Dissociation of carbonic acid: Gas phase

THE JOURNAL OF CHEMICAL PHYSICS 126, 204315 共2007兲

Dissociation of carbonic acid: Gas phase energetics and mechanism from ab initio metadynamics simulations P. Padma Kumar,a兲 Andrey G. Kalinichev, and R. James Kirkpatrick Department of Geology, University of Illinois at Urbana-Champaign, 245 Natural History Building, Urbana, Illinois 61801

共Received 24 January 2007; accepted 25 April 2007; published online 31 May 2007兲 A comprehensive metadynamics study of the energetics, stability, conformational changes, and mechanism of dissociation of gas phase carbonic acid, H2CO3, yields significant new insight into these reactions. The equilibrium geometries, vibrational frequencies, and conformer energies calculated using the density functional theory are in good agreement with the previous theoretical predictions. At 315 K, the cis-cis conformer has a very short life time and transforms easily to the cis-trans conformer through a change in the O v C – O – H dihedral angle. The energy difference between the trans-trans and cis-trans conformers is very small 共⬇1 kcal/ mol兲, but the trans-trans conformer is resistant to dissociation to carbon dioxide and water. The cis-trans conformer has a relatively short path for one of its hydroxyl groups to accept the proton from the other end of the molecule, resulting in a lower activation barrier for dissociation. Comparison of the free and potential energies of dissociation shows that the entropic contribution to the dissociation energy is less than 10%. The potential energy barrier for dissociation of H2CO3 to CO2 and H2O from the metadynamics calculations is 5 – 6 kcal/ mol lower than in previous 0 K studies, possibly due to a combination of a finite temperature and more efficient sampling of the energy landscape in the metadynamics calculations. Gas phase carbonic acid dissociation is triggered by the dehydroxylation of one of the hydroxyl groups, which reorients as it approaches the proton on the other end of the molecule, thus facilitating a favorable H–O–H angle for the formation of a product H2O molecule. The major atomic reorganization of the other part of the molecule is a gradual straightening of the O v C v O bond. The metadynamics results provide a basis for future simulation of the more challenging carbonic acid-water system. © 2007 American Institute of Physics. 关DOI: 10.1063/1.2741552兴 INTRODUCTION

Carbon dioxide and its derivative aqueous species are major players in many natural phenomena of fundamental importance to a broad range of scientific disciplines including biology, geochemistry, astrophysics, and atmospheric sciences, as well as to technological applications ranging from power generation to the food and beverage industries. In particular, a more detailed understanding of the molecular mechanisms of CO2 hydration by formation of carbonic acid, H2CO3, and its further dissociation to HCO−3 and CO2− 3 assumes new significance in the context of carbon sequestration efforts in deep saline aquifers and deep sea environments.1 Deep sea sequestration could, for instance, have a direct effect on the oceanic pH and consequent deleterious impact on marine life. Although the presence of small amounts of carbonic acid in water containing dissolved CO2 has been assumed for many decades, the species resisted direct experimental observation, because it is very short lived.2,3 Carbonic acid also attracted a significant amount of theoretical attention, but the question of whether bare carbonic acid can exist as a stable species remained a topic of discussion for many years.2,4,5 a兲

Author to whom correspondence should be addressed. Electronic mail: [email protected]

0021-9606/2007/126共20兲/204315/7/$23.00

The mass spectroscopic studies by Terlouw et al.3 in the late 1980’s provided the first evidence for the formation of stable carbonic acid molecules in the gas phase during the decomposition of ammonium bicarbonate, NH4HCO3.3 A series of more recent developments has led to the preparation of crystalline forms of carbonic acid, which can sublime at about 220 K and recondense in a water-free atmosphere without decomposition to CO2 and H2O.6 Recent computational studies using improved quantum chemical techniques have shown that the gas-phase decomposition of carbonic acid to H2O and CO2 is exothermic by about 10 kcal/ mol and has an activation barrier of about 43 kcal/ mol with respect to the reactant.4 Despite this high activation barrier against dissociation in the gas phase, the species is too short lived to be observed in aqueous environments. Quantum chemical studies of carbonic acid microsolvated by water molecules, H2CO3 · nH2O, where n = 0 , . . . , 3, have provided valuable insight into the catalytic role of water in this dissociation reaction.5,7,8 These studies observed a systematic reduction of the activation barrier with increasing n, provided a plausible mechanism of dissociation involving the active participation of two water molecules, and emphasized the important role of “spectator” water molecules in stabilizing the H2O molecules actively participating in the dissociation.5,7,8

