Hydrogen-Bonding Structure and Dynamics of Aqueous Carbonate Species fromCar-Parrinello Molecular Dynamics Simulations

P. Padma Kumar,*,† Andrey G. Kalinichev,*,‡ and R. James Kirkpatrick§

Department of Geology, UniVersity of Illinois at Urbana-Champaign, Urbana, Illinois 61801

ReceiVed: October 14, 2008; ReVised Manuscript ReceiVed: NoVember 17, 2008

A comprehensive Car-Parrinello molecular dynamics (CP-MD) study of aqueous solutions of carbonic acid(H2CO3), bicarbonate (HCO3

-), carbonate (CO32-), and carbon dioxide (CO2) provides new quantitative insight

into the structural and dynamic aspects of the hydrogen-bonding environments for these important aqueousspecies and their effects on the structure, H-bonding, and dynamical behavior of the surrounding watermolecules. The hydration structures of the different carbonate species depend on their ability to accept anddonate H-bonds with H2O. The H-bonds donated by the C-O-H sites of the carbonate species to watermolecules are generally stronger and longer-lived than those accepted by these sites from water molecules.The structural relaxation among the water molecules is dominated by diffusional (translational) motion ofH2O, whereas the H-bond reorganization is dominated by the librational motion of the water molecules andthe carbonate species. The rates of structural relaxation of the H2O molecules and the rates of H-bondreorganization among them are slower in systems containing carbonate species, consistent with previous studiesof simple salt solutions. The strengths and lifetimes of H-bonds involving the carbonate species positivelycorrelate with the total negative charge on the species. H-bond donation from H2O to CO2 is weak, but thepresence of CO2 noticeably affects the structure and structural relaxation of the surrounding H-bonding networkleading to generally stronger H-bonds and slower relaxation rates, the behavior typical of a hydrophobicsolute.

1. Introduction

There is strong evidence that the local hydration structurearound a solute molecule in aqueous solution and the responseof the water molecules to the changes in the geometric andelectronic structure of the solute have significant influence onthe reactivity of solutes in the solution.1,2 Advances in under-standing the thermodynamics and kinetics of aqueous solutions,however, require a dynamical treatment that goes beyond theconventional statistical approach and that also uses a moleculardescription of the solute rather than a dielectric continuumapproach.1,2 The experimental microscopic temporal and spatialresolution of solution structure and dynamics sufficient tosupport such theoretical development has not been available inthe past. Recent advances in time-resolved spectroscopictechniques and computer simulations are, however, now deliver-ing such a molecular level description. Recent spectroscopicinvestigations of pure water3 and alkali halide and Na/Mgperchlorate (ClO4

-) solutions4-6 provide valuable insight intothe hydrogen-bonding and relaxation dynamics of water mol-ecules in the bulk and in the solvation shell around solutemolecules. A detailed microscopic picture of the solvationstructure and dynamics of a variety of atomic and molecularspecies in aqueous solutions is also emerging from recentmolecular dynamics simulations.7-17

Aqueous solutions containing dissolved CO2 and the variouscarbonate species are ubiquitous in the natural environment andare major players in a broad range of processes of criticalimportance in chemistry, biology, geochemistry, atmosphericsciences, astronomy, and environment sciences.18-22 Under-standing the reactivity of aqueous carbonate species is especiallycritical to understanding the role of CO2 in the global carboncycle and climate change and in developing viable carbonsequestration technology. Despite the importance of aqueouscarbonate species, surprisingly little is known about theirstructural environments and dynamical behavior in aqueoussolution. It has been known for many decades that when CO2

dissolves in water, about 1% of it converts to carbonic acid,H2CO3.23,24 It is also well-known that aqueous carbonic aciddeprotonates to bicarbonate, HCO3

-, and carbonate, CO32-, with

pKa values of 6.4 and 10.3, respectively. Direct spectroscopicdata for H2CO3 date from the early 1990s,25 and there is morerecent spectroscopic evidence for its presence on calciumcarbonate surfaces.26,27 Carbonic acid can be synthesized byirradiation of frozen films of CO2/H2O mixtures with high-energy He ions or protons25,28 and by protonation of HCO3

-/CO3

2- solutions at low temperatures.29 Crystalline H2CO3 canbe sublimated and recondensed without decomposition to CO2

and H2O.30 There have been several recent quantum chemicalstudies of the structure, energetics, and reactivity of carbonatespecies using self-consistent field Hartree-Fock methods (SCF-HF), coupled cluster methods (CCM), Møller-Plesset (MP)perturbation theory, and density functional theory (DFT).31-43

Because these computational techniques are expensive, theyhave been limited largely to gas phase systems consisting of amolecule of carbonic acid or carbon dioxide either in the barestate or microsolvated by a few water molecules.31-39 Quantum

* To whom correspondence should be addressed. E-mail: padmakumarp@iitg.ernet.in; kalinich@chemistry.msu.edu.

† Current address: Department of Physics, Indian Institute of TechnologyGuwahati, Guwahati, Assam 781039, India.

‡ Current address: Department of Chemistry, Michigan State University,East Lansing, MI 48824.

§ Current address: College of Natural Science, Michigan State University,East Lansing, MI 48824.

