On the Origin of Potential Barrier for the Reaction OH- +

1734

J. Phys. Chem. B 2002, 106, 1734-1740

On the Origin of Potential Barrier for the Reaction OH- + CO2 f HCO3- in Water: Studies by Using Continuum and Cluster Solvation Methods Alexander V. Nemukhin,‡ Igor A. Topol,*,† Bella L. Grigorenko,‡ and Stanley K. Burt† AdVanced Biomedical Computing Center, SAIC Frederick, National Cancer Institute at Frederick, P.O. Box B, Frederick, Maryland 21702-1201, and Chemistry Department, Moscow State UniVersity, Moscow 119899, Russian Federation ReceiVed: NoVember 12, 2001

The energy profiles for the reaction OH- + CO2 f HCO3- are analyzed following the results of calculations carried out using both a continuum solvation model and a cluster approach. The minimum energy path, computed with the quantum chemistry LMP2 and B3LYP approximations, corresponds to the activation-less process in the gas phase but shows a barrier on the way from the reactants to the product in the dielectric continuum medium. In the cluster approach, the reacting species were completely surrounded by 30 water molecules, each considered as an effective fragment potential (EFP) acting on the quantum system. Positions of all particles were optimized along the reaction coordinate in this quantum mechanical-molecular mechanical (QM/MM) approximation. The energy profile obtained with the QM/MM(EFP) approach is in remarkable agreement with the results of the continuum model, showing the barrier in the same region. An analysis of the arrangements of the water molecules around the reacting species, as well as changes in geometry configurations and electronic distributions of the solute species, allows us to conclude that on the segment of the reaction path close to the potential barrier a considerable fraction of the negative charge on OH- transfers to CO2, accompanied by a sharp bending of the O-C-O species. As a result, the hydroxide anion loses water molecules from its hydration shell. We show that the height of the barrier on the free energy curve for the reaction OH- + CO2 f HCO3- in water can be estimated within the limits 8-13 kcal/mol, and its precise quantity depends on the reference value of experimental free energy of solvation of OH-.

1. Introduction OH-

-

+ CO2 f HCO3 constitutes a stage of The reaction the reversible hydration of carbon dioxide, a process involved in transportation of CO2 in living organisms. In humans, carbonic anhydrase efficiently catalyzes the corresponding reactions,1 and it is important to understand the role of environment at different steps of the catalytic cycle.2,3 Previous theoretical studies4,5 revealed that the gas-phase reaction of hydroxide anion with carbon dioxide proceeded without a potential barrier. Experimental estimates for this reaction in aqueous solution showed an activation barrier on the free energy profile.6,7 Palmer and van Eldik summarized the experimental works for the reaction and quoted the activation enthalpy and entropy as 13.0 ( 0.6 kcal/mol and 2.9 ( 1.9 cal/(mol K), respectively.7 Correspondingly, the free energy reaction barrier in aqueous solvent at T ) 298.15 K is estimated as 12.1 kcal/ mol. Existence of the reaction barrier was qualitatively described within a continuum solvation model.8 Liang and Lipscomb discussed the gas-phase reaction path for OH- + CO2 f HCO3by using semiempirical and low level ab initio quantum chemistry approaches and qualitatively considered the role of the solvent.5 Peng and Merz constructed ab initio total energy profile for the gas-phase reaction, and following the results of molecular dynamics simulations of rigid OH-...CO2 complexes in TIP3P waters, calculated the free energy profile in aqueous solvent.9,10 These authors determined the theoretical free energy barrier to be 17 ( 29 or 19.2 kcal/mol in the later work.10 † ‡

National Cancer Institute. Moscow State University.