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Kumar, Kalinichev, and Kirkpatrick

The need to extend these calculations with explicit incorporation of water molecules in the first few hydration shells is apparent. While such calculations are prohibitively expensive within traditional quantum chemical treatments, recent developments in density functional theory 共DFT兲based ab initio techniques offer a viable alternative. Ab initio molecular dynamics, such as the popular Car-Parrinello scheme, is, in principle, capable of describing a very large subset of chemical reactions that are adiabatic.9,10 However, the computationally expensive nature of these simulations restricts them to relatively short durations, typically a few tens of picoseconds, often too short to observe most chemical reactions of interest. Very recently, Laio and Parrinello proposed an ingenious approach, called metadynamics, to circumvent this practical limitation.11 By periodically imposing external repulsive potentials on the simulated system, the technique encourages the system to perform a self-avoiding exploration of the phase space, resulting in accelerated barrier crossing. However, since the natural dynamics is perturbed, direct temporal information about the reaction is lost in this approach and interpretations about reaction mechanisms must be based on the computed free energy surface alone. Because the volume of the “excluded phase space” is a direct measure of the free energy, the technique allows for mapping of the free energy surface of the reaction in the space of the relevant reaction coordinates.12,13 The importance of free energy computations, even for gas-phase reactions, is emphasized in recent studies, which show that entropic contributions can be decisive in the choice of the actual reaction path.14 Metadynamics is now being widely employed in studies of a variety of chemical reactions.15 We are currently pursuing a detailed investigation on the dissociation of carbonic acid in both gas-phase and aqueous solution environments employing Car-Parrinello molecular dynamics9 共CPMD兲 and metadynamics.10 This paper presents results for the energetics and mechanisms of the gasphase conformational changes and dissociation of carbonic acid based on CPMD and metadynamics techniques. The solution phase calculations will be presented elsewhere.

METHODS

The metadynamics approach employs an extended Lagrangian of the form10 LMTD = LCP +

␮ k s˙␣2 − 兺关S␣共r兲 − s␣兴2 − V共t,s兲, 兺 2 ␣ 2 ␣

共1兲

where LCP is the standard Car-Parrinello Lagrangian and S共r兲 is a collective dynamical variable, or simply “collective variable,” of the system that defines the reactant and product states. s and ␮ are, respectively, the coordinates and the mass of fictitious particles that are coupled to the collective variable S共r兲 through a harmonic spring of constant k. V共t , s兲 is the history-dependent repulsive potential acting on the fictitious particles, which is usually chosen as a Gaussian,

