Autocatalytic Isomerizations of the Two Most Stable Conformers of

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Autocatalytic Isomerizations of the Two Most Stable Conformers of Carbonic Acid in Vapor Phase: Double Hydrogen Transfer in Carbonic Acid Homodimers Sourav Ghoshal, and Montu K Hazra J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp5024873 • Publication Date (Web): 30 May 2014 Downloaded from http://pubs.acs.org on June 7, 2014

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The Journal of Physical Chemistry

Autocatalytic Isomerizations of the Two Most Stable Conformers of Carbonic Acid in Vapor Phase: Double Hydrogen Transfer in Carbonic Acid Homodimers Sourav Ghoshal and Montu K. Hazra * Chemical Sciences Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata-700 064, India ABSTRACT The cis-cis [(cc)] and cis-trans [(ct)] conformers of carbonic acid (H2CO3) are known as the two most stable conformers based on the different orientations of two OH functional groups present in the molecule. To explain the interconversion of the (cc)–conformer to its (ct)–conformer, the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer has been shown until now as the effective isomerization mechanism. Moreover, the (ct)–conformer, which is slightly energetically disfavored over the (cc)–conformer, has been considered as the starting point for the decomposition of H2CO3 into CO2 and H2O molecules. Experimentally, on the other hand, the infrared (IR) and Raman spectroscopy of the crystalline H2CO3 polymorphs suggest that the most possible basic building blocks of H2CO3 polymorphs consist of only and exclusively the (cc)–conformers. However, the sublimations of these crystalline H2CO3 polymorphs result both the (cc)– and (ct)–conformers in vapor phase with the (cc)–conformer being as the major species. In this article, we first report the high level ab initio calculations investigating the energetics of the autocatlytic isomerization mechanism between the two most stable conformers of carbonic acid in the vapor phase. The calculations have been performed at the MP2 level of theory in conjunction with aug-cc-pVDZ, aug-cc-pVTZ, and 6311++G(3df,3pd) basis sets. The results of present study specifically and strongly suggest that double hydrogen transfer within the eight-membered cyclic doubly hydrogen-bonded (H-bonded) ring interface of the H2CO3 homodimer formed between two (cc)–conformers is ultimately the starting mechanism for the isomerization of the (cc)–conformer to its (ct)–conformer, especially, during the sublimation of the H2CO3 polymorphs, which result the vapor phase concentration of the (cc)–conformer at highest levels.

Keywords: Hydrogen-Bonded Dimer, Isomerization Reaction, Autocatalytic Reaction Mechanism, and Intermolecular Hydrogen Transfer. * Address correspondence to: [email protected]

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1. Introduction Carbonic acid (H2CO3), a small molecule of six atoms involving three elements in the periodic table, is right at the interface between organic and inorganic chemistry. This molecule is known as the key species in the dissolution of carbonate compounds and as well as of fundamental importance for the regulation of blood pH and acidification of the oceans.1-19 Moreover, this molecule is believed to be present in cirrus clouds on Earth atmosphere, on Venus and Martian surfaces as well as in Comets and the Galilean satellites.3,5,14-29 Thus, the H2CO3 molecule also gets profound astrophysical as well as environmental significance as both the water (H2O) and carbon dioxide (CO2) molecules coexist in various astrophysical environments such as ice grain mantles in the interstellar medium as well as in various environments of outer space.3,5,14-37 However, it is surprising that it has not been detected yet in interstellar clouds or at outer space either in the solid or in the gas phase.18-19,38 Indeed, we note that the detection of gas-phase interstellar H2CO3 as well as in earth’s troposphere has become an exciting challenge for a new generation of scientists,18,24 as scientists get success in measuring the infrared spectra of the vapor phase H2CO3 resulting from its polymorphs via the sublimation at cold temperatures (210-260K).19,28 From theoretical calculations,15,39-44 it is seen that the H2CO3 monomer has three conformers based on the different orientations of two OH functional groups present in the molecule. Among the three conformers, the cis-cis [(cc)] and cis-trans [(ct)] conformers, as shown in the Fig. 1, are respectively the global minimum and the second most stable one—those have been characterized recently by rotationally resolved spectra.39,41 Moreover, the (ct)–conformer, which is slightly energetically disfavored over the (cc)–conformer, has been considered as the starting point for the decomposition of H2CO3 into CO2 and H2O molecules.44-47 The predicted relative energy difference between these two conformers at the high levels of ab initio calculations including zero point vibrational energy (ZPE) corrections is ~1.5-1.7 kcal/mol with the (cc)–conformer being at lower energy.39,44,48 Theoretical calculations including ZPE corrections39,44,48 also predict that the barrier height for the ACS Paragon Plus Environment

