trajectories showed rearrangement for Y33A, Q58A,
and Y33A/Q58A mutants, respectively. The fraction of trajectories without reaction is plotted against simulation time for
the wild-type trHbN along with its three mutants, see Figure
8D. The time constants associated with the rearrangement
reaction are determined as 193, 20, and 262 ps for Y33A, Q58A,
and Y33A/Q58A mutants, respectively (see Table 3).
In summary, the rearrangement of peroxynitrite complex of
trHbN to its nitrato complex is studied with four values of ∆
between ∆ ) 60 and 80 kcal/mol. For ∆ ) 80 kcal/mol, the
rearrangement reaction shows biphasic kinetics with time
constants of 10 and 46 ps. Whereas for ∆ ) 75 kcal/mol, a
single exponential function with a time constant of 80 ps is
found to explain the underlying kinetics. With comparison of
the results of wild-type trHbN and three mutants, it is found
that the rearrangement reaction is strongly influenced by the
mutation of Tyr33 residue whereas Gln58 residue is found to
have rather small effects on the reaction, see Table 3.
Discussion and Conclusions
Nitric oxide plays a pivotal role in various physiological
processes. It is now widely believed that oxy-bound globins
can oxidize toxic NO to harmless nitrate. Here we have used
J. AM. CHEM. SOC.
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Mishra and Meuwly
Figure 8. (A) Time series of the energy of the reactant and product, the O1-O2 and O1-N bond distances, and the O1-O2-N and O1-N-O2 angles
during an example ARMD trajectory for OONO rearrangement reaction. In this trajectory, reaction occurs after 38 ps of simulation with ∆ ) 80 kcal/mol.
(B) Probability distribution of the energy of the reactant (solid line) and the product (dashed line) obtained from 300 independent ARMD trajectories. The
distributions p(E) shown by black, red, and green lines correspond to ∆ ) 80, 75, and 60 kcal/mol, respectively. The region where the reactant and product
distributions overlap represents the crossing region. (C) Two-dimensional plot showing the correlated distribution of crossing points along the (i) O1-N
distance and O1-O2 distance and the (ii) O1-O2-N angle and O1-O2 distance for ∆ ) 80 (black), 75 (red), and 70 (green) kcal/mol. (D) Time distribution
of fraction of unreacted trajectories for wt-trHbN (black), Y33A (red), Q58A (green), and Y33A + Q58A (blue) mutants for ∆ ) 80 kcal/mol.
Figure 9. Relative potential energies determined from DFT calculation of
snapshots corresponding to the reactant, product, and the crossing points
obtained from five ARMD trajectories for the reaction step I.
atomistic and molecular dynamics simulations to characterize
the NO dioxygenation in truncated hemoglobin of Mycobacterium tuberculosis by considering two pathways, A and B.
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Pathway A follows earlier suggestions14,15,18,38 where the entire
reaction consists of four steps: (I) NO (re)binding to oxy-trHbN,
(II) homolytic cleavage of the peroxide bond in trHbN-OONO,
(III) NO2 rebinding to oxo-ferryl trHbN, and (IV) dissociation
of nitrate from trHbN-ONO2 complex, whereas pathway B
involves a rearrangement reaction from peroxynitrite-trHbN
to the trHbN-ONO2 complex.12,59 The reactive steps were
followed by employing the adiabatic reactive MD method which
was found earlier to provide a detailed atomistic understanding
of NO rebinding in myoglobin.42,43 For the reactant and product
state of each step, associated force-fields were determined from
electronic structure calculations. For pathway A, steps I, III,
and IV yield rate constants on the picosecond time scale. To
assess the sensitivity of the results, the simulations for each of
the reaction steps are run for a range of ∆ values around the ab
initio determined value. The results obtained from these
simulations are found to be robust and show little dependence
on the precise value of ∆. However, it is possible that more
elaborate treatments of ∆, such as including an explicit
conformational dependence, provides additional insight.
Atomistic Simulation of NO Dioxygenation
To further characterize step II (not reactive so far), 30
additional trajectories 200 ps in length with an oxygen-van der
Waals radius of σO ) 1.55 Å were analyzed. None of them
were reactive. Thus, for typical and realistic values of σO, the
rate for homolytic cleavage is slower than nanoseconds. To
quantify the activation energy associated with NO2 dissociation,
the free-energy profile along the O1-O2 distance was calculated
from three independent umbrella sampling simulations at 300
K and analyzed with the weighted histogram analysis method.63,64
The resulting free energy profiles (Figure S6 in the Supporting
Information) exhibit NO2 dissociation barriers of 12-15 kcal/
mol, which are in qualitative agreement with an estimated barrier
of 6.7 kcal/mol from previous DFT calculations.18 On the other
hand, for pathway B, the rearrangement reaction, rate constants
were found to be in the picosecond range, which readily explains
the rapid overall NO dioxygenation that is associated with a
second order rate constant of 7.5 × 108 M-1 s-1 in trHbN.29
Moreover, Herold et al. were unable to observe any dissociated
NO2 which should emerge along pathway A. All these observations suggest that pathway B may be preferred.12,16 It is also of
interest to put such rates into context with caged radical
reactions, which are characteristic of cytochrome P450 catalyzed
oxidations. Employing trans-2-phenyl-methylcyclopropane as
a radical clock-substrate of a P450 enzyme mimic, i.e., a
synthetic Fe(IV)dO porphyrin radical cation, a lifetime of 625
fs for the radical intermediate was estimated.65
A detailed analysis of the energetics of pathway B is shown
in Figure 8B, which reports the probability distribution pR(E)
of the energy of the reactant (peroxynitrite complex) and that
of the product (nitrato complex) pP(E) as sampled by reactive
MD simulations (average over 300 independent trajectories, each
100 ps in length). As can be seen, the product state is stabilized
by 24 kcal/mol, which is in reasonable agreement with the
relative stabilization energy obtained from quantum chemical
calculations of the model heme systems from both, the present
work (37.1 kcal/mol), and by Blomberg et al.18 (35.6 kcal/mol).
The distributions pR(E) (solid line) and pP(E) (dashed line)
overlap at 8.6 kcal/mol above the most probable energy of the
reactant, see Figure 8B. This low probability region corresponds
to the crossing from reactant to product and is only a little
influenced by the choice of ∆. To more quantitatively characterize the forward and reverse barriers, the transition state structure
was optimized by quantum chemical calculations of the model
system using the quadratic synchronous transit method.66,67 The
calculated TS barrier is 8.3 kcal/mol, which supports the results
from the simulations. However, the quantum chemical calculations do not include entropy corrections and interactions with
the protein and solvent environment whereas ARMD includes
such effects. The TS structure obtained from quantum chemical
calculations (Supporting Information) has striking similarities
with the crossing geometries obtained from the ARMD simulations of the rearrangement reaction, which further validates the
parametrization of the force fields.
It is also of interest to more carefully compare the structure
and spectroscopic properties of the NO2 fragment in the TS
structure and free NO2 from B3YLP/6-31G(d,p) calculations.
(63) Kumar, S.; Rosenberg, J. M.; Bouzida, D.; Swendsen, R. H.; Kollman,
P. A. J. Comput. Chem. 1995, 16, 1339–1350.
(64) Roux, B. Comput. Phys. Chem. 1995, 91, 275–282.
(65) Sbaragli, L.; Woggon, W. D. Synthesis 2005, 1538–1542.
(66) Halgren, T. A.; Lipscomb, W. N. Chem. Phys. Lett. 1977, 49, 225–
232.
(67) Peng, C.; Ayala, P. Y.; Schlegel, H. B.; Frisch, J. J. Comput. Chem.
1996, 17, 49.
ARTICLES
While free NO2 has two symmetric N-O bonds (1.26 Å) and
an ONO angle of 101°, NO2 at the TS is asymmetric with NO
bond distances of 1.26 and 1.21 Å and an ONO angle of 124°.
Additionally, the bending and stretching frequencies of NO2 in
the two structures differ considerably (764, 766, 1486 cm-1 for
free NO2 and 797, 1180, 1552 cm-1 for NO2 at the TS; a
frequency analysis of the entire model complex at the TS yields
vibrations with strong involvement of the NO2 at 739, 748, 1088,
and 1609 cm-1). Thus, NO2 at the TS of the NO dioxygenation
has properties quite different from that of “free” NO2 as has
been pointed out previously.18
Comparing the two pathways studied in this work, there is
strong evidence that pathway B is favorable and realistic both
in view of the energetics and the geometrical properties which
compare favorably with electronic structure calculations. However, given that observing the dissociation of NO2 (step II) in
pathway A depends on the van der Waals parameters used (see
above), more detailed analysis of this step may be required to
rule out pathway A. Finally, the barriers for individual crossing
events can be controlled through the force field parametrizations
for the product and the reactant states.
It is known that the rate of NO dioxygenation varies
substantially in different heme proteins,32,68,69 suggesting that
the particular environment around the active site is important.
Here, the role of the protein environment is assessed through
simulations of alanine mutants Y33A and Q58A and their
combination. From previous experimental and computational
studies it is known that Tyr33 and Gln58 residues participate
in a dynamic H-bonding network with the heme-bound and free
ligands.33,70-72 A previous QM/MM study of the reactive steps
along pathway A suggested that Y33 does not play a significant
role in the reaction,38 although experimental studies using the
Y33F mutant observe an increase in NO2 dissociation and a
decrease in NO dioxygenation rates compared to wild-type
trHbN.29 Similar results are also obtained in Escherichia coli
flavohemoglobin where the rate of NO dioxygenation decreases
by ≈30-fold upon Y33F mutation.73 Finally, in Hbs of parasitic
worm Ascaris lumbricodes (also known as Ascaris Hb or AHb),
the strategic positioning of a Cys residue in the distal side74
enables the organism to carry out the cysteine-mediated dioxygenase reaction in the presence of NO via an S-nitrosothiol
intermediate.75 This illustrates the diversity of interaction of NO
with Hb of different organisms, which has been discussed in
more detail in a recent review.30
A detailed picture of the role of active site residues on the
NO dioxygenation in trHbN emerges from the present simulations. They show that step I is minimally influenced by the
protein environment, which is in agreement with previous
observations where NO is found to be extremely reactive toward
oxygenated globins because the bound oxygen has a dominant
superoxide character.11,56 Similar to the wild-type protein,
(68) Ascenzi, P.; Bolognesi, M.; Milani, M.; Guertin, M.; Visca, P. Gene
2007, 398, 42–51.
(69) Ascenzi, P.; Visca, P. Methods Enzymol. 2008, 436, 317–337.
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J. Biol. Chem. 2000, 275, 12581–12589.
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ARTICLES
reaction II did not occur in the mutants. Unlike reaction I, our
simulations reveal that NO2 rebinding (step III) is strongly
influenced by Tyr33 and Gln58. For the Y33A mutant, the time
constant differs by an order of magnitude from that of wildtype trHbN (see Table 3). This can be explained by noting that
in wild-type trHbN the oxygen atom of the oxo-ferryl species
is stabilized via H-bonding to Gln58, and the free NO2 radical
participates in H-bonding with both Tyr33 and Gln58 which
arrest the free ligand and make it available for reaction. Thus
step III is not entirely diffusion controlled. Instead, the reaction
in the wild-type protein is facilitated by the presence of Tyr33
and Gln58. Nitrate dissociation (step IV) as well as the
rearrangement of trHbN-OONO to trHbN-ONOO are also
found to be influenced by residues Tyr33 and Gln58. In general,
Tyr33 and Gln58 facilitate the reaction by preorienting the
ligands via H-bonding, which is not possible for the corresponding alanine mutants. This is contrary to previous findings
which reported that the protein environment plays no role in
the NO dioxygenation reaction.38 Our simulations reflect the
importance of Tyr33, which is conserved across the trHb family,
suggesting an evolutionary significance of the residue.76 One
possible origin for the different conclusions concerning the role
of the protein environment is that the QM/MM calculations
involved restrained energy minimizations along a predefined
progression coordinate instead of a fully flexible and sufficiently
long explicit dynamics simulations, which is not possible with
QM/MM for large systems.38
Until now, no generally accepted scheme for the elementary
steps involved in NO dioxygenation is available. The nature of
the intermediate is expected to be different for different globins
and will also depend on the experimental conditions such as
concentration of NO and O2 and pH, as well as the existence,
proximity, and nature of the reductase domain.8,30 In other
words, given the differences between Hbs of different organisms
on one side and differences between various globins on the
other,30 mechanistic insight from the reaction investigated here
(conversion of NO to nitrate in trHbN) cannot straightforwardly
be generalized to NO dioxygenation in other proteins. Extensive
experimental work over the past few years has led to the
conclusion that under physiological conditions flavohemoglobin
binds NO at the heme, reduces it to nitroxyl, and reacts with
O2 to form nitrate,8 although the intermediates of this pathway
have as yet not been studied. In FHbs, the ferric heme is reduced
to the ferrous form by methemoglobin reductases together with
NADH and the FAD prosthetic group, thus completing the
catalytic cycle.24 The kinetics for NO dioxygenation in oxytrHbN is studied in vitro under aerobic conditions,29 although
in vivo trHbN operates at microaerobic conditions. Thus, the
relevance of single step turnover studies starting from O2-bound
heme to the in vivo situation should be seen in this context.
Nonetheless, the in vitro NO dioxygenation of trHbN, which
possesses high O2 affinity (P50 ) 0.013), suggests that trHbN
protects aerobic respiration from NO inhibition.29
(76) Nardini, M.; Pesce, A.; Milani, M.; Bolognesi, M. Gene 2007, 398,
2–11.
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In the present work, we have investigated the mechanistic
details of NO dioxygenation in oxy-trHbN by studying two
pathways. While proposed pathway A occurs via peroxide bond
cleavage, pathway B involves a rearrangement of heme-OONO
to heme-ONO2. Experimentally determined second order rate
constants for NO dioxygenation are of the order of 108 M-1
s-1 for oxy-trHbN. Since the diffusion controlled migration of
NO to the heme-active site is generally believed to be the
slowest process, it is conceivable that the elementary reactive
steps at the active site should be fast, i.e., on the order of picoto nanoseconds. This is also the case in Mbs, where the
rebinding times for NO and CO are between several tens of
picoseconds and hundreds of nanoseconds.77-84 In the present
simulations, which explicitly include nuclear dynamics, solvation, and protein environmental effects, all elementary steps were
found to be in this time range, except for step II. For this step,
the product (NO2) could not be characterized experimentally
and electronic structure calculations give a high barrier leading
to microsecond time scales, which is probably too slow to be
compatible with the measured rate constants. Thus, pathway
B, the rearrangement of the Fe(III)OONO intermediate to nitrate,
appears to be favorable for NO dioxygenation in trHbN. Future
experiments using time-resolved methods both in vivo as well
as in vitro should be able to discriminate between pathways A
and B, which will lead to fundamental understanding of the
NO dioxygenation reaction. It will also be of considerable
interest to study NO dioxygenation in different proteins,
including Mb and Hb, to obtain insights into similarities and
differences in the mechanistic aspects of the reaction.
Acknowledgment. The authors thank Stephan Lutz for many
helpful discussions, Profs. P. E. M. Siegbahn and K. M. Merz for
stimulating comments and useful suggestions from an anonymous
reviewer. Generous allocation of computing time at the Centro
Svizzero di Calcolo Scientifico (CSCS) is gratefully acknowledged.
This work has been supported through Grant 200021-117810 by
the Swiss National Science Foundation.
Supporting Information Available: A brief discussion on the
force field parameters obtained from ab initio calculations,
optimized geometries of the reactive intermediates in Cartesian
coordinates, some additional tables and figures, and complete
citation for refs 44, 52, and 79. This material is available free
of charge via the Internet at http://pubs.acs.org.
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Biophysical Journal Volume 96 March 2009 2105–2118
2105
Nitric Oxide Dynamics in Truncated Hemoglobin: Docking Sites, Migration
Pathways, and Vibrational Spectroscopy from Molecular Dynamics
Simulations
Sabyashachi Mishra and Markus Meuwly*
Department of Chemistry, University of Basel, Basel, Switzerland
ABSTRACT Atomistic simulations of nitric oxide (NO) dynamics and migration in the trHbN of Mycobacterium tuberculosis are
reported. From extensive molecular dynamics simulations (48 ns in total), the structural and energetic properties of the ligand
docking sites in the protein have been characterized and a connectivity network between the ligand docking sites has been built.
Several novel migration and exit pathways are found and are analyzed in detail. The interplay between a hydrogen-bonding
network involving residues Tyr33 and Gln58 and the bound O2 ligand is discussed and the role of Phe62 residue in ligand migration
is examined. It is found that Phe62 is directly involved in controlling ligand migration. This is reminiscent of His64 in myoglobin,
which also plays a central role in CO migration pathways. Finally, infrared spectra of the NO molecule in different ligand docking
sites of the protein are calculated. The pocket-specific spectra are typically blue-shifted by 5–10 cm1, which should be detectable in future spectroscopic experiments.
INTRODUCTION
In recent years, the microbial hemoglobins (Hbs) have
received much attention due to their wide range of functions
in microorganisms (1,2). Three groups of Hbs have been
identified in microorganisms, namely, flavohemoglobins
(FHbs), single domain Hbs, and truncated Hbs (trHbs) (3).
The FHbs contain a globin domain with a classical threeover-three a-helical structure and an additional flavin-containing reductase domain covalently attached to it. While
the single domain Hbs share high sequence and structure
homology with the globin domain of the FHbs, the trHbs,
on the other hand, are much smaller with z110–140
amino-acid residues and exhibit a two-over-two a-helical
structure (3–10).
The trHbs are phylogenetically divided into three
groups—group I (trHbN); group II (trHbO); and group III
(trHbP) (3)—which are 20–40 amino-acids shorter than the
mammalian Hbs due to the presence of several shortened
a-helices in trHbs. However, the residue deletions, insertions, and replacements relative to the vertebrate globin
sequences are distributed throughout the globin chain. The
trHbs host the heme in a two-over-two a-helical sandwich
based on four helices, corresponding to the B, E, G, and H
helices of the classical globin fold. The B/E and G/H helix
pairs run antiparallel and surround the heme group to keep
the latter safe from solvents. As compared to the classic
globin fold, the trHbs show a drastically shortened A helix
(absent in some cases, e.g., group III trHb). The D helix of
classic globin fold is usually absent and the proximal F helix
is almost completely replaced by an extended pre-F helix.
Submitted September 26, 2008, and accepted for publication November 18,
2008.
*Corresponding [email protected]
Editor: Gregory A. Voth.
Ó 2009 by the Biophysical Society
0006-3495/09/03/2105/14 $2.00
The stabilization in the shortened helices to build a properly
structured heme crevice is provided by three glycine-based
motifs in group I and II trHbs (7).
Pesce et al. (10) and Milani et al. (11,12) have analyzed
the crystal structures of several group I trHbs, including
the crystal structure of group I trHb of Mycobacterium tuberculosis, which is the primary focus of this work. One in every
three human beings in today’s population is latently infected
by M. tuberculosis (13,14), the causative agent of tuberculosis. It is now widely believed that the microorganism overcomes the toxicity of nitric oxide (NO) by converting it to
harmless nitrates (15,16).
