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Carbonic Acid Formation from Reaction of Carbon Dioxide and Water Coordinated to Al(OH)3: A Quantum Chemical Study Jonas Baltrusaitis†,‡ and Vicki H. Grassian*,† Department of Chemistry and Central Microscopy Research Facility, UniVersity of Iowa, Iowa City Iowa 52242 ReceiVed: October 12, 2009; ReVised Manuscript ReceiVed: December 18, 2009
Density functional and ab initio calculations have been performed on CO2-nH2O and Al(OH)3-CO2-nH2O (where n ) 1, 2, 3) cluster models to elucidate the catalytic effect of a hydroxylated metal center on the formation of carbonic acid (H2CO3). B3LYP/6-311++G(d,p)-calculated geometries and RI-SCS-MP2/augcc-pVTZ//B3LYP/6-311++G(d,p)-calculated energies with respect to isolated gas-phase molecules and various H2O, CO2, and H2CO3-Al(OH)3 complexes are presented. It is shown here that H2CO3 formation proceeds via direct CO2 and nH2O reaction with very high activation barriers in the gas phase, 51.40, 29.64, and 19.84 kcal/mol for CO2-H2O, CO2-2H2O, and CO2-3H2O clusters, respectively, decreasing in magnitude with an increase in the number of H2O molecules. The energetics as well as the reaction mechanism and energy landscape change significantly when carbonic acid is formed from CO2 and nH2O in the presence of Al(OH)3, a hydroxylated metal center. Results presented here show important details of the influence of the coordinating metal center in the formation of H2CO3. Introduction Carbonic acid formation in the gas phase from reaction of CO2 and H2O has been of interest in many fields of chemistry including biochemistry,1,2 atmospheric chemistry,3 mineral surface chemistry,4 and solid H2CO3 formation in ice.5,6 Carbonic acid has been proposed as a new candidate for CO2 capture and sequestration,7 as CO2 removal from coal plant emissions remains a challenge.8 A large number of theoretical studies have been performed since the 1970s to estimate the energetics of the direct formation of H2CO3 with increasingly accurate computational methods.9,10 The number of H2O molecules involved in direct CO2 reaction is still, however, under debate.11 High-level QCISD(T)/6-31G(d,p)//MP2/6-31G(d,p) calculations have shown that three or more H2O molecules are needed for direct reaction in the gas phase, with the second H2O molecule acting as a catalyst in the formation of carbonic acid.12 Experimentally, gaseous carbonic acid was observed to be present in interstellar icy grains as well as in Earth’s upper atmosphere.13 A reversible CO2 reaction with H2O in human carbonic anhydrases (HCAs) is of essential importance in respiration.14,15 The mechanism has been investigated both theoretically and experimentally.16-23 The widely accepted reaction mechanism involves (a) binding of H2O to Zn followed by deprotonation, (b) reaction between Zn-OH with CO2 to form bicarbonate and (c) proton migration via Lipscomb and/or Lindskog mechanism.23 All of these steps proceed in physiological buffer with bulk water facilitating proton transfer reactions. Far less attention has been devoted to carbonic acid formation from CO2 and H2O in the presence of a metal center present on a particle surface or in a metal oxide cluster. The interactions of CO2 and H2O on metals and metal oxides are of importance due to the possible formation of key intermediates in catalytic * To whom correspondence should be addressed. E-mail: vicki-grassian@ uiowa.edu. † Department of Chemistry. ‡ Central Microscopy Research Facility.