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isomerization of the (cc)–conformer to its (ct)–conformer [(cc)–H2CO3 → (ct)–H2CO3] via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer is ~9.4-9.9 kcal/mol. Therefore, the formation of the (ct)–conformer of H2CO3 from its most stable (cc)–conformer via the rotation of the OH functional group, as mentioned above, is a hindered process in vapor phase. It is important to note here that the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer has been considered until now as the effective mechanism for the formation of (ct)–conformer from its most stable (cc)–conformer of H2CO3.39-46,48 On the other hand, experimentally, the noble gas matrix isolated infrared spectroscopy of carbonic acid vapors, produced via the sublimations of crystalline α- and β-polymorphs of H2CO3, show that the population of the (ct)–conformer with respect to the (cc)–conformer in case of vapor over the α– polymorph of carbonic acid28 is 10% at 210K and for the vapor over the β–polymorph of carbonic acid, this population varies from 10% to 20% at 230-260K.19 It is worthwhile to note that the crystalline αand β-polymorphs of H2CO3 are known to date as the two distinct polymorphs of H2CO3.16,19 Furthermore and more importantly, the infrared (IR) and Raman spectroscopy of the crystalline α– and β–polymorphs of H2CO3 suggest that the most possible basic building blocks of the crystalline α– and β–polymorphs of H2CO3 consist of only and exclusively the (cc)–conformers, as shown in Fig. 2.12,16,19,27-29 However, as noted above, the sublimation of both the crystalline α– and β–polymorphs of H2CO3 results the (ct)–conformer in view of the above note that the interconversion of the (cc)– conformer to its (ct)–conformer in vapor phase via the rotation of the OH functional group is a hindered process. Therefore, it is important to investigate the effective and correct isomerization mechanism by which the (ct)–conformer of H2CO3 is formed from its (cc)–conformer during the sublimation of crystalline H2CO3 polymorphs that result the vapor phase (cc)–conformer at the highest levels of concentration.


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In this article, we present high level ab initio calculations investigating the energetics of the double hydrogen transfer within the doubly hydrogen-bonded (H-bonded) interface of the homodimers of H2CO3. Below, we specifically show that the isomerization of (cc)–conformer to its (ct)–conformer [(cc)–H2CO3 →

(ct)–H2CO3] is autocatalytic and the double hydrogen transfer within the eight-

membered cyclic doubly H-bonded ring interface of the homodimer formed between two (cc)– conformers is ultimately the starting mechanism, especially, during the sublimation of the H2CO3 polymorphs that result the concentration of the (cc)–conformer in vapor phase at highest levels.12,16,19,2729

To the best of our knowledge, there have been no previous studies reported in the literature

investigating the double hydrogen transfer within the doubly H-bonded interface of the H2CO3 homodimers as the isomerization mechanism for the interconversion of the (cc)–conformer to its (ct)– conformer in view of the current detail that the molecular subunit in the most possible basic building blocks of the crystalline H2CO3 polymorphs is only and exclusively the (cc)–conformer. Indeed, we note that the study of energetics associated with the double hydrogen transfer within the doubly H-bonded interface of the H2CO3 homodimer is inevitably underestimated.

2. Computational Methods Gaussian-09 suite of program with “opt=tight” convergence criteria has been used to carry out all the quantum chemistry calculations presented here.49 Both the geometry optimizations and frequency calculations of the monomers and homodimers have been performed using the second order Møller– Plesset (MP2) perturbation theory in conjunction with aug-cc-pVDZ, aug-cc-pVTZ and 6311++G(3df,3pd) basis sets. It is worthwhile to note that the geometry optimizations using the larger basis sets are required to reduce basis set superposition error (BSSE), even though full (100%) counterpoise corrections often underestimate binding energies of dimeric complexes.15,50-53 Transition states (TS) have been located using the QST2/QST3 routines as implemented in Gaussian-09 program. Furthermore, Intrinsic Reaction Coordinate (IRC) calculations were performed at the MP2/aug-ccpVDZ level of theory to unambiguously verify that the transition states found connect with the desired ACS Paragon Plus Environment

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reactants and products. Normal mode vibrational frequencies have been used to estimate the zero point vibration energy (ZPE) corrections for the reactants, products and TS. The computed total electronic energies (Etotal) and ZPE corrected electronic energies [Etotal(ZPE)] for the monomers, homodimers and the transition states are given in Table S1, Supporting Information. In addition, normal mode vibrational frequency analyses have been performed for all the stationary points to verify that the stable minima have all positive vibrational frequencies and that the transition states have only one imaginary frequency (see Table S2, Supporting Information).