J. Phys. Chem. B 2009, 113, 794–802794

10.1021/jp809069g CCC: $40.75 2009 American Chemical SocietyPublished on Web 12/24/2008

chemical calculations for carbonate species in solution haveeither treated the solvent implicitly by mean-field or dielectriccontinuum approximations or have used empirical force fields.40-42

The hydrogen-bonded structures and vibrational frequencies ofisolated H2CO3 dimers and larger clusters have also been studiedby quantum chemical techniques.44,45

The stability of the bare carbonic acid molecule was acontroversial topic43 until the mass spectroscopic studies byTerlouw et al. confirmed its existence in 1987.46 Theoreticalcalculations of the dissociation of gas-phase H2CO3 to CO2 andH2O have estimated the reaction to be exothermic by about9-10 kcal/mol, but with an activation barrier of about 43 kcal/mol, thus explaining the observed stability of gas phaseH2CO3.33,37-39 More recent theoretical studies by Liedl andco-workers37,38 have shown that the activation barrier for H2CO3

dissociation decreases as the number of solvating water mol-ecules increases, suggesting that hydrogen-bonding with H2Omolecules plays a significant catalytic role in this reaction. Theirtransition state theoretical (TST) approach based on a coupledcluster method estimated an activation barrier of 43 kcal/molfor the dissociation of a bare H2CO3 molecule with this valuedecreasing monotonically to ∼21 kcal/mol when three H2Osolvate the molecule.37,38

There have been several classical molecular dynamics (MD)and Monte Carlo (MC) computer simulation studies ofCO2-H2O solutions,47-52 but this work focused largely on thethermodynamic properties and developing better equations ofstate for CO2-H2O mixtures. The molecular-scale structure andhydrogen-bonding in such solutions have attracted much lessinterest. Classical molecular simulations of this type employpredefined intermolecular potentials and can efficiently probethe structural and dynamic properties of bulk aqueous solutions,but their applicability is limited when chemical reactions occur.The development of “reactive” intermolecular potentials capableof modeling the formation and breaking of chemicals bonds insuch situations has proven to be difficult.53,54 In addition, recentstudies have observed that classical MD methods tend tooverestimate the size of the solvation sphere.7,8,10,14 Explicitincorporation of ionic polarizability in the intermolecularpotentials may improve the results but does not solve thedifficulty in describing the chemical reactivity.

Given the prohibitively large computational cost of traditionalhigh-level quantum chemical methods in modeling bulk solventenvironments and the limited applicability of classical molecularsimulation techniques, several compromise ways to incorporatechemical reactivity into the molecular modeling of aqueoussystems have been developed. The important advantage of theseapproaches over traditional quantum chemical techniques is inthe explicit incorporation of finite temperature effects and thefeasibility of performing calculations on large enough systemsthat the effects of the solution environment can be morerealistically modeled. The QM/MM technique separates thesolvent and solute system into two parts: (i) the QM (forquantum mechanical) part is treated using high-level quantumchemical methods but includes only the reaction center and thesolvent molecules in its immediate vicinity and (ii) the MM(for molecular mechanics) part, which includes the rest of thesystem and is treated using a classical force field approach. Rodeand co-workers16 have recently successfully applied this methodin the form of quantum mechanical charge field moleculardynamics (QMCF-MD)55 to study the structure and dynamicsof a number of oxo anions in water. A limitation of this approachis that the “classical” solvent molecules can frequently exchangepositions with their “quantum” counterparts near the solute

during a typical simulation time of a few tens of picoseconds.This exchange partially eliminates the capability of some solventmolecules to react with the solute.

The Car-Parrinello molecular dynamics technique (CP-MD),55 sometimes also called ab initio molecular dynamics(AIMD), appears to be a more universal molecular modelingapproach to the study of chemical reactions in many aqueoussystems. In contrast to the QM/MM approach, all solventmolecules are treated equivalently in the CP-MD simulation,and all are capable of participating in chemical reactions in anyregion of the simulated system. Admitably, the gain is partiallythrough the utility of density functionals developed within thelocal density approximation (LDA). CP-MD is superior toclassical MD methods because the intermolecular interactionsare computed “on the fly” at the DFT level, thus incorporatingmany-body interactions and ion polarizability. Leung et al.57

have recently used this approach to investigate the nucleophilicattack of hydroxide on CO2 in the aqueous environment, andRustad et al.57 have used a combination of CP-MD with quantumchemical calculations of large supermolecular clusters to studycarbon isotope fractionation in CO2(g), aqueous carbonatespecies, and carbonate minerals.

Here we present a detailed CP-MD study of the structure anddynamics of hydrogen-bonding around molecules of carbonicacid (H2CO3), bicarbonate (HCO3

-), carbonate (CO32-), and

CO2, in aqueous solutions. The objective of these simulationsis to provide new fundamental insight into the hydrationstructures, H-bond environments and lifetimes, and dynamicalbehavior of these important species, which are a required basisfor future study of their molecular scale reactivity. In a recentstudy39 employing a metadynamics algorithm59 based on theCar-Parrinello technique,56,60 we reported the energetics of theconformational rearrangements of gas-phase carbonic acid andits dissociation to H2O and CO2. The results are in goodagreement with previous theoretical studies, provide a detaileddissociation mechanism for gas phase H2CO3, and demonstratethe usefulness of the technique. These results, together with thepresent study, lay the foundation for ongoing efforts tounderstand the chemical reactivity of carbonate species inaqueous environment on a fundamental atomistic time andlength scale.