In this work we apply quantum chemistry methods at continuum solvation and cluster levels to study the energy profiles for this reaction and suggest a detailed picture of the changes in hydration shells of the solute species during the reaction. An appearance of the activation barrier in water can be rationalized from these studies, taking advantage of both theoretical approaches (continuum and discrete) applied for modeling condensed phase phenomena. For solvation calculations we apply the Jaguar program,11 which realizes the procedure based on an estimation of the solvent response to the solute charge distribution by the Poisson-Boltzmann equation. The localized Møller-Plesset second-order perturbation theory (LMP2)12 and the conventional B3LYP density functional theory approaches13,14 were selected for our calculations. The dielectric constant of pure water ( ) 80) was used. In the cluster model, the solvent molecules are considered explicitly, and their interactions with the solute species as well as between themselves are described at different levels ranging from empirical pairwise potentials to complete ab initio treatment. Formulation of the effective fragment potential (EFP) approach15,16 and its implementation in the GAMESS program17 allows one to apply a new level of modeling solvation phenomena within the cluster approximation. In this quantum mechanical-molecular mechanical (QM/MM) approach, the solvent molecules are explicitly included into the system, but their influence on the solute species is described through the potentials, parameters of which should be determined at preliminary stages by the results of trial ab initio calculations. The EFPs are expressed as the sums of electrostatic, polarization,

10.1021/jp0141629 CCC: $22.00 © 2002 American Chemical Society Published on Web 01/18/2002

Energy Profiles for OH- + CO2 f HCO3-

Figure 1. Gas-phase and continuum model energy profiles for the reaction OH- + CO2 f HCO3- computed in the LMP2/6-311++G(d,p) approximation.

and exchange-repulsion terms. The first one is represented by a distributed multipole expansion, and the atom centers and bond midpoints are used as expansion points. The second one is expressed in terms of localized polarizability tensors centered at their centroids. A treatment of the third one presents the most difficult problem, and presently, the fitting procedure to independent ab initio data seems to be the best choice. The EFP parameters for water were carefully selected and included in the GAMESS program. It was demonstrated that for pure water clusters, applications of these EFPs led to very successful results. Day et al. employed the Monte Carlo simulated annealing technique to locate the lowest energy structures for water clusters (H2O)n (n up to 20).18 They found that the interaction energies of water clusters calculated with the EFP model agree very well (within 1-2 kcal/mol) with ab initio data, and the equilibrium geometries of water clusters are also consistent with ab initio results. Ability of the QM/MM(EFP) approach to describe correctly hydrogen-bonded networks is especially promising for modeling structure and dynamics of molecular species in water clusters. Chen and Gordon used this method to study the internal rotation barrier in formamide solvated by water molecules.19 Krauss and Webb applied it for studies of the excited states of formamide with three water molecules.20 Preliminary results of QM/MM(EFP) calculations for the reaction OH- + CO2 f HCO3- in water clusters are described in ref 21. Section 2 contains the results of the gas phase and continuum model calculations. Section 3 is devoted to calculations in the cluster model. Discussion and conclusions are given in section 4. 2. Gas Phase and Continuum Model Energy Profiles Like in all previous studies of this reaction, we select the distance between oxygen in OH and carbon in CO2 as the reaction coordinate. Figure 1 shows the results of calculations at the LMP2/6-311++G(d,p) level for the gas-phase energies and energies in aqueous solvent. For each value of R, all remaining internal coordinates of the OH- + CO2 system have been optimized in the gas-phase calculations (lower curve in Figure 1), and these geometry parameters have been passed into the continuum model (upper curve in Figure 1).

J. Phys. Chem. B, Vol. 106, No. 7, 2002 1735

Figure 2. Gas-phase and continuum model energy profiles for the reaction OH- + CO2 f HCO3- computed in the B3LYP/6-311++G(d,p) approximation.