3. Results and Discussion The MP2/aug-cc-pVTZ level optimized geometries of the cis-cis [(cc)] and cis-trans [(ct)] conformers of H2CO3 have been shown in Fig. 1. It has been mentioned before that the H2CO3 monomer has three conformers based on the different orientations of two OH functional groups present in the molecule and among the three conformers; the (cc) and (ct) conformers, as shown in Fig. 1, are respectively the global minimum and the second most stable one.15,39-43 The predicted geometrical parameters and rotational constants for both of these two conformers at the MP2 level of calculations in conjunction with aug-cc-pVDZ, aug-cc-pVTZ and 6-311++G(3df,3pd) basis sets have been presented in Table 1. Recently, the rotationally resolved spectra for both the conformers have been measured by Mori et al. in the cold supersonic jet environment.39,41 Therefore, we also present the experimental microwave values in Table 1 for the direct comparison with theoretically predicted values. From the comparison between experimental and theoretically predicted values, it is seen that all the calculations are in good agreement from each other as well as with experiment regarding both the structural parameters and rotational constants. However, a detail scrutiny of the results presented in Table 1 shows that the MP2/aug-cc-pVTZ and MP2/6-311++G(3df,3pd) calculations are achieving a remarkably good agreement between themselves. Moreover, the comparison of experimental results with the predicted results obtained at the MP2/aug-cc-pVTZ and MP2/6-311++G(3df,3pd) level of calculations shows that in a number of cases, the MP2/aug-cc-pVTZ level of calculation is somewhat better and in number of ACS Paragon Plus Environment

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other cases, the MP2/6-311++G(3df,3pd) level of calculation outperforms over the MP2/aug-cc-pVTZ level of calculation. Therefore, both the MP2/aug-cc-pVTZ and MP2/6-311++G(3df,3pd) calculations are equally reliable in predicting the geometrical parameters of the isolated H2CO3 molecule. In Fig. 3, we present the potential energy profile calculated at the MP2/aug-cc-pVTZ level including zero point energy (ZPE) correction for the isomerization of the (cc)–conformer of H2CO3 to its (ct)–conformer [(cc)–H2CO3 → (ct)–H2CO3] via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer (Fig. 1). It is worthwhile to note that the energetics of the potential energy profile associated with the rotation of OH functional group has been reinvestigated here only to compare the energetics of the potential energy diagrams for the autocatalytic isomerizations of the (cc)–conformer in presence of both the (cc)– and (ct)–conformers (see below) on equal footing. It has been mentioned before that the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer has been shown until now as the effective mechanism for the (cc)–H2CO3 → (ct)–H2CO3 interconversion among the two most stable conformers (Fig. 1).39-46,48 From the figure, it is seen that the calculated relative energy difference between the two conformers including zero point vibrational energy (ZPE) correction, as expected, is ~1.6 kcal/mol with the (cc)–conformer being at lower energy. This value is comparable with the values predicted at the CCSD(T) level of calculations. The relative energy differences between the above mentioned two most stable conformers at the CCSD(T) level of calculations in conjunction with cc-pVDZ,

cc-pVTZ, cc-pVQZ and with the

extrapolated basis limit (EBL) are respectively ~2.0, 1.6, 1.5 and 1.6 kcal/mol.48 From our MP2/aug-ccpVTZ level of calculation including ZPE corrections, it is seen that the predicted barrier height for the isomerization of the (cc)–conformer to its (ct)–conformer via the rotation of the OH functional group is ~9.6 kcal/mol and this value is also comparable with the values (~9.4-9.9 kcal/mol) predicted at the CCSD(T) level of calculations in conjunction with basis sets of high angular momentum and diffuse functions.39,44,48 Therefore, as pointed out before that the isomerization of the (cc)–conformer to its (ct)– conformer [(cc)–H2CO3 → (ct)–H2CO3] via the rotation of OH functional group is a hindered process in ACS Paragon Plus Environment

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vapor phase. The predicted barrier heights for the (cc)–H2CO3 → (ct)–H2CO3 isomerization via the rotation of the OH functional group, as mentioned above, and the relative energies between the (cc)– and (ct)–conformers at the MP2 level of calculations with three different basis sets have been given in the Table S3, Supporting Information. We note that apart from the rotation of OH functional group required for the (cc)–H2CO3 → (ct)–H2CO3 isomerization process between the two most stable conformers, the isomerization of the (cc)–conformer to its (ct)–conformer may also occur via the intramolecular hydrogen atom transfer from either one of the two OH functional groups to oxygen atom of the C=O functional group present within the (cc)–conformer, as shown in Fig. 4. We also point out that as the transfer of hydrogen atom from the OH group to oxygen atom of the C=O group of the (cc)–conformer requires overall an O—H bond breaking and making process, the barrier height for this process is substantially higher4 than the ~ 9.6 kcal/mol barrier height associated with the rotation of OH functional group as mentioned above. However, the study of the gas phase unimolecular isomerization reactions involving hydrogen atom transfer in the formation of H2SO4 from the SO3…H2O complex,54-55 isomerization of methoxy and HOCO radicals,56-57 keto—enol

tautomerization of vinyl alcohol58 and as well as the study of

tautomerizations of model biologically relevant molecules59-60 in presence of formic acid (HC(O)OH) suggest that the hydrogen atom transfer in the doubly or multiply hydrogen-bonded interfaces via the O—H bond breaking and making process is very efficient, as both the hydrogen donor and acceptor functional groups present in HC(O)OH simultaneously facilitate the hydrogen atom transfer process required for the isomerization of the parent molecules or the complexes of interest. Therefore, as both the (cc) and (ct) conformers of H2CO3 have both the hydrogen donor and acceptor units like those present in HC(O)OH, it is expected that the H2CO3 itself can also act as an autocatalyst to promote the hydrogen transfer process required for its isomerization as described above. Thus, we next focus upon the study of the potential energy diagrams for the autocatalytic isomerizations of the (cc)–conformer of H2CO3 to its (ct)–conformer [(cc)–H2CO3 → (ct)–H2CO3] in ACS Paragon Plus Environment