The trHbN of M. tuberculosis has a dimeric assembly. The
dimer has an elongated shape, positioning the two hemes
22 Å apart. The interface area between two trHbN chains
is ~310 Å2 (11). The crystal structure reveals the presence
of an almost continuous tunnel through the protein matrix
connecting the heme distal pocket to the protein surface at
two distinct sites (11). The tunnel is composed of two
orthogonal branches, stretching 20 Å and 8 Å from the
respective access sites to the heme ligand site, and has
a diameter of 5–7 Å, thus covering a volume of z330–
360 Å3 (11). The crystal structure of trHbN with Xe
atoms under pressure shows eight Xe atoms with different
occupancy levels, three of which fall in the shorter
branch of the tunnel and two in the longer branch of the
tunnel (12).
There have been a number of experimental studies devoted
to the spectroscopic aspects of several diatomic ligands (CO,
O2, NO, and CN) binding to the trHbN in M. tuberculosis
(15,17–20). These authors have studied several mutants of
the wt-trHbN and have proposed that the ligand binding is
largely controlled by a pair of interacting amino acids
(Gln58 and Tyr33) in the heme active site by participating
doi: 10.1016/j.bpj.2008.11.066
2106
in H-bonding with the heme-bound diatomic O2 ligand. In
addition to the spectroscopic investigations, there exist
several kinetic studies on ligand binding to trHbN (9). In
trHbN, the O2 binding is faster by a factor of two compared
to sperm whale Mb whereas O2 dissociation is two-ordersof-magnitude slower in trHbN, due to the presence of a tunnel in the trHbN for a faster ligand diffusion to the heme
active site and the presence of ligand stabilizing
residue Tyr33 (15). It has also been shown that the ligand
binding is much faster in group I trHbs compared to the
group II trHbs, which lack a tunnel for ligand diffusion (5).
Nitric oxide has been found to play a pivotal role in
various physiological processes such as neurotransmission,
regulation of vasodilation, inhibition of mitochondrial respiration, and immune response to bacterial infection (21,22).
Overproduction of NO is potentially toxic (23). Important
biological functions of NO involve its interaction with metal
centers of heme and other metal-containing proteins (24).
Additionally, nitric oxide is also known to participate in
the reaction with superoxide to form peroxynitrite, the
moiety that triggers several reactions such as lipid peroxidation, DNA damage, or thiol oxidization (25). For heme
proteins, NO is a special ligand as it binds to both ferrous
and ferric iron on the picosecond timescale in a variety of
proteins including nitric oxide synthetase, guanylate cyclase,
hemoglobin, and myoglobin (24,26).
From crystallographic studies, it is proposed that residue
Phe62 exists in two conformations. In one, the benzene
side chain of the residue blocks the longer channel of the
tunnel path (the so-called closed state) and in the other it
does not (the open state) (11,12). By long MD simulations
(0.1 ms), Bidon-Chanal et al. have proposed that in deoxytrHbN, the Phe62 adopts the closed conformation and hence
the O2 ligand enters the protein via the short channel. In case
of oxygenated trHbN, the Phe62 prefers the open conformation, thus facilitating the entrance of the second ligand (NO)
via the long channel (27,28).
The active sites of heme proteins are often buried inside
the globin chain, which prevents direct contact with solvent.
Therefore, the ligand has to trace its way to the heme by
traversing through the globin chain. The driving force underlying the ligand migration is commonly believed to be due to
thermal fluctuations of the proteins (29). The migration pathways and ligand access sites are located in, most likely,
evolutionarily optimized well-defined regions of proteins
that can be identified with systematic experimental and
computational efforts (30). With the development of timedependent crystallographic methods, it is now possible to
investigate the time evolution of the ligand distribution after
flash photolysis of heme-bound ligand (31–34). While such
experimental methods are yet to be used routinely, computer
simulations have complemented our understanding of ligand
migration pathways, for example, in myoglobins by the socalled ligand implicit sampling method (35). In ligand
implicit sampling, locating ligand migration pathways is
Biophysical Journal 96(6) 2105–2118
Mishra and Meuwly
based on a free-energy perturbation approach applied to
simulations of the dynamical fluctuations of the protein in
the absence of a ligand. The method provides complete
three-dimensional maps of the potential of mean force for
ligand placement anywhere in the protein. By using this
method, several novel possible exit pathways have been suggested for myoglobin (35). The idea underlying potential of
mean force-based implicit ligand sampling is the fact that
diatomic ligands, often approximated as apolar, only interact
weakly with the protein, and hence their impact on conformational changes of the protein are approximated as a small
perturbation or even neglected. This approximation is,
however, vulnerable when the ligand is either charged or
possesses significant higher multipole moments, as is the
case for CN or NO. In such cases, an explicit ligand
sampling of the protein is required.
It is well known that NO can rapidly diffuse through the
protein matrix (36), can easily cross membranes (37), and
has a small barrier to escape to the bulk solvent (38). Hence,
it can be used as a probe to explore the interior of proteins,
such as active site conformations, ligand docking sites, or
solvent-accessible regions. Moreover, since the molecule
has an appreciable dipole moment, the NO stretching
frequency can also be used as a spectroscopic probe. Unfortunately, because of its weak absorption cross section and
spectral overlap with the amide bands (when it is bound to
ferrous heme), measuring the NO stretching vibration has
always remained a challenging experimental problem (39–
42). Under such circumstances, computational investigations
of NO in the protein environment are of considerable interest
(26,43).
In this work, we use the NO ligand as a structural and
spectroscopic probe for the trHbN of M. tuberculosis and
employ the recently developed three-point fluctuating
charge model for NO (43) and a suitable Morse potential
for the N-O bond. The three-point fluctuating charge model,
obtained by fitting to high-level ab initio dipole and
quadruple moments, provides an accurate description of
the electrostatic interactions between the ligand and the
protein environment by correctly describing the variation
of the multipole moments of the ligand as a function of its
bond length (43).
COMPUTATIONAL METHODS
The initial structure of the protein is the x-ray crystal structure (Protein Data
Bank entry 1IDR) and only monomer A of this homodimeric protein is
considered in this study. Hydrogen atoms are added and the internal coordinates are built by using the appropriate modules of the CHARMM program
(44). The protein contains 131 amino-acid residues, a prosthetic heme group
as well as O2 and NO ligands. All histidine residues are treated as d-protonated. The heme group is covalently bound to the N of residue His81 and the
dioxygen molecule is ligated to the FeII atom of the heme group, while the
NO ligand remains unbound. A water box with dimension 62.1 52.8 68.3 Å3 is used to solvate the protein. The water molecules are represented
via the modified TIP3P potentials (45). The water box was heated and equilibrated for 50 ps at 300 K before the protein was solvated. After deleting the
NO Migration in Truncated Hemoglobin
2107
TABLE 1
Force-field parameters for NO molecule
VNO ¼ De(1 exp(b(r r0)))2
qN ¼ a0 þ a1r þ a2r2 þ a3r3
qO ¼ a0 þ a1r þ a2r2 þ a3r3
qCoM ¼ qN þ qO
Nonbonded parameters (N)
Nonbonded parameters (O)
De ¼ 152.6 kcal/mol,
b ¼ 2.636 Å1, r0 ¼ 1.151 Å
a0 ¼ 6.3 e, a1 ¼ 11.5 eÅ1,
a2 ¼ 7.3 eÅ2, a3 ¼ 1.6 eÅ3
a0 ¼ 10.7 e, a1 ¼ 19.0 eÅ1,
a2 ¼ 11.4 eÅ2, a3 ¼ 2.4 eÅ3
3N ¼ 0.20 kcal/mol, rN ¼ 2.00 Å
3O ¼ 0.16 kcal/mol, rO ¼ 2.05 Å
The Morse potential, the atomic (fluctuating) charges, and the nonbonded
parameters (the van der Waals well depth 3 and radii r) are taken from the
literature (43,49,50), respectively.
centered point-charge model in the sense that the latter are the 0th order
expansion terms of the electrostatic potentials of the electron-density distribution. The expansion converges by considering the higher order expansion
terms, which are essentially the higher order multipole moments of the
ligand molecule. The charge model employed in this work is accurate up
to the NO-quadrupole moment and thereby has the additional advantage
of providing a more realistic description of the electrostatic interactions
between the ligand and the protein environment. While the van der Waals
parameters for the NO ligand are taken from Meuwly et al. (49), the
N-O bond is described by a Morse potential,
VM ¼ De ½1 expð bðr re ÞÞ2 ;
(1)
with dissociation energy De ¼ 152.6 kcal/mol, b ¼ 2.636 Å1, and equilibrium bond distance re ¼ 1.151 Å (50). All force field parameters for the
NO molecule are given in Table 1.
The free-energy profile along a progression coordinate (q) is estimated
from the probability distribution P(q) via the relation
DGðqÞ ¼ kB T In PðqÞ;
(2)
3
FIGURE 1 Ribbon representation of trHbN showing the structural
elements. The heme group is shown with sticks and the ligand docking sites
are shown by spheres. The docking sites are labeled according to the corresponding Xe pocket indices. The sphere-labeled PDS indicates the ligand
docking site in the proximal side of the heme group, which is not seen in
the crystallographic study of Milani et al. (11). The Phe62 residue, which
acts as a gate for ligand migration from Xe5 pocket to Xe1 pocket, is shown
with black sticks.
where kB is the Boltzmann constant (1.9875 10 kcal/mol/K) and T is the
temperature in Kelvin.
The infrared absorption spectrum of the NO molecule is calculated by
using the relation
Zu
AðuÞ ¼ u 1 exp kB T
CðuÞ;
(3)
where C(u) is the Fourier transform of the dipole-dipole autocorrelation
function,
CðtÞ ¼
water molecules overlapping the protein atoms, the simulation contains 6619
water molecules and the entire system has 21,975 atoms.
All MD simulations are carried out with the CHARMM22 force field (46)
and the CHARMM program (44). Nonbonded interactions are truncated at
a distance of 14 Å by using a shift function for the electrostatic terms and
a switch algorithm for the van der Waals terms (47). All bonds involving
hydrogen atoms are kept fixed by using SHAKE (48). The system was slowly
heated to 300 K and equilibrated for at least 300 ps before free dynamics is
performed at a constant temperature of 300 K. We have considered six starting
structures of the protein by taking snapshots when the NO ligand is in one of
the Xe1–Xe5 pockets and in the proximal docking site (PDS) (see Fig. 1 for
the locations of the NO ligand in these six snapshots, represented by spheres).
Four trajectories of 2-ns duration each were initiated from each of the six snapshots, which gives 24 trajectories each of 2-ns time length.
The recently developed three-point fluctuating charge model (43) for the
dissociated NO molecule is used to describe the electrostatics of NO. All
other interactions are treated with the CHARMM22 force field (46). The
three-point fluctuating charge model is an improvement over the atom
mð0Þ~
mðtÞi
h~
;
mð0Þ~
mð0Þi
h~
(4)
obtained from the dipole moment time series of the NO molecule accumulated from a given trajectory. For further details on the calculation of infrared
spectra, see Nutt and Meuwly (51).
RESULTS
Characterization of the ligand docking sites
The crystal structure of trHbN exhibits a continuous tunnel
through the protein matrix with two perpendicularly placed
channels. One end of each of the channels opens to the
solvent while the other toward the heme. The entrance of
the longer channel (channel I) is defined by residues Ile19,
Ile25, Val28, and Leu102 whereas the entrance of the shorter
channel (channel II) is surrounded by residues Phe91,
Biophysical Journal 96(6) 2105–2118
2108
Mishra and Meuwly
FIGURE 3 Three-dimensional view of the probability distribution of the
NO ligand during the entire period of simulation. The heme group, proximal
His81, bound O2, and Phe62 are shown and the ligand docking sites are indicated. The population of Xe4 pocket is too low to appear in the figure. The
figure is prepared using Surfplot software (67).
FIGURE 2 Contour plots in the xy-, xz-, and yz planes showing the probability
distribution of the NO ligand from all the simulations. The heme plane is along
the xy plane and the origin is shifted to the center of mass of the four N atoms of
the porphyrin ring of the heme group. The ligand situated in different Xe pockets
are labeled. The population of Xe4 pocket is too low to appear in the figure.
Ala95, Leu116, Ile119, and Ala120. All residues defining the
tunnel entrances and their inner surface are apolar. From
Xe-pressurized protein samples three docking sites along
channel II (the Xe2, Xe3, and Xe4 pockets) and two docking
sites along channel I (the Xe1 and Xe5 pockets) were found
Biophysical Journal 96(6) 2105–2118
(12). In addition to these five Xe pockets, these simulations
reveal the presence of an additional stable docking site
(called proximal docking site: PDS) situated in the proximal
side of the heme group in trHbN. A schematic diagram
showing the Xe pockets and the PDS site in the trHbN is
given in Fig. 1.
The cumulative probability distribution of the NO molecule in the three Cartesian planes from all 24 trajectories is
shown in Fig. 2. The average heme plane is in the xy plane
and the origin is at the center of mass of the four N atoms
of the porphyrin ring of the heme group. In the two-dimensional projection of the ligand density distribution, some of
the ligand docking sites overlap. In the xy plane, the Xe2
pocket (due to its proximity to the heme group) and the
Xe3 pocket can be distinguished from other pockets.
However, a distinction between the Xe1 and Xe5 pockets
is difficult in the xy plane. In the xz plane, however, the
Xe1 and Xe5 pockets can be differentiated. The spatial proximity of the Xe2 and the Xe1 pocket is best seen in the yz
plane (Fig. 2).
For a spatial description of the probability distribution of
the NO ligand from all simulations, Fig. 3 shows a threedimensional probability density of the NO ligand in trHbN
shown in its crystal structure conformation. While the
density of the ligand is shown by mesh, the heme group,
the bound O2, the proximal His81, and the Phe62 residues
are shown by sticks. In the three-dimensional projection,
the ligand docking sites as well as their relative positions
NO Migration in Truncated Hemoglobin
2109
FIGURE 4 Time evolution of the x-, y-, and z coordinates (from top to bottom at time t ¼ 0) of the position
vector of N atom of the NO ligand, with respect to the
center-of-mass of the four N atoms of the porphyrin ring
of the heme group, in four trajectories chosen to illustrate
ligand migration. The trajectories shown in panels a–d
are started from snapshots with the NO ligand in the
Xe1, Xe2, Xe3, and Xe5 pockets, respectively. The locations of the NO ligand during the simulations are marked
in each of the figures. The intermediate site in between G
and H helices is indicated by IS1 and the asterisk refers
the ligand at the entrance of channel I.
and the degree of overlap with each other are discernible.
In the distal side of the heme group, nearest to the bound
O2 ligand is the Xe2 pocket. The Xe5 and Xe1 pockets
show overlapping density, which reflects the continuity of
channel I. The Phe62 residue is situated between these two
pockets. The region of the Xe1 pocket most distant from
the heme plane corresponds to the entrance of channel I.
The Xe4 pocket has negligible ligand density in these simulations, since the ligand upon arrival at the Xe4 pocket
rapidly diffuses to bulk solvent via the opening of channel
II. The Xe3 pocket is spatially close to the Xe2 and Xe5
pockets. The ligand docking site in the proximal side of
the heme group and close to the His81 ring is the proximal
pocket, which is not seen in crystallographic studies
(11,12) and earlier simulations.
Fig. 4 shows the time evolution of the x-, y-, and z coordinates of the N atom of the NO molecule in four representative trajectories. For this purpose, the entire protein was
reoriented so that the least-squares plane containing the four
nitrogen atoms of the heme group lies in the xy plane, with
the center-of-mass of the four nitrogen atoms placed at the
origin. In the trajectory shown in Fig. 4 a, the NO ligand
is initially in the Xe1 pocket. The ligand is found to move
very rapidly from the Xe1 pocket to the Xe5 pocket and
remains there briefly (for <10 ps) before returning to the
Xe1 pocket. This process is completed within the first
50 ps of the simulation. Afterwards, the NO ligand remains
in the Xe1 pocket for ~1 ns, then proceeds toward the Xe3
pocket via an intermediate site (IS1) between helices G
and H (see Fig. 4 b). At ~1800 ps, the ligand migrates to
the Xe4 pocket and further moves along channel II. In the
trajectory shown in Fig. 4 b, the NO ligand starts in the
Xe2 pocket. The ligand remains in the Xe2 pocket for
~500 ps and then proceeds to the Xe1 pocket. After this,
rapid transitions between Xe1 and Xe3 pockets occur.
Finally, via the intermediate site between helices G and H
(IS1), the ligand moves to the Xe4 pocket and from there
it escapes to the bulk water. In the example trajectory shown
in Fig. 4 c, the ligand starts from the Xe3 pocket and rapidly
moves toward the Xe2 pocket (along channel II). The ligand
is then found to make several transitions between the Xe2
and Xe1 pockets. During the last 400 ps of the simulation,
the ligand remains in IS1. In the last trajectory (Fig. 4 d)
the ligand is initially in the Xe5 pocket and the ligand movement in this trajectory is primarily restricted to channel I
(i.e., Xe5 and Xe1 pockets; see Fig. 4 d). In several of the
calculated trajectories (i.e., 14 out of 24), the ligand escapes
to the bulk solvent in <2 ns.
The primary ligand docking sites, their distance from the
Fe atom of heme, the residues surrounding the docking sites,
and the connectivity of the docking sites with other docking
sites are given in Table 2.
The Xe1 pocket connects the Xe5 pocket with the entrance
of channel I. Starting from the Xe1 pocket, the ligand
migrates along three primary pathways: 1), to the Xe5
pocket; 2), toward the opening of channel I; or 3), toward
the Xe3 pocket. The transfer of the ligand from the Xe1
pocket to the Xe5 pocket is assisted by the rotation of the
phenyl ring of Phe62 residue. From Xe1 to Xe3, the ligand
moves via the intermediate site (IS1) in between the helices
G and H of trHbN. This intermediate site is surrounded by
Ala95, Leu98, Ala99, Ile112, Ile115, and Leu116 amino acids.
The NO ligand is found to traverse this region of the protein,
which connects the Xe1 pocket in channel I with the Xe3 and
Xe4 pockets in channel II, in several trajectories.