In Figure 2 we show the corresponding potential energy curves computed using the B3LYP/6-311++G(d,p) approximation. Also, at the first stage the gas-phase energies have been obtained by optimizing internal coordinates along the reaction path. However, in this approach it is practical to perform geometry optimizations within solvation calculations; therefore two potential curves are presented for the continuum model, namely, with and without adjustment of geometry configurations of solute species in the solvent. As expected, the computed energy curves and geometry parameters of gas-phase calculations of the LMP2 and B3LYP approximations are very similar. Upon the reagents approach to each other, the potential curves gradually decrease and reach the minimum value at R ) 1.45 Å. If the energy at the farthest considered point R ) 6 Å is taken as a reference, then the well depths are estimated as 42.2 kcal/mol for LMP2 and 46.7 kcal/ mol for B3LYP. These values are consistent with the calculation results of Peng and Merz at the MP4/6-311++G(d,p)//RHF/6311++G(d,p) level.9,10 Optimized geometry parameters vary smoothly; the most noticeable are the changes in configurations of the carbon dioxide fragment from linear in the entrance channel to bent in the product state. The potential curves in the dielectric solvent for both approaches also show similar features. Due to differences in solvation energies of the reactants (OH- + CO2) and the product (HCO3-), the energy of the global minimum, occurring at a shorter value of R (1.4 Å), with respect to our “dissociation limit” at R ) 6 Å is now -24.2 kcal/mol for LMP2 and -22.0 kcal/mol for B3LYP. Peng and Merz estimated the experimental free energies of solvation at 298.15 K for OH-, CO2, and HCO3- as -113, 0.11, and -81.5 kcal/mol, respectively.9,10 Therefore, such changes (∼20 kcal/mol) in reaction energies when going from the gas phase to aqueous solvent were expected. A clear occurrence of the potential barrier in the vicinity of 2-2.4 Å, again in both approximations, LMP2 and B3LYP, is the most important result for the goals of this work. As cited by Peng and Merz,9 a previous study based on a continuum solvation model also showed a solvation-induced activation

1736 J. Phys. Chem. B, Vol. 106, No. 7, 2002

Nemukhin et al.

TABLE 1: Thermodynamic Parameters for the Reaction OH- + CO2 f HCO3- in the Gas Phase (g) and in Aqueous Solvent (aq) at T ) 298.15 K, Computed in the B3LYP/ 6-311++G(d,p) Approximation (Enthalpy (∆H), Free Energy (∆G), Free Energy Reaction Barrier (∆G#) in kcal/mol, and Entropy (∆S) in cal/(mol K)) parameter this work (g) ∆H

-45.47

∆S ∆G

-28.23 -37.06

∆G#

lit. (g)

this work (aq)

-46.9a -21.03 -49.0b -46c -29.2a -19.73 -38.2 ( 0.7a -15.15 -37.5c 8.22

lit. (aq)

TABLE 2: Solvation Free Energies ∆Gsolv (kcal/mol) of the Reagents and the Product of the Reaction OH- + CO2 f HCO3B3LYP/6-311++G(d,p) lit.

-10.2a -10.9a -7.05a 13.5 ( 0.2a 12.1d 17 ( 2e 19.2f

a Estimates by experimental data cited by Peng and Merz.9 b Experimental estimate cited by Liang and Lipscomb.5 c Calculations by Peschke, Blades, and Kebarle.28 d Experimental estimate by Palmer and van Eldik.7 e Molecular dynamics calculations by Peng and Merz.9 f Molecular dynamics calculations by Peng and Merz.10