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presence of both of its (cc) and (ct) conformers. However, in particular, as the vapor phase concentration of the (cc)–conformer reach its highest levels during the sublimation of H2CO3 polymorphs and as the sublimation of α–polymorph of H2CO3 results the eight-membered cyclic doubly hydrogen-bonded (Hbonded) centrosymmetric (cc)–H2CO3…(cc)–H2CO3 homodimer in vapor phase,28 we first investigate the energetics for the potential energy diagram associated with the double hydrogen transfer within the eight-membered cyclic doubly H-bonded ring interface formed between two (cc)–conformers of H2CO3. The autocatalytic isomerization of the (cc)–conformer of H2CO3 in presence of another (cc)–conformer, which result two (ct)–conformers of H2CO3 together from the concurrent isomerization of the two (cc)– conformers involved in the reaction in terms of bimolecular collision, can explicitly be written as follows: (cc)–H2CO3 + (cc)–H2CO3 ⇌ (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 ⇌ (ct)–H2CO3 + (ct)–H2CO3

(1)

In the above reaction, the (cc)–H2CO3…(cc)–H2CO3 species is the pre-reactive entrance channel eight-membered cyclic doubly H-bonded homodimer that undergoes double hydrogen transfer via an eight-membered ring cyclic transition state (TS) to form the eight-membered cyclic doubly H-bonded (ct)–H2CO3…(ct)–H2CO3 homodimer in the exit channel. The MP2/aug-cc-pVTZ level optimized geometries of the starting (cc)–H2CO3…(cc)–H2CO3 reactant homodimer, the exit channel (ct)– H2CO3…(ct)–H2CO3 product homodimer and the TS associated with the (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step via the double hydrogen transfer reaction, are shown in Fig. 5A. Analysis of the optimized geometrical parameters for both the (cc)–H2CO3…(cc)– H2CO3 and (ct)–H2CO3…(ct)–H2CO3 homodimers shows that these homodimers are cetrosymmetric in nature (see Table S4, Supporting Information). The calculated binding energies for the formation of all the H2CO3 homodimers those are reported in this article have been given in Table 2. From Table 2, the comparison of predicted values at the MP2 level of calculations with three different basis sets shows that


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the predicted values match well from each other. Therefore, to keep the discussion simple, we prefer to highlight in text only the results predicted at the MP2/aug-cc-pVTZ level of calculations including zero point vibrational energy (ZPE) corrections. In Fig. 6, we present the potential energy diagram for the double hydrogen transfer within the eight-membered cyclic doubly H-bonded ring interface of the (cc)– H2CO3…(cc)–H2CO3 homodimer that result in two (ct)–conformers from the concurrent isomerization of the two (cc)–conformers involved in the Reaction-1. The MP2 level calculated barrier heights for the (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step via the double hydrogen transfer within the eight-membered cyclic doubly H-bonded ring interface have been given in Table 3. From Fig. 6, it is seen that the barrier height for the unimolecular isomerization step, which is the rate limiting step for the autocatalytic isomerization process as discussed above, is only ~2.4 kcal/mol. This value is approximately four times lower than the ~9.6 kcal/mol barrier height associated with the above mentioned bare (cc)–H2CO3 → (ct)–H2CO3 isomerization reaction via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer (Fig. 3). Furthermore, the energetics of the potential energy diagram suggests that the bimolecular collision between two (cc) conformers of H2CO3 at room temperature is highly effective for the formation of (ct)– conformer as the energy of the TS associated with the rate limiting (cc)–H2CO3…(cc)–H2CO3 → (ct)– H2CO3…(ct)–H2CO3 unimolecular isomerization step is 15.1 kcal/mol lower than the total energy of the isolated starting (cc)–H2CO3 + (cc)–H2CO3 reactants. However, as the energy of the (cc)–H2CO3…(cc)– H2CO3 reactant homodimer is lower than the energy of (ct)–H2CO3…(ct)–H2CO3 product homodimer and also, as the total energy of the isolated starting (cc)–H2CO3 + (cc)–H2CO3 reactants is lower than the total energy of the isolated final (ct)–H2CO3 + (ct)–H2CO3 products, the reaction equilibrium would be in favor of reactants not only at cold temperature but also at the room temperature. From our calculated potential energy diagram, it is seen that the energy difference between the initial starting (cc)–H2CO3 + (cc)–H2CO3 reactants and the final (ct)–H2CO3 + (ct)–H2CO3 products is ~3.2 kcal/mol. It is important to note here that this 3.2 kcal/mol energy difference corresponds to the concurrent isomerization of the two ACS Paragon Plus Environment