再

V共t,s兲 = W 兺 exp − ti⬍t

再

⫻exp −

共s − si兲2 2共⌬s⬜兲2

冎

冎

关共si+1 − si兲 · 共s − si兲兴2 . 2共⌬s储兲4

共2兲

The collective variable S共r兲 is a smooth-differentiable function of the ionic coordinates and determines the “direction” of the reaction progress. Typical examples of collective variables include bond lengths, bond angles, dihedral angles, and suitable coordination numbers, the specific choice being strongly dependent on the reaction of interest. There are several parameters that control the character of the dynamics and need be tuned to optimize the quality and efficiency of the calculations. These parameters include the height and spread of the history-dependent Gaussian “hills” and the masses ␮ and spring constants k of the fictitious particles. Ensing et al.16 provided guidelines for choosing these parameters and demonstrative examples. The following are the details concerning the electronic structure optimization and the Car-Parrinello kernel of the metadynamics calculations used here. A single molecule of carbonic acid, H2CO3, in a cubic cell of 11⫻ 11⫻ 11 Å3 forms the reactant species. Periodic boundary conditions are applied, but the box size is large enough to ensure negligible interaction between the periodic images. The valence electrons are treated explicitly within the DFT formalism employing the gradient-corrected Becke, Lee, Yang, and Parr 共BLYP兲 functional.17 The BLYP functional facilitates systematic extension of the calculations to aqueous environments, since bulk water is known to be best represented by this exchange-correlation functional.18 The interaction of the valence electrons with the nuclei and core electrons are represented by ultrasoft pseudopotentials originally proposed by Vanderbilt.19 The Kohn-Sham orbitals are expanded using plane wave basis sets with a cutoff of 30 Ry. An electronic mass of 600 a.u. and a time step of 4 a.u. 共⬇0.1 fs兲 are used. A temperature of 315 K for the ions and a fictitious kinetic energy of 0.0018 a.u. for the electronic degrees of freedom are controlled using Nosé-Hoover thermostats. The choice of the fictitious electronic kinetic energy is based on its “natural value” for the given setup, as estimated from a short CPMD run without the thermostats. The physically uninteresting overall translations and rotations of the molecule are removed every ten CPMD steps by the procedure described in Ref. 20. All simulations are performed using the CPMD software.21 We have carried out the metadynamics simulations to study two distinct activated processes 共rare events兲 of interest in the context of gas-phase carbonic acid, conformation changes and dissociation to carbon dioxide and water. For the study of conformation changes, the collective variables are the two O v C – O – H dihedral angles of H2CO3, and for dissociation, they are the C–O and O–H coordination numbers. Note that smooth-differentiable functional forms, as described in the CPMD manual version 3.9.2, need to be adapted for the definition of the coordination numbers.21 Further details about the metadynamics simulations are given in the appropriate context in the next section.


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Gas phase dissociation of carbonic acid

TABLE II. Harmonic frequencies 共in cm−1兲 of trans-trans 共TT兲, cis-trans 共CT兲, and cis-cis 共CC兲 conformers from normal mode analysis.

FIG. 1. The optimized geometry of H2CO3 conformers: 共a兲 trans-trans, TT; 共b兲 cis-trans, CT, and 共c兲 cis-cis, CC, 共d兲 shows the product of H2CO3 dissociation, CO2 + H2O.

RESULTS AND DISCUSSION Carbonic acid conformers

Previous theoretical studies have shown that carbonic acid has three conformers, trans-trans 共TT兲, cis-trans 共CT兲, and cis-cis 共CC兲.4,22–24 The optimized geometries from our DFT calculations 共Fig. 1兲 are in good agreement with previous quantum chemical studies.4,22,23 The convergence criteria used for the maximum gradients, respectively, of the wave functions and ions, were 10−7 and 10−4 a.u. The relative energies ⌬E of the conformers, without the zero point energy correction, together with previously reported values 共Table I兲 show that the TT conformer is the most stable structure in the gas phase and that the energies of the CT and CC conformers are, respectively, about 1 and 9 kcal/ mol higher. Our results suggest smaller differences in the relative energies of the conformers than in previous studies. However, given the variation among the values from previous reports, the present DFT-based prediction is very satisfactory. In the TT conformer both hydrogens are about 2.37 Å from the oxygen that is double bonded to the carbon, and in the CT structure one of the hydrogens is at about the same distance 共⬇2.37 Å兲 from the double bonded oxygen, TABLE I. The gas-phase energies 共in kcal/mol兲 of geometry-optimized cistrans 共CT兲 and cis-cis 共CC兲 conformers with respect to the trans-trans 共TT兲 conformer. The relative energy of the geometry-optimized CO2 + H2O is also given with respect to the same reference. cis-trans

cis-cis

CO2 + H2O

DFT-BLYP/PW HF-SCF/3-21G DFT-PBE/PW

0.97 0.96 1.50

8.72 13.8 10.0 14.19

−9.58 ¯ −7.1a ¯

HF/ 6-31G* MP2 / 6-31G* MP2 / 6-311+ + G** CCSD共T兲/VDZ

2.44 2.14 1.86 ¯

13.51 11.76 ¯

¯ −9.67 −9.05

Method

a

Including zero point energy correction.