reactions involving hydrocarbon formation and carbon sequestration.24 CO2 and H2O have been found to react with Pd, Al, and TiO2 to form CO2-surface complexes possessing negative charge with bent structures and/or bicarbonates.24-28 In a study from our laboratory, we proposed the formation of H2CO3 following reaction of CO2 and H2O on hydroxylated iron and aluminum oxide surfaces as an intermediate in the formation of adsorbed carbonate.29,30 Here we present results from quantum chemical studies where we use a mononuclear metal hydroxide species to provide some insight into reactions of H2O and CO2 in the presence of a hydroxylated metal center. In particular, we show that coordination of reactant molecules, CO2 and H2O, to Al(OH)3 reduces the activation barrier and facilitates the formation of H2CO3 via a bicarbonate intermediate. Theoretical Methods All molecules and clusters were optimized using spin-restricted calculations with the B3LYP functional and 6-311++G(d,p) basis set. No symmetry constraints were imposed during geometry optimization. Vibrational frequencies were calculated after optimization at the same level of theory to confirm that the optimized geometry was a minimum in the potential-energy surface. No negative vibrational frequencies were observed for minimum structures and only one for all transition-state structures. Singlepoint energies were calculated at B3LYP/6-311++G(d,p) geometry with the RI-SCS-MP2 level of theory with “resolution of the identity” approximation (RI)31,32 using the augmented correlationconsistent polarized triple-valence zeta (aug-cc-pVTZ)33,34 basis set to better account for electron correlation effects. The RI-MP235 method provides negligible loss in accuracy at a fraction of a cost of full MP2 calculations. For example, Feyereisen et al. showed a relatively small 0.18 kcal/mol error at a Dunning’s correlationconsistent triple-ζ (cc-TZ) basis set when compared to the full MP2 calculations performed on a H2O dimer.36 An auxiliary aug-ccpVTZ basis set was used in all RI calculations. All primitives in the aug-cc-pVTZ basis set were contracted to basis functions as follows: hydrogen (6s,3p,2d) f [4s,3p,2d], carbon and oxygen (19s,6p,3d,2f) f [5s,4p,3d,2f], aluminum (42s,17p,3d,2f) f
10.1021/jp9097809 2010 American Chemical Society Published on Web 01/27/2010
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TABLE 1: RI-SCS-MP2/aug-cc-pVTZ//B3LYP/ 6-311++G(d,p)-Calculated Energies of the Carbonic Acid Formation from H2O and CO2
TABLE 2: RI-SCS-MP2/aug-cc-pVTZ//B3LYP/ 6-311++G(d,p)-Calculated Energies of Carbonic Acid Formation from H2O and CO2 Coordinated to Al(OH)3
RI-SCS-MP2/aug-cc-pVTZ// B3LYP/6-311++G(d,p) energies clusters and molecules (reaction coordinate)
total energy, Hartreesa
H 2O H2O dimer H2O trimer
Reactantsb -76.304860 -152.613439 -228.928568
CO2
-188.290372
Al(OH)3
-469.314109
interaction energy, kcal/mol
-2.33 -8.78
H2O (I) H2O TS (II) 2H2O (I) 2H2O TS (II) 3H2O (I) 3H2O TS (II)
Intermediatesb -264.597471 -264.513320 -340.909192 -340.852860 -417.222942 -417.173340
-1.41 51.40 -5.71 29.64 -11.29 19.84
H2CO3 (III) H2CO3 + H2O (III) H2CO3 + 2H2O (III)
Productsb -264.576415 -340.890988 -417.205510
11.81 5.71 -0.35
CO2 CO2 CO2 CO2 CO2 CO2
+ + + + + +
RI-SCS-MP2/aug-cc-pVTZ// B3LYP/6-311++G(d,p) energies
a Gas-phase ZPE corrected using B3LYP/6-311++G(d,p) calculated values. b Clusters and molecules shown in Figures 1 and 2, respectively.
interaction energy, kcal/mol
reaction coordinate
total energy, Hartreesa
I II III IV (TS) V VI
CO2 + H2Ob -733.947777 -733.929712 -733.934947 -733.890588 -733.947289 -733.916385
-24.12 -12.78 -16.07 11.77 -23.81 -4.42
I II III IV (TS) V VI
CO2 + 2H2Ob -810.273568 -810.244511 -810.254186 -810.240945 -810.263264 -810.235599
-37.25 -19.02 -25.09 -16.78 -30.79 -13.43
I II III IV (TS) V VI
CO2 + 3H2Ob -886.593591 -886.553944 -886.572538 -886.559318 -886.580767 -886.549698
-46.77 -21.89 -33.56 -25.26 -38.72 -19.23
a Gas-phase ZPE corrected using B3LYP/6-311++G(d,p)calculated values. b Cluster models shown in Figure 4.