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(cc)–conformers of H2CO3 into their corresponding two (ct)–conformers. Further inspection of the potential energy diagram suggests that the population ratio of the (ct)–conformer with respect to its (cc)– conformer, produced via the sublimation of H2CO3 polymorphs, will go down at cold temperatures such as that present in cryogenic environment of the matrix isolation infrared spectroscopy or in the jet expansion. This is because at cold temperature, the bimolecular collision between two (ct)–conformers eventually would result the formation of (cc)–H2CO3…(cc)–H2CO3 homodimer and this is the most probable reason why only the (cc)–H2CO3…(cc)–H2CO3 homodimer, among the (cc)–H2CO3…(cc)– H2CO3 and (ct)–H2CO3…(ct)–H2CO3 homodimers, has been detected in the matrix isolated infrared spectroscopy of H2CO3 vapors, even though the binding energy of the (ct)–H2CO3…(ct)–H2CO3 homodimer is 1.7 kcal/mol higher than the binding energy of the (cc)–H2CO3…(cc)–H2CO3 homodimer. Given that the energetics of potential energy diagram is consistent with the experimental observation in the matrix isolated infrared spectroscopy of H2CO3 vapors, it is worthwhile to note here that the crystalline α–polymorph of H2CO3 is stable up to at least 200K, and the sublimation of the α– polymorph above the temperature 200K results its decomposition.28 Similarly, in case of the crystalline β–polymorph of H2CO3, this temperature is 230K.19 Therefore, for further support of the above mentioned interpretations of the potential energy diagram associated with the double hydrogen transfer within the eight-membered cyclic doubly H-bonded ring interface formed between two (cc)–conformers of H2CO3, we also analyze the MP2/aug-cc-pVTZ level calculated free energy profiles associated with this reaction mechanism in the temperature range from 180 to 280K. From our analysis, it is seen that results are consistent with the above mentioned interpretations of the potential energy diagram. The MP2/aug-cc-pVTZ level calculated values of free energies, enthalpies and entropies of all the species involved in the above mentioned potential energy diagram in the temperature range from 180 to 280K have been given in the supporting information (see Table S5). In supporting information, we also present the MP2/aug-cc-pVTZ level predicted relative values of enthalpies, entropies and free energies of the (ct)–conformer with respect to its (cc)–conformer and as well as the corresponding population ACS Paragon Plus Environment

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ratios between these two conformers in the temperature range from 180 to 280K (see Table S6); though it is known from the vast literature of carbonic acid that all the high levels of ab initio calculations overestimate unexpectedly the energy difference or the corresponding free energy difference between the two most stable conformers of H2CO3.48 Thus, keeping in mind that all the high levels of ab initio calculations including the calculations performed here overestimate unexpectedly only the relative energy difference between two most stable conformers of H2CO3, the energetics of the above mentioned potential energy diagram associated with the autocatalytic double hydrogen transfer reaction suggests that the isomerization of the (cc)–conformer via the double hydrogen transfer within the eightmembered cyclic doubly H-bonded ring interface formed between two (cc)–conformers of H2CO3 is allowed and potentially effective in comparison to the above mentioned bare (cc)–H2CO3 → (ct)– H2CO3 isomerization reaction via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer. Given that the above said autocatalytic path is energetically allowed and potentially effective for the isomerization of the (cc)–conformer to its (ct)–conformer, we next investigate the energetics of another possible autocatalytic mechanism in vapor phase that may also isomerize the (cc)–conformer to its (ct)–conformer. In this autocatalytic mechanism, we also consider the isomerizion of the (cc)– conformer in presence of the (cc)–conformer as represented by Reaction-1; but with the mechanism where one of the two identical OH functional groups present in the (cc)–conformer act as both the hydrogen donor and acceptor units like what water molecule does in the water assisted hydrogen transfer reaction.44-46 Therefore, it is worthwhile note here that this autocatalytic mechanism is different from the autocatalytic mechanism discussed above in terms of the numbers of atoms involved in the doubly Hbonded interface formed between the two (cc)–conformers of H2CO3. In the present mechanism, we have considered the double hydrogen transfer within the six-membered cyclic doubly H-bonded ring interface formed between the two (cc)–conformers, whereas the double hydrogen transfer in the above mentioned mechanism has been considered within the eight-membered cyclic doubly H-bonded ring ACS Paragon Plus Environment