2. Methods

The CP-MD calculations here employ the Car-Parrinellomolecular dynamics algorithm as implemented in version 3.11.1of the CPMD software.61 The simulated systems are isoelec-tronic, with a single molecule of H2CO3, HCO3

-, or CO32-

embedded in a box with 45 water molecules or a single moleculeof CO2 embedded in 46 water molecules. Pure water is modeledusing 48 water molecules. In all cases, periodic boundaryconditions are used with the cubic cell edge of 11.3 Å. For purewater these parameters yield the experimental density of 1 g/cm3

(0.033 molecules/Å3). The starting configurations for the CP-MD simulations were well equilibrated structures from 100 psclassical MD simulations using SPC62 and CVFF63 force fieldparameters. A further equilibration was carried out for ∼15 psusing CP-MD before 14 ps long equilibrium CP-MD trajectorieswere produced for detailed analysis of structure and dynamics.

Note that with no counterions present the HCO3- and CO3

2-

systems are not electrostatically neutral, and the structures anddynamics obtained for them do not account for the effects ofdissolved cations. For the sake of convenience, however, weuse the terms solute and solution to refer to the carbonate speciesand aqueous systems containing all the carbonate species. These

Structure and Dynamics of Aqueous Carbonate Species J. Phys. Chem. B, Vol. 113, No. 3, 2009 795

two non-neutral systems are handled by adding a neutralizingcharge to the simulation cell together with Ewald summation.61

The added charge is uniformly distributed in the simulation cellsuch that it has no spatial gradient and imparts no force on theions and, hence, does not affect the dynamics of the ions.

The valence electrons are treated explicitly within the DFTformalism employing the gradient-corrected Becke, Lee, Yang,and Parr (BLYP) functional.64,65 The interactions of the valenceelectrons with the nuclei and core electrons are represented byultrasoft pseudopotentials originally proposed by Vanderbilt.66

The use of ultrasoft pseudopotentials (USPP) greatly reducesthe number of plane waves necessary in DFT calculationsrelative to norm-conserving pseudopotentials.67 Therefore, inour simulations, the Kohn-Sham orbitals are expanded usingplane wave basis sets,with a cutoff of 40 Ry. An electronic massof 600 au and a time step of 4 au (≈0.1 fs) are used. Atemperature of 310 K for the molecules and a fictitious kineticenergy of about 0.02 au for the electronic degrees of freedomare controlled using Nose-Hoover thermostats. The physicallyuninteresting bulk translations of the system are removed every100 MD steps.

The H2CO3 molecule occurs in three different conformations,trans-trans (TT), cis-trans (CT), and cis-cis (CC), and wehave undertaken calculations for the TT and CT conformers.The three conformers differ in the orientation of the hydroxylgroups with respect to the carbonyl group.33,39 Previous theoreti-cal calculations suggest that in the gas phase TT is the moststable species but is only about 1-2 kcal/mol lower in energythan CT.33,39 This energy difference is small enough that theirrelative stability could be easily changed by H-bonding withwater molecules, and it is not known which of these two speciesis the most stable in aqueous solution. The CC conformer isabout 9 kcal/mol higher in energy than CT in the gas phaseand is expected to be much less stable than the other two evenin solution.

This study focuses on the structural and dynamic aspects ofhydrogen-bonding, and we use a uniform definition for theexistence of an H-bond between two species that requiressimultaneously satisfying three criteria: (i) the donor-acceptorO · · ·O distance is less than 3.5 Å, (ii) the donor-acceptorH · · ·O distance is less than 2.45 Å, and (iii) the hydrogen-donor-acceptor angle is less than 30°.11 We examine thestructural relaxation of hydrogen bonds in our simulated systemsusing two suitably defined time correlation functions. Thefunction

describes the structural relaxation of hydrogen bonds. Here h(t)is unity if an H-bond as defined above exists between a pair ofdonor-acceptor sites at time t and zero otherwise. A similarlydefined function

is based only on the distance criterion (i) and thus describesthe structural relaxation of the H-bonds due to translationaldiffusion. Chandra11 has used these functions in a study ofrelaxation in NaCl and KCl solutions and found evidence forslower structural relaxation of H-bonds among water moleculesin the presence of ions.

We estimate the lifetimes of the H-bonds between specificdonor-acceptor pairs using two similar time correlation functions:

and

where H(t) is unity if a tagged pair of donor-acceptor sitesremain continuously H-bonded for a period t and zero otherwise.SHB(t) probes the sum of all rotational and translational motionsaffecting H-bonding, whereas Sd

HB(t) probes only the transla-tional contribution to the H-bond lifetimes, since it, like Cd

HB(t),is defined based only on the distance criterion (i) above. Thepower spectra of the carbonate species were calculated as Fouriertransforms of their velocity autocorrelation functions over the14 ps production trajectories of the CP-MD simulations.