Xe2 pocket is the closest docking site in the distal side of the
heme group and hence is crucial for ligand rebinding and
ligand chemistry such as oxidation of NO. Xe2 pocket is the
intersection of channels I and II. Starting from the Xe2 pocket,
the ligand can either move along channel II to the Xe3 pocket
Biophysical Journal 96(6) 2105–2118
2110
TABLE 2
Pocket
Xe1
Xe2
Xe3
Xe4
Xe5
PDS
Mishra and Meuwly
Ligand docking sites in trHbN of Mycobacterium tuberculosis
Distance (Å)
13
6
12
15
9
6
Surrounding residues
62
25
115
Connectivity
28
29
98
Phe , Ile , Ile , Val , Val , Leu
Phe32, Leu98, Ala94, Phe62, Tyr33, Gln58
Phe62, Leu98, Leu66, Ile115 Ile119, Val118, Ala65
Met88, Phe91, Ser92, Ala95, Gly96, Ala123
Phe62, Ala65, Leu66, Leu98, Ile115, Val118
Ile119, Phe91, His81, Val124, Ala123, Asp125, Val126, Met77
IS1, Xe5, Xe2, Xe3
Xe5, Xe3, Xe1, Solvent
Xe1, Xe2, Xe4, IS1, Solvent
Xe3, IS1, Solvent
Xe1, Xe1, Solvent
Xe2
The averaged distance of N atom of NO to Fe when NO is in a particular docking site of the protein is given in Å.
or along channel I to the Xe5 pocket. In addition, we also
observed less frequent transitions from the Xe2 pocket to
the Xe1 pocket. In some cases, the ligand from the stable
Xe2 pocket was also found to move toward the C helix and
escape to the bulk water via an exit pathway situated between
helices C and F, and surrounded by Phe46, Thr49, Met51, and
Leu54 residues. The ligand remains in the Xe2 pocket for a
longer period of time as compared to the other docking sites
of the protein. This supports the proposal for multiligand
chemistry taking place in the active site of the protein (16,52).
The Xe3 pocket, situated in the midway of channel II, has
close access to bulk water and connects pockets Xe2 and
Xe4. The ligand from the Xe3 pocket can move toward the
Xe2 and Xe4 pockets along channel II or can move toward
IS1 before reaching Xe1. In some cases, the ligand is found
to move directly from the Xe3 pocket to the Xe1 pocket.
Since the ligand spends typically a few tens of picoseconds
in Xe3 pocket, this site is considered to be metastable.
This is in agreement with the crystallographic observation
that the Xe3 pocket is not a well-defined pocket in the A
monomer of the trHbN dimer (12).
Starting from the Xe4 pocket, the ligand either moves
along channel II toward the Xe3 pocket or escapes to the
solvent. In addition to the movement along channel II, the
ligand from Xe4 pocket is also seen to move toward IS1.
The Xe5 pocket is found in between the Xe1 and Xe2
pockets along channel I. From the Xe5 pocket, the ligand
travels along channel I either toward the Xe1 pocket or
toward the Xe2 pocket. Additionally, the ligand from the
Xe5 pocket is also found to proceed to the bulk water via
a region between the helices E and F, surrounded by Pro71,
Tyr72, Phe62, Ala65, and Pro121 residues.
The PDS is extremely stable and the ligand exhibits no
migration from this pocket during our 8 ns of simulation of
the protein with NO in this pocket. The ligand in this docking
site is surrounded by hydrophobic residues and has very little
probability to escape the docking site.
Summarizing all ligand migration pathways from the
simulations leads to a connectivity diagram for NO ligand
transfer in trHbN, which is shown in Fig. 5. Although the
apolar channels are the most preferred pathways for the
ligand migration, the NO ligand does follow pathways in
addition to the two channels, e.g., the transitions between
Xe3/Xe2 and Xe1, and transitions between Xe4/Xe3 and
Biophysical Journal 96(6) 2105–2118
Xe1 via IS1. There exist at least four different pathways
via which the ligand can migrate through the protein to the
bulk water. Two of these pathways are the openings of channels I and II, and the other two are the exit channels outside
the tunnel of the protein (in between helices E and F and
helices C and F).
Fig. 6 shows the free energy profile for the migration of
the NO ligand in the trHbN protein matrix, estimated from
the probability density of the Fe-N distance averaged over
all the calculated trajectories as described in the previous
section. The energy profile exhibits two distinct minima
separated by a barrier of 1.2 kcal/mol. While the minimum
at the lower value of Fe-N distance (~5 Å) corresponds to
the Xe2 pocket and the proximal docking site of the protein,
the broad minimum at the higher Fe-N distance corresponds
to the Xe1, Xe3, and Xe5 pockets. These three pockets
are indistinguishable in the free-energy profile along the
Fe-N distance due to frequent transitions among these
pockets that lead to a wide local minimum associated with
the corresponding pockets, making an energetic distinction
of these pockets along the Fe-N coordinate difficult. An energetically distinct characterization of individual docking sites
can be achieved by nonequilibrium sampling methods such
as umbrella sampling along some progression coordinates
that can effectively distinguish the ligand docking sites.
FIGURE 5 Connectivity network between the NO ligand docking sites
within the trHbN protein matrix. The observed ligand transitions among
various protein pockets are indicated by arrows. The loss of ligand to the
bulk solvent is indicated by arrows toward water.
NO Migration in Truncated Hemoglobin
2111
FIGURE 6 Free-energy profile for the migration of the NO ligand in the
trHbN protein matrix. The progression coordinate is the distance between
Fe atom of the heme and N atom of the NO ligand. The minimum at smaller
Fe-N distance corresponds to the Xe2 pocket and the PDS, while the broad
minimum at larger Fe-N separation corresponds to the Xe1, Xe3, and Xe5
pockets.
FIGURE 7 Time series of distances between (a) O2 of the bound O2 and
the phenolic O of the Tyr33; (b) the phenolic O of the Tyr33 and the amide
N of the Gln58; (c) the phenolic O of the Tyr33 and the amide O of the Gln58;
and (d) O2 of the bound O2 and the amide N of the Gln58, for an example
trajectory illustrating H-bonding pattern among Tyr33, Gln58, and the bound
O2 molecule.
H-bonding between O2, Gln58, and Tyr33
Fig. 8 b. It is seen that Tyr33 exhibits two conformations
with respect to the bound O2 ligand, regulating the H-bond
between the phenolic O of Tyr33 and O2. The energy barrier
between the H-bonded Tyr33-O2 pair to the free Tyr33 and O2
ligand is z1 kcal/mol. In contrast, the energy barrier to
break the H-bonding between the phenolic O of the Tyr33
and carbonyl O of the Gln58 is z2 kcal/mol (see Fig. 8 b).
As shown in Fig. 8 a, the amide group of Gln58 and the
phenol ring of Tyr33 are found in three different conformations that also differ in their relative orientation. The
minimum found at 3 Å corresponds to the situation where
the amide O of Gln58 acts as an H-bond acceptor of the
phenolic H of Tyr33 and the phenolic O of Tyr33 acts as an
H-bond acceptor of the amide H of Gln58 (Fig. 8 a(II)).
The intermediate minimum at 4.8 Å corresponds to the
situation shown in Fig. 8 a(I), in which Tyr33 participates
in H-bonding to the bound O2 ligand as well as with the
amide group of Gln58. The conformation with the distance
between the N atom of Gln58 and the O atom of Tyr33 at
6.5 Å reflects the situation where the amide group of Gln58
is engaged in H-bonding with O2 of the O2 ligand and
Tyr33 participates in the H-bonding with the amide O of
Gln58 (Fig. 8 a(III)).
The experimental spectroscopic and kinetic studies suggest
the presence of an H-bonding network involving Tyr33,
Gln58, and bound O2 in the heme active site (15,17,18).
Computational studies have been carried out to further characterize the H-bonding network in the heme active site for
deoxy- and oxy-trHbN (28). In the following, we corroborate
the experimental findings regarding the H-bonding network
between the bound O2 ligand and Tyr33 and Gln58 residues
by analyzing the time evolution of their interactions and
provide energetic estimates for these H-bonds. Fig. 7 illustrates the H-bonding pattern from a typical MD simulation
and shows the time series of the distance between 1), the
O2 atom (of O2) and the phenolic O of the Tyr33; 2), the
amide N of the Gln58 and the phenolic O of the Tyr33; 3),
the phenolic O of the Tyr33 and the amide O of the Gln58;
and 4), the O2 of the bound O2 and the amide N of the
Gln58, are given for such an example trajectory. Initially,
H-bonds between the O2 and the phenolic O of the Tyr33,
and the phenolic O of the Tyr33 and the amide N of the
Gln58, are present (see Fig. 7 a). This situation is graphically
illustrated in Fig. 8 a(I). After 60 ps, the phenolic O of the
Tyr33 approaches the carbonyl O of the Gln58 (see the
reduced bond distance in Fig. 7 c), leading to the breaking
of the H-bond between the Tyr33 and the O2 atom and the
formation of the H-bond between the amide O of the Gln58
and the phenolic O of the Tyr33 (shown in Fig. 8 a(II)). After
z500 ps, the Tyr33 separates further from the O2 ligand,
while the amide group of Gln58 moves closer with the possibility to form an H-bond between the amide N of Gln58 and
O2 of the bound O2 (Fig. 7 c).
The free-energy profiles, associated with the H-bonded
network calculated from all 24 trajectories, are shown in
Phe62 controlled ligand migration along channel I
We have analyzed the trajectories calculated in this work to
discuss the opening and closing of the Phe62 gate and its
effects on the ligand migration. Similar to previous studies
(11,12,27,28), we find the Phe62 residue exhibiting two
conformations. In one of the conformations, the phenyl
ring of the residue blocks the channel I while in the other
it lets the ligand move along channel I. Our simulations
revealed that the Phe62 residue in the oxy-trHbN exhibits
Biophysical Journal 96(6) 2105–2118
2112
Mishra and Meuwly
FIGURE 8 (a) Schematic representation of orientation
of Tyr33, Gln58, and the bound O2 molecule during the
trajectory shown in Fig. 7. (b) Free-energy profiles for
H-bonding among Gln58, Tyr33, and the bound O2 molecule. (Inset) Progression coordinates associated with the
energy curves.
primarily the open conformation (probability >70%), see
Fig. 9 a, where the averaged probability distribution of the
dihedral angle Ha-Ca-Cb-Cg of Phe62 residue provides
a comparison between the populations of the closed and
open conformations. By analyzing individual trajectories,
we found that the change in conformation is a less frequent
event. The conformational change from an open state to
a closed state is more rare than the opposite, indicating the
presence of a larger energy barrier for an open-to-closed transition. This is verified from the free energy profile calculated
for the ring torsion of the Phe62 residue. For the oxy-trHbN,
the open state conformer is found 1.5 kcal/mol more stable
than the closed conformer. The energy barrier for closedto-open transition is ~1.2 kcal/mol whereas the reverse
energy barrier is >3 kcal/mol (see Fig. 9 b). The barrier
for ring torsion originates from a combination of 1), Hbond breaking and formation between Tyr33 and Gln58
residue pair; and 2), steric interactions between Phe62 and
Gln58 residues.
To illustrate the ligand migration associated with the
open-closed transition of the Phe62 residue, we present an
Biophysical Journal 96(6) 2105–2118
example trajectory in Fig. 9, c and d, where the ligand movement and Phe62 ring torsion are visibly correlated. The time
series of the dihedral angle Ha-Ca-Cb-Cg of Phe62 is plotted
in Fig. 9 c and the time series of the x-, y-, and z coordinates
of the NO ligand in the trajectory is plotted in Fig. 9 d. (The
ligand transition between the Xe5 and the Xe1 pockets is
indicated by the vertical dashed lines in Fig. 9, c and d.)
During this simulation, the phenyl ring adopts both closed
and open conformations and during the first nanosecond of
the simulation, three transitions occur between the two
conformations. The ligand is initially found in the Xe5
pocket, where it stays for ~240 ps before it moves along
channel I toward the Xe1 pocket. During the transition of
the ligand from the Xe5 pocket to the Xe1 pocket, the
Phe62 residue exhibits open conformation and soon after
the transition, the residue adopts the closed conformation
(see Fig. 9 c at 300 ps). The ligand remains in the Xe1 pocket
for next 250 ps, during which the Phe62 remains in the closed
conformation. At ~475 ps, Phe62 adopts the open conformation and 5 ps later, the ligand moves along the open channel
toward Xe5 pocket. This example trajectory clearly
NO Migration in Truncated Hemoglobin
2113
FIGURE 9 (a) Average probability distribution of the
conformations of the dihedral angle Ha-Ca-Cb-Cg of
Phe62 residue in oxy-trHbN. (b) Free-energy profile associated with the ring torsion of the Phe62 residue. The dihedral
angle of 50 and þ50 corresponds to the open and
closed states of the Phe62 residue, which refer to the situations when the phenyl ring of Phe62 residue blocks and
unblocks, respectively, the passage between the Xe5 and
Xe1 pockets along channel I. Time series of (c) Phe62
phenyl ring torsion and (d) x-, y-, and z coordinates of
the NO ligand in an example trajectory to illustrate the
correlation between the movement of Phe62 and ligand
migration. The vertical dashed lines at 240 ps and 480 ps
indicate the migration of the ligand from the Xe5 to the
Xe1 pocket and the reverse migration, respectively.
demonstrates the ligand migration being controlled by the
change in the Phe62 conformation.
Infrared spectra of NO in trHbN
The harmonic (ue) and the fundamental (ne) frequency associated with a Morse potential (Eq. 1) are given by
sffiffiffiffiffiffiffiffi
2De
ue ¼ Zb
;
m
"sffiffiffiffiffiffiffiffi
#
2De Zb
:
ð5Þ
ne ¼ Zb
m
m
With the Morse potential used in this work, the analytic
fundamental and harmonic frequencies of NO are (ne)
1798.8 cm1 and (ue) 1830.1 cm1, respectively. To
investigate the performance of the Morse potential used for
N-O bond in the MD simulations, we calculated the infrared
spectrum of an isolated NO molecule in vacuum. The resulting spectrum shows a sharp peak at 1837.5 cm1. The difference of 39 cm1 compared to the calculated fundamental
frequency (ne) is consistent with the previous investigations
for similar systems (51,53) and is related to two factors: 1),
the classical treatment of the Morse potential; and 2), the
use of Verlet integrator with the time step of 1 fs employed
to integrate the equations of motion in the MD simulations
(51,53). The experimental gas phase infrared spectrum of
NO shows absorption at 1875.9 cm1 (50). In myoglobin,
the infrared spectrum of photodissociated NO exhibits two
peaks at 1857 and 1867 cm1 and spreads over a spectral
window of 10–30 cm1 between 1840 and 1880 cm1
(39,42).
The infrared spectrum of NO in the protein environment
averaged over all 24 individual trajectories is broad with
extended tails to both sides of the central, most intense
feature, and exhibits several peaks as shown in Fig. 10 a.
It spans over a spectral region of 20 cm1 between 1830
and 1850 cm1, centered around the gas phase NO absorption peak at 1837.5 cm1 (see dashed line in Fig. 10 a).
The averaged infrared spectrum shows an intense peak at
1837.5 cm1 with a shoulder at 1839 cm1. Two additional
peaks with moderate-to-high intensity are seen to the red (at
1835.5 cm1) and blue (at 1840.5 cm1) side of the central
peak. The position, relative intensity, and width of six
Gaussian functions fitted to the spectral features of
Fig. 10 a are given in Table 3.
Fig. 10 b shows NO-infrared spectra from four trajectories, which differ in the ligand sampling particular regions
FIGURE 10 (a) Infrared spectrum of NO ligand averaged over 24 spectra
calculated from individual trajectories. (b) NO infrared spectra from four
trajectories, which differ in the regions of protein sampled by the ligand.
(c) Averaged infrared spectra of NO in the Xe1 (black), Xe2 (red),
Xe5 (green), and the proximal pocket (blue). The absorption of NO molecule in the gas phase is indicated by the dashed line at 1837.5 cm1.
Biophysical Journal 96(6) 2105–2118
2114
Mishra and Meuwly
TABLE 3 Position, intensity, and full width at half-maximum
(FWHM) of the Gaussian functions describing the profile of the
averaged infrared spectrum of NO in trHbN (shown in Fig. 10 a)
1
Frequency (cm )
1834.3
1835.8
1837.5
1838.9
1840.6
1842.0
Intensity (%)
FWHM
45.5
75.5
100.0
90.0
92.3
52.0
1.97
2.05
3.14
1.88
2.88
3.16
inside the protein. The black line is an infrared spectrum
calculated from a trajectory where NO primarily remains in
the Xe1 and Xe5 pockets, with occasional migration to
Xe3. The red spectrum corresponds to a trajectory in which
NO migrates between Xe2 and Xe4, whereas the broad and
structured green spectrum corresponds to a trajectory in
which the NO molecule migrates between Xe5 and Xe1,
and the entrance of channel I. Finally, the blue spectrum in
Fig. 10 b arises from a trajectory with the NO molecule in
Xe2. This information alone is not sufficient to assign particular spectral features to specific pockets sampled. To this
end, Fig. 10 c shows the averaged NO spectra when the
ligand movement is restricted to a given ligand docking
site. Such docking-site specific spectra provide a means for
a spectroscopic identification of ligand docking sites in
a protein. To achieve this, we collected the time series of
the dipole moments of NO from those parts of trajectories
where the ligand was localized in a given docking site
from which pocket-specific spectra were obtained. By averaging over all such pocket-specific spectra from different
trajectories, we obtained averaged infrared spectrum of NO
ligand in particular docking sites. Since the ligand was not
found in the Xe3 and the Xe4 for a sufficiently long time
to calculate meaningful pocket-specific infrared spectra, the
analysis is only carried out for Xe1, Xe2, Xe5, and the proximal docking site (see Fig. 10 c). By combining the information from Fig. 10, b and c, the following assignments are
proposed: for NO in the Xe1 pocket, an infrared absorption
occurs at 1837.5 cm1 (i.e., unshifted with respect to free
NO), whereas the infrared absorption of the ligand in the
Xe5 pocket leads to signals at 1835 and 1841 cm1. The
ligand in Xe2 pocket shows three distinct absorption maxima
located at 1834, 1839, and 1842 cm1. The ligand in Xe3 or
Xe4 pocket shows red-shifted absorption (at <1834 cm1).
Finally, for the NO molecule in the PDS, a blue-shifted broad
infrared peak at 1847 cm1 is found. In conclusion, the
infrared spectrum for unbound NO inside truncated hemoglobin is expected to exhibit a relatively broad (z20 cm1)
spectrum with largely unresolved bands centered around the
absorption of free NO. For a spectroscopic characterization
of the ligand docking sites, however, site-specific infrared
spectra need to be recorded. This may also include investigation of suitably mutated proteins to block particular ligand
migration pathways.
Biophysical Journal 96(6) 2105–2118
DISCUSSION AND CONCLUSIONS
By using the ligand as a probe, the present simulations have
characterized the internal structure of trHbN including active
site conformation, ligand migration pathways, ligand docking sites, and solvent-accessible regions. The connectivity
network given in Fig. 5 shows the possible transition pathways of the ligand within the protein matrix. The tunnel
system of trHbN plays an important role in determining
and controlling ligand entrance, migration, and rebinding.