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interface formed between the two (cc)–conformers. Therefore, to keep the discussion simple, we designate the autocatalytic path associated with the isomerization of the (cc)–conformer in presence of another (cc)–conformer via eight-membered cyclic doubly H-bonded ring interface formed between the two (cc)–conformers of H2CO3 as the Mechanism-1; and the autocatalytic path associated with the isomerization of the (cc)–conformer in presence of its (cc)–conformer via six-membered cyclic doubly H-bonded ring interface formed between the two (cc)–conformers of H2CO3 as the Mechanism-2. Like before, for the Mechanism-2, the MP2/aug-cc-pVTZ level optimized geometries of the starting (cc)– H2CO3…(cc)–H2CO3 reactant homodimer, the exit channel (ct)–H2CO3…(ct)–H2CO3 product homodimer and the six-membered ring cyclic TS associated with the (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)– H2CO3 unimolecular isomerization step via the double hydrogen transfer reaction have been shown in Fig, 5B. Similarly, for the Mechanism-2, the potential energy diagram for the double hydrogen transfer within the six-membered cyclic doubly H-bonded ring interface formed between the two (cc)– conformers of H2CO3, which result in two (ct)–conformers from the concurrent isomerization of the two (cc)–conformers, has been presented in Fig. 7. The MP2 level calculated barrier heights for the (cc)– H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step associated with the Mechanism-2 have been given in Table 3. From Fig. 7, it is seen that the MP2/aug-cc-pVTZ level predicted barrier height for the unimolecular isomerization step, which is the rate limiting step for the isomerization process as discussed above in case of the Mechanism-2, is ~10.6 kcal/mol. This value is substantially higher than the ~2.4 kcal/mol barrier height associated with Mechanism-1. Furthermore, we note that this barrier height is also higher than the barrier height associated with the above mentioned bare (cc)–H2CO3 → (ct)–H2CO3 unimolecular isomerization reaction via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer (Fig. 3). As noted above, the MP2/aug-cc-pVTZ level predicted barrier height for the bare (cc)–H2CO3 → (ct)–H2CO3 unimolecular isomerization step via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer is ~9.6 kcal/mol. It is also worthwhile to note here that the binding energy of the sixACS Paragon Plus Environment

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membered cyclic (cc)–H2CO3…(cc)–H2CO3 reactant homodimer, which determines its probability of formation via the bimolecular encounters between the two (cc)–conformers of H2CO3 associated with the Mechanism-2, is ~8.6 kcal/mol. This value is ~8.9 kcal/mol lower than the binding energy of the eight-membered cyclic (cc)–H2CO3…(cc)–H2CO3 reactant homodimer (~17.5 kcal/mol) associated with the Mechanism-1. Therefore, we conclude that the Mechanism-2, which eventually represents the simultaneous isomerization of two (cc)–conformers of H2CO3 into two (ct)–conformers, is not the effective one and a hindered process in the vapor phase in comparison to the Mechanism-1, as mentioned above. Next, it has been mentioned before from the results of noble gas matrix isolated infrared spectroscopy of carbonic acid vapors that the population of the (ct)–conformer with respect to the (cc)– conformer in case of vapor over the α–polymorphs of carbonic acid28 is 10% at 210K and for the vapor over the β–polymorphs of carbonic acid, this population varies from 10% to 20% at 260K.19 Therefore, we next investigate another possible autocatalytic mechanism by which the (cc)–H2CO3 → (ct)–H2CO3 isomerization may occur in presence of the (ct)–conformer. However, as noted above that the double hydrogen transfer process via the six-membered cyclic H-bonded ring interface (Mechanism-2) in comparison to the eight-membered cyclic doubly H-bonded ring interface (Mechanism-1) is substantially hindered, we consider here the autocatalytic (cc)–H2CO3 → (ct)–H2CO3 isomerization in presence of (ct)–conformer via only the eight-membered cyclic doubly H-bonded ring interface of the H2CO3 homodimer formed between the (cc)– and (ct)–conformers. Again, to keep the discussion simple, we designate this autocatalytic isomerization path as the Mechanism-3. Therefore, the Mechanism-3 or the autocatalytic mechanism by which the (cc)–conformer of H2CO3 isomerizes to its (ct)–conformer in presence of the (ct)–conformer in vapor phase can be explicitly written as follows: (cc)–H2CO3 + (ct)–H2CO3 ⇌ (cc)–H2CO3…(ct)–H2CO3 → (ct)–H2CO3…(cc)–H2CO3 ⇌ (ct)–H2CO3 + (cc)–H2CO3

(2)