3. Results and Discussion

3.1. Hydration Structure and Hydrogen-Bonding. The CP-MD results show significant differences in the local hydrationstructure and hydrogen-bonding of the different carbonatespecies, as illustrated by the computed 3-dimensional spatialatomic density distributions for the hydrogens (gray) andoxygens (red) of water molecules around them (Figure 1a-e).In these diagrams, the first shells of hydrogen and oxygeninclude those directly H-bonded to the solute assuming asimplified H-bonding criterion of 2.4 Å between the donor andacceptor sites. The second shell includes the oxygens andhydrogens bonded to the atoms in the first shell. The enclosedvolumes represent number densities of 0.109/Å3 or more aroundH2O (Figure 1f) and all the carbonate species except CO2. Thisthreshold value corresponds to 3.5 times the average numberdensity of water. For CO2 (Figure 1e) the number densityvisualization threshold is 0.0109/Å3 because this species makestoo few H-bonds with H2O to be effectively visualized at thelarger density, and there is only weak H-bond acceptance bythe oxygens of CO2. The atomic density distributions of thehydrogen and oxygen of water in the hydration shell around anarbitrarily chosen H2O molecule from the pure water simulation(Figure 1f) are directly comparable with the CP-MD (BLYP/pw) results of Mantz et al.68 for 64 water molecules, exceptthat we use a 5% lower threshold density.

The computed hydration structures involve three kinds ofH-bonds: (i) OH-HO · · ·Ow, donated by the hydroxyl groups(-C-OH) of the carbonate species to water, (ii) Ow-Hw · · ·OH,donated by water to the hydroxyl oxygens of the carbonatespecies, and (iii) Ow-Hw · · · )O, donated by water to thecarbonyl groups (-CdO). Symbols )O, OH, HO refer respec-tively to carbonyl oxygens, hydroxyl oxygens, and hydroxylhydrogens of the carbonates. Ow and Hw refer to the oxygensand hydrogens of water molecules, respectively. The structureof the solute also affects the hydration structure, as demonstratedby the differences in the atomic density distributions for theTT and CT conformers of H2CO3 (Figure 1a,b). Thus, thehydration structures appear to result from the complex interplayof slightly different energetics and dynamics of the acceptedand donated H-bonds between the different sites of the solutemolecules and water molecules and among water moleculesthemselves.

The atom-atom radial distribution functions (RDFs; g(r))between different solute sites and H2O molecules provide a moredetailed quantitative description of the hydration structures(Figure 2). For all the carbonate species except CO2, the C-Ow

RDFs all contain a nearest-neighbor peak near 3.5 Å that

CHB(t) ) ⟨h(0) ·h(t)⟩ /⟨h⟩ (1)

CdHB(t) ) ⟨h(0) ·hd(t)⟩ /⟨h⟩ (2)

SHB(t) ) ⟨h(0) ·H(t)⟩ /⟨h⟩ (3)

SdHB(t) ) ⟨h(0) ·Hd(t)⟩ /⟨h⟩ (4)

796 J. Phys. Chem. B, Vol. 113, No. 3, 2009 Kumar et al.

becomes progressively sharper as the charge of the carbonatespecies increases (Figure 2a). This result indicates a progres-sively stronger and more ordered solvation structure withincreasing net solute charge. The C-Ow RDFs of TT- and CT-H2CO3 conformers are similar. The C-Ow RDF of CO2 is quite

different, with a low-intensity feature (shoulder) at ∼2.75 Åand a broad peak between 3 and 5 Å. These structural resultsare in generally good agreement with calculations of Leung atal.57 and Rustad et al.58

The RDFs for the carbonyl oxygens and hydrogens of water()O-Hw) show a first peak at ∼1.8 Å that shifts to shorterdistances and becomes more intense with increasing negativecharge of the species (Figure 2b). This trend clearly indicates aprogressively increasing H-bond strength for this type of sitewith increasing net charge on the ion. Compaction of the 3-Dhydration structure around the )O oxygens (Figure 1a-d) wasalso recently observed around the oxygens of perchlorite, sulfate,and phosphate in QMCF-MD simulations.16

The differences in the RDFs of the TT and CT conformersof H2CO3 are related to their structures and the observation thatthere are two groups of water molecules in the hydration shell:those donating H-bonds to the carbonate species and thoseaccepting H-bonds from the carbonate species. Water moleculesin these two groups do not make favorable H-bonds with watermolecules in the other group. For the TT conformer, the watermolecules donating H-bonds to )O are located between thoseaccepting H-bonds from the -OH groups. For TT and CTconformers the H-bonds donated by the -OH groups to watermolecules (HO · · ·Ow) are stronger and presumably more “rigid”than those donated by H2O to the )O, as evidenced by theirmuch shorter HO-Ow distances (Figure 2d). This configurationposes a significant structural constraint on the “basin” of watermolecules around )O, resulting in fewer H-bonds accepted bythe site. This effect is less pronounced for the CT conformerbecause the water molecules donating H-bonds to )O are locatedbetween those forming HO · · ·Ow H-bonds (strong) on one sideand those forming the relatively weaker OH · · ·Hw bonds on theother side. The smaller steric hindrance could be partiallyresponsible for the higher )O-Hw RDFs peaks for HCO3