The ligand is also seen to follow migration pathways besides
the tunnel, for example, migration from Xe1 and Xe3 pocket
via IS1 (see Fig. 5). In addition to the five Xe pockets found
in the crystallographic study of Milani et al. (12), the present
simulations find another ligand docking site in the proximal
side of the heme group in trHbN. The simulations reveal four
different regions of the protein from which the ligand can
escape the protein matrix to the bulk water. Two of these
pathways are the openings of channel I and II, surrounded
by apolar residues. The other two exit channels fall outside
the tunnel of the protein, accessible from the Xe2 and Xe5
pockets. While the exit pathway close to the Xe5 pocket
lies between helices E and F (surrounded by Pro71, Tyr72,
Phe62, Ala65, and Pro121 residues), the exit path close to
the Xe2 pocket is situated between the helices C and F (surrounded by Phe46, Thr49, Met51, and Leu54). Both of these
extratunnelar exit paths are surrounded by at least one polar
residue, e.g., Thr, Pro, or Tyr. The exit channels surrounded
by polar residues are expected to be the preferred escape
channel for charged or highly polar ligands. Recently, a study
involving the release of NO3 (the product of NO detoxification) from the heme distal side to solvent finds that the polar
nitrate anion does not escape the protein via the well-characterized apolar tunnels. Instead, the anion prefers a path
close to the Met51 and Thr49 residues in between helices C
and F (54).
The above discussion opens the possibility for competing
ligand-migration pathways operating in the protein matrix. A
nonpolar ligand, such as O2, prefers protein channels delineated by apolar residues. On the contrary, a highly polar
ligand, such as the nitrate anion (NO3), follows exit pathways surrounded by polar residues. The three-point fluctuating charge model, employed in this work for NO, correctly
describes the strong quadrupole moment of the ligand.
Therefore, NO represents an intermediate case, where the
ligand is neither apolar nor highly polar. In such a case,
a competition between polar and nonpolar pathways is
possible, as is seen in this work (see Fig. 5).
Other recent studies exploring the interior of oxy-trHbN
were carried out with a grid-based MD method for fast and
unsupervised exploration of protein channels (55). In this
method, a precomputed grid of forces for protein conformations interact with the rigid probe (ligand). Although such an
approach is computationally efficient, it ignores the influence
of the ligand on the protein dynamics, which, in the present
NO Migration in Truncated Hemoglobin
work, is found to be important. Consequently, this study,
although it reports the presence of the exit pathway between
E and F helices, failed in locating the proximal docking site,
the intermediate site (IS1) between Xe1 and Xe3 pocket, and
the nonpolar exit pathway (between C and F helices), shown
to exist in the present work. All experimentally and computationally characterized pathways are found from a single
computational model in the present study, which is not the
case for previous simulations (28,54,55). The additional exit
channels are expected to be important for removing the products of NO detoxification reaction from the protein matrix.
Although our simulations are not sufficiently long to capture
the reentrance of the NO ligand from bulk to protein, by
observing four exit routes of the ligand, we anticipate that
the ligand can also enter the protein matrix via these pathways.
This can be verified by running long simulations with ligand
outside the protein matrix. The increased number of access
routes of the ligand should also increase the probability of
capturing nitric oxide for efficient detoxification.
Most likely, the novel observations of the proximal docking site as well as the exit channels, besides the tunnel openings, are consequences of using an accurate electrostatic
model for the ligand. The Xe pockets and tunnel branches
observed from crystallographic studies suggest possible
ligand migration sites within and through the protein (56).
However, other and additional sites might be found from
atomistic simulations. The interactions between protein residues and the ligand mutually influence their dynamics and
may open additional localization sites and migration pathways. This has been previously shown for myoglobins
(35,57), and this study is an additional example. In this
context, it should be noted that simulations, in which the
ligand location is determined implicitly from the classical
molecular interaction potential (as in (27,28,52,55)), are
liable to failure in capturing the novel phenomena that arise
solely due to explicit interaction of the ligand with the fluctuating protein.
In this work, the presence, energetics, and dynamics of the
active-site hydrogen-bonding network has been characterized explicitly. The resonance Raman spectrum of the oxytrHbN shows the Fe-O2 stretching mode at 562 cm1
(17,18). Upon mutation of the Tyr33 to Leu33, this peak
shifted to 540 cm1, which is the Fe-O2 stretching frequency
observed in most other hemoglobins and myoglobins
(17,18). One possible reason for this observation is the presence of an H-bonding between Tyr33 and the bound O2
ligand. Furthermore, a red shift of the Fe-O2 stretching
frequency was seen upon Gln58Val mutation, indicating an
H-bond between the bound O2 and the Gln58 residue
(17,18). Finally, the kinetic and equilibrium constants for
the reaction of ferrous HbN with O2 compared to those of
other proteins reveal that the O2 binding is twofold faster
in trHbN compared to sperm whale Mb, whereas O2 dissociation is two-orders-of-magnitude slower in trHbN. This is
because of the presence of a tunnel in the trHbN for a faster
2115
ligand diffusion to the heme active site and the presence of
a ligand-stabilizing residue (Tyr33) restricting ligand dissociation (15). The spectroscopic and kinetic studies thus suggest
the presence of an H-bonding network in the heme active
site. Previously, the existence of such a network has been
indirectly characterized through Tyr33Phe and Gln58Ala
mutational studies (28).
The present simulations show the presence of a dynamic
H-bonding network between the bound O2 ligand and
Tyr33 and Gln58 residues. From detailed analysis of the
residue movements, it is concluded that the phenolic O of
Tyr33 plays the role of both H-bond donor and acceptor
with the amide N of Gln58. Additionally, the phenolic O of
Tyr33 also participates as an H-bond donor to the amide O
of Gln58. This is in contrast to previous results (28) where,
from one 50-ns trajectory for oxy-trHbN, it was found that
Tyr33 acts exclusively as H-bond acceptor of the amide H
of Gln58 and as H-bond donor to bound O2. On the contrary,
our simulations suggest that the O2 ligand acts as H-bond
acceptor of both the phenolic H of Tyr33 as well as the amide
H of Gln58, and the H-bond between Tyr33 and O2 is
dynamic in nature. Three different conformations arising
from the mutual H-bonds between these moieties have
been identified (see Fig. 8 a) and energetic estimations of
the involved H-bonds have been provided (Fig. 8 b). While
the breaking of H-bond between O2 and Tyr33 pertains
a barrier of 1.2 kcal/mol, the barriers involving the breaking
of H-bonds between Tyr33 and amide N and amide O of
Gln58 amounts to 1 kcal/mol and 2 kcal/mol, respectively.
The H-bonds among these moieties are frequently formed
and broken during simulations. The small energy barriers
indicate that the H-bonds in the heme active site are not
energy-demanding. The dynamic H-bonds involving small
energy requirements support the ligand chemistry that takes
place in the heme active site. Since the stability and mobility
of the intermediates and the products of the NO detoxification process depend on the surrounding residues, the low
energy barriers are desirable for accommodation of different
reactive conformations that may play a role in the detoxification reaction.
The Phe62 residue situated in the helix E of the trHbN lies
in a strategic position to control the ligand migration between
Xe5 and Xe1 pockets along channel I. From crystallographic
studies it is known that Phe62 adopts two conformations,
differing by a rotation around the Ca-Cb bond (11,12).
This aspect has been further studied by MD simulations
(27,28). By comparing the energy barriers associated with
ligand migration along the two channels, a dual path mechanism has been postulated, stating that O2 enters the deoxytrHbN from channel II, while NO enters the oxy-trHbN from
channel I (27,28). The present simulations substantiate this
observation with additional facts such as energy barrier
between the two conformations and direct observation of
the role of the Phe62 in ligand migration. We have estimated
the energy barrier for closed-state-to-open-state transition as
Biophysical Journal 96(6) 2105–2118
2116
1.2 kcal/mol, whereas the reverse energy barrier is z3 kcal/
mol. Owing to the larger barrier, open-to-closed transition is
less frequent than the opposite. Our simulations revealed that
the open state of the Phe62 residue is prevalent in the case of
oxy-trHbN. It has been found that ligand migration between
pockets Xe1 and Xe5 along the channel I is correlated to
a conformational change of the Phe62 residue. The role of
Phe62 in trHbN as a gate controlling the ligand migration
along channel I is reminiscent of His64 in myoglobin, where
no permanent channel exists in the molecular structure of the
protein that connects the active site to the outside, but an
outward movement of the His64 imidazole side chain may
transiently open a pathway through which ligands may enter
or exit the distal heme cavity (58–61).
Using an anharmonic potential for the bond-stretching and
accurate electrostatic interactions including higher multipole
moments, for several diatomic ligands (such as CO, CN,
and NO) in myoglobin, it has been shown that the experimentally observed splittings of the ligand absorption spectrum can be understood from MD simulations (51,53,
62–64). The averaged infrared spectra of NO, calculated in
this work (Fig. 10 a), is broad and extends over a spectral
window of 20 cm1 with a central intense peak at
1837.5 cm1. The averaged spectrum is broad with tails at
both sides of the maximum and exhibits several splittings;
these are typically 1.5–2 cm1. The considerable width of
the spectrum is in qualitative agreement with the experimental infrared spectrum of NO in myoglobin (39,42), where
both blue and red shifts of the central intense peak are
observed. Similar to this spectra (see Fig. 10 a), the experimental spectra of dissociated NO in myoglobin (39,42) are
broad and structured with peaks separated by a few wave
numbers. As for photodissociated CO in myoglobin, these
peaks most likely correspond to conformational substates
which, however, have not yet been unambiguously assigned.
In addition to the averaged infrared spectra of NO, the
individual spectra arising from trajectories, where ligand
samples different regions of protein, are also analyzed. In
recent years with the development of experimental techniques, it is now possible to record infrared spectra of ligands
in specific ligand docking sites and spectroscopically characterize the docking sites of the protein (65,66). This has also
been achieved in this computational work where pocketspecific NO infrared spectra have been calculated. By
comparing the spectra shown in Fig. 10, a–c, the following
attempt to correlate structure and spectroscopy is made:
The central part of the averaged spectrum originates from
NO in Xe1, Xe2, and Xe5, which are buried inside the
protein and close to the heme active site. The peaks toward
the red side of the averaged spectrum are primarily due to
the ligand in Xe3, Xe4, and the opening of channel I. These
positions are away from the heme active site and close to the
surrounding bulk solvent, which gives rise to the red-shifted
peaks. On the other hand, the blue-shifted tail of the averaged
infrared spectrum is primarily due to the ligand in the proxBiophysical Journal 96(6) 2105–2118
Mishra and Meuwly
imal pocket, which consists of hydrophobic residues such
as Ile119, Phe91, His81, Val124, Val126, Ala123, Met77, and
Asp125. The polar side chain of Asp125 lies close to the
surrounding solvent molecules and away from the proximal
docking site, thus keeping the proximal docking site hydrophobic. The contribution of the Xe3, Xe4, and the proximal
docking sites to the overall spectrum is expected to be rather
minimal, whereas the overall spectrum is expected to be
dominated by the ligand located in Xe1, Xe2, and Xe5.
In summary, we have studied nitric oxide migration in the
trHbN of M. tuberculosis via molecular-dynamics simulation, by using a fluctuating three-point charge model and
a Morse potential for the NO molecule. By analyzing the
ligand probability density, we have characterized the primary
ligand docking sites in the protein matrix. In addition to the
five Xe pockets found in the crystallographic study of Milani
et al. (12), our simulations find another ligand docking site
on the proximal side of the heme group in trHbN. By
studying the ligand dynamics, a connectivity network could
be determined that describes transition pathways of the
ligand in the protein matrix including novel migration pathways and exit channels. A structural and energetic account of
dynamic H-bonding network (among Tyr33, Gln58, and
bound O2) operating in the heme active site has been found
and characterized and the pivotal role of Phe62 in ligand
migration has been confirmed. Finally, the simulations allow
prediction of the (site-specific) infrared spectra of NO in
trHbN, which as yet have not been observed experimentally.
The different bands of the infrared spectrum have been assigned through comparison with pocket-specific infrared
spectra of NO ligand and it will be interesting to compare
these findings with experiments.
The authors thank Mr. Christian Wäckerlin for helpful discussions.
Financial support from the Swiss National Science Foundation is gratefully
acknowledged.
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9164
J. Phys. Chem. A 2007, 111, 9164-9168
Theoretical Calculation of the Photodetachment Spectra of XAuY- (X, Y ) Cl, Br, and I)
Sabyashachi Mishra*
Department of Chemistry, Technical UniVersity of Munich, D-85747, Garching, Germany
ReceiVed: May 14, 2007; In Final Form: July 8, 2007
The photodetachment spectra of the title molecules have been calculated, taking electron correlation and
spin-orbit coupling into account and employing improved relativistic effective core potentials for gold and
the halogen atoms. The calculated spectra have been compared with existing experimental spectra. The spinorbit splitting of several degenerate electronic states has been calculated. The composition of the spin-orbit
eigenstates are analyzed in terms of scalar relativistic electronic states. A comparison of the relative position
of peaks in the calculated photodetachment spectra of the title molecules has been made.
Introduction
The chemistry of gold compounds has always been a hot topic
due to the unique properties of gold, which are influenced by
relativistic effects, and for its potential applications in material
science, medicine, and catalysis. The multiple personalities of
gold have been described in a recent review by Pyykkö, where
a detailed account of the gold chemistry can be found.1
Recently, we assigned the photodetachment spectra (PDS)
of Schröder et al.2 for AuX 2 , X ) Cl, Br, and I, by taking
spin-orbit (SO) coupling into account and employing improved
relativistic effective core potentials (RECP) for gold and the
halogen atoms.3 We also emphasized the relevance of SO
coupling in the spectroscopy of heavy elements by comparing
our results with experiment2 and with other scalar relativistic
theoretical studies;4 see ref 3.
While the symmetric gold dihalides (AuX 2 ) have received
some attention,2-8 the nonsymmetric gold dihalides (XAuY-,
X * Y), to our knowledge, have remained unexplored.
In the present study, we have performed ab initio electronic
structure calculations on XAuY- (X, Y ) Cl, Br, and I), taking
the SO coupling explicitly into account. Unlike the symmetric
dihalides, the excited-state spectroscopy of the nonsymmetric
dihalides cannot be properly described via single-reference
correlation methods. Therefore, in contrast to our previous
work,3 where the coupled-cluster method was used, we have
employed multireference methods to calculate the photodetachment spectra of the title molecules. In addition to a reassignment
of the experimental PDS of the symmetric gold dihalides, our
results lead to a theoretical prediction of the PDS of nonsymmetric gold dihalides, namely, ClAuBr-, ClAuI-, and BrAuI-.
Ab Initio Calculations
The structural and electronic properties of XAuY- have been
determined by using quantum chemical methods where the gold
and halogen atoms are described by RECP. While the gold atom
is described by two-component relativistic pseudopotentials (i.e.,
scalar relativistic and SO potentials) of the energy-consistent
variety supplemented by an energy-optimized (12s12p9d3f2g)/
[6s6p4d3f2g] valence basis set,9 we have used one-component
(i.e., SO averaged) semilocal energy-adjusted pseudopotentials
* To whom correspondence
[email protected].
should
be
addressed.
E-mail:
for the halogen atoms.10 The valence electrons of Br and I are
described by basis sets of augmented quadruple-ζ quality,
composed of optimized contracted s, p, d, f, and g functions,10
whereas the valence shell of Cl is described by optimized
contracted s and p functions of augmented quadruple-ζ quality.11
The d, f, and g polarization functions are obtained from the
augmented correlation-consistent polarized valence quadruple-ζ
(aug-cc-pVQZ) basis set of Woon and Dunning.12 A core
polarization potential (CPP)13 calculation for the halogen centers
is performed during every calculation using the CPP parameters
taken from ref 10.
The geometries of the XAuY anions have been optimized in
their respective ground states by a scalar relativistic (neglecting
SO effects) coupled-cluster calculation with singles and doubles
and perturbative account of triple excitations (CCSD(T)). The
calculations are performed in the largest Abelian point group
of the corresponding systems, that is, D2h for the symmetric (X
) Y) and C2V for the nonsymmetric (X * Y) linear gold
dihalides. The closed-shell anionic species possess an electronic
ground state of 1Σ +
g symmetry with the following valenceshell electronic configuration: 1σ 2g 1σ 2u 1π 4u 2σ 2g 2σ 2u 3σ 2g 1π 4g
1δ 4g 3σ 2u 2π 4u 4σ 2g 2π 4g (g/u notation applies to the symmetric
dihalides only). Detachment of one electron from the highestoccupied 2πg molecular orbital of the anion gives rise to the
X̃2Πg ground state of the neutral species. We employ the
multireference configuration interaction (MRCI) method, which
uses state-averaged (over the lowest two 2Π, two 2Σ+, and one
2∆ states) complete active space self-consistent field (SACASSCF) orbitals as the N-electron basis, for a scalar relativistic
description of the lowest eight electronic states at the reference
geometry of the anion. The active space involves all but 8
valence electrons, correlated in 14 orbitals.
The SO interaction was treated by the contracted SO
configuration interaction method after the electron correlation
step, diagonalizing the SO matrix in the space of all SO-free
electronic states of interest.14 The scalar relativistic orbitals
obtained from the MRCI calculations are used to calculate the
SO matrix elements. The SO matrix elements are computed
using the SO pseudopotential cited above9 for gold and SO
pseudo-operators by Dolg,11 adapted to the scalar RECP used
for the halogen atoms.10 All calculations have been performed
using the MOLPRO program suite.15
10.1021/jp0736645 CCC: $37.00 © 2007 American Chemical Society
Published on Web 08/22/2007
Photodetachment Spectra of XAuY- (X, Y ) Cl, Br, I)
TABLE 1: Optimized Bond Distances in Å at the CCSD(T)
Level for XAuYXAuY-
X-Au
Au-Y
AuCl 2
AuBr 2
AuI 2
ClAuBr-
2.2836
2.4086
2.5754
2.2622
2.2700
2.4184
2.3984
2.5564
2.5647
ClAuIBrAuI-
TABLE 2: Scalar Relativistic Detachment Energies (in eV)
from the X̃ 1Σ+ State of XAuY- Computed by the MRCI/
SA-CASSCF Methoda
state
2
AuCl2
state
2
AuBr2
AuI2
X̃ Πg
Ã2Σ +
g
B̃2∆g
2
C̃ Πu
D̃2Σ +
u
4.618
4.863 (0.245)
6.243 (1.625)
6.319 (1.701)
6.561 (1.943)
X̃ Πg
Ã2Σ +
g
B̃2Πu
2 +
C̃ Σ u
D̃2∆g
4.721
5.221 (0.500)
6.005 (1.284)
6.236 (1.515)
6.548 (1.827)
5.220
6.107 (0.887)
6.127 (0.907)
6.332 (1.112)
7.411 (2.191)
X̃2Π
Ã2Σ+
B̃2Π
C̃2∆
D̃2Σ+
ClAuBr
4.761
5.165 (0.404)
6.358 (1.597)
6.508 (1.747)
6.529 (1.768)
X̃2Π
Ã2Σ+
B̃2Π
C̃2Σ+
D̃2∆
ClAuI
4.603
5.259 (0.656)
6.147 (1.544)
6.170 (1.567)
6.570 (1.967)
BrAuI
4.610
5.343 (0.733)
5.757 (1.147)
5.918 (1.308)
6.659 (2.049)
a Values in parentheses refer to the MRCI/SA-CASSCF results with
the vertical detachment energy of the X̃2Π adjusted to zero.