barrier.8 In our calculations the barrier heights with respect to the point R ) 6 Å are 6.9 kcal/mol (LMP2) and 5.8 kcal/mol (B3LYP). We notice a nonmonotonic behavior of the solvation energy curves in the region of R between 3.5 and 5.5 Å. Figure 2 demonstrates that the consequences of geometry optimizations of the solute species in the dielectric medium do not lead to noticeable differences (compared to the single point calculations) for short O-C distances (R < 2 Å), when the reactants OHand CO2 are close. When they are separated (R > 2 Å), we see an effect of structural changes in solutes on the reaction profile. Most likely, the features in the potential curves (local barriers and minima) reflect certain rearrangements in hydration shells around reactants. Since CO2 is a hydrophobic species, changes in the hydration state of the hydroxide anion are responsible for the shape of the solvation energy potentials. To clarify these issues, we performed studies of this reaction in the cluster approach, described in section 3. We conclude this section by discussing the value of the free energy barrier of the title reaction in water at 298.15 K. To estimate this quantity, we computed in the B3LYP/6-311++G(d,p) approximation the thermodynamic parameters, enthalpy, entropy, and free energy of reagents and products in the gas phase and in aqueous solvent. We also found the transition state structure in aqueous solvent, as a point with exactly one imaginary frequency. The results are collected in Table 1 together with the literature data. The computed gas-phase parameters are in excellent agreement with the literature values; however, our result for the activation free energy (8.2 kcal/mol) is noticeably smaller than that cited as an experimental estimate 12.1 kcal/mol7 or theoretical estimates by Peng and Merz (17 ( 2 kcal/mol)9 or 19.2 kcal/mol.10 We clarify the reasons for such discrepancies, by considering the solvation free energies of the reagents (OHand CO2) and the product (HCO3-). The corresponding data are collected in Table 2. Clearly, the main problem is the OH- solvation energy, for which several different experimental evaluations are known in the literature. Our B3LYP/6-311++G(d,p) result (-105.47 kcal/ mol) is close to the value of -104.92 kcal/mol estimated by Marcus.22 However, it is larger that the value -110 kcal/mol suggested by Hawkins, Cramer, and Truhlar,23 following their analysis of experimental data. If we take the last value as a true one, then our computed barrier should be increased by 4.5

CO2

OH-

HCO3-

-1.07 0.11a 0.31b -1.0c

-105.47 -113 a -112.9b -104.92d -110.0e -105.0f

-81.47 -81.5a -83.8b

a Estimates by experimental data cited by Peng and Merz.10 b Calculations bt Peng and Merz.10 c Experimental estimation by Ben-Naim and Marcus.29 d Experimental estimation by Marcus (Table 5.10).22 e Estimates by experimental data cited by Hawkins, Cramer and Truhlar.23 f Estimates by experimental data cited by Pliego and Riveros.30

kcal/mol and it would reach the value of 12.7 kcal/mol. Besides, such scaling would decrease our computed thermodynamic parameters for aqueous solvent (Table 1) by 4.5 kcal/mol and bring them closer to the literature data. Peng and Merz used for the solvation energy of OH- the value (-113 kcal/mol),10 which led them to the overestimation of the barrier height by 3.5 kcal/mol. As a conclusion, we estimate the free energy barrier for the title reaction as a quantity between 8.2 and 13.5 kcal/mol, depending on the reference value of the solvation free energy of the hydroxide ion. 3. Cluster Calculations As discussed in the Introduction, we applied the effective fragment potential (EFP) theory to model geometry configurations of the reacting species inside a shell of explicitly considered solvent molecules. We applied the set of EFP parameters for water as they are tabulated in GAMESS17 (H2Oef2 option) without an additional refinement. We also applied the same method for the QM part, namely, the restricted Hartree-Fock (RHF) approximation with the Dunning-Hay double-ζ-based basis set DH+(d,p), as used in calibrating EFPs for water. We first performed a series of test calculations for the particles occurring in our system. The well-known equilibrium geometry configuration of the water dimer, obtained in the EFP approximation agrees very well with high-level ab initio calculations. The largest discrepancy was noticed for the intermolecular O...H distance in (H2O)2: the one obtained with the EFP waters was 2.05 Å, while in the MP2/aug-cc-pVTZ calculations the value 1.95 Å was computed. Since the RHF/DH(d,p) level of theory has been employed for calibration of EFP parameters of water,15 and the frozen geometry of water monomers is assumed in the EFP model, some discrepancies are expected in such comparisons. Next we performed a series of QM/MM(EFP) test calculations, in which from one to five water molecules were considered as effective fragments, and CO2, OH-, and HCO3species were described in the ab initio RHF/DH+(d,p) approximation. Comparisons were made with the results of MP2 or B3LYP calculations. Equilibrium geometry configuration of the complex CO2...H2O is also correctly reproduced in this QM/MM(EFP) model compared to the ab initio data. The main isomer of the complex is a planar C2V structure with the oxygen atom from water closest to an almost linear CO2 species. The QM/MM(EFP) approach gives an O-C-O angle of 178°, a distance between carbon and the water oxygen of 2.90 Å, and distances between the oxygens in CO2 and the hydrogens in water of 3.51 Å. The corresponding parameters, obtained after full optimization in