- andCO3

2-. As also seen in the C-Ow RDF discussed above, the

Figure 1. 3-D atomic density distributions of hydrogens (gray) and oxygens (red) of water molecules H-bonded to carbonate species (or to anarbitrarily chosen water molecule in the case of pure H2O simulation) obtained from CP-MD simulations. The first shell of hydrogens (gray) oroxygens (red) of water molecules included in the atomic density calculation are within 2.4 Å of the oxygens or hydrogens of the solute molecule,which is a simplified H-bonding criterion. The second shell of density includes the water hydrogens or oxygens bonded to those in the first shell.Clockwise from top-left corner: (a) trans-trans (TT) H2CO3, (b) cis-trans (CT) H2CO3, (c) bicarbonate, HCO3

-, (d) carbonate, CO32-, (e) CO2, (f)

pure H2O. A uniform threshold number density of 0.109/Å3 is chosen for the isosurface in all plots, except for the case of CO2 where the thresholdis set to 0.0109/Å3 (see text for details).

Figure 2. Atom-atom radial distribution functions between selectedsites of the carbonate species and water molecules at 310 K. Thesymbols C, )O, OH, and HO refer respectively to carbon, carbonyloxygen, hydroxyl oxygen, and hydroxyl hydrogen of the carbonatespecies. Ow and Hw refer to the oxygens and hydrogens of watermolecules, respectively. Legends in (a) are common to all.

Structure and Dynamics of Aqueous Carbonate Species J. Phys. Chem. B, Vol. 113, No. 3, 2009 797

)O-Hw RDF for CO2 is markedly different from the others.There is little intensity at distances less than 2 Å, suggestingvery weak H-bonding between CO2 and H2O molecules. Thisconclusion is in qualitative agreement with the low solubilityof CO2 in water and has been observed in previous MDsimulations.57,58

The OH-Hw RDFs of HCO3- and the TT and CT conformers

of H2CO3 (Figure 2c) have much smaller first peaks at a largerdistance than the HO · · ·Ow RDFs (Figure 2d). This result clearlyshows that the H-bonds accepted by the -OH groups (OH · · ·Hw)are much weaker than those donated by them. The donatedHO · · ·Ow H-bonds are shorter (stronger) for both conformersof carbonic acid than for HCO3

-, which is indicative of therelative ease of deprotonation of carbonic acid, as shown by itslower pKa value.

The RDFs between oxygens of water molecules (Ow),gOwOw(r), for the carbonate-containing solutions (Figure 3) arenot greatly different from that of pure water. The Ow-Ow RDFsfor the solutions, except that of CT-H2CO3, have slightly highermaxima and deeper minima, suggesting a somewhat moreordered solvent structure compared to pure water. It is not clearat this point whether the small structural differences of thedifferent systems is due entirely to the differences in the firsthydration shell around the solute molecules or to longer rangeeffects. For pure H2O, the position (2.75 Å) and height (2.98)of the first peak of gOwOw(r) are in good agreement with themost recently published CP-MD simulations of 64 H2O mol-ecules employing the BLYP/pw functional and at a comparabletemperature.68,69 The values for the first minimum and secondmaximum for pure water are ∼3.35 Å, 0.6 and ∼4.45 Å, 1.35,respectively, and are also in good visual agreement with previousreports.68,69 The relatively flat first minimum and secondmaximum make it difficult to locate their positions accurately.

The time-averaged H-bonding statistics of the various sitesof the aqueous carbonate species computed using the three-pointcriterion discussed in section 2 show that the number of H-bondsaccepted and donated by the different sites varies significantlyfrom species to species (Figure 4). For the TT and CTconformers of H2CO3 and for HCO3

-, the number of H-bondsdonated by each -OH group to water (HO · · ·Ow) is essentiallyunity, reflecting the large relative strength and stability of theseH-bonds described above. The number of H-bonds accepted bythe )O sites increases from CT-H2CO3 to HCO3

-, to CO32-,

reflecting the increasing negative charge on the )O sites. The

OH sites of TT-H2CO3 accept a greater number of H-bonds thanthose of CT-H2CO3 and HCO3

-. The number of H-bondsaccepted by the two symmetrically inequivalent -OH groupsof the CT conformer are also different: 0.27 per OH site for theone oriented toward the )O and 0.49 per OH for the one orientedaway from it. Similarly, the )O of the bicarbonate closer to theHO accepts fewer H-bonds from water (2.19 per )O site) thanthe other )O (2.52 per site). These differences can be rational-ized in terms of steric constraints arising from (i) the inabilityof the water molecules in the first hydration shell to formcompact structures favorable for H-bonding among themselvesand (ii) the relative strength of the H-bonds donated by thecarbonate species, as discussed above. The presence of thecarbonate species decreases the number of H-bonds betweenH2O molecules relative to pure water, except for CO2 whichincreases this number. Thus, CO2 behaves in this respect as atypical hydrophobic solute.