Results and Discussion
The optimized geometries of the ground state of the symmetric and nonsymmetric XAuY anions are given in Table 1.
For the comparison of calculated and experimental bond
distances of AuX 2 species, see ref 3. The Au-Cl bond length
is found to be around 2.27 Å, whereas the Au-Br and Au-I
bond distances are around 2.40 and 2.56 Å, respectively, for
all of the species; see Table 1.
The vertical detachment energies of the lowest eight electronic
states with respect to the electronic ground state of the anion
(X̃ 1Σ+) determined by performing MRCI/SA-CASSCF calculations are reported in Table 2. Since the energy spacing of the
electronic states of the neutral XAuY matters, rather than the
absolute values of the vertical detachment energies, we have
also reported, in Table 2, the difference in vertical detachment
energies of the excited states of the neutral XAuY with respect
to its ground state. This allows a comparison of the relative
positions of the scalar relativistic band heads of the PDS. The
relative energies of the excited scalar relativistic electronic states
of the neutral XAuY are plotted against their molecular weight
in Figure 1. It is found that the electronic energies are a linear
function of molecular mass, to a good approximation. While
the energy difference of the (1) 2Σ+ state and the (1) 2∆ state
with respect to the (1) 2Π state (the ground state) increases
linearly with molecular mass, a reverse trend is observed for
the (2) 2Σ+ and (2) 2Π states; see Figure 1. Several changes
occur in the ordering of the electronic states when going from
AuCl2 to AuI2. In particular, the 2∆ state, which lies high in
the energy for AuI2, is the second excited state in AuCl2; see
Figure 1. This electronic state was overlooked in our earlier
work.3 Although the 2∆ state will have a negligible effect on
the observed spectroscopy of AuI2 and, to some extent, AuBr2,
for AuCl2, however, it is indispensable.
The calculated SO splittings in the two 2Π states and the 2∆
state of XAuY are given in Table 3. The SO splitting of both
of the 2Π states increases, as expected, from AuCl2 to AuI2,
with the exception of the small SO splitting of the (2) 2Π state
J. Phys. Chem. A, Vol. 111, No. 37, 2007 9165
of AuBr2. In Table 3, the numbers in parentheses are the SO
splittings of the corresponding degenerate state when their
coupling with neighboring states is neglected, that is, when they
are assumed isolated. When compared with the true SO splitting,
these numbers reveal the extent of interaction between different
SO-free states via the SO coupling operator. In AuCl 2, the X̃2Π
state interacts significantly with the Ã2Σ+ state via the SO
interaction. The SO splitting of the former state decreases
substantially (from its value in the isolated 2Π state approximation) as a result of the repulsion of first two 1/2 states, which
arise mainly from the Ã2Σ+ and X̃ 2Π states; see Tables 3 and
4. This degree of interaction gets reduced for the heavier gold
dihalides since the energy separation between the X̃ 2Π and
the Ã2Σ+ increases from AuCl2 to AuI2; see Figure 1. In AuI2,
for example, this mixing almost vanishes and so does the
difference between the true SO splitting and the SO splitting
from the isolated-state approximation; see Table 3. By comparing the true SO splitting and the SO splitting calculated with
the inclusion of the SO contributions of only halide atoms (i.e.,
SO contributions from the Au atom are neglected), it is found
that the halogen centers contribute about 80% of the total SO
splitting of the (1) 2Π state.
While the (1) 2Π state arises from an orbital with antibonding
overlap of gold and the halogen centers, the (2) 2Π state
emanates from the orbital centered primarily on the halogen
centers. Therefore, the true SO splitting as well as the SO
splitting obtained in the isolated-state approximation of the (2)
2Π state, of which more than 98% are due to the halogen centers,
increase from AuCl2 to AuI2. By comparing the SO splittings
obtained from these two methods, it can be seen that the isolatedstate approximation of the (2) 2Π state gets poorer as one
approaches heavier systems due to the increasing interaction
of this state with the (2) 2Σ+ state via the SO operator. Although
the scalar relativistic energy difference between these two
electronic states of all of the systems remains nearly the same,
see Figure 1, for the heavier halides due to the large SO splitting
in the (2) 2Π state, the (2) 2Σ+ state lies in between the 3/2 and
1/2 components of the (2) 2Π state, and the repulsion between
the low-lying 2Σ +
1/2 state and the high-lying 1/2 component of
the (2) 2Π state increases the true SO splitting compared to the
SO splitting in the isolated-state approximation.
The SO splitting of the 2∆ state remains nearly the same,
that is, around 1.3 eV for all molecules. The calculated SO
splitting in the 2∆ state of XAuY is quite similar to the atomic
SO splitting of the 5d orbital of Au (1.5 eV), which is due to
the fact that the 2∆ state originates from the molecular orbital
localized on the central Au atom. The true SO splitting is only
slightly different from the SO splitting obtained in the isolatedstate approximation since the 2∆ state mixes only to a minor
extent with the neighboring states via the SO operator.
Using the SO splittings given in Table 3 and the scalar
relativistic MRCI energies given in Table 2, we have assigned
the experimental PDS of the AuX 2 and predicted the PDS of
the nonsymmetric gold dihalides; see Tables 4 and 5, respectively. The calculated energy of the SO eigenstates is presented
with respect to the energy of the (1) 3/2 state, which indicates
the origin of the spectrum. The assignment of the spectra has
been carried out by investigating the composition of the SO
eigenstate in terms of scalar relativistic electronic states.
Similar to the previous study,3 we assign the first two peaks
(which are not completely resolved in the experimental spectrum
of AuCl 2 , see Figure 1a of ref 2) as the 3/2g and 1/2g SO
components of the X̃2Πg state, followed by the narrow and
intense peak assigned as the Ã2Σ +
g,1/2 state; see Table 4. The
9166 J. Phys. Chem. A, Vol. 111, No. 37, 2007
Mishra
Figure 1. The relative energies of the scalar relativistic electronic states of the neutral XAuY with respect to the (1) 2Π ground state, see Table
2, as a function of molecular weight. The calculated energies of the (1) 2Σ+, (1) 2∆, (2) 2Π, and (2) 2Σ+ states are shown by circles, squares,
triangles, and crosses, respectively.
TABLE 3: SO Splitting (in eV) of the (1) 2Π, (2) 2Π, and (1)
2∆ States of XAuY, Computed in the Basis of the (1) and (2)
2Π, (1) 2∆, (1) and (2) 2Σ+ SO-Free Statesa
AuCl2
ClAuBr
AuBr2
ClAuI
BrAuI
AuI2
(1) 2Π
(2) 2Π
(1) 2∆
0.0864 (0.4117)
0.2273 (0.4590)
0.3340 (0.4792)
0.4328 (0.5956)
0.5179 (0.5914)
0.6555 (0.6492)
0.0970 (0.0975)
0.3199 (0.2728)
0.1815 (0.3140)
0.6370 (0.4371)
0.7025 (0.4440)
0.9350 (0.5939)
1.3193 (1.2265)
1.3666 (1.2485)
1.3120 (1.2447)
1.3699 (1.2476)
1.3044 (1.2452)
1.2809 (1.2420)
a Values in parentheses refer to the results obtained when the
concerned state is assumed to be isolated.
assignment of the next two peaks with very low intensity seen
at higher energy differs from the assignment in ref 3. While
the present multiconfigurational study reveals these two peaks
as the lower SO components of the B̃2∆g and the C̃2Πu, that is,
the (1) 5/2g and the (1) 3/2u states, respectively, the results from
ref 3, where the 2∆g state is not considered, assigned these two
peaks as two SO components of the 2Πu state. An experimental
probe at higher energy is hoped to detect the peaks due to the
upper SO components of the B̃2∆g and the C̃2Πu states in the
energy range given in Table 4. Similar conclusions can be made
for AuBr 2 as well, where we assign the first two moderately
intense peaks (Figure 1b of ref 2) as the two SO components
of the X̃2Πg state followed by the intense and narrow peak due
to the Ã2Σ +
g,1/2 state. In contrast to the assignment in ref 3, the
present study leads to the assignment of the next two wellseparated and equi-intense peaks as due to the (1) 3/2u and (1)
5/2g states, respectively. These two peaks were assigned as the
two SO components of the 2Πu state in ref 3. The assignment
of the PDS of AuI 2 remains unchanged from ref 3 since the
2∆ state, in this case, lies high in energy. The matching between
g
the energies of the experimental photoelectron peaks and the
energies obtained from present calculations is excellent in all
three cases; see Table 4.
In Table 5, the calculated PDS of the nonsymmetric gold
dihalides are presented. Similar to the AuX 2 , the first three
SO eigenstates in all three nonsymmetric gold dihalides correspond to the two SO components of the X̃2Π and the Ã2Σ+
states, respectively. The higher-energy SO eigenstates, however,
are less ordered in different systems; see Table 5. Notice, for
TABLE 4: Assignment of Photoelectron Bands of
Symmetric Gold Dihalides (AuX2) and Composition of the
SO Eigenstates in Terms of SO-Free States; All Energies in
eV
SO state
calcd
(1) 3/2g
(1) 1/2g
(2) 1/2g
(1) 5/2g
(1) 3/2u
(1) 1/2u
(2) 1/2u
(2) 3/2g
0.00
0.09
0.96
1.31
1.95
2.05
2.24
2.63
(1) 3/2g
(1) 1/2g
(2) 1/2g
(1) 3/2u
(1) 5/2g
(1) 1/2u
(2) 1/2u
(2) 3/2g
0.00
0.34
1.02
1.44
1.51
1.62
1.95
2.82
(1) 3/2g
(1) 1/2g
(1) 3/2u
(1) 1/2u
(2) 1/2g
(2) 1/2u
(1) 5/2g
(2) 3/2g
0.00
0.66
0.97
1.14
1.28
1.91
1.93
3.21
exptl
AuCl2
0.00
0.20
0.99
1.44
1.57
AuBr2
0.00
0.35
1.03
1.26
1.50
AuI2
0.00
0.62
0.90
1.13
1.44
1.98
composition (weight in %)
X̃2Πg (95); B̃2∆g (5)
X̃2Πg (55); Ã2Σ +
g (45)
X̃2Πg (45); Ã2Σ +
g (55)
B̃2∆g (100)
C̃2Πu (100)
C̃2Πu (100)
D̃2Σ +
u (100)
X̃2Πg (5); B̃2∆g (95)
X̃2Πg (95); D̃2∆g (5)
X̃2Πg (70); Ã2Σ +
g (30)
X̃2Πg (30); Ã2Σ +
g (70)
B̃2Πu (100)
D̃2∆g (100)
B̃2Πu (60); C̃2Σ +
u (40)
B̃2Πu (40); C̃Σ 2+
u (60)
X̃2Πg (5); D̃2∆g (95)
X̃2Πg (100)
X̃2Πg (100)
B̃2Πu (100)
B̃2Πu (45); C̃2Σ +
u (55)
Ã2Σ +
g (100)
B̃2Πu (55); C̃2Σ +
u (45)
D̃2∆g (100)
D̃2∆g (100)
the symmetric dihalides, where the calculations are performed
under D2h point group, the 2∆ state with gerade symmetry mixes,
to a small extent, with the (1) 2Π state but not with the (2) 2Π
state since the latter has ungerade symmetry. In the case of the
nonsymmetric dihalides, on the other hand, where the g/u
symmetry is absent, the (1) 2∆ state mixes with the close-lying
(2) 2Π state rather than with the far-lying (1) 2Π state; see Tables
4 and 5.
The calculated SO eigenenergies of all six systems studied
here are plotted against their molecular weights in Figure 2.
The energies of the SO eigenstates, like the scalar relativistic
Photodetachment Spectra of XAuY- (X, Y ) Cl, Br, I)
J. Phys. Chem. A, Vol. 111, No. 37, 2007 9167
Figure 2. The relative energies of the SO eigenstates of the neutral XAuY with respect to the (1) 2Π3/2 state as a function of molecular weight.
The calculated energies of the SO components of the (1) 2Π, (1) 2Σ+, (1) 2∆, (2) 2Π, and (2) 2Σ+ states are shown by stars, circles, squares,
triangles, and crosses, respectively. Although the SO eigenstates are a mixture of the SO-free states and the orbital angular momentum quantum
number, Λ (Σ, Π, etc.) is no longer a good quantum number, and the states are labeled with the Λ value of the largest contributing SO-free
electronic state; see Tables 4 and 5.
TABLE 5: Theoretical Prediction of the Photoelectron
Bands of Nonsymmetric Gold Dihalides (XAuY, X * Y) and
Composition of the SO Eigenstates in Terms of SO-Free
States; All Energies in eV
SO state
energy
composition (weight in %)
(1) 3/2
(1) 1/2
(2) 1/2
(1) 5/2
(2) 3/2
(3) 1/2
(4) 1/2
(3) 3/2
0.00
0.23
0.96
1.43
1.73
2.05
2.13
2.80
ClAuBr
X̃2Π (97); C̃2∆ (3)
2
X̃ Π (60); Ã2Σ+ (40)
X̃2Π (40); Ã2Σ+ (60)
C̃2∆ (100)
B̃2Π (96); C̃2∆ (4)
B̃2Π (60); D̃2Σ+ (40)
B̃2Π (40); D̃2Σ+ (60)
X̃2Π (3); B̃2Π (4); C̃2∆ (93)
(1) 3/2
(1) 1/2
(2) 1/2
(2) 3/2
(1) 5/2
(3) 1/2
(4) 1/2
(3) 3/2
0.00
0.43
1.02
1.61
1.70
1.99
2.25
3.06
ClAuI
X̃2Π (100)
X̃2Π (76); Ã2Σ+ (20); C̃2Σ+ (4)
X̃2Π (18); Ã2Σ+ (72); B̃2Π (6); C̃2Σ + (4)
B̃2Π (95); D̃2∆ (5)
D̃2∆ (100)
X̃2Π (6); Ã2Σ+ (3); B̃2Π (13); C̃2Σ+ (78)
Ã2Σ+ (5); B̃2Π (81); C̃2Σ+ (14)
B̃2Π (5); D̃2∆ (95)
(1) 3/2
(1) 1/2
(2) 1/2
(2) 3/2
(3) 1/2
(1) 5/2
(4) 1/2
(3) 3/2
0.00
0.52
1.10
1.26
1.51
1.77
1.96
3.07
BrAuI
X̃2Π (100)
X̃2Π (85); Ã2Σ+ (15)
X̃2Π (10); Ã2Σ+ (75); B̃2Π (10); C̃2Σ + (5)
B̃2Π (100)
X̃2Π (5); Ã2Σ+ (10); B̃2Π (35); C̃2Σ+ (50)
D̃2∆ (100)
B̃2Π (55); C̃2Σ+ (45)
D̃2∆ (100)
energies in Figure 1, change linearly with the molecular mass.
Figure 2 provides a graphical presentation of the change in SO
splitting of the (1) and (2) 2Π and (1) 2∆ states as one goes
from AuCl2 to AuI2. As discussed earlier, the SO splitting of
the 2∆ state remains unchanged, whereas that of the (1) and (2)
2Π states increases with increasing relativistic effects; see Figure
2. There are several instances of reordering of energy levels as
a function of the molecular weight (or relativistic effects).
Conclusions
We have determined the geometries of anionic XAuY (X, Y
) Cl, Br, and I) at the CCSD(T) level, employing an improved
RECP for Au and the halogens. The SO-free vertical detachment
energies of the ground as well as of the excited states of the
neutral species have been determined using the MRCI method,
where eight electronic states are averaged, via a SA-CASSCF
calculation, to generate the N-electron basis. We have also
determined SO coupling parameters of these complexes by
calculating the matrix elements of the SO operator over the SOfree CI vectors. The SO splittings in the degenerate states have
been compared for different species.
We have not only reported a revised assignment of the
experimentally recorded PDS of symmetric gold dihalides, that
is, when X ) Y, but we also have provided a theoretical
prediction of PDS of the nonsymmetric gold dihalides (X *
Y). For symmetric gold dihalides, we have compared the present
assignment with the previous assignment where the presence
of the excited 2∆g state was overlooked.3 While this state has a
negligible effect on the observed spectroscopy of AuI2, for
AuBr2 and AuCl2, the inclusion of this state is found to be
necessary. Interestingly, the energy of the SO eigenstates of
these molecules are found to change linearly with increasing
molecular weight. It is hoped that this theoretical study will
stimulate the recording of PDS of both symmetric as well as
nonsymmetric gold dihalides over an extended range of photodetachment energies.
Acknowledgment. The author is grateful to Professor
Wolfgang Domcke and Dr. Valérie Vallet for useful comments
on the manuscript. This paper is dedicated to Professor
Wolfgang Domcke, who introduced the author to this field of
study, on the occasion of his 60th birthday.
References and Notes
(1) Pyykkö, P. Angew. Chem., Int. Ed. 2004, 43, 4412.
(2) Schröder, D.; Brown, R.; Schwerdtfeger, P.; Wang, X. B.; Yang,
X.; Wang, L.; Schwarz, H. Angew. Chem., Int. Ed. 2003, 42, 311.
(3) Mishra, S.; Vallet, V.; Domcke, W. ChemPhysChem 2006, 7, 723.
9168 J. Phys. Chem. A, Vol. 111, No. 37, 2007
(4) Dai, B.; Yang, J. Chem. Phys. Lett. 2005, 379, 512.
(5) Schwerdtfeger, P.; Boyd, P. D. W.; Burrell, A. K.; Robinson, W.
T.; Taylor, M. J. Inorg. Chem. 1990, 29, 3593.
(6) Schwerdtfeger, P.; McFeaters, J. S.; Stephens, R. L.; Liddell, M.
J.; Dolg, M.; Hess, B. A. Chem. Phys. Lett. 1994, 218, 362.
(7) Schwerdtfeger, P.; McFeaters, J. S.; Liddell, M. J.; Hrušák, J.;
Schwarz, H. J. Chem. Phys. 1995, 103, 245.
(8) Seth, M.; Cooke, F.; Schwerdtfeger, P.; Heully, J. L.; Pelissier, M.
J. Chem. Phys. 1998, 109, 3935.
(9) Figgen, D.; Rauhut, G.; Dolg, M.; Stoll, H. Chem. Phys. 2005, 311,
227.
Mishra
(10) Bergner, A.; Dolg, M.; Kuechle, W.; Stoll, H.; Preuss, H. Mol.
Phys. 1993, 80, 1431.
(11) Dolg, M. Ph.D. Thesis, University of Stuttgart, Germany, 1989.
(12) Woon, D. E.; Dunning, T. H., Jr. Chem. Phys. 1993, 98, 1358.
(13) Dolg, M. In RelatiVistic Electronic Structure Theory, Part 1.
Fundamentals; Schwerdtfeger, P., Ed.; Elsevier: Amsterdam, The Netherlands, 2004.