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Like before, in the above reaction, the (cc)–H2CO3…(ct)–H2CO3 species is the pre-reactive entrance channel eight-membered cyclic doubly H-bonded homodimer that undergoes double hydrogen transfer via an eight-membered ring cyclic transition state (TS) to form the eight-membered cyclic doubly H-bonded (ct)–H2CO3…(cc)–H2CO3 homodimer in the exit channel. It is worthwhile to note here that like the (ct)–H2CO3…(ct)–H2CO3 homodimer, as mentioned above, the (cc)–H2CO3…(ct)–H2CO3 homodimer has not also been observed in the cold environment of matrix isolated infrared spectroscopy of the H2CO3 molecule.19,28 The MP2/aug-cc-pVTZ level optimized geometries of the starting (cc)– H2CO3…(ct)–H2CO3 reactant homodimer, the exit channel (ct)–H2CO3…(cc)–H2CO3 product homodimer and the TS associated with the (cc)–H2CO3…(ct)–H2CO3 → (ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization step of the Mechanism-3, are shown in Fig. 5C. In Fig. 8, we present the potential energy diagram for the double hydrogen transfer within the eight-membered cyclic doubly H-bonded ring interface formed between (cc) and (ct) conformers of H2CO3 that results the isomerization of both the (cc) and (ct) conformers into their respectively (ct) and (cc) conformers. The MP2 level calculated barrier heights for the (cc)–H2CO3…(ct)–H2CO3 → (ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization step via the double hydrogen transfer have been given in Table 3. From Fig. 8, it is seen that the autocatalytic double hydrogen transfer in the doubly H-bonded interface formed between the (cc) and (ct) conformers of H2CO3 occurs within symmetric double well potential. This is because the autocatalytic Mechanism-3, defined as the path by which the (cc)–conformer of H2CO3 isomerizes to its (ct)–conformer in presence of the (ct)–conformer, in the forward direction is identical with its reversed one—the isomerization of the (ct)–conformer of H2CO3 to its (cc)–conformer in presence of the (cc)– conformer. From our calculations, it is seen that the MP2/aug-cc-pVTZ level predicted barrier height for the (cc)–H2CO3…(ct)–H2CO3 → (ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization step is only 1.6 kcal/mol including ZPE correction. This value is lower than the value associated with the (cc)– H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step of the Mechanism-1. As noted above, the MP2/aug-cc-pVTZ level predicted barrier height for the (cc)–H2CO3…(cc)–H2CO3 ACS Paragon Plus Environment

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→ (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step associated with the Mechanism-1 is 2.4 kcal/mol. Therefore, it appears that the autocatalytic isomerization of the (cc)–conformer of H2CO3 via the Mechanism-3 is energetically favorable over the Mechanism-1. However, we note that the present autocatalytic Mechanism-3 is not the one to have an impact in the isomerization of the (cc)–conformer to its (ct)–conformer to begin with, especially, at the sources of H2CO3. This is because as the most possible structural motifs of crystalline H2CO3 polymorphs16,19 consist of only and exclusively the (cc)– conformers and also, as the sublimation of H2CO3 polymorphs result mostly the (cc)–conformer in vapor phase.19,28 Moreover, we note that if in any case the concentration of the (ct)–conformer goes up such as that observed in the noble gas matrix isolated infrared spectroscopy of carbonic acid vapors under the influence of UV/Vis radiation;19,28 it is most likely that the reverse reaction of the Mechanism-1 will be competitive and finally, the Mechanism-3 will be suppressed by the reversed reaction of the Mechanism1. This is not only because of the larger binding energy of the (ct)–H2CO3…(ct)–H2CO3 homodimer over the binding energy of the (cc)–H2CO3…(ct)–H2CO3 homodimer but also because of the low barrier height of the reversed (ct)–H2CO3…(ct)–H2CO3 → (cc)–H2CO3…(cc)–H2CO3 unimolecular isomerization step of the Mechanism-1 in comparison to the barrier height associated with the (cc)–H2CO3…(ct)– H2CO3 → (ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization step of Mechanism-2. Moreover, it is also worthwhile to note that the Mechanism-2 would not have any impact to change population ratio between the (cc) and (ct) conformers of H2CO3, as the reaction in the forward direction is equally probable with its reversed reaction. Therefore, we finally conclude that the autocatalytic Mechanism-1 via double hydrogen transfer within the eight-membered cyclic doubly H-bonded ring interface formed between two (cc)–conformers of H2CO3, as represented by the Reaction-1, is ultimately the starting path by which the isomerization of the (cc)–conformer of H2CO3 to its (ct)–conformer occurs, especially, during the sublimation of the H2CO3 polymorphs that result in the concentration of the (cc)–conformer in vapor phase at highest levels.19,28 It is worthwhile to note here that the most possible basic building blocks of crystalline H2CO3 polymorphs consist of only and exclusively the (cc)–conformers16,19 and the ACS Paragon Plus Environment

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sublimations of these crystalline H2CO3 polymorphs result in both the (cc)– and (ct)–conformers in vapor phase with the (cc)–conformer being as the major species.19,28 It is also worthwhile to note here that the energetics of the Mechanism-1, as revealed by the theoretical calculations presented here, is consistent with experimental observations of the matrix isolated infrared spectroscopy of the H2CO3 vapors.19,28

4. Summary and Conclusions: Carbonic acid (H2CO3), a small molecule of six atoms involving three elements in the periodic table, is right at the interface between organic and inorganic chemistry. We note what already has been noted by other research groups that this molecule is among several ubiquitous molecules of huge fundamental importance in many fields including astrophysics, marine-chemistry, geochemistry and medicine.1-48,61-64 Moreover, the detection of gas-phase interstellar H2CO3 as well as in earth’s troposphere has become an exciting challenge for a new generation of scientists.18-19,24 Theoretically, it has been shown in the literature15,39-46,48 that the cis-cis [(cc)] and cis-trans [(ct)] conformers of carbonic acid (H2CO3) are the two most stable conformers with the (cc)–conformer being at lower energy. These two conformers are different with respect to the orientations of two OH functional groups present in the molecule and the (ct)–conformer, which is slightly energetically disfavored over the (cc)–conformer, has been considered as the starting point for the decomposition of H2CO3 into CO2 and H2O molecules.39,4447