3.2. Structural Relaxation and H-Bonding Lifetimes. Thehydrogen-bonding time correlation functions, CHB(t) and Cd

HB(t)(eqs 1 and 2), describe respectively the overall structuralrelaxation and the structural relaxation due only to translationaldiffusion. The decay of both functions is faster than exponentialduring the first 1-2 ps but approaches exponential at longertimes (Figure 5). This behavior is in agreement with the resultsof previous classical MD simulations of simple salt solutionsusing the SPC/E water potential.11 For pure water, the CHB(t)and Cd

HB(t) relaxation times, τc and τcd, obtained from linear

fits to the exponential portion of our results are 5.0 and 5.1 ps,respectively (Table 1). Given the technical differences betweenthe methods, these values agree favorably with the values of6.6 and 7.6 ps from the previous classical MD studies.11

For the carbonate solutions, the structural relaxation times(Table 1) are all larger than for pure water and increase fromCT-H2CO3 to TT-H2CO3 to HCO3

- to CO32-. The CT-H2CO3

solution exhibits a longer nonexponential regime than the othersand relaxes significantly faster than that of the TT conformer.The behavior of the CT conformer is unexpected but consistentwith the less ordered structure of its hydration shell (Figures 1and 2). The logarithmic nature of the relaxation plots in Figure5 suggests that longer simulation times are needed for preciseestimates of the structural relaxation times for CT-H2CO3. The

Figure 3. Oxygen-oxygen radial distribution functions for water, pureas well as containing different carbonate species from the CP-MDsimulations at 310 K. Bins of size 0.02 Å are used in all cases.

Figure 4. Statistics of the H-bonds between different sites of carbonatespecies with water molecules together with those between watermolecules at 310 K averaged over the entire 14 ps long CP-MDtrajectories. The numbers are per site of the carbonate species for thecarbonate-water H-bonds. The number of H2O · · ·H2O H-bonds is perwater molecule.

798 J. Phys. Chem. B, Vol. 113, No. 3, 2009 Kumar et al.

longer relaxation times of the HCO3- and CO3

2- solutionscorrelate well with their increasing net charge and increasingH-bonding strength. This observation is again consistent withthe results of classical MD simulations for simple salt solutions,in which increasing salt concentration causes slower relaxation.11

In both cases, the increasing ionic strength (or the charge/volumeratio) leads to strengthening of the ion atmosphere felt by thewater molecules and slows the H-bonding relaxation. The CO2

system also exhibits increased structural relaxation times despitethe relatively weak CO2 · · ·H2O H-bonding. This behavior isconsistent with the increased structural ordering of watermolecules in the CO2 hydration shell (Figure 2), typical for ahydrophobic solute.

The two relaxation times obtained from these results, τc andτc

d (Table 1), are equal for all the systems studied here withintypical statistical errors. This result demonstrates that the longertime structural relaxation (t > 2 ps) is due principally totranslational diffusion of H2O molecules and not to theirrotational or librational motion.

The SHB(t) and SdHB(t) correlation functions (eqs 3 and 4) that

probe H-bond lifetimes also exhibit nonexponential behaviorat t < 0.5 ps and exponential decay at longer times (Figure 6,Table 2). These functions provide detailed insight into theH-bond dynamics. For all of our systems, the Sd

HB(t) lifetimes,τs

d, are significantly longer than the SHB(t) ones, τs, in contrastto the structural relaxation for which Cd

HB(t) decays at the samerate as CHB(t). This result demonstrates that librational modesplay a more important role than translational diffusion modesin breaking of water H-bonds (H2O · · ·H2O) in both pure water70

and the carbonate solutions.As for the structural relaxation, the τs and τs

d H-bond lifetimesbetween H2O molecules are generally longer in the solutionsthan in pure water (Table 2). Again, the only exception is theCT-H2CO3 system, which relaxes faster than pure water. Wedo not have a clear understanding of this result. A second CP-MD run, starting from the final structure of the first run forCT-H2CO3, revealed that this feature is persistsent. This behavior

may be due to the system not being completely at equilibrium,but it may also be due to the natural behavior of the reactant(CT-H2CO3) being close to a reaction event (H2CO3T HCO3

-

+ H3O+). This reaction could have a low activation barrier butwith the product unstable due to pH considerations. CO2

increases the H2O · · ·H2O H-bond lifetimes despite the veryweak CO2 · · ·H2O H-bond interaction, again consistent with thestructural relaxation described above and with the hydrophobicnature of CO2 in solution. For pure water, our τs and τs

d valuesfrom CP-MD (0.88 and 2.57 ps, respectively) are in reasonableagreement with those from the previous classical MD simula-tions by Chandra (0.54 and 1.75 ps, respectively).11

The lifetimes of H-bonds accepted from water molecules bythe OH and )O sites of the carbonate species are shorter thanthose between water molecules, except for )O of CO3

2- (Table2), and the lifetimes of OH · · ·Hw H-bonds are shorter than thosefor )O · · ·Hw bonds for all relevant species. This latter behavioris consistent with the relatively long OH · · ·Hw bond lengths

Figure 5. Time correlation functions, CHB(t) and CdHB(t) (see text for

details), showing the structural relaxation of H-bonds between watermolecules for different solutions of carbonate species at 310 K. Legendsin the lower panel are common to both.