(14) Berning, A.; Schweizer, M.; Werner, H. J.; Knowles, P. J.; Palmieri,
P. Mol. Phys. 2000, 98, 1823.
(15) Molpro 2002.6, a package of ab initio programs; see http://
www.molpro.net.
DOI: 10.1002/cphc.200500554
Importance of Spin–Orbit Coupling for the
Assignment of the Photodetachment Spectra of
AuX2 (X = Cl, Br, and I)
Sabyashachi Mishra,[b] Valerie Vallet,*[a] and Wolfgang Domcke[b]
Recently, photodetachment spectra of AuX2 , X = Cl, Br, and I,
have been reported [D. Schrçder et al., Angew. Chem. Int. Ed.
2003, 42, 311] followed by a scalar-relativistic theoretical study
of the assignment of these spectra [B. Dai, J. Yang, Chem. Phys.
Lett. 2003, 379, 512]. Herein, the photodetachment spectra of
the title molecules are reassigned, taking spin–orbit coupling into
account and employing relativistic-effective core potentials for
gold and the halogen atoms. The composition of the AuX2 electronic states are further analyzed in terms of scalar-relativistic
electronic states. The relevance of spin–orbit coupling in the
spectroscopy of heavy elements is emphasized by comparing the
results of this work with experiment and with other scalar-relativistic theoretical studies.
1. Introduction
In recent years, many experimental and theoretical studies
have been devoted to the determination of the properties of
small metal-containing molecules in the gas phase. Much attention has been paid to one of the most precious elements of
the periodic table, that is, gold. Several spectroscopic,[1–8] crystallographic,[9–11] and theoretical[6, 12–22] studies have been performed on gold complexes with different ligands. In particular,
it is known that the chemical and physical properties of gold
are quite different from that of the other Group XI elements
copper and silver. For example, the most common coordination number of AuI, which is a soft Lewis acid, is two, forming
linear AuL2 molecules, L being a wide variety of polarizable
Lewis bases. Ag and Cu, on the other hand, tend to form complexes with higher coordination numbers. The special properties of gold can be explained by the importance of relativistic
effects which lead to a contraction of the 6s orbital and a
slight expansion of the 5d orbital.[20, 21] In addition, fine-structure effects are important for the 5d and 6p shells; spin–orbit
(SO) coupling amounts to about 0.5 eV for the 6p orbital (Au
2
P1/2–2P3/2) and 1.5 eV for the 5d orbital (Au 2D3/2–2D5/2). These
effects are important for the electronic structure of Au compounds.
Recently, Schrçder et al. reported an experimental study of
gaseous gold dihalides AuX2, (X = Cl, Br, and I) using photodetachment spectroscopy (PDS) of the corresponding anions and
sector-field mass spectrometric techniques.[23] They also performed theoretical calculations which were mostly focused,
however, on structural aspects, thus leaving the PDS unassigned.[23] This inspired Dai and Yang to perform a theoretical
calculation to assign the photoelectron bands of the AuX2
compounds.[24] They performed calculations for AuX2 in neutral
and anionic states using scalar-relativistic (spin-independent)
time-dependent density functional theory (TD-DFT). The agreement between the computed detachment energies and the
ChemPhysChem 2006, 7, 723 – 727
experimental spectra is satisfactory for AuCl2, but deteriorates
for the complexes with heavier halides, Br and I. These discrepancies may be explained in terms of SO coupling effects,
which were not considered by Dai and Yang. In addition to the
strong SO effects in the gold atom, the magnitude of the SO
interaction in the valence p shells of the halide atoms increases
with increasing nuclear charge. They may have important consequences, as it is known that SO coupling is not completely
quenched for heavy halogen compounds such as iodides.[22]
In the present study, we have performed ab initio electronic
structure calculations on AuX2 and AuX2 (X = Cl, Br, and I),
taking the SO coupling explicitly into account. Our results lead
to a reassignment of the experimental PDS of Schrçder et al.
for AuX2.
2. Ab Initio Calculations
In this section, we will discuss the strategy of the ab initio electronic-structure calculations of the structural and electronic parameters of neutral as well as anionic AuX2, X = Cl, Br, and I.
The gold and halogen atoms are described by relativistic-effective core potentials (RECP). The explicit quantum chemical
treatment is thus restricted to the valence shells, while the
core shells are simulated by the pseudopotentials. The use of
computationally convenient nodeless pseudopotentials for the
[a] Dr. V. Vallet
Laboratoire PhLAM, UMR CNRS 8523, CERLA
University of Sciences and Technologies of Lille
59655 Villeneuve d’Ascq (France)
Fax: (+ 33) 32033-7020
E-mail: [email protected]
[b] S. Mishra, Prof. W. Domcke
Department of Chemistry, Technical University of Munich
85747, Garching (Germany)
C 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
723
V. Vallet et al.
valence shell leads to the transfer of most of the contributions
from the important relativistic operators to the pseudopotentials. The Au atom is described by a small-core effective pseudopotential basis set described by Figgen et al.,[25] where the
1s–4f core shells (containing 60 electrons) are replaced by
two-component relativistic pseudopotentials (i.e. scalar-relativistic as well as SO potentials) of the energy-consistent variety,
being supplemented by an energy-optimized (12s12p9d3f2g)/
[6s6p4d3f2g] valence basis set. For the halogen atoms, onecomponent (i.e. SO averaged) semilocal energy-adjusted pseudopotentials are used to describe the core, that is, 1s–2p for Cl
(10 electrons), 1s–3d for Br (28 electrons), and 1s–4d for I (46
electrons).[26] The valence electrons of Br and I are described by
basis sets of augmented quadruple-zeta quality, composed of
optimized contracted s, p, d, f, and g functions,[26] while the valence shell of Cl is described by optimized contracted s and p
functions of augmented quadruple-zeta quality.[27] The d, f, and
g polarization functions are obtained from the augmented correlation-consistent polarized valence quadruple-zeta (Aug-ccpVQZ) basis set of Woon and Dunning.[28] A core-polarizationpotential (CPP) calculation for the halogen centers is performed during every calculation, using the CPP parameters
taken from ref. [26].
Using the above mentioned RECPs, the geometries of neutral and anionic AuX2 have been optimized in their respective
ground states by a scalar-relativistic (neglecting SO effects)
coupled-cluster calculation with singles and doubles and perturbative account of triple excitations (CCSD(T)).[29] The closedshell anionic species AuX2 possess an electronic ground state
of 1Sg + symmetry with the following valence-shell electronic
configuration: 1sg2 1su2 1pu4 2sg2 2su2 3sg2 1pg4 1dg4 3su2 2pu4
4sg2 2pg4. Detachment of one electron from the highest occupied 2pg molecular orbital (MO) of the anion gives rise to the
X̃ 2Pg ground state of the neutral species. For the neutral systems, we employ spin-unrestricted open-shell coupled-cluster
theory, in which singles, doubles, and perturbative triple corrections are obtained by excitation out of a high-spin restricted-Hartree–Fock (RHF) reference wavefunction, abbreviated
RHF-UCCSD(T)[29, 30] for a scalar-relativistic description of the
lowest six electronic states. The lowest four orbitals, that is,
1sg2 1su2 1pu4 (essentially being the 5s and 5p orbitals of Au)
were kept frozen in all calculations.
The SO interaction was treated by the contracted SO configuration interaction method after the electron-correlation step,
diagonalizing the SO matrix in the space of all SO-free electronic states of interest.[31] For this purpose, the SO-free states
were obtained from a state-averaged (over 2Pg, 2Sg + , 2Pu, and
2
Su + states) complete-active-space self-consistent-field (CASSCF)
calculation,[32, 33] where all but eight valence electrons were
kept in the active space. Thus, 25 electrons have been correlated in 14 orbitals, that is, a (25,14) CASSCF. The SO matrix elements were computed using the SO pseudopotential cited
above[25] for gold and SO pseudo-operators by Dolg,[27] adapted to the scalar RECP used for the halogen atoms.[26] It is sufficient to calculate the SO matrix elements at a lower level of
theory and to replace the SO-free energies by values precomputed by a higher level of theory. Here, we have used the RHF-
724
www.chemphyschem.org
UCCSD(T) energies for this purpose. All calculations were performed using the MOLPRO program suite.[34]
3. Results and Discussion
The optimized geometries of neutral as well as anionic AuX2
are given in Table 1 together with the experimental and other
calculated values. Both the neutral and the anionic species are
Table 1. Optimized bond distances [N] at the CCSD(T) and RHF-UCCSD(T)
level for AuX2 and AuX2, respectively.
This work
CCSD(T)
AuX2
[24]
B3LYP
[19]
CISD
Expt.
AuX2
This work
RHF-UCCSD(T)
2.2836
2.4086
2.5754
2.381
2.506
2.705
2.353
2.487
2.668
2.28[9]
2.40[10]
2.53[11]
2.1814
2.3081
2.5035
X
Cl
Br
I
linear in their respective ground states. Our calculated bond
distances are in excellent agreement with the crystallographic
measurements,[9, 10, 11] see Table 1. The bond distances obtained
by Dai and Yang[24] at the DFT/B3LYP level and by Schwerdtfeger et al.[19] at the configuration interaction with single and
double excitations (CISD) are longer. This difference might be
the result of the use of less accurate effective-core-potentials
than used in the present study. In all cases, the anions have a
longer bond distance than the corresponding neutral species,
as a result of the antibonding character of the 2pg MO of the
anion. The 2pg MO is essentially an antibonding linear combination of the px(py) orbitals of the halogen atoms and the dxz(dyz) orbital of Au. This overlap is larger in AuCl2 than in AuBr2.
In AuI2, this MO is almost halogen centered, with little overlap
of the gold and iodine atomic orbitals, see Figure 1. Hence, the
change in bond distance from anion to neutral is smaller in
the case of AuI2 than in AuCl2 and AuBr2.
Figure 1. The 2pg MO (highest occupied MO) in a) AuCl2 and b) AuI2.
The lowest six electronic states (the two nondegenerate 2S +
states and two doubly degenerate 2P states) of the neutral
species have been calculated via RHF-UCCSD(T) at the reference geometry of the anion. The difference in energy of these
doublet electronic states from the X̃ 1Sg + electronic ground
state of the anion (i.e. the vertical detachment energies) are reported in Table 2. The ffi 2Sg + electronic state is found 0.5 eV
C 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ChemPhysChem 2006, 7, 723 – 727
Assigning the Photodetachment Spectra of AuX2
The repulsion between the first
two 1/2g states composed of
the X̃ 2Pg and ffi 2Sg + states and
the first two 1/2u SO states,
which are mixtures of the B̃ 2Pu
and C̃ 2Su + states, decreases the
SO splitting in the X̃ 2Pg and B̃
2
Pu states, respectively, see
Tables 3 and 5. In the case of
AuI2, the ffi 2Pu state mixes with
the B̃ 2Su + state through the SO
operator. The repulsion between the 1/2u components of
the B̃ 2Su + and ffi 2Pu states
Table 2. Scalar-relativistic detachment energies [eV] from the X̃ 1Sg + state of AuX2 computed by the RHFUCCSD(T) method (this work) and by DFT/B3LYP (ref. [24]). Values in parentheses refer to the RHF-UCCSD(T) results with the vertical detachment energy of the X̃ 2Pg adjusted to its experimental value as done by Dai and
Yang for the corresponding DFT/B3LYP values.[24]
State
X̃ 2Pg
ffi 2 Sg +
B̃ 2Pu
C̃ 2Su +
2
Pu
2
Dg
AuCl2
UCCSD(T)[a]
B3LYP[24]
AuBr2
UCCSD(T)[a]
B3LYP[24]
State
5.070
5.559
6.515
6.833
4.918
5.636
6.026
6.332
X̃ 2Pg
ffi 2 Pu
B̃ 2Su +
C̃ 2Sg +
2
Pu
2
Dg
(4.740)
(5.229)
(6.185)
(6.503)
4.740
5.220
5.652
6.266
6.214
6.243
(4.610)
(5.328)
(5.718)
(6.024)
4.610
5.342
5.322
5.942
5.866
6.313
AuI2
UCCSD(T)[a]
4.658
5.481
5.757
5.778
(4.280)
(5.103)
(5.379)
(5.400)
B3LYP[24]
4.280
4.820
5.391
5.276
5.323
6.206
[a] This work.
above the X̃ 2Pg state in AuCl2. This X̃ 2Pg–ffi 2Sg + energy gap
increases to 0.75 eV for AuBr2. A complete change in the ordering of states occurs in the case of AuI2, where the 2Sg +
state lies higher in energy than the 2Pu and 2Su + states. This
finding can be understood from an analysis of the MOs. The
3su and 2pu MOs are mostly centered on the halogen atoms
(pz and px/y respectively), while the 4sg orbital is the bonding
linear combination of the pz orbitals of the halogen atoms and
the dz2 orbital of Au atom. This bonding is stronger in case of
AuI2 than in AuBr2 and AuCl2, because of the comparable sizes
of the Au and I atomic orbitals, which leads to a good overlap,
thus lowering the energy of the 4sg orbital in the case of AuI2,
see Table 2.
To compare the computed RHF-UCCSD(T) values to the DFT/
B3LYP values obtained by Dai and Yang,[24] we adjusted the
vertical detachment energy of the X̃ 2Pg state to the experimental value[23] and added this constant shift to the computed
vertical-detachment energies of higher electronic states. There
are significant deviations, up to 0.5 eV, between the detachment energies obtained by the RHF-UCCSD(T) method and the
TD-DFT/B3LYP method. The TD-DFT/B3LYP method assigns
some peaks in the 5–6 eV region to excited states of AuX2,
which are predicted at much higher energy by RHF-UCCSD(T).
As discussed later, these peaks should rather be assigned as
fine structure levels of the 2Pg,u and 2Sg,u electronic states.
The calculated SO splittings in the 2Pg and 2Pu states of
AuX2 are given in Table 3. The SO splitting in the 2Pg state increases, as expected, from AuCl2 to AuI2. However, the increase
in the SO splitting of the 2Pu state is less uniform. The numbers in parentheses are the SO splitting calculated for the 2P
state when an isolated 2P state is assumed, see Table 3. When
compared with true SO splitting, these numbers reveal the
extent of interaction between different SO-free states via the
SO coupling operator. In AuCl2, the X̃ 2Pg state interacts with
the ffi 2Sg + state. The SO splitting of the former state decreases
substantially (from its value in the isolated 2P state approximation) as a result of the repulsion of the first two 1/2g states,
which arise mainly from the ffi 2Sg + and X̃ 2Pg states, see
Tables 3 and 4. The B̃ 2Pu state of AuCl2, on the other hand,
mixes only weakly with neighboring electronic states via the
SO operator. In the case of AuBr2, the X̃ 2Pg and ffi 2Sg + states
as well as the B̃ 2Pu and C̃ 2Su + states mix via SO coupling.
ChemPhysChem 2006, 7, 723 – 727
Table 3. SO splitting [eV] of the 2Pg and 2Pu states of AuX2, computed in
the basis of the 2Pg, 2Pu, 2Sg + , and 2Su + SO-free states. The first column
refers to the splitting obtained with the SO-operator for both gold and
halide atoms; the second column refers to the splitting obtained with
the SO-operator of the halide atoms only. Values in parentheses refer to
the results obtained when considering isolated 2P SO-free states.
State
Au-SO and X-SO
X̃ 2Pg
B̃ 2Pu
0.1062 (0.3388)
0.0953 (0.0954)
X̃ 2Pg
B̃ 2Pu
0.3414 (0.4295)
0.1993 (0.3086)
X̃ 2Pg
ffi 2 Pu
0.6453 (0.6465)
1.0104 (0.6110)
X-SO
AuCl2
0.0465 (0.0470)
0.0625 (0.0738)
AuBr2
0.2082 (0.2169)
0.1286 (0.2875)
AuI2
0.2082 (0.2169)
1.0473 (0.5908)
Table 4. Assignment of photoelectron bands of AuCl2 and composition
of the SO eigenstates in terms of L-S SO-free states. All energies in eV.
SO state
Calc.[a]
Expt.[23]
Composition (weight in %)
(1)
(1)
(2)
(1)
(1)
(2)
4.74
4.85
5.63
6.31
6.40
6.67
4.74
4.97
5.73
6.18
6.31
X̃ 2Pg (100)
X̃ 2Pg(70); ffi 2Sg + (30)
ffi 2Sg + (70); X̃ 2Pg (30)
B̃ 2Pu (100)
B̃ 2Pu (100)
C̃ 2Su + (100)
3/2g
1/2g
1/2g
3/2u
1/2u
1/2u
[a] Vertical detachment energy of the (1) 3/2g state adjusted to the experimental value.
pushes the latter even further up. Hence, the SO splitting of
the ffi 2Pu state increases, compared to its value in the isolated
2
P state approximation. The upper 1/2u SO component of the
ffi 2Pu state comes at higher energy than the B̃ 2Su + and C̃
2
Sg + states, see Table 6.
The third column of Table 3 contains the SO splitting of the
2
Pg and 2Pu states, calculated with inclusion of the SO contribution from only the halide atoms. The comparison of this
value to the true SO splitting reveals the relative contribution
of the gold SO coupling and the halide SO coupling. The SO
coupling of the halide atom largely contributes to the SO split-
C 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
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725
V. Vallet et al.
Table 5. Assignment of photoelectron bands of AuBr2 and composition
of the SO eigenstates in terms of L-S SO-free states. All energies in eV.
SO state
Calc.[a]
Expt.[23]
Composition (weight in %)
(1)
(1)
(2)
(1)
(1)
(2)
4.61
4.95
5.63
5.78
5.98
6.35
4.61
4.96
5.64
5.87
6.11
X̃ 2Pg (100)
X̃ 2Pg (87); ffi 2Sg + (13)
ffi 2Sg + (87); X̃ 2Pg (13)
B̃ 2Pu (100)
B̃ 2Pu (70) C̃ 2Su + (30)
C̃ 2Su + (70); B̃ 2Pu (30)
3/2g
1/2g
1/2g
3/2u
1/2u
1/2u
[a] Vertical detachment energy of the (1) 3/2g state adjusted to the experimental value.
Table 6. Assignment of photoelectron bands of AuI2 and composition of
the SO eigenstates in terms of L-S SO-free states. All energies in eV.
SO state
Calc.[a]
Expt.[23]
Composition (weight in %)
(1)
(1)
(1)
(1)
(2)
(2)
4.28
4.93
5.12
5.30
5.72
6.13
4.28
4.90
5.18
5.41
5.72
6.26
X̃ 2Pg (100)
X̃ 2Pg (100)
ffi 2Pu (100)
B̃ 2Su + (52); ffi 2Pu (48)
C̃ 2Sg + (100)
ffi 2Pu (52); B̃ 2Su + (48)
3/2g
1/2g
3/2u
1/2u
1/2g
1/2u
[a] Vertical detachment energy of the (1) 3/2g state adjusted to the experimental value.
ting of the 2Pu state and to a smaller extent to the 2Pg state.