Present work Ref. 22 Ref. 23 Ref. 24 Ref. 24 Ref. 4 Refs. 7 and 5

trans-trans

cis-trans

cis-cis

493 532 562 565 739 916 1061 1235 1375 1721 3667 3670

461 513 534 573 729 893 1060 1209 1309 1779 3648 3656

74 413 532 594 724 863 1015 1196 1235 1806 3652 3674

whereas the other is about 2.2 Å from the oxygen of the other hydroxyl group. These values are within the typical hydrogen bonding distances for most aqueous species.25 The energetic stabilization of the TT conformer with respect to the CT form, thus, suggests that the double bonded oxygen forms stronger intramolecular hydrogen bonds than the oxygens of the hydroxyl groups do. The rather short distance 共⬇2.1 Å兲 between the hydrogens in the CC conformer, together with the relatively weaker intramolecular hydrogen bonding of hydroxyl oxygens, explains its less favorable energy with respect to the other two structures. Since the difference in the relative gas-phase energies of CT and TT conformers is smaller than typical hydrogen bond energy, the relative stabilities or abundances of the two conformers in solution environment are not obvious from these results. The vibrational frequencies of the three conformers from the present study are given in Table II. Unlike TT and CT conformers, the CC conformer is nonplanar, with the hydrogens making angles of about 5° to either side of the plane containing the carbon and the three oxygens, resulting in the different vibrational frequencies. Energetics of conformation changes

The geometries of the three carbonic acid conformers differ largely in the orientation of the hydroxyl groups and can be readily distinguished in terms of the pair of O v C – O – H dihedral angles, the terminal oxygen being double bonded to carbon. We used this pair of dihedral angles as the collective variables in a detailed metadynamics simulation to examine the mechanism and energetics of the interconversion of the conformers. Symmetric Gaussian hills 0.627 kcal/ mol high and approximately 10° wide were used to drive the fictitious particles, which had “masses” of 40 amu bohr2. A harmonic spring constant of 0.2 hartree was used to couple the fictitious particles to the collective variables S共r兲. The hills were added every 20 CPMD steps, and velocities of the fictitious particles were scaled to maintain a temperature of 315 K. This setup is a bit “hard driven,” because the interest is to explore the entire potential energy surface in the dihedral angle space using a reasonable amount of computer time. The electronic degrees of freedom were quenched to the Born-Oppenheimer surface whenever


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FIG. 2. 共Color online兲 The potential energy surface for the conformation changes of carbonic acid averaged over 20 ps long metadynamics trajectory.

the fictitious kinetic energy exceeded 0.003 hartree to ensure accurate description of the ion-ion interactions. The metadynamics simulation at 315 K was started from a thermally equilibrated configuration in the TT potential well, and Gaussian hills were added periodically. As the initial well was progressively filled with the hills, the system crossed the barrier to the CT basin. This basin also fills as the metadynamics proceeds further, and the system executes several crossings and recrossings between the two wells until the total energy is comparable to the barrier to the CC conformation. With a sufficiently long metadynamics run the entire dihedral angle space is explored. The potential energy surface 共PES兲 thus mapped 共Fig. 2兲 is in good agreement with that of Weight and Boldyrev obtained from MP2 calculations.4 Note that we have used a definition of the dihedral angle in which its value ranges from −180° to +180° through zero, and the ±180° configurations are identical. Further, the inversion symmetry of the dihedral angle space in this definition allows the PES to be reduced to the range of 0°–180° in one of the dimensions. Our PES contains three symmetrically unrelated energy minima that correspond to the TT 关near 共0,0兲兴,, CT 关near 共 0 , ± 180兲 and 共180,0兲兴, and CC 关near 180, ± 180兲兴 conformers. The minima of the CT and CC basins are roughly 1.5 and 9.0 kcal/ mol higher than that of the TT basin, consistent with the relative energies of the respective geometryoptimized structures. The minimum energy path connecting the TT and CT wells involves a change of one of the dihedral angles through 180°, as the other remains fixed, and has a barrier of about 9.6 kcal/ mol relative to the TT conformer. The interconversion of the CT to CC conformers involves a change of the other dihedral angle with a barrier of about 11.4 kcal/ mol relative to the TT energy. Direct conformational change from the TT to the CC conformer through simultaneous changes of both dihedral angles is energetically unfavorable. The energetics of such a mechanism also depends on whether both hydrogens move to the same side of the plane of the molecule or not. In the former case, the larger repulsion between the hydrogens costs more energy, which is reflected in the height of the PES near 共+90, −90兲 of the dihedral angles. The potential energy landscape shown in Fig. 2 also provides valuable insight into the nature of the energy basins of the different conformers. Independent Car-Parrinello MD