Figure 6. Time correlation functions, SHB(t) and SdHB(t) (see text for

details), describing the lifetimes of H-bonds between water moleculesfor different solutions of carbonate species at 310 K.

TABLE 1: Structural Relaxation Times τc and τcd of

H-Bonds between Water Molecules Computed from theCorrelation Functions CHB(t) and Cd

HB(t), Respectively

system τc (ps) τcd (ps)

pure H2O 4.9 5.1TT-H2CO3 8.8 9.2CT-H2CO3 6.0 6.4HCO3

- 13.8 13.4CO3

2- 40.4 40.0CO2 10.7 10.0

TABLE 2: Lifetimes of Different H-Bonds, τs, Computedfrom the Correlation Function SHB(t)a

system H2O · · ·H2O (ps) )O · · ·Hw (ps) OH · · ·Hw (ps)

pure H2O 0.88 (2.57)TT-H2CO3 1.10 (3.32) 0.31 0.22CT-H2CO3 0.68 (2.28) 0.51 0.15HCO3

- 1.10 (3.61) 0.99 0.13CO3

2- 1.43 (6.82) 2.05CO2 1.14 (4.04) ∼0.01

a For the H-bonds between water molecules, the relaxation times,τs

d, computed from SdHB(t) are given in parentheses. The Sd

HB(t)relaxation times, τs

d, of the other H-bonds and the τs values forHO · · ·Ow H-bonds are not reported because of statisticaluncertainty.

Structure and Dynamics of Aqueous Carbonate Species J. Phys. Chem. B, Vol. 113, No. 3, 2009 799

(compared with the )O · · ·Hw bonds) in the corresponding RDFs(Figure 2b,c). The OH · · ·Hw H-bonds are, thus, clearly weakerthan )O · · ·Hw H-bonds for all the species studied. The increas-ing lifetimes of )O · · ·Hw bonds from TT to CT to HCO3

- toCO3

2- correlate positively with shorter )O · · ·Hw bond distances(Figure 2b) and thus correspond to progressively stronger)O · · ·Hw H-bonds. These trends also parallel the increase inthe total number of H-bonds accepted by )O (Figure 4).

For all of the systems studied, the H-bonds donated by theC-OH groups to H2O (HO · · ·Ow) are much longer lived thanthose accepted by the C-OH (OH · · ·Hw) and )O sites ()O · · ·Hw)from water molecules. In fact, very few events of HO · · ·Ow

H-bond breakage were observed during the 14 ps long simula-tions. This behavior is consistent with the relatively shortHO · · ·Ow bond lengths (Figure 2) and demonstrates that(HO · · ·Ow) H-bonds are quite strong and may have averagelifetimes of several picoseconds. Because the HO · · ·Ow H-bondsin our simulations are few in number and have lifetimescomparable to the duration of the simulation runs, these lifetimeshave large statistical uncertainties and are not reported in Table2. In contrast, the H-bonds accepted by the C-OH groups ofthe carbonic acid and bicarbonate species (OH · · ·Hw) are, ingeneral, the weakest and the shortest lived in these systems.

3.3. Vibrational Density of States. The power spectra ofatomic motions for the aqueous carbonate are calculated asFourier transforms of the velocity autocorrelation functions forthe respective atoms from the 14 ps production trajectories of theCP-MD simulations. They provide additional insight into therelationships among the structure, H-bonding, and spectroscopiccharacteristics of these species (Figure 7). However, a detailedcomparison of the full vibrational spectra for all the speciesand discussion of the origins of the differences betweencomputed and observed71,72 frequencies is beyond the scope ofthis paper.

The large red shift of the O-H stretching frequencies of theTT and CT conformers of carbonic acid in solution relative tothe computed gas-phase values39 of about 3660 cm-1 (Figure7a) is a clear signature of the strong HO · · ·Ow H-bonding thatis evidenced in the RDFs and H-bond lifetimes discussed above.

These O-H stretching bands are very broad, spreading over afrequency range from 2100 to 3100 cm-1. This result is inqualitative agreement with the pioneering IR study by Mooreand Khanna,25 who reported vibrational frequencies of 2614,2840, and 3030 cm-1 for the O-H stretching modes of H2CO3/H2O(ice) at 250 K. Our results are also consistent with morerecent FTIR spectroscopic data73-75 for solid amorphous H2CO3

below 230 K which show a broad O-H stretching band between2600 and 3200 cm-1. Recent CBSB7 B3LYP quantum chemicalcalculations45 of the vibration frequencies for the hydrogen-bonded H2CO3 dimers in implicit PCM continuum solvent-mimicking water also give 2728, 2820, and 3232 cm-1 for theIR-active stretching vibrations of these species.

Over the 14 ps duration of the TT and CT H2CO3 solutionsimulations, there were a few instances of O-H breakingleading to the formation of contact ion pairs of HCO3

- andH3O+. These transient deprotonation events contribute to thelarge computed red shifts and frequency ranges. In all suchevents the same proton recombined with the parent carbonicacid in a short span of time. At near-neutral pHs the HCO3

-

concentration is much higher than that of H2CO3 and isthermodynamically favored. At the high concentrations in oursimulations, however, formation of HCO3

- from H2CO3 isunlikely to be favorable. The presence of a single H3O+

molecule corresponds to a very low macroscopic pH, whichgreatly inhibits the forward reaction. Microscopically, the backreaction may also be more common than the forward reactionbecause the latter requires a reorganization of the hydrationstructure while the former only requires a proton hop along asingle H-bond.