[6s,5p,3d,2f]. Uncontracted primitives in the auxiliary aug-cc-pVTZ basis set were as follows: hydrogen (5s,4p,3d,2f), carbon and oxygen (9s,7p,6d,4f,2g), aluminum (11s,9p,8d,6f,3g). Total energies calculated at RI-SCS-MP2/aug-cc-pVTZ were corrected for zeropoint energies (ZPE) calculated at B3LYP/6-311++G(d,p) according to eq 1
Etotal ) Eelectronic + EZPE
(1)
where Eelectronic is the computed RI-SCS-MP2/aug-cc-pVTZ// B3LYP/6-311++G(d,p) energy and EZPE the B3LYP/6311++G(d,p)-computed vibrational zero-point energy correction. Calculated total energies, Etotal in Hartrees, as well as interaction energies (total energy difference between the calculated cluster and those of isolated molecule, in kcal/mol) for all reactants, transitions states, and products discussed here are presented in Tables 1 and 2. Additionally, polarizability is calculated using the RI-SCS-MP2/ aug-cc-pVTZ//B3LYP/6-311++G(d,p) method by numerically differentiating the dipole moment using a finite field increment of 10-4 Hartrees as shown in Supporting Information Tables 1 and 2. Geometry optimization and frequency calculations were performed using Spartan’08 run on a dual-core Linux workstation.37,38 Single-point RI-SCS-MP2/aug-cc-pVTZ calculations were performed in the gas phase. The COSMO solvation model39 was implemented in ORCA 2.7.0.40 All structures were visualized using commercially available Chemcraft software.41 Results and Discussion Gas Phase Reactants. B3LYP/6-311++G(d,p)-optimized structures of CO2, H2O, H2O-H2O, H2O-H2O-H2O, and Al(OH)3 are shown in Figure 1 together with the corresponding geometrical parameters. The corresponding RI-SCS-MP2/aug-
Figure 1. B3LYP/6-311++G(d,p)-optimized structures of H2O, H2O dimer, H2O trimer, CO2, and Al(OH)3. Corresponding bond lengths and interatomic distances are given in Angstroms. Bond angles are given in degrees.
cc-pVTZ total energies in Hartrees as well as the interaction energies for H2O-H2O and H2O-H2O-H2O complexes in kcal/ mol are shown in Table 1. Water molecules bind via hydrogen bonding, the interaction energy being weakly exothermic with a binding energy of -2.33 kcal/mol for H2O-H2O and -8.78 kcal/mol for the triple-bonded homodromic H2O-H2O-H2O ring. The B3LYP/6-311++G(d,p)-optimized CO2 molecule is completely linear with C-O bond lengths of 1.16 Å. The distortion in the O-C-O angle in the CO2 molecule is of utmost importance in CO2 activation as the bending of the O-C-O
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Figure 2. B3LYP/6-311++G(d,p) optimized structures of CO2 and H2O reaction complexes together with the corresponding transition states. Additionally, final structures of H2CO3 with zero, one and two H2O molecules are shown. Bond lengths and interatomic distances are given in Angstroms. Bond angles are given in degrees.
Figure 3. RI-SCS-MP2/aug-cc-pVTZ//B3LYP/6-311++G(d,p) interaction energies of CO2 with one, two and three H2O molecules complexed together with corresponding transition states and final reaction structures of H2CO3 with one and two H2O molecules are shown. All energies are with respect to the isolated CO2 and H2O molecules. Interaction energies are taken from Table 1.
angle will cause the degenerate π orbitals of CO2 to split.42 The energy of the out-of-plane 2πu orbital falls sharply in the bent molecule and changes symmetry, becoming a 6a1 orbital.42 The occupancy of this valence orbital will lead to a decrease in the O-C-O angle away from 180°, which will have increasing reactivity toward other molecules. B3LYP/6-311++G(d,p)optimized Al(OH)3 is planar with C3h geometry with O-H bond lengths of 0.96 Å. Gas-Phase Intermediates and Reaction Products in the Absence of Al(OH)3. Structure and binding energy calculations of the gas-phase CO2-nH2O clusters have been extensively studied before.2,3,11,12,43 Here we re-evaluate these data at the RI-SCS-MP2/aug-cc-pVTZ//B3LYP/6-311++G(d,p) levels for