This results from the fact that the 2pu MO is mostly centered
on the halide atom. The gold 6p orbital has a slight positive
effect on the 2Pu SO splitting. The highest occupied 2pg MO
(HOMO), on the other hand, has contributions from the gold
5d orbital and the halide valence p orbitals.
Using the SO splittings given in Table 3 and the scalar-relativistic RHF-UCCSD(T) energies given in Table 2, we assigned
the experimental PDS of AuCl2, see Table 4. Since the energy
spacing of the electronic states of the neutral AuX2 matters,
rather than the absolute values of the vertical detachment energies, we have adjusted the vertical detachment energy of
the 3/2g state to the experimental value and added this constant shift to the all computed values.[23] We assign the first
two peaks (which are not completely resolved in the experimental spectrum, see Figure 1 a of ref. [23]) as the 3/2g and 1/
2g SO components of the X̃ 2Pg state. The following narrow
and intense peak is assigned as the ffi 2Sg,1/2 + state and the
two peaks of low intensity seen at higher energy are assigned
as the two SO components of the B̃ 2Pu state. In AuBr2, we
assign the first two moderately intense peaks (which are isolated from other peaks, see Figure 1 b of ref. [23]) as the two SO
components of the X̃ 2Pg state. The next intense and narrow
peak is assigned as the ffi 2Sg,1/2 + state, followed by the two
peaks corresponding to the two SO components of the B̃ 2Pu
state, which are well separated because of larger SO splitting
in this state, see Table 3. In the case of AuI2, we assign the first
two peaks with equal intensities as the two SO components of
the X̃ 2Pg state. The third and the sixth peaks of the experi-
726
www.chemphyschem.org
mental spectrum (Figure 1 c of ref. [23]), are assigned as the
two components of the ffi 2Pu state. This assignment is further
supported by the rule that the two SO components of an otherwise degenerate electronic state appear with equal intensities.[35] The two narrow peaks in between the two SO components of the ffi 2Pu state are assigned as the B̃ 2Su,1/2 + and C̃
2
Sg,1/2 + states, see Table 6. The matching between the energies
of the experimental photoelectron peaks and the calculated
energies is excellent in all three cases. Our assignment of the
PDS of AuX2 differs from the assignments of Dai and Yang,[24]
which have been derived from SO-free calculations, in several
instances.
4. Conclusions
We have determined the geometries of anionic and neutral
AuX2, which are in excellent agreement with the crystallographic data. We have determined the SO-free vertical detachment energy of the ground as well as of the excited states of
the neutral species using a RHF-UCCSD(T) method. We have
also determined SO coupling parameters of these complexes
for the first time. We have reported a revised assignment of
the PDS of AuX2, (X = Cl, Br, and I) based on an accurate ab
initio treatment of electron-correlation and SO coupling effects. The results reveal the importance of the SO interaction
in the spectroscopy of heavy elements. It has been shown that
the scalar-relativistic treatment omitting the SO effects can
lead to incorrect results when the molecule contains one or
more heavy elements.
Acknowledgements
This work was supported by the Deutsche Forschungsgemeinschaft and the Fonds der Chemischen Industrie.
Keywords: ab initio calculations · electronic structure ·
photoelectron spectroscopy · relativistic effects · spin–orbit
coupling
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Assigning the Photodetachment Spectra of AuX2
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[18] C. Janiak, R. Hoffmann, Inorg. Chem. 1989, 28, 2743.
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Inorg. Chem. 1990, 29, 3593.
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Comput. Phys. Commun. 1980, 21, 207.
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Received: October 11, 2005
C 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
www.chemphyschem.org
727
THE JOURNAL OF CHEMICAL PHYSICS 123, 124104 共2005兲
Spectroscopic effects of first-order relativistic vibronic coupling in linear
triatomic molecules
Sabyashachi Mishra
Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
Valerie Vallet
Institute of Laboratoire de Physique des Lasers Atomes et Molécules (PhLAM), University of Lille 1,
F-59655 Villeneuve d’Ascq, France
Leonid V. Poluyanov
Institute of Chemical Physics, Academy of Sciences, Chernogolovka, Moscow 14232, Russia
Wolfgang Domckea兲
Department of Chemistry, Technical University of Munich, D-85747 Garching, Germany
共Received 31 May 2005; accepted 13 July 2005; published online 27 September 2005兲
It has recently been shown that there exists, in addition to the well-known nonrelativistic
Renner-Teller coupling, a linear 共that is, of the first order in the bending distortion兲
vibronic-coupling mechanism of relativistic 共that is, spin-orbit兲 origin in 2⌸ electronic states of
linear molecules 关L. V. Poluyanov and W. Domcke, Chem. Phys. 301, 111 共2004兲兴. The generic
aspects of the relativistic linear vibronic-coupling mechanism have been analyzed in the present
work by numerical calculations of the vibronic spectrum for appropriate models. The vibronic and
spin-orbit parameters have been determined by accurate ab initio electronic-structure calculations
for the X̃ 2⌸ states of a series of triatomic radicals and radical cations. It is shown for the example
of GeCH that the relativistic linear vibronic-coupling mechanism provides a quantitative
explanation of the pronounced perturbations in the vibronic spectrum of the X̃ 2⌸ state of GeCH,
which previously have been termed “Sears resonances” 关S.-G. He, H. Li, T. C. Smith, D. J.
Clouthier, and A. J. Merer, J. Chem. Phys. 119, 10115 共2003兲兴. The X̃ 2⌸ vibronic spectra of the
series BS2, CS+2 , OCS+, and OBS illustrate the interplay of nonrelativistic and relativistic
vibronic-coupling mechanisms in Renner-Teller systems. © 2005 American Institute of Physics.
关DOI: 10.1063/1.2018702兴
I. INTRODUCTION
The combined effects of Renner-Teller 共RT兲 and spinorbit 共SO兲 coupling in 2⌸ electronic states of linear molecules have been extensively investigated experimentally
and theoretically for decades see, e.g., Refs. 1–6 and references therein.
In the present work, we address certain perturbations of
the usual pattern of RT-SO vibronic energy levels, which
have been observed in 2⌸ electronic states of several triatomic systems, in particular, NCO, NCS, and GeCH.7–9
These perturbations have been termed “Sears resonances”.9
An explanation of these perturbations has been given in
terms of a perturbative analysis of RT and SO coupling effects of the 2⌸ state, invoking 共nonrelativistic兲 vibroniccoupling effects of the 2⌸ state with a distant 2⌺+ state.7,9
Here, we show that these perturbations can quantitatively be
described by a linear 共that is, of first order in the bending
radial coordinate兲 vibronic-coupling mechanism of relativistic 共that is, SO兲 origin within the 2⌸ state.
The existence of this relativistic linear coupling term has
been pointed out recently, based on an analysis of the “mia兲
Electronic mail: [email protected]
0021-9606/2005/123共12兲/124104/8/$22.50
croscopic” Breit-Pauli SO operator for quasilinear triatomic
molecules.10 This coupling term is absent when the usual
phenomenological form of the SO operator, introduced long
ago by Pople,1
HSO = ALZSZ ,
is assumed. It seems that this simplified form of the SO
operator has been employed in most subsequent treatments
of the RT-SO effect, with the consequence that the relativistic
linear coupling term has not been taken into account in previous calculations of RT-SO vibronic spectra.1–6
In Secs. II and III, the fundamentals of the RT-SO effect
in 2⌸ states and the numerical calculation of the vibronic
spectra are discussed. In Sec. IV, the generic effects of relativistic linear vibronic coupling are investigated for the socalled resonant case, where the spin-orbit splitting of the 2⌸
state and the bending vibrational frequency are approximately equal. In Sec. VI, the vibronic spectrum of the X̃ 2⌸
state of GeCH is analyzed in some detail. Both ab initio
electronic-structure calculations as well as the fitting of the
measured energy-level spectrum within the vibronic model
reveal the existence of a significant relativistic linear
vibronic-coupling term in the X̃ 2⌸ state of GeCH. In Sec.
VII, the relevance of the relativistic linear coupling term in
123, 124104-1
© 2005 American Institute of Physics
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124104-2
J. Chem. Phys. 123, 124104 共2005兲
Mishra et al.
⫹spin兲 3 / 2, 1 / 2, −1 / 2, and −3 / 2. These four electronic
states constitute a complete electronic basis. The vibrational
motion is represented by a degenerate 共harmonic兲 bending
mode.
The vibronic Hamiltonian of the RT problem including
SO coupling has been derived in a previous publication up to
second order in the bending coordinate.10 In a diabatic electronic representation, it reads 共ប = 1兲
the 2⌸ ground state of a series of radicals and radical cations
with 15 valence electrons 共BS2, CS+2 , OCS+, and OBS兲 is
briefly discussed.
II. VIBRONIC HAMILTONIAN
Let us consider the RT vibronic-coupling problem in a
⌸ electronic state of a linear triatomic molecule with a
single unpaired electron. We shall not consider the stretching
modes because they decouple from the bending mode when
one restricts the discussion to an isolated ⌸ electronic state.
The single unpaired electron, having orbital angular momentum ⌳ = ± 1 and spin angular momentum ␴ = ± 1 / 2, gives rise
to four electronic states with total angular momenta 共orbital
2
Hel =
冢
0
d ␳ e i␾
1 2 2i␾
g␳ e
2
0
d␳e−i␾
␨
0
1
− g␳2e2i␾
2
1 2 −2i␾
g␳ e
2
0
␨
0
1
− g␳2e−2i␾
2
d␳e−i␾
d␳e
0
i␾
冣
Here ␳ and ␾ are the radial and angular components of
the dimensionless degenerate bending mode, respectively, h0
is the two-dimensional isotropic harmonic oscillator, and 1 is
the 4 ⫻ 4 unit matrix. g is the well-known nonrelativistic RT
coupling constant, ␨ is the SO splitting of the ⌸ state, and d
is the linear vibronic-coupling constant of relativistic origin,
see Ref. 10. ␻ is the averaged harmonic bending frequency
of the 2⌸ state which is related to the harmonic frequencies
共␻+ and ␻−兲 associated with the two components of the bending potential-energy surface in the following way:11
␻=
冑
1
关共␻+兲2 + 共␻−兲2兴.
2
共4兲
In the literature, the RT coupling is often characterized by
the dimensionless RT parameter ⑀. It is defined as11
⑀=
共 ␻ +兲 2 − 共 ␻ −兲 2
.
共 ␻ +兲 2 + 共 ␻ −兲 2
共5兲
This dimensionless parameter ⑀ is related to the nonrelativistic coupling constant g via
␻g
⑀= 2
␻ + 共g2/4兲
共6兲
The electronic Hamiltonian Hel of Eq. 共3兲 has the following symmetry properties:
关Hel,T兴 = 0,
共7兲
关Hel, jz兴 = 0.
共8兲
H = h01 + Hel ,
h0 = −
冉
共1兲
冊
1 ⳵2
␻ 1 ⳵ ⳵
␻
␳ + 2 2 + ␳2 ,
2 ␳ ⳵␳ ⳵␳ ␳ ⳵ ␾
2
共2兲
共3兲
.
Here, T is the time-reversal operator and jz is z projection of the total electronic angular momentum operator,
jz =
1 ⳵
+ ␴z ,
i ⳵␪
共9兲
where ␪ is the electronic angular coordinate.
The adiabatic potential terms and the adiabatic electronic
states have been discussed in Ref. 10. It has been shown that
the adiabatic electronic states carry a nontrivial topological
phase despite the absence of conical intersection of the adiabatic potential-energy surfaces.10
The full Hamiltonian H of Eq. 共1兲 satisfies, in addition
to the time-reversal property, the axial symmetry property
关H,Jz兴 = 0,
共10兲
where
Jz = j z +
1 ⳵
.
i ⳵␾
共11兲
The eigenvalues 共␮兲 of Jz are half-integral numbers
共␮ = ± 1 / 2 , ± 3 / 2 , …兲. The eigenvalues of H are doubly degenerate 共Kramers degeneracy兲. If d = 0, the Kramers degeneracy is trivial in so far as it reduces to spin degeneracy. If
d ⫽ 0, the electronic orbital and spin projection quantum
numbers 共⌳ and ␴兲 are no longer good quantum numbers; in
this case the degeneracy of vibronic eigenvalues with angular momentum quantum numbers ±␮ is solely a consequence
of time-reversal symmetry.
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124104-3
J. Chem. Phys. 123, 124104 共2005兲
Relativistic vibronic coupling
III. CALCULATION OF THE SPECTRUM
We solve the vibronic Schrödinger equation
H⌿␯ = E␯⌿␯
共12兲
by the expansion of ⌿␯ in a complete basis which is constructed as the product of electronic 共兩␺⌳,␴典兲 and vibrational
共兩nl典兲 basis functions. The 兩␺⌳,␴典, ⌳ = ± 1, and ␴ = ± 1 / 2 are
the four diabatic electronic states which correspond to the
representation 共3兲 of the Hel. The 兩nl典, n = 0 , 1 , 2 , …, and l
= −n , −n + 2 , ¯n − 2 , n are the eigenfunctions of the twodimensional isotropic harmonic oscillator.12
Since ␮ is a good quantum number, the real symmetric
Hamiltonian matrix is constructed and diagonalized for a
given value of ␮. The vibrational basis is increased until
convergence of the eigenvalues of interest has been
achieved. A standard diagonalization method for real symmetric matrices has been used. The eigenvalues represent the
vibronic energy levels E␯ with vibronic angular momentum
quantum number ␮. The square of the first component of the
eigenvector represents the spectral intensity within the Condon approximation, assuming that the optical excitation takes
place from the vibrational ground state 兩00典.13
IV. GENERIC ASPECTS OF RELATIVISTIC LINEAR RT
COUPLING
In this section, we discuss the generic effects of the relativistic linear vibronic-coupling term d␳e±i␾ on RT spectra.
Since d will be small for molecules with not too heavy atoms, the effect of the relativistic linear vibronic-coupling
term is expected to become significant only when the potentially interacting unperturbed levels are nearly degenerate.
Since d couples, in first order, levels with different spin
quantum numbers which differ by one quantum of the bending frequency, we expect near-degeneracy effects when ␻
⯝ ␨. We shall refer to the case ␻ ⯝ ␨ as the “resonant case” in
the following.
As is well known in RT theory,1–6 two limiting cases can
be considered. In case A, the spin-orbit splitting ␨ is small
compared with the nonrelativistic RT coupling constant g,
which in turn is small compared with the bending frequency
␻. In case B, the SO splitting ␨ is comparable to or larger
than ␻ and/or g. We shall be concerned here with a special
case of case B, in which ␨ ⯝ ␻ and g ⬍ ␻.
Figure 1 shows the energy levels of such a system with
d = 0. The parameter values are ␨ / ␻ = 0.8 and g / ␻ = 0.15. The
unperturbed bending levels are shown in column 共a兲. Column
共b兲 gives the energy levels of the nonrelativistic RT system.
The energy levels obtained with inclusion of the spin-orbit
splitting ␨ are given in column 共c兲, assigned by usual spectroscopic terms.1–8
It is seen that the energy levels 共000兲 2⌸1/2 and
共010兲␮ 2⌺1/2 are close in energy, as a consequence of ␻ ⯝ ␨
and g ⬍ ␻,␨. The same applies for the level pairs
共020兲␮ 2⌸3/2, 共010兲 2⌬3/2 and 共010兲␬ 2⌺1/2, 共020兲␮ 2⌸1/2.
These quasidegenerate energy levels interact with each other
when the coupling term d␳e±i␾ is taken into account.
Figure 2 displays the energy levels of this system 共complete up to two quanta in the bending mode兲 as a function of
FIG. 1. Energy levels of a RT system with SO coupling in the resonant case
共␨ ⯝ ␻兲.
the dimensionless parameter d / ␻. The energy levels corresponding to different values of ␮, i.e., ␮ = ± 1 / 2, ±3 / 2, ±5 / 2,
are shown by the full, dash-dotted, and dashed lines, respectively. The figure reveals significant level repulsions within
the ␮ = 1 / 2 manifold: the pairs 共000兲 2⌸1/2 / 共010兲␮ 2⌺1/2,
共010兲␬ 2⌺1/2 / 共020兲␮ 2⌸1/2, and 共030兲␮ 2⌺1/2 / 共020兲␬ 2⌸1/2
are seen to repel each other with increasing d / ␻. Similar, but
less pronounced level-repulsion effects are seen in the ␮
= 3 / 2 manifold. The lowest 2⌬5/2 level, on the other hand, is
isolated and its energy is essentially independent of d / ␻. As
a result, the 共010兲␮ 2⌺1/2 and 共010兲 2⌬5/2 levels cross as a
function of d / ␻. Numerous other level crossings occur
among the higher energy levels, see Fig. 2.
Figure 2 reveals that even weak relativistic linear vibronic coupling 共d Ⰶ ␻ , ␨兲 can lead to a significant rearrangement of the vibronic energy levels in resonant cases 共␨ ⯝ ␻兲.
As mentioned in the Introduction, such perturbations of the
vibronic energy levels of 2⌸ states of linear triatomic molecules with moderate RT and SO coupling have been observed experimentally, in particular, in the spectra of NCS
and GeCH, and have been termed “Sears resonances”.7,9
The mixing of the zero-order energy levels also has a
FIG. 2. Effect of d on the vibronic levels. The solid, dash-dotted, and
dashed lines represent the energy levels with ␮ = 1 / 2, 3 / 2, and 5 / 2,
respectively.
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124104-4
J. Chem. Phys. 123, 124104 共2005兲
Mishra et al.
istic adiabatic states, which correspond to the diagonalization
of the nonrelativistic fixed-nuclei electronic Hamiltonian,
H共nr兲
el
=
V. AB INITIO CALCULATION OF THE PARAMETERS
In the present work, we have determined the parameters
␻, ⑀, ␨, and d by ab initio electronic-structure calculations
for the X̃ 2⌸ state of a number of linear triatomic molecules.
For molecules with not too heavy atoms, it is a good approximation to compute the nonrelativistic electronic wave
functions and to determine the matrix elements of the SO
operator 共the Breit-Pauli operator兲 with these nonrelativistic
wave functions. The electronic basis states obtained by the
ab initio electronic-structure calculations are the nonrelativ-
0
1 2 2i␾
g␳ e
2
0
0
0
0
1
− g␳2e2i␾
2
1 2 −2i␾
g␳ e
2
0
0
0
0
1
− g␳2e−2i␾
2
0
0
冣
.
共13兲
共nr兲
, i.e.,
The unitary matrix S which diagonalizes Hel
FIG. 3. Redistribution of the spectral intensity by the linear relativistic
vibronic-coupling parameter d. The solid and dash-dotted lines represent the
energy levels with ␮ = 1 / 2 and ␮ = 3 / 2, respectively.
significant effect on the intensity of the spectral lines. We
shall consider here the case of electronic excitation from the
共000兲 vibrational ground state of some nondegenerate electronic state into the 2⌸ manifold. In the Condon approximation, only the 共000兲 2⌸3/2 and 共000兲 2⌸1/2 zero-order levels
then carry spectral intensity. As is well known,3–6 the RT
coupling leads to a redistribution of intensity, but only
among levels with an even number of quanta in the bending
mode, reflecting the second-order 共quadratic in ␳兲 character
of the RT coupling. The relativistic vibronic coupling term
d␳e±i␾, on the other hand, being of first order in ␳, transfers
spectroscopic intensity to vibronic levels with an odd number of quanta in the bending mode.