Depending upon the methods of calculations used, the calculated value of the relative energy

difference between these two most stable conformers including zero point energy correction (ZPE) is ~1.5-1.7 kcal/mol. Similarly, theoretical calculations also predict that the barrier height for the isomerization of the (cc)–conformer to its (ct)–conformer [(cc)–H2CO3 → (ct)–H2CO3] via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer is ~9.4-9.9 kcal/mol.39,44,48 Therefore, the formation of the (ct)–conformer of H2CO3 from its most stable (cc)– conformer via the rotation of the OH functional group, as mentioned above, is a hindered process in vapor phase. Experimentally, on the other hand, the infrared (IR) and Raman spectroscopy of the ACS Paragon Plus Environment

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crystalline H2CO3 polymorphs suggest that the most possible basic building blocks of the H2CO3 polymorphs12,16,19,27-29 consist of only and exclusively the (cc)–conformers and the sublimation of the crystalline H2CO3 polymorphs19,28 results the (cc)–H2CO3 → (ct)–H2CO3 interconversion in the view of the above note that the interconversion of the (cc)–conformer to its (ct)–conformer in vapor phase via the rotation of the OH functional group is a hindered process. In this article, we first report the high level of ab initio calculations investigating the energetics of the potential energy diagrams associated with the double hydrogen transfer within the doubly hydrogen-bonded (H-bonded) interface of the H2CO3 homodimers. More specifically, we have studied the energetics for the autocatalytic isomerizations of the (cc)–conformer to its (ct)–conformer [(cc)– H2CO3 → (ct)–H2CO3] in presence of both the (cc)– and (ct)–conformers those represent the simultaneous isomerizations of the two reactant conformers of H2CO3 into their two corresponding product conformers. In case of the autocatalytic (cc)–H2CO3 → (ct)–H2CO3 isomerization in presence of the (cc)–conformer, we have considered the isomerization mechanisms via double hydrogen transfer within both the six- and eight-membered cyclic doubly H-bonded ring interfaces formed between the two (cc) conformers. The calculations have been performed at the MP2 level of theory in conjunction with aug-cc-pVDZ, aug-cc-pVTZ, and 6-311++G(3df,3pd) basis sets. It is seen from our calculations at the MP2 level including zero point energy (ZPE) correction that the double hydrogen transfer within eight-membered cyclic doubly H-bonded ring interface is highly favorable over the double hydrogen transfer via six-membered cyclic doubly H-bonded ring interface. Moreover, we also find that the barrier height associated with the double hydrogen transfer within six-membered cyclic doubly H-bonded ring interface is higher than the above mentioned ~9.4-9.9 kcal/mol barrier height associated with the bare (cc)–H2CO3 → (ct)–H2CO3 isomerization reaction via the rotation of one of the two indistinguishable OH functional groups present in the (cc)–conformer. Therefore, we conclude that the double hydrogen transfer within six-membered cyclic doubly H-bonded ring interface, which eventually represents the simultaneous isomerization of two (cc)–conformers of H2CO3 into their two corresponding (ct)– ACS Paragon Plus Environment

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conformers, is not the effective and correct one. On the other hand and in contrary, it is seen from our calculation at the MP2/aug-cc-pVTZ level including ZPE correction that the barrier height for the double hydrogen transfer within the eight-membered cyclic doubly H-bonded ring interface of the (cc)– H2CO3…(cc)–H2CO3 homodimer, associated with the rate limiting (cc)–H2CO3…(cc)–H2CO3 → (ct)– H2CO3…(ct)–H2CO3 unimolecular isomerization step for autocatalytic isomerization of the (cc)– conformer in presence of another (cc)–conformer, is only ~2.4 kcal/mol. Similarly, in case of another possible autocatalytic isomerization mechanism via the double hydrogen transfer within the eightmembered cyclic doubly H-bonded ring interface of the (cc)–H2CO3…(ct)–H2CO3 homodimer formed between the (cc)– and (ct)–conformers of H2CO3, the barrier height for the rate limiting (cc)– H2CO3…(ct)–H2CO3 →

(ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization step, is only ~1.6

kcal/mol. Clearly, these values are substantially lower than the ~9.4-9.9 kcal/mol barrier height associated with the bare (cc)–H2CO3 → (ct)–H2CO3 isomerization via the rotation of one of the two indistinguishable OH functional groups as mentioned above. It is worthwhile to note that the predicted barrier height for the bare (cc)–H2CO3 → (ct)–H2CO3 isomerization via the rotation of one of the two indistinguishable OH functional groups present within the (cc)–H2CO3 at the MP2/aug-cc-pVTZ level of calculation including ZPE correction is ~9.6 kcal/mol. Moreover, it appears that among the two above mentioned autocatalytic mechanisms via the eight-membered cyclic doubly H-bonded ring interfaces, the autocatalytic isomerization of the (cc)–conformer to its (ct)–conformer in presence of the (ct)– conformer is