Figure 3. Comparison of equilibrium geometry configurations of the test systems, obtained in the customary quantum chemical approximations and in the QM/MM(EFP) technique.

the MP2/6-311++G(d,p) approximation are 178°, 2.77, and 3.38 Å, respectively. The panels of Figure 3 show comparisons of the QM/MM(EFP) and QM configurations obtained by full optimizations of geometry parameters in both approaches. Panels a and b refer to the isomers of the hydrogen-bonded complexes of the hydroxide anion with water molecules, OH-(H2O)4 and OH-(H2O)5, in which all waters are directly coordinated to OH-, but do not form a second solvation shell above the basic unit OH-(H2O)3.24 As discussed later, such structures play the key role for the reaction under consideration. Panels c and d show two isomers of the complex of HCO3- with a single water molecule. A general conclusion that can be drawn from these tests (Figure 3) is that the set of parameters for H2O excellently reproduces the hydrogen bond networks but leads to a systematic overestimation of the hydrogen bond O...H lengths by 0.10.15 Å compared to pure quantum results. Then we proceeded to calculations of the reaction profile by surrounding the solute species (OH- + CO2 f HCO3-) by 30 EFP waters. Novoa et al.24 concluded that only 17 water molecules form the complete hydration shell for OH-. In our pilot QM/MM(EFP) calculations, neither 17, nor 20 water molecules were enough to surround the reacting complex. Tuckerman et al.25 carried out molecular dynamics studies of OH- embedded in a 31-water cluster. With the QM/MM(EFP) approach we found that 30 waters can form a cavity completely covering the OH- + CO2 system at R ) 6 Å separation. For each value of R, the positions of all particles, including 30 EFP waters, were optimized by using standard optimization algorithms implemented in GAMESS.17 We understand that such an approach does not guarantee finding the global minimum for these systems, and most likely, we located one of the numerous local minima available. A proper tool for a complete investigation of such clusters might be simulated annealing or related procedures.3,18 However, we believe that the arrangements of inner water molecules immediately coordinated to the reacting species are predicted correctly in this approach and that the closest hydration shells of the charged species (OH- in the entrance channel, or the product HCO3-) can be analyzed after such calculations. To minimize the errors,

Figure 4. Energy profiles for the reaction OH- + CO2 f HCO3- in the cluster of 30 EFP water molecules.

we varied the reaction coordinate R slowly and started optimization of each point from the coordinates of the previous one. After the passage from large R to short distances, we recomputed the reaction profile in the opposite direction, and at several points the new coordinates of somewhat (within 1 kcal/mol) lower energy were obtained. As expected, the general trend is the following: at large distances (6 > R > 2.5 Å) the water molecules are systematically grouped around OH- and much less regularly at the CO2 side, but at R < 2 Å, where the product HCO3- is formed, the shells of water molecules behave more systematically. Our focus in this work is on understanding the structures of reacting species with the closest water molecules. The computed RHF potential is shown in Figure 4 (upper curve). Its shape is in remarkable qualitative agreement with the results of the continuum model (Figures 1 and 2). The barrier before the potential well occurs at the value R ) 2 Å, while in continuum models it happens at 2.2 Å (LMP2), and 2.1 Å (B3LYP) in the QM calculations. The coordinates of all particles, including 30 water molecules, were then used to recompute the reaction energy profile at the QM level in the


Nemukhin et al.