J. Chem. Phys. 126, 204315 共2007兲

runs 共without the metadynamics algorithm兲 at 315 K starting from the TT and CT conformers indicate that these species remain in their respective basins over the entire ⬃10 ps simulation period. In contrast, the CPMD runs starting from the CC basin move to the CT basin within 2 ps, and the system remains there for the rest of the simulation. Such a short lifetime is evidently due to the shallow nature of the CC energy basin, which has a separatrix with the CT basin of less than 2 kcal/ mol with respect to the bottom of the CC basin. The low frequency harmonic mode of the CC conformer 共about 80 cm−1; Table II兲 is another manifestation of the shallow nature of this basin.

Dissociation of carbonic acid

The dissociation of carbonic acid is key to understanding the behavior of all the carbonate species in aqueous solution, and the mechanism of dissociation in the gas phase described below is an essential reference point for the processes in solution. The comparable stabilities of the TT and CT carbonic acid conformers shown above make them the important structures for understanding this dissociation. The CC conformer is too short lived with respect to conformational change to the CT conformer at 315 K to be of significance in this regard. The most direct way of dissociating the H2CO3 molecule that involves breaking the fewest bonds is to cleave one of the O–H bonds and the other C–OH bond. The proton and the hydroxyl group thus formed then combine to form H2O while the other ions reorganize to form CO2. Intuitively, a relatively short path for the detaching proton or hydroxyl group to combine with the hydroxyl group or proton on the other side of the molecule should be important in controlling the ease of dissociation of the two conformers. This suggests that the CT conformer is the most likely starting point for the reaction. We have, however, carried out several independent metadynamics runs starting from both the TT and CT conformers to confirm this perception. The results show that the TT conformer resists direct dissociation to CO2 and H2O and undergoes a conformation change to CT through a dihedral angle change before finally dissociating. Thus, the following discussion of the energetics and mechanism of the carbonic acid dissociation are based on the CT conformer simulations. Because the CT conformer lacks mirror symmetry, there are two inequivalent ways to attempt the bond cleavage. These are 共i兲 C共1兲–O共4兲H共6兲 together with O共3兲–H共5兲 and 共ii兲 C共1兲–O共3兲H共5兲 together with O共4兲–H共6兲关see Fig. 1共b兲 for atom labeling兴. However, in our metadynamics simulations the latter choice did not yield the CO2 + H2O product state, despite long metadynamics runs, suggesting that it does not have an energetically favorable path for dissociation. The metadynamics simulations of H2CO3 dissociation employed C–O and O–H coordination numbers as collective variables to affect the cleavage of C–OH and O–H bonds. A differentiable function of the kind


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TABLE III. The parameters employed for the different metadynamics runs of the dissociation of cis-trans 共CT兲 carbonic acid and the corresponding estimated free energy barriers 共see text for more details兲.

Cij =

Runs

dC–O 0

dO–H 0

⌬s⬜ = ⌬s储

W 共kcal/mol兲

⌬F 共kcal/mol兲

run1 run2 run3 run4 run4/ext. run4/ext. run4/ext. run4/ext. run5/ext.