This phenomenon is illustrated in Fig. 3, for a resonant
case with the parameter values ␨ / ␻ = 1, g / ␻ = 0.4, and d / ␻
= 0,0.1,0.2. The full and dashed-dotted lines represent the
levels with ␮ = 1 / 2 and ␮ = 3 / 2, respectively. Figure 3共a兲 reveals that the 共020兲␮ 2⌸1/2 level borrows intensity from the
共000兲 2⌸1/2 level via RT coupling 共the intensities of the other
vibronic levels are too low to be visible in the figure兲. Figures 3共b兲 and 3共c兲 illustrate an example of strong mixing of
the quasidegenerate 共000兲 2⌸1/2 and 共010兲␮ 2⌺1/2 levels via
linear relativistic vibronic coupling. In such cases of quasidegeneracy of nonrelativistic RT vibronic levels, the intensity
of the levels with an odd number of quanta of the bending
mode 关such as 共010兲␮ 2⌺1/2兴 can become comparable to
those with an even number of quanta, see Fig. 3.
冢
0
S+H共nr兲
el S =
is
S=
1
冢
冑2
冢
1
− g␳2
2
0
0
0
0
1
− g␳2
2
0
0
0
0
1 2
g␳
2
0
0
0
0
1 2
g␳
2
e−i␾
0
0
e
i␾
e i␾
0
0
− e i␾
e−i␾
0
e−i␾
0
0
e−i␾
0
e−i␾
冣
冣
共14兲
,
共15兲
.
The correspondingly transformed relativistic vibronic
Hamiltonian reads
共SO兲
S=
S+Hel
冢
0
0
0
0
␨
i
2
id␳e
id␳e
i␾
−i
␨
2
− id␳ei␾
−i␾
␨
−i
2
− id␳e−i␾
i
␨
2
0
0
0
0
冣
.
共16兲
The matrix 共16兲 represents the matrix elements of the
Breit-Pauli operator with nonrelativistic adiabatic electronic
states. The SO splitting is directly obtained from the SOmatrix elements at the linear geometry 共␳ = 0兲. The parameter
d can be extracted from the slope of the corresponding SOmatrix elements as a function of the bending coordinate.
The electronic-structure calculations were carried out using the MOLPRO package.14 The ground-state geometry of the
system under consideration is first optimized with the
coupled-cluster method including single and double excitations with perturbative triple excitations 关CCSD共T兲兴,15 em-
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124104-5
J. Chem. Phys. 123, 124104 共2005兲
Relativistic vibronic coupling
TABLE I. Vibrational, vibronic-coupling, and SO-coupling parameters for
the X̃ 2⌸ state of GeCH. ␻, ␨, and d are given in cm−1, ⑀ is dimensionless.
Parameter
Expt.
Calc.
␻
Fitted
a
⑀
␨
⫺334.6
d
500.7
500b
⫺0.0940a
⫺0.1046b
⫺325.0a
41.06a
d
GeCH
Obs. - Calc.
a
435.6
434.8c
⫺0.1090a
⫺0.1135c
⫺348.76a
⫺383.8c
40.48a
a
This work.
Reference 19.
Reference 9.
d
Reference 18.
b
c
ploying the cc-pVQZ 共Refs. 16 and 17兲 basis set. The nonrelativistic parameters ␻ and ⑀ are obtained from the bending
force constants of the two components of the potentialenergy 共PE兲 surface of the degenerate ⌸ state, using Eqs. 共4兲
and 共5兲. The SO-matrix elements have been computed with
complete-active-space self-consistent-field 共CASSCF兲 wave
functions. A state-averaged full-valence CASSCF calculation
of the two components of the 2⌸ state has been performed.
These wave functions are then used to calculate the matrix
elements of the Breit-Pauli operator. These calculations were
performed for a few bent geometries and the parameter d
was extracted as described above. For the SO calculations,
the g-type orbitals had to be omitted because of the inability
of the MOLPRO program to calculate SO integrals over functions of this type.
VI. RESULTS FOR GeCH
GeCH is a linear radical with an orbitally degenerate
X̃ ⌸ electronic ground state. Apart from the RT effect, there
are other effects which complicate the vibronic structure of
the X̃ 2⌸ state. The SO splitting of the X̃ 2⌸ state is significant, being of the order of the bending frequency. A Fermi
resonance between the bending mode and the Ge–C stretching mode and possible vibronic interactions with the closelying electronically excited à 2⌺ state are further
perturbations.18
The geometry of GeCH in the electronic ground state
has been optimized at the CCSD共T兲/cc-pVQZ level. GeCH is
found to be a linear molecule with r0共HC兲 = 1.079 Å,
r0共CGe兲 = 1.769 Å, in good agreement with the experimental
values 1.067 and 1.776 Å,18 respectively. These results agree
with the results obtained by other authors19 with the same
basis set and method. The bending vibrational frequencies
associated with the 2A⬘ and 2A⬙ components of the X̃ 2⌸
state are found to be 476.6 and 523.7 cm−1, respectively. The
averaged harmonic bending frequency 共␻兲 is obtained as
500.7 cm−1, in good agreement with Ref. 19. The RT parameter ⑀1, defined in Eq. 共5兲, is obtained as ⫺0.0940, which
compares well with the value of ⫺0.1046 reported in Ref.
19. The negative sign of ⑀ reflects the fact that the 2A⬘ energy
lies below the 2A⬙ energy.
2
TABLE II. The X̃ 2⌸ vibronic energy levels of GeCH. The differences between the calculated and experimentally observed values are given in cm−1.
共 ␯ 1␯ 2␯ 3兲
共000兲
共010兲
共010兲
共010兲
共010兲
共020兲
共020兲
共020兲
State
Obs.
⌸1/2
⌬5/2
␮ 2⌺1/2
␬ 2⌺1/2
2
⌬3/2
␮ 2⌸3/2
␮ 2⌸1/2
␬ 2⌸1/2
334.9
440.0
444.5
755.6
765.1
869.7
889.8
1193.0
2
2
with
1.8
6.1
⫺1.0
⫺5.5
⫺1.1
⫺1.4
⫺1.6
⫺4.8
d
without d
⫺12.6
4.1
15.1
⫺34.1
⫺13.9
12.5
28.8
⫺34.5
The relativistic parameters were determined with the
procedure described in Sec. V. The SO splitting is found to
be 325 cm−1, in good agreement with the spectroscopically
determined value of 334.6 cm−1.18 The parameter d is calculated as 41.06 cm−1, which is more than 10% of the SO
splitting. The calculated parameters are given in Table I.
Although we have employed elaborate electronicstructure methods and an extended basis set in the ab initio
electronic-structure calculations, one cannot expect that the
obtained vibronic and SO parameters are of the spectroscopic
accuracy. We therefore have performed an independent determination of the parameters by a least-squares fit of the
energy levels of the Hamiltonian 共1兲–共3兲 to the observed energy levels.9 The fitted parameters are also given in Table I.
The fitted bending frequency 共435.6 cm−1兲 is lower than the
ab initio calculated value 共500.7 cm−1兲. The fit of Ref. 9 has
given a similar value of bending frequency 共434.8 cm−1兲.
The fitted value of a ⑀共−0.1090兲 is in good agreement with
the fitted value 共⫺0.1135兲 of Ref. 9.
The fitted and ab initio calculated values for ⑀ are in
satisfactory agreement with each other. For the SO splitting,
the present fitting yields 348.76 cm−1 which is quite close to
the ab initio calculated value 共325 cm−1兲 and the observed
共334.6 cm−1兲 splitting of the 共000兲 2⌸3/2 and 共000兲 2⌸1/2
levels.18 In Ref. 9, anharmonic as well as Fermi resonance
FIG. 4. Comparison of the calculated and observed energy levels for GeCH.
The solid, dash-dotted, and dashed lines represent the energy levels with
␮ = 1 / 2, 3 / 2 and 5 / 2, respectively.
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124104-6
J. Chem. Phys. 123, 124104 共2005兲
Mishra et al.
TABLE III. Structural, vibrational, vibronic-coupling, and SO-coupling parameters for BS2, CS+2 , OCS+, and
OBS. The numbers in parentheses are the values in units of ␻.
Parameter
r1共Å兲
r2共Å兲
␻共cm−1兲
⑀
g共cm−1兲
␨共cm−1兲
d共cm−1兲
CS+2
BS2
1.6760
¯
284.78
⫺0.2257
65.12共0.23兲
⫺394.90共1.39兲
13.31
OCS+
1.5647
¯
331.84
⫺0.1912
64.04共0.19兲
⫺417.40共1.26兲
13.39
effects were included in the fit, resulting in a somewhat
larger value of the SO splitting. The parameter d is obtained
as 40.48 cm−1 from the fit of the experimental spectrum,
which is in very good agreement with its ab initio calculated
value 共41.06 cm−1兲.
The X̃ 2⌸ vibronic energy levels obtained with the fitted
parameters are compared in Table II with the observed energy levels.9 We have restricted our analysis to the lowest
few bending excitations because at higher excitation levels
anharmonicity effects, which are not included in our vibronic
model, may become important. The overall quality of the fit
is determined from the square root of the mean-squared deviation of the calculated energy levels from the observed
energy levels, which is found to be 3.5 cm−1. To reveal the
effect of relativistic linear vibronic coupling, we have included in Table II the deviations of the calculated from the
observed energy levels obtained with and without inclusion
of d. As can be seen, most of the calculated vibronic levels
are in good agreement with the observed values. In most
cases, the difference is below 2 cm−1 which is well within
the experimental error. It can be seen that the levels obtained
with the inclusion of d match the observed levels much better than for d = 0. Several levels are shifted measurably by the
effect of the relativistic linear vibronic coupling. The
共000兲 2⌸1/2 and 共010兲␮ 2⌺1/2 levels, for example, exhibit significant level repulsion. A similar level repulsion can be observed for the 共010兲␬ 2⌺1/2 and 共020兲␮ 2⌸1/2 levels. The ordering of the 共010兲 2⌬3/2 and 共010兲␬ 2⌺1/2 levels is
interchanged by the inclusion of d 共see Fig. 4兲.
OBS
1.1583
1.5690
442.65
⫺0.1590
70.83共0.16兲
⫺347.55共0.78兲
26.96
1.2142
1.7583
370.04
⫺0.1383
51.44共0.14兲
⫺345.04共0.93兲
29.08
The X̃ 2⌸ state of GeCH clearly represents a resonant
case, ␨ / ␻ = 0.88. The Renner-Teller coupling is relatively
weak. As discussed earlier, these circumstances are favorable
for the observation of the relativistic linear vibronic-coupling
effects.
In studies of the vibronic spectrum of the X̃ 2⌸ state of
NCS, Northrup and Sears7 have analyzed the repulsion of
certain levels, e.g., 共010兲 2⌬3/2 and 共020兲␮ 2⌸3/2 in terms of a
mixed second-order perturbation treatment, considering the
SO coupling within the 2⌸ state as well as nonrelativistic
vibronic coupling of the 2⌸ state with a distant 2⌺ state.
Since the ⌺-⌸ coupling is of first order in ␳ and the SO
coupling is of zeroth order in ␳, the combined effect of both
perturbations is of first order in ␳.7 The analysis of Northrup
and Sears thus is equivalent to a perturbative treatment of the
linear relativistic vibronic-coupling term d␳e±i␾. It should be
noted that the perturbative approach of Ref. 7 is bound to
break down when the energy gap of the 2⌺ and 2⌸ states is
of the order of 共or smaller than兲 the SO splitting of the 2⌸
state.
VII. RESULTS FOR OTHER MOLECULES
We consider relativistic vibronic coupling in molecules
with a second-row atom 共S兲: BS2, CS+2 , OCS+, and OBS. All
four systems possess a well-isolated X̃ 2⌸ ground state. The
ab initio calculated vibrational, vibronic-coupling, and SOcoupling parameters of the four systems are given in Table
III.
TABLE IV. Calculated X̃ 2⌸ vibronic energy levels 共in cm−1兲. ␦ is the difference in energy with and without
inclusion of the linear relativistic vibronic coupling.
CS+2
BS2
共␯1␯2␯3兲 State
with
共000兲 ⌸1/2
共010兲␮ 2⌺1/2
共010兲 2⌬5/2
共010兲 2⌬3/2
共010兲␬ 2⌺1/2
共020兲␮ 2⌸3/2
共020兲␮ 2⌸1/2
共020兲 2⌽7/2
共020兲 2⌽5/2
共020兲␬ 2⌸1/2
共020兲␬ 2⌸3/2
386.09
272.69
280.03
648.60
680.98
543.02
558.30
557.83
812.18
821.11
852.56
2
d
␦
1.4
⫺1.4
⫺0.3
1.1
2.2
⫺1.5
⫺2.2
⫺0.5
⫺1.5
⫺1.6
⫺2.5
with
d
412.72
320.27
327.75
728.30
754.98
639.12
649.70
653.58
956.88
960.93
986.54
OCS+
␦
1.9
⫺1.8
⫺0.2
1.7
3.0
⫺1.8
⫺2.9
⫺0.5
⫺1.8
⫺2.3
⫺3.6
with
d
338.26
435.87
437.62
772.47
785.88
860.40
878.60
873.22
1202.76
1227.90
1233.51
OBS
␦
⫺6.6
7.3
⫺0.9
⫺5.7
⫺15.6
5.9
16.3
⫺1.8
⫺4.4
⫺20.3
⫺25.4
with
d
323.45
382.81
366.40
687.30
685.69
742.23
764.11
731.60
1049.25
1049.89
1052.21
␦
⫺19.4
20.3
⫺1.2
⫺18.9
⫺34.8
19.3
35.7
⫺2.3
⫺17.2
⫺32.3
⫺45.2
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124104-7
J. Chem. Phys. 123, 124104 共2005兲
Relativistic vibronic coupling
VIII. CONCLUSIONS
FIG. 5. Comparison of the vibronic energy levels of the X̃ 2⌸ state of OBS,
calculated with and without inclusion of linear relativistic vibronic coupling,
respectively.
In the case of BS2, the SO splitting of the X̃ 2⌸ state is
calculated to be 395 cm−1, which is larger than the bending
frequency 共285 cm−1兲. This is accompanied by a relatively
strong Renner-Teller coupling g / ␻ = 0.23. The calculations
predict a rather small value of d 共13.3 cm−1兲. The differences
between the energies of the vibronic levels with and without
inclusion of d are given in Table IV.
In the case of BS2, we observe a very small effect of d
on the energy levels 共less than 2 cm−1兲. This is the consequence of the nonresonant character of BS2 共␨ / ␻ ⯝ 1.4兲 and
the rather small value of d 共d / ␨ ⬍ 0.03兲. The situation is
similar in CS+2 , although ␨ / ␻ is closer to unity than in BS2.
In addition, the Renner-Teller coupling is weaker in CS+2 .
However, this system still is too far from resonance to exhibit strong relativistic vibronic-coupling effects.
In OCS+, the bending frequency 共443 cm−1兲 is larger
than the SO splitting 共348 cm−1兲. The Renner-Teller coupling
is weaker than in BS2 and CS+2 . The value of d is 27 cm−1.
The more favorable ␨ / ␻ ratio of 0.78, weaker RT coupling,
and the larger value of d render relativistic vibronic-coupling
effects more conspicuous than in BS2 and CS+2 共see Table
IV兲. The difference in the energy levels is sometimes as large
as 20 cm−1. The relativistic vibronic-coupling effects are
largest in OBS. It has a favorable ␨ / ␻ ratio 共0.93兲, a weak
Renner-Teller coupling 共g / ␻ = 0.14兲, and a relatively large
value of d 共29 cm−1兲. The calculated vibronic levels of OBS
with and without inclusion of d are depicted in Fig. 5. It can
be seen that the levels are shifted by up to 30 cm−1 by the
relativistic vibronic coupling. Moreover, a complete rearrangement of the energy levels takes place.
It is worthwhile to point out some observations which
are common to all four systems. In all cases, we observe a
very small change in the energy of the 共010兲 2⌬5/2 level upon
the inclusion of d 共cf. Sec. IV兲. A similar observation applies
for the 共020兲 2⌽7/2 level. Both levels are little affected because of the absence of close-lying levels of the same symmetry. Another common observation is the nearly symmetric
splitting of the energy levels which are coupled by the linear
relativistic term, for example, 共010兲␮ 2⌺1/2 and 共000兲 2⌸1/2.
This symmetric splitting is also observed for higher levels
共see Fig. 5兲.
The spectroscopic effects of the relativistic linear
vibronic-coupling term derived from the Breit-Pauli SO operator have been analyzed for a series of linear triatomic
radicals and radical cations with 2⌸ electronic ground states.
It has been shown that the relativistic vibronic-coupling
mechanism can lead to significant perturbations of the vibronic spectra when the 2⌸ SO splitting and the bending
vibrational frequency are of similar magnitude.
For the example of the X̃ 2⌸ state of GeCH, we have
determined the relativistic linear vibronic-coupling parameter d as well as the other parameters of the RT vibronic
model with accurate ab initio electronic-structure methods.
These parameters were independently determined by a leastsquares fitting of the experimentally observed RT vibronic
energy levels. The excellent agreement of the ab initio and
empirically determined values provides convincing evidence
that the strong perturbations of vibronic spectrum of the
X̃ 2⌸ state of GeCH, which previously have been termed
“Sears resonances,”9 are effects of the relativistic linear
vibronic-coupling mechanism. The effects of the relativistically induced vibronic coupling are comparatively pronounced in GeCH, since the SO splitting ␨ and the bending
frequency ␻ are nearly equal and the nonrelativistic RT coupling is comparatively small 共g / ␻ Ⰶ 1兲, while the ratio d / ␨ is
relatively large. The latter fact may have its electronicstructure origin in the existence of a rather low-lying à 2⌺+
state in GeCH, which mixes strongly with the X̃ 2⌸ state
upon bending. This mixing affects the SO-matrix elements of
the X̃ 2⌸ state.
A brief survey of the ab initio calculated relativistic linear vibronic-coupling constants and the resulting vibronic
spectra of the series BS2, CS+2 , OCS+, and OBS has been
given. The survey illustrates the interplay of the parameters
␨ / ␻, g / ␻, and d / ␨ in the RT-SO spectra. Near degeneracy of
␨ and ␻ 共␨ / ␻ ⯝ 1兲 as well as weak nonrelativistic RT coupling 共g / ␻ Ⰶ 1兲 are favorable circumstances for significant
perturbations of RT-SO spectra by the relativistically induced
vibronic coupling.
ACKNOWLEDGMENTS
This work has been supported by the Deutsche
Forschungsgemeinschaft and the Fonds der Chemischen
Industrie.
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