the relative comparison of the geometries as well as the interaction energies with similar CO2-nH2O clusters coordinated to Al(OH)3 (vide infra). The B3LYP/6-311++G(d,p)-optimized structures of the CO2-H2O clusters as well as the corresponding transition states and resulting H2CO3-H2O complexes are shown in Figure 2 together with the corresponding geometrical parameters. The corresponding RI-SCS-MP2/pVTZ total energies in Hartrees as well as the interaction energies for CO2-H2O and H2CO3-H2O complexes in kcal/mol are shown in Table 1. All CO2-H2O interactions, except transition states, are exothermic with calculated interaction energies of -1.41, -5.71, and -11.29 kcal/mol for CO2-H2O, CO2-2H2O, and CO2-3H2O, respectively, relative to the isolated molecules. For comparison, CO2-H2O binding energies have been calculated within the range from -1.77 to -3.27 kcal/mol with augmented correlation-consistent basis sets (aug-cc-pVTZ) (Jena et al.2 and references therein). Similarly, binding energies per water molecule in CO2-2H2O complexes were reported in the range from -3.67 to -5.74 kcal/mol (Jena et al.2 and references therein). The first H2O molecule has a distance of 2.78 Å from the C atom in CO2 with a decrease to 2.69 Å in the CO2-3H2O complex. C(CO2)-O(H2O) distances for one and two H2O molecule clusters have been determined experimentally to be 2.84 and 2.86 Å for CO2-H2O and CO2-2H2O, respectively, from radiofrequency and microwave spectra.44,45 Calculations tend to underestimate the C(CO2)-O(H2O) bond distances in CO2-nH2O complexes, especially when calculated with highly correlated ab initio methods. For example, MP2/6-311++G(d,p) and MP2/aug-cc-pVDZ calculations showed C(CO2)-O(H2O) distances of 2.78 and 2.75 Å, respectively, for a CO2-H2O complex,2 the same as the distances presented in this work for 1 and 2 H2O complexes. Furthermore, a complete basis set calculation (CBS-Q) underestimates the C(CO2)-O(H2O) distance even more at 2.71 Å.3 The energetics of the transition state involved in the direct hydration of CO2 in the gas phase to form H2CO3 are large with RI-SCS-MP2/aug-cc-pVTZ//B3LYP/6-311++G(d,p)-computed energies of 51.40, 29.64, and 19.84 kcal/mol with respect
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Figure 4. B3LYP/6-311++G(d,p) optimized structures of CO2 and nH2O reaction (where n ) 1, 2, 3) coordinated to Al(OH)3 (I and II) together with the corresponding intermediates (III and IV) and transition states (IV). Final reaction structures of H2CO3 coordinated to Al(OH)3 are also shown (VI). Bond lengths and interatomic distances are given in Angstroms. Bond angles are given in degrees.
to the isolated gas-phase CO2-H2O, CO2-2H2O, and CO2-3H2O clusters, respectively (see Figure 3). The true activation barriers with respect to the bound CO2-nH2O complexes are even higher at 52.81, 35.35, and 31.13 kcal/mol. For comparison, various computed literature values range from 70.2 to 50.1 kcal/mol for CO2-H2O and 49.0 to 29.2 kcal/mol for CO2-2H2O.2 While inclusion of the second water molecule reduced the activation barrier by ∼33%, there is no further pronounced effect when three water molecules are present. All of these activation barrier values are higher than the experimental solution-phase CO2 hydration value of 17.7 kcal/mol,46 with three water molecules determined to be very close to the experimental value, thus providing some evidence that the three H2O molecule complex can describe the direct CO2 reaction. Finally, H2CO3 and H2CO3-nH2O complexes are endothermic or slightly exothermic in the case of the H2CO3-2H2O system with respect to both isolated gas-phase molecules and CO2-nH2O clusters. H2CO3 formation is unfavored by 11.81 kcal/mol with respect to the isolated molecules with gradually decreasing energy by ∼5.7 kcal/mol for each stabilizing H2O molecule (Figure 3). Gas-Phase Intermediates and Reaction Products in the Presence of Al(OH)3. CO2-H2O coordinated to Al(OH)3 has been modeled to account for any catalytic effects in the formation of H2CO3 due to the presence of a hydroxylated metal center, for example, on a metal oxide surface. Structures for various stages of reactive CO2-H2O, CO2-2H2O, and CO2-3H2O complexes when coordinated to Al(OH)3 are shown in Figure 4. Several coordination modes were modeled. In particular, all reactions were modeled so that in the first step of the reaction H2O coordinated to the Al atom, as this is a stronger interaction than that with CO2, and CO2 weakly coordinated to the OH group. This is a very exothermic step with calculated