2.08 1.60 2.08 1.80 1.80 1.80 1.80 1.80 1.80

1.60 1.24 1.60 1.40 1.40 1.40 1.40 1.40 1.40

0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.02 0.01

5.020 2.510 1.255 1.255 0.627 0.439 0.251 0.125 0.0627

36.6 34.8 35.3 39.2 36.8 37.1 36.8 37.2 37.1

1 − 共dij/d0兲 p 1 − 共dij/d0兲 p+q

1 2 3 4 5

共3兲

is used to define a smooth coordination number of the atom labeled i with respect to j. dij is the instantaneous distance between atoms labeled i and j. d0 is a constant for a given type of bond that controls the shape of the function p and q are positive integers, respectively set to values of 6 and 12 in the present study. Fictitious particles s of mass 50 amu bohr2 were coupled to the collective variables S共r兲, coordination numbers as in Eq. 共3兲 in the present case, through spring constants of 2.0 hartree. The metadynamics of the fictitious particles was driven by symmetric Gaussian hills, that is, ⌬s⬜ = ⌬s储关see Eq. 共2兲兴. New hills are added at irregular intervals of CPMD steps based on the criterion that the fictitious particles must diffuse at least 1.5 times the width of the Gaussian employed. However, hard limits of 50 and 200 CPMD steps were enforced, respectively, for the minimum and maximum intervals for the placement of Gaussian hills. The velocities of the fictitious particles were scaled to maintain a temperature of 315 K. We carried out several metadynamics runs for different values of d0 关see Eq. 共3兲兴 and Gaussian heights W 关see Eq. 共2兲兴 to derive an accurate free energy estimate for the gas phase dissociation of the CT conformer. The values of these parameters and the corresponding Helmholtz free energy es-

FIG. 3. The free energy estimates from the metadynamics runs as a function of the inverse height of the Gaussian hills employed. The corresponding hill heights in kcal/mol are indicated along the X axis on the top. The circles with crosses denote runs employing different definitions of the coordination numbers.

timates are given in Table III. Runs 1–4 were independent, and their metadynamics parameters were kept constant throughout the entire dissociation reaction. The runs labeled run4/ext.1–5 were designed to test the convergence of the free energy estimates with respect to progressively smaller Gaussian hills. To save the increasing computational expense with smaller hill heights, these runs were made by restarting from a configuration from the metadynamics trajectory run4 共that employed larger hills兲 at the point when the reactant well was filled to about 70%. The computed Helmholtz free energy barriers for the dissociation of carbonic acid 共Fig. 3兲 show excellent convergence for hill heights comparable to or smaller than a thermal energy of 3 / 2kT 共⬃0.9 kcal/ mol兲 of the ions, with the undulations well within the inherent sensitivity of the technique 共⬃kT兲. Such smaller hills allow the system to overcome the imposed Gaussian potential without being confined to a local minimum and significantly improve the sampling procedure. The computed free energy landscapes for carbonic acid dissociation all show the same general features. Figure 4 shows a typical surface based on run4. The relatively shallow and broad basin near coordinates 共1, 1兲 represents the reactant H2CO3, and the deep and narrow well near 共0,0兲 represents the product CO2 and H2O. The two basins are connected by a narrow valley depicting the reaction path. The green contour is the separatrix of the reactant and product basins and measures, for this particular case, a free energy barrier of 39.2 kcal/ mol with respect to the reactant carbonic acid in the CT conformation. In this representation, the free energy values are given relative to an arbitrary reference, and free energy surface is constructed as a function of the reaction coordinates s = 共s1 , s2兲, using the expression F共s兲 = −limr→⬁ V共t , s兲. The reaction coordinates, s1 and s2, are synonymous with the collective variables, the C共1兲–O共4兲 and O共3兲–H共5兲 coordination numbers, respectively. The smallest metadynamics hill height of 0.0627 kcal/ mol employed here, predicts an accurate estimate of 37.05 kcal/ mol for the free energy barrier for dissociation with respect to the reactant CT conformer. The potential energy 共Kohn-Sham energy兲 profiles U共s兲 for the dissociation were also calculated in the same reaction coordinate space from the present metadynamics runs 共not shown兲. This potential energy surface suggests a barrier of


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FIG. 4. 共Color兲 A typical free energy landscape 共taken from run4; see text for details兲 for the dissociation of H2CO3 to CO2 + H2O in the space of the reaction coordinates. The blue and green contours mark the free energies of the reactant, cis-trans carbonic acid, and the transition state with respect to the same arbitrary reference.