The O-H stretching modes of HCO3- occur near 3200 cm-1

(Figure 7a) and are less red-shifted and have a narrowerfrequency range than the H2CO3 conformers. These differencesare consistent with the longer HO · · ·Ow distances and hence withweaker HO · · ·Ow H-bonds for HCO3

- (Figure 2d). Our valueof ∼3200 cm-1 is somewhat lower than that from recentquantum chemical calculations59 using the self-consistent reac-tion field method with the PCM continuum solvation model(3423.5 cm-1). However, both are significantly larger that theexperimentally observed value for the solvated bicarbonate ion,2620 cm-1.71,72 Accurate calculation of O-H vibrationalfrequencies for the hydrated bicarbonate ion remains a signifi-cant challenge.72

The CdO stretching of the various carbonate species havebeen the signature modes for identification of carbonic acid inseveral experimental IR studies of samples containing carbonicacid together with other carbonates species.25-27 Our calculationsshow that the CdO stretch is at about 1500 cm-1 for HCO3

-

and at about 1600 cm-1 for CT- and TT-H2CO3 (Figure 7c,d).For CO3

2- our calculated CdO stretching band is at about 1300cm-1 (blue line in Figure 7d), well separated from those of thecarbonic acid species. Thus, the CdO stretching featureemployed by Moore and Khanna25 (in their case, at 1705 cm-1)in identifying the presence of carbonic acid in an ensemble ofother carbonates embedded in an ice matrix is clearly visiblein our simulated solution environment. However, intensity atthis frequency is also observed in the HO power spectrum (Figure7a), suggesting that the mode at 1650 cm-1 is not a pure CdOstretch, but also involves motion of hydrogens of the -OHgroup. The )O and C power spectra of CO2 (Figure 7c,d) havedistinct peaks near 2200 cm-1 for the asymmetric stretching ofthe CdO bond.

The computed Hw vibrational density of states are nearlyidentical for all simulated systems, suggesting that the presence

Figure 7. Power spectra of the atomic motions for different carbonatespecies in aqueous environment at 310 K. Trajectories were stored every0.5 fs, and the spectra are computed from the full 14 ps productionrun. Symbols: C, )O, OH, and HO refer respectively to carbon, carbonyloxygens, hydroxyl oxygens, and hydroxyl hydrogens. The open andfilled triangles are respectively the harmonic frequencies of the gas-phase TT and CT conformers of H2CO3. The legends are common toall the panels.

800 J. Phys. Chem. B, Vol. 113, No. 3, 2009 Kumar et al.

of dissolved carbonate species largely affects the relatively lowfrequency translational and librational processes of H2O, forwhich 14 ps CP-MD simulations are not very sensitive.

4. Conclusions

CP-MD calculations provide new quantitative insight into thestructure and dynamics of hydrogen-bonding environments forhydrated carbonic acid (H2CO3), bicarbonate (HCO3

-), carbon-ate (CO3

2-), and carbon dioxide (CO2) and the effects of thesespecies on the structure, H-bonding, and dynamical behaviorof the surrounding water molecules. The hydration structuresof the different carbonate species depend in detail on their abilityto accept and donate H-bonds with H2O. One important controlon the hydration structure and dynamics is that H-bonds betweenwater molecules that donate H-bonds to the carbonate speciesand those that accept H-bonds from the carbonate species areoften difficult to form due to steric constraints in the firsthydration shell around the carbonate species. H-bonds donatedby the -OH groups of the carbonate species to water moleculesare stronger and longer lived than those accepted by these sitesfrom water molecules. The rates of structural relaxation of thewater molecules and the rates of H-bond reorganization amongthem are slower in systems containing carbonate species,consistent with previous classical MD simulations of simpleaqueous salt solutions.11 On time scales longer than 2 ps therate of structural relaxation among the water molecules isdominated by diffusional motion of H2O, whereas the rate ofH-bond reorganization of the water molecules and the carbonatespecies is dominated by librational motion. The strengths andlifetimes of H-bonds involving the carbonate species generallyincrease with increasing net charge in the system. Solvated CO2

experiences only very weak H-bond donation from surroundingwater molecules, but its presence in solution significantly affectsthe structure and structural relaxation of water, resulting instronger H-bonds among the water molecules and slowerrelaxation rates. In this sense, dissolved CO2 exhibits propertiescharacteristic of a typical hydrophobic solute.

Acknowledgment. This research was supported by the DOEBES Geoscience Program (Grants DE-FG02-00ER-15028 andDE-FG02-08ER-15929), and the computational resources wereprovided by the DOE National Energy Research ScientificComputing Center, National Center for Supercomputing Ap-plications, and other NSF TeraGrid supercomputing facilities.P.P.K. thankfully acknowledges Axel Kohlmeyer and NisanthN. Nair for useful technical discussions. We acknowledge theuse of VMD software for visualizations of MD trajectories.

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