energies of -24.12, -37.25, and -46.77 kcal/mol for one, two, and three water molecules, respectively. Step I is then followed by a rearrangement whereby CO2 coordination is through the oxygen lone pair to Al and H2O water coordination via a hydrogen bond to the surface oxygen atom (Figure 4, Step II). This rearrangement is endothermic by ∼12 kcal/mol for one water molecule and increases to ∼25 kcal/ mol for three water molecules. These coordination modes account for CO2 and H2O interactions with Al(OH)3. These weak binding configurations are close enough to the CO2-H2O complex structures discussed in the previous section, thus allowing for the direct comparison of the catalytic effect of a hydroxylated metal center on the next steps in the reaction mechanism. Although differences include the fact, that the C(CO2)-O(H2O) distances in Al(OH)3-CO2-H2O and Al(OH)3-CO2-2H2O complexes are shorter than those in the absence of Al(OH)3 by 0.16 and 0.21 Å, respectively. Three water complexes have very similar C(CO2)-O(H2O) distances (2.69 and 2.68 Å) alone and when coordinated to Al(OH)3. This can be explained by steric hindrance of three H2O molecules, competing for one bond with the carbon atom. Additionally, a local configuration of three H2O molecule binding is somewhat different in both cases, since with no Al(OH)3 present all three water molecules form a homodromic ring starting with the molecule donating electron density to the carbon atom, whereas in Al(OH)3-CO2-3H2O cluster one water molecule interacts with the oxygen atom in Al(OH)3, thus CO2-3H2O assuming a T-shaped configuration. It can also be observed from the structures shown in Figure 4, when compared with the structures shown in Figure 2, that the O-C-O angle in CO2 is slightly more distorted in CO2-H2O complexes when coordinated to the Al(OH)3 than in the absence of Al(OH)3. In particular, while CO2-H2O complexes alone have O-C-O angles of 177.6°,
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Figure 5. RI-SCS-MP2/aug-cc-pVTZ//B3LYP/6-311++G(d,p) calculated energies for CO2 and one, two and three H2O molecules reaction complexes on Al(OH)3 together with the corresponding transition states. Additionally, final product structures of H2CO3 and with one and two H2O molecules are shown. All interaction energies are with respect to the CO2, H2O and Al(OH)3 isolated molecule energies. Interaction energies taken from Table 2.
176.7°, and 175.9° for one, two, and three H2O molecules, respectively, the same complexes when coordinated to Al(OH)3 have angles of 174.6°, 174.0°, and 174.6°, respectively. However, this is only true for the Al(OH)3-CO2-H2O complexes initially. As the reaction coordinate proceeds, H2O interacts more strongly with Al(OH)3, donating a hydrogen atom and effectively producing a hydroxyl group with an O-H bond length of 0.99 Å. This transition is thermodynamically favored by 3.29, 6.07, and 11.67 kcal/mol (Step II f III in Figure 5). As the reaction further proceeds along the reaction coordinate, as seen in III, O-C-O bond angles are 129.2°, 126.8°, and 125.7° for one, two, and three H2O molecule complexes, respectively. Here CO2 is clearly activated by donation of the lone pair of electrons from H2O oxygen atom. This step essentially results in the formation of bicarbonate with the simultaneous strong H2O interaction. This resulting structure is that of bicarbonate, HCO3-, with a newly formed C-O6 bond length decreasing from 1.41 to 1.37 Å with an increase in the number of reacting water molecules (Figure 4, Step III). These data show the stabilization of the activated CO2 product, bicarbonate ion, with increasing hydrogen bonding. Additionally, it shows an alternative thermodynamically favorable route to CO2 activation from that of anionic species, CO2-, formation. The O-C-O angle in CO2- isolated in alkali halide matrix has been experimentally determined to be 127 ( 8°,48 within the range of that of the bicarbonate species in Step III. The autodetachment of the electron from the CO2- is 9.22 kcal/mol (0.4 eV) with a measured anion lifetime of 60-90 µs.42,49,50 Since the activation barrier is quite low, the short-lived CO2can serve as an intermediate of the bicarbonate structure like that obtained in Figure 4, Step III. Calculated in Step IV of the Al(OH)3-CO2-H2O reaction pathway is a transition state for proton transfer. From the data presented in Figure 5, it can be clearly seen that the relative energy needed for this step is 11.77, -16.78, and -25.26 kcal/ mol. With the exception of the monohydrate, this process is exothermic with respect to the isolated molecules. The true activation barrier, i.e., the energy needed for Step III f IV, is