about 38 kcal/ mol relative to the CT conformer. The similarity of the free energy and potential energy barriers indicates that the entropic contribution to the magnitude of the barrier to dissociation near room temperature is well less than 10%. The potential energy of the product state, CO2 + H2O, estimated from the metadynamics sampling is about −10 kcal/ mol with respect to the CT conformer, consistent with the potential energy of the geometry-optimized species given in Table I. Our computed potential energy barrier of 38 kcal/ mol is 5 – 6 kcal/ mol less than those in the most recent studies of the dissociation of gas-phase carbonic acid. For example, the MP2 level, 0 K quantum chemical calculations of Wight and Boldyrev4 suggest a value of about 45.7 kcal/ mol, and the more recent DFT-based calculations by Loerting et al.7 suggest a value of 43.55 kcal/ mol. Note that the level of electronic structure calculation by Loerting et al.7 is very similar to ours, although it does not explicitly include finite temperature effects. Together, these results suggest that the lower activation barrier in our calculations is largely due to a finite temperature. It is also plausible, however, that thermalization of the ions in the metadynamics calculations enhances the relaxation rate of the system along the degrees of freedom normal to the reaction coordinate, thus assisting the system in more efficiently locating the minimum energy path. This is likely to be important for gas-phase carbonic acid in view of the narrow reaction pathway 共of low entropy兲 near the transition state and the highly cooperative nature of the reaction mechanism. The superimposed snapshots of carbonic acid dissociation from near the transition region in the metadynamics trajectory illustrate the dissociation mechanism of the CT conformer 共Fig. 5兲. The reactant H2CO3 molecule and the products, CO2 and H2O 共shown in a slightly different shade兲, are represented as ball and stick models. The intermediate stages of the most “active ions” in the reaction are shown

with slightly smaller balls and without sticks. The major positional changes are for the hydrogens represented by small while spheres. The reaction is triggered by dehydroxylation, and the detaching hydroxyl group 关–O共4兲H共6兲兴 subsequently changes its original in-plane orientation to form a larger angle with the plane of the three oxygens. Initially, the –O共4兲H共6兲 hydroxyl group swings up as the other hydroxyl group swings down with respect to the plane of the oxygens. However, as the reaction proceeds, both hydroxyl groups reverse their orientations cooperatively. This is clearly an attempt by the system to facilitate a favorable H–O–H bond angle for the water molecule to be formed. The formation of CO2 involves largely the straightening of the O v C v O bonds, and this process continues until the proton from the 关CO2H兴+ is transferred to the detached hydroxyl group form-

FIG. 5. 共Color online兲 Superimposed snapshots from the transition fragment of a metadynamics CPMD trajectory, illustrating the mechanism of gasphase H2CO3 dissociation 共see text for details兲.


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J. Chem. Phys. 126, 204315 共2007兲


ing a water molecule. The mechanism is thus highly cooperative in nature, which is not surprising for such a small system.

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CONCLUSIONS

The geometries, relative energies, and vibrational frequencies of the gas-phase conformers of carbonic acid 共H2CO3兲 calculated at the DFT/BLYP level are in good agreement with previous studies. The mechanism and energetics of the conformational changes at 315 K are examined in detail using the metadynamics technique. The cis-cis conformer has a very short lifetime at this temperature and transforms easily to the cis-trans conformer through a change in the O v C – O – H dihedral angle. The energy difference between the trans-trans and cis-trans conformers is very small 共⬇1 kcal/ mol兲, but the trans-trans conformer is resistant to dissociation to carbon dioxide and water. The cis-trans conformer has a relatively short path for one of its hydroxyl groups to accept the proton from the other end of the molecule, resulting in a lower activation barrier for dissociation. The dissociation mechanism is triggered by the dehydroxylation of one of the hydroxyl groups. The detaching hydroxyl reorients as it approaches the proton on the other end of the molecule, thus facilitating a favorable H–O–H angle for the formation of a product H2O molecule. The major atomic reorganization of the other part of the molecule is a gradual straightening of the O v C v O bond. The present metadynamics calculations yield a free energy barrier of 37.1 kcal/ mol at 315 K for the gas-phase dissociation of cis-trans carbonic acid to carbon dioxide and water. The potential energy barrier for the reaction is 5 – 6 kcal/ mol lower than the most recent 0 K calculations.4,7 The entropic contribution to the reaction free energy is less than 10%, in qualitative agreement with the observed narrow reaction pathway on the potential energy surface. This feature, together with the highly cooperative nature of the reaction mechanism, emphasizes the importance of system relaxation as the reaction progresses. The results here set the stage for future studies of the complex chemical reactivity of carbonate species in the more challenging aqueous environments. ACKNOWLEDGMENTS

One of the authors 共P.P.K.兲 thankfully acknowledges Nisanth N. Nair and Axel Kohlmayer for invaluable discussions. The financial support by the DOE BES Geoscience Program 共Grant No. DEFGO2-00ER-15028兲 is gratefully acknowledged. The computational resources were provided by the DOE National Energy Research Scientific Computing