Figure 6. Geometry configurations of the system (OH- + CO2)@(H2O)30 at R ) 6 Å (panel a) and R ) 4 Å (panel b).

Figure 5. Geometry configurations of the system (OH- + CO2)@(H2O)30 at R ) 2.75 Å (panel a), R ) 2 Å (panel b), and R ) 1.4 Å (panel c).

B3LYP/6-31G* approximation. This curve is also shown in Figure 4. Again, the shape of the potential curve, computed at the cluster level, agrees with that of the continuum model, placing the barrier at R ) 2.2 Å. 4. Discussion The arrows in Figure 4 indicate the points along the reaction path where the geometry configurations of the cluster (Figure 5) are analyzed. Namely, we consider the configuration before the barrier (R ) 2.75 Å, Figure 5a), close to the top of the barrier (R ) 2 Å, Figure 5b), and at the potential well (R ) 1.4 Å, Figure 5c). We select the closest water molecules coordinated by hydrogen bonds to the solute species within the distances 1.8-2.2 Å. Comparison of structures at points R ) 2.75 Å (Figure 5a) and R ) 2 Å (Figure 5b) leads to a conclusion that moving along the reaction path during this segment the hydroxide anion loses one water molecule from its hydration shell. Five water molecules are attached to OH- at distances R between 4 and 2.75 Å, and only four at R ) 2 Å. Of course, this process of stripping off the solvent molecule from the immediate solvation shell is accompanied by energy growth, and occurrence of the barrier is understandable. At the point of the global minimum R ) 1.4 Å (Figure 5c) the hydrogen bond network becomes

completely different. The OH moiety keeps only 3 water molecules while 4 water molecules are attached by hydrogen bonds to the oxygens from CO2. The energy is lowered due to formation of the O-C chemical bond. Let us consider other (or related) reasons for the potential barrier in the reaction OH- + CO2. It is reasonable to assume that activation energy is required to push water molecule(s) out of the space between initially separated reactants. However, examination of the structures of particles in the cluster shows that this process is complete at much longer separations. In Figure 6 we show the arrangements of species at R ) 6 Å (Figure 6a) and R ) 4 Å (Figure 6b) and point out, as in Figure 5, hydrogen bond networks involving the water molecules closest to the hydroxide anion. For R ) 6 Å (Figure 6a), the water molecule, clearly seen between OH- and CO2, resides in an almost perfect central position. The distance from oxygen in this water molecule to oxygen in OH is 3.10 Å, and to carbon in CO2 it is 3.12 Å. However, already at R ) 4 Å (Figure 6b) there is no space for water molecules between the reagents, but the energy is rising at shorter (R < 4 Å) distances. It is interesting that on the way from R ) 6 Å to R ) 4 Å the hydroxide anion loses one hydrogen-bonded water molecule, and instead of the unit OH-(H2O)6 the pentacoordinated species OH-(H2O)5 is formed. The features in the potential curves obtained in both continuum (Figures 1 and 2) and cluster (Figure 4) approaches in the region 6 > R > 3 Å are most likely due to this change in the hydrogen bond network. It is also interesting to note that the gas-phase cluster OH-(H2O)6 shows a variety of isomers, all of which have 5 water molecules coordinated directly to OH-, and the sixth one belongs to the second hydration shell. In the cluster with 30 water molecules we observe the unit with 6 waters closest to the hydroxide anion. It is appropriate to make one more comment about the region


Figure 7. Geometry configurations of OH- + CO2 at R ) 4 Å in the gas-phase calculations (panel a), continuum model (panel b), and cluster model (panel c).