27.84, 8.31, and 8.30 kcal/mol for Al(OH)3-CO2-H2O, Al(OH)3-CO2-2H2O and Al(OH)3-CO2-3H2O complexes, respectively. These energies are much lower than those compared to CO2-H2O clusters in the absence of Al(OH)3. The main difference enabling a low energy barrier transition state is the stabilization of bicarbonate when coordinated to the metal center with a C-O distance of 1.32 Å. This, in turn, shortens the distance for the hydrogen atom to react with the other oxygen atom in HCO3- from 1.48 to 1.39 Å in the three water molecule TS case (Figures 2 and 4, respectively). When coordinated, there is a strong interaction between CO2 and H2O to form HCO3ion by lone pair donation to the CO2 LUMO orbital. This interaction weakens the O-H bond, thus requiring less energy to transfer the proton in the TS. This can be illustrated by comparing SCS-MP2/aug-cc-pVTZ//B3LYP/6-311++G(d,p)computed Mulliken charges for the Al(OH)3-CO2-H2O system. In the weakly coordinated structure (Figure 4, Step II) Mulliken charges on O6 and H4 atoms are -0.579 and 0.176, respectively, with an O-H bond distance of 0.96 Å. In the bicarbonate structure (Figure 4, Step III) those are -0.319 and 0.205, respectively, with a concomitant elongation of the O-H bond distance by 0.006 Å. The positive charge increase on the hydrogen atom means less electron density overlap with the O6 atom and a lower energy needed to transfer H4 in the transition state (Step IV). Structures of the coordinated complex following proton transfer are shown in Step V of Figure 4. Here the coordinated bicarbonate ion is rotated 180° from that in Step III; consequently, an alternative transition state by bicarbonate ion rotation can be involved. From microscopic reversibility,51,52 it follows that an intramolecular proton transfer is required. In the case of a larger metal cluster or a hydroxylated surface, an alternative mechanism to intramolecular proton transfer is intermolecular proton transfer, a mechanism that we proposed in an early paper which involves proton transfer to the neighboring adsorbed hydroxyl groups before transferring back to the carbonate ion to yield bicarbonate.53
Carbonic Acid Formation The final structure for coordinated carbonic acid is shown in Step VI (Figure 4). This final process results in a lower energy state with respect to the separated molecules by -4.42, -13.43, and -19.23 kcal (Figure 5). The formation of carbonic acid, however, involves additional protonation involving a H2O molecule coordinated to Al(OH)3. This is an unfavorable process by 19.39, 17.36, and 19.49 kcal/mol with respect to Step V. The direct deprotonation transition between Steps V and VI involves an unidentified complex transition state involving hydrogen transfer from the Al-coordinated water molecule to bicarbonate as well as breaking of the H bond between C-O-H (HCO3-) and H2O followed by C-O-H rotation (Figure 4, Step VI). This reorientation can be envisioned as very unfavorable due to the distortion of the homodromic H2O ring. The results presented in this section show that coordinated CO2 has a much smaller activation barrier than CO2-H2O complexes alone. Additionally, the reaction proceeds via a bicarbonate intermediate before formation of carbonic acid. This mechanism differs from that of HCA in several ways as water reacts directly with coordinated carbon dioxide to yield bicarbonate. Consequently, the hydroxyl group is not bound to the metal atom during reaction with CO2. This is different from the well-known HCA mechanism, where both hydroxyl and CO2 are bound to the same Zn atom prior to reaction.23 COSMO Solvation Calculations COSMO single-point solvation calculations were performed on all models shown in Figures 1, 2, and 4 to account for the solvation effects. These data were interpreted in terms of solvation energies, e.g., the difference between the total energies of the COSMO method solvated and the gas-phase data. The most negative solvation energy would constitute the species that is the most stabilized by electrostatic forces in aqueous solution. B3LYP/6-311++G(d,p) geometries were used from gas-phase structure optimizations. Single-point COSMO energies were calculated using the RI-SCS-MP2/aug-cc-pVTZ level of theory with water as the solvent. The solvent dielectric constant and refractive index used in COSMO energy calculations were 80.4 and 1.33, respectively. SCS-MP2/aug-cc-pVTZ//B3LYP/6-311++G(d,p)-calculated COSMO solvation single-point calculations are shown in Supporting Information Tables 1 and 2 together with the total energies of the structures. To further aid the interpretation of solvation energies, dipole moments and isotropic polarizabilities were calculated both in the gas phase and using the COSMO solvation model. These are also shown in Supporting Information Tables 1 and 2. Total energy values shown have been corrected using a gas-phase zero-point energy calculated at the B3LYP/6-311++G(d,p) level of theory. Solvation energies calculated for the reactant molecules, H2O, H2O dimer, and H2O trimer, as well as CO2 are -6.95, -11.66, -10.83, and -1.88 kcal/mol with a very good agreement with the values recently published by Nguyen et al.11 at the MP2/aug-cc-pVTZ level of theory. Al(OH)3 alone has a large solvation energy of -32.24 kcal/mol. While there is no dipole moment associated with the planar Al(OH)3 molecule, calculated polarizability values in both the gas phase and COSMO solvated are high, 30.185 and 37.197, respectively. Calculated solvation energies for CO2-H2O clusters in both the gas phase and COSMO solvated show that in all cases either H2CO3 formation product or the corresponding transition state is stabilized more strongly by electrostatic forces in aqueous solutions than the reactants. For example, data shown in Supporting Information Tables 1 and 2 show a solvation energy
J. Phys. Chem. A, Vol. 114, No. 6, 2010 2355 of H2CO3 of -10.37 kcal/mol while that of CO2 + H2O is -6.80 kcal/mol. Interestingly, for two and three H2O molecule systems a corresponding transition state is stabilized in solution more than the final product or reacting complex (-14.25, -13.24 and -19.27, -15.33 kcal/mol for two and three H2O molecules, respectively). This again can be related to the different isotropic polarizabilities, which are less for the carbonic acid complexes by ∼2 and 3 with respect to the corresponding transition state (Supporting Information Tables 1 and 2). Different solvation of CO2 + H2O and those on Al(OH)3 depend greatly on the polarity of the system. An increase in the dipole moment value with COSMO screening has been previously reported for the H2O molecule from 1.74 to 2.06 D, close to the values shown in Supporting Information Table 1.39 This is consistent with the fact that a larger dipole moment should lead to a higher polarizability and a larger solvation energy.11 Solvation energies calculated for Al(OH)3-CO2-H2O complexes show that carbonic acid formation Step VI has the greatest solvation energy. This is an important finding contributing to the gas-phase calculations presented above. While Step V is more favorable thermodynamically, inclusion of solvent effects shows that the carbonic acid molecule in Step VI can be stabilized by solvation forces. This is also accentuated by the large dipole moment for the structures formed in Step VI. It is larger by a factor of 2-3 than dipole moments in all other steps on PES. Conclusions Density functional and ab initio calculations have been performed on CO2-nH2O and Al(OH)3-CO2-nH2O (where n ) 1, 2, 3) clusters to elucidate the catalytic effect of a metal center, e.g., in the case of a metal oxide cluster or surface, on the formation of H2CO3. High activation barriers are seen in the gas phase for the direct H2O + CO2 reaction. The barrier is observed to decrease in magnitude with the number of H2O molecules involved in reaction (CO2-nH2O, where n ) 1, 2, 3). In particular, the second H2O molecule decreases the activation barrier by 40%, whereas addition of the third H2O molecule decreases the activation barrier a lower amount by 60% with respect to the one H2O molecule reaction. Activation barriers for all the CO2-nH2O (where n ) 1, 2, 3) clusters coordinated to Al(OH)3 were much less than those in the absence of Al(OH)3. Additionally, H2CO3 formation proceeded via adsorbed bicarbonate intermediate. Inclusion of solvation effects via the COSMO model showed an increase in the solvation energy of structures adsorbed on Al(OH)3 compared to those of the gas phase. This was explained by the larger polarizability of Al(OH)3 when compared to CO2 and H2O. Acknowledgment. This material is based on the work supported by the National Science Foundation under grant CHE0503854. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Professor Jan H. Jensen is acknowledged for useful discussions in result interpretation. Supporting Information Available: Supporting Information contains: RI-SCS-MP2/aug-cc-pVTZ(COSMO)//B3LYP/6311++G(d,p) calculated total energies and solvation energiers, as well as calculated gas and solvated (COSMO) dipole moments, µ (in Debye, D) and isotropic polarizability, (in Hartrees3), from the reaction of H2O and CO2 to form carbonic acid in the presence and absence of Al(OH)3. This material is available free of charge via the Internet at http://pubs.acs.org.
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