of fairly large separations between OH- and CO2 in water. We implicitly assume that OH- can migrate through water toward CO2 without reacting with water molecules. Literature data provide some support to this assumption. Studies of Tun˜on et al.26 showed that OH- could participate in proton-transfer reactions with surrounding water molecules, but the energy barriers might be noticeable. Tuckerman et al.25 performed molecular dynamics investigations of the OH-(H2O)31 clusters and concluded that the units OH-(H2O)4 were basically stable along trajectories, while proton transfers could occur when these units were rearranged. Structural changes in the solute system due to interactions with solvent molecules may also modify the reaction energy profile in the environment in comparison to the gas-phase path. Our study shows that such changes may be considerable. In Figure 7 we compare the snapshots of the OH-...CO2 structures at R ) 4 Å, optimized in the gas-phase calculations (panel a), in the B3LYP continuum model calculations (panel b), and in the cluster calculations with 30 EFP water molecules (panel c). We note a remarkable agreement of the results of two latter approaches (Figure 7b,c). Clearly, energies of the solute structures in the condensed phase differ from those in the gas phase. To check the role of this factor, we carried out the following calculations. For each value of R we extracted geometry configurations of OH-...CO2 from the clusters with 30 water molecules and computed energies for these systems at the MP2 level. Then the energies of the gas-phase optimized structures of OH-...CO2 were subtracted from those values. The so obtained difference curve ∆(R) is shown in Figure 8, taking the value ∆ at R ) 6 Å as zero. We also constructed the hypothetical potential curve, by combining the gas-phase profile (Figure 1) with ∆(R), and plotted it in Figure 8. Despite the fact that the difference curve passes through a maximum at R ) 2 Å, the resulting hypothetical potential does not resemble the true condensed-phase curve of Figure 1. In particular, the barrier does not appear in the hypothetical energy path. Now we analyze the changes in electronic structure of the solute species along the reaction coordinate. Figure 9 shows the graphs of the charges on all atoms computed by the natural bond orbital analysis.27 We see that the most noticeable changes occur for the oxygen centers at distances R less than 2.5 Å. Namely, the natural charge on the hydroxide oxygen decreases


Figure 8. Energy differences (∆) due to distinct geometry configurations of OH- + CO2 in the gas phase and inside water cluster, and the hypothetical (gas-phase + ∆) potential.

Figure 9. Natural charges on atoms in the reacting system in the cluster calculations.

from -1.4 to -0.8 units, while the charges on the carbon dioxide oxygens increase from -0.64 to -0.95 units. The corresponding curves intersect at about R ) 1.5 Å. Changes in charges on hydrogen and carbon in the course of the reaction are less pronounced. Clearly, the reaction has certain features of the electron transfer from OH- to CO2. The CO2 moiety is able to accommodate an electron only if its geometry configuration changes from linear to bent with a corresponding increase of the dipole moment. This actually happens in the vicinity of the potential barrier (Figure 10). We see that the change from linearity occurs rapidly at R < 2 Å. The inflection point of the curve corresponds to the value R ) 1.85 Å. Therefore, the following events occur at the segment of the reaction path close to the position of the potential barrier, i.e., approximately between 2.5 and 1.85 Å: a considerable fraction of the negative charge from OH- transfers to CO2, what is accompanied by a sharp bending of the O-C-O species. As a result, the hydroxide anion loses water molecules from its hydration shell. Fifteen years ago, Liang and Lipscomb wrote in their paper5 devoted to gas-phase ab initio calculations of the OH- + CO2 reaction: “... the appearance of the barrier in solution may be associated with displacement of water from hydration stabilized


Figure 10. Optimized values of the O-C-O angle along the reaction coordinate (geometry configurations of the cluster calculations).

OH-...”. The results of the present modeling provide direct evidence of this statement. Acknowledgment. We thank the staff and administration of the Advanced Biomedical Computing Center for their support of this project. This project has been funded in whole or in part with Federal funds from the National Cancer Institute, National Institutes of Health, under Contract No. NO1-CO-56000. A.V.N and B.L.G. thank the Russian Foundation for Basic Researches for partial support (Project No. 99-03-33178). The content of this publication does not necessarily reflect the views or policies of the Department of Health and Human Services, nor does mention of trade names, commercial products, or organization imply endorsement by the U.S. Government. References and Notes (1) Silverman, D. N.; Lindskog, S. Acc. Chem. Res. 1988, 21, 30.

Nemukhin et al. (2) Warshel, A. Computer Modeling of Chemical Reactions in Enzymes and Solutions; John Wiley & Sons: New York, 1991. (3) Cramer, C. J.; Truhlar, D. G. Chem. ReV. 1999, 99, 2161. (4) Jo¨nsson, B.; Karlstro¨m, G.; Wennerstro¨m, H. J. Am. Chem. Soc. 1978, 100, 1658. (5) Liang, J.-L.; Lipscomb, W. N. J. Am. Chem. Soc. 1992, 108, 5051. (6) Pinsent, B. R. W.; Pearson, L.; Roughton, F. J. W. Trans. Faraday Soc. 1956, 52, 1512. (7) Palmer, D. A.; van Eldik, R. Chem. ReV. 1983, 83, 651. (8) Miertus, S.; Kysel, O.; Krajcik, K. Chem. ZVesti 1981, 35, 3. (9) Peng, Z.; Merz, K. M. J. Am. Chem. Soc. 1992, 114, 2733. (10) Peng, Z.; Merz, K. M. J. Am. Chem. Soc. 1993, 115, 9640. (11) Jaguar 3.5, Schro¨dinger, Inc., Portland, OR, 1998. (12) Sæbø, S.; Pulay, P. Annu. ReV. Phys. Chem. 1993, 44, 213. (13) Lee, C.; Yang, W.; Parr R. G. Phys. ReV. B 1988, 37, 785. (14) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (15) Day, P. N.; Jensen, J. H.; Gordon, M. S.; Webb, S. P.; Stevens, W. J.; Krauss, M.; Garmer, D.; Basch, H.; Cohen, D. J. Chem. Phys. 1996, 105, 1968. (16) Gordon, M. S.; Freitag, M. A.; Bandyopadhyay, P.; Jensen, J. H.; Kairys, V.; Stevens, W. J. J. Phys. Chem. A. 2001, 105, 293. (17) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347. (18) Day, P. N.; Pachter, R.; Gordon, M. S.; Merrill, G. N. J. Chem. Phys. 2000, 112, 2063. (19) Chen, W.; Gordon, M. J. Chem. Phys. 1996, 105, 11081. (20) Krauss, M.; Webb, S. P. J. Chem. Phys. 1997, 107, 5771. (21) Grigorenko, B. L.; Knyazeva, M. A.; Nemukhin, A. V. Bull. M. V. LomonosoV Moscow State UniVersity, Chem. 2001, 42, 92. (22) Marcus, Y. Ion SolVation; John Wiley & Sons: New York, 1985. (23) Hawkins, G. D.; Cramer, C. J.; Truhlar, D. G. J. Phys. Chem. B 1998, 102, 3257. (24) Novoa, J. J.; Mota, F.; Perez del Valle, C.; and Planas, M. J. Phys. Chem. 1997, 101, 7842. (25) Tuckerman, M.; Laasonen, K.; Sprik, M.; and Parrinello, M. J. Phys. Chem. 1995, 99, 5749. (26) Tun˜on, I.; Rinaldi, D.; Ruiz-Lopez, M. F.; Rivail, J. L. J. Phys. Chem. 1995, 99, 3798. (27) Reed, A. E.; Curtiss, L. A.; Weinhold, F. Chem. ReV. 1988, 88, 899. (28) Peschke, M.; Blades, A. T.; Kebarle, P. J. Am. Chem. Soc. 2000, 122, 1492. (29) Ben-Naim, A.: Marcus, Y. J. Chem. Phys. 1984, 81, 2016. (30) Pliego, J. R.; Riveros, J. M. J. Phys. Chem. B 2000, 104, 5155.

On the Origin of Potential Barrier for the Reaction OH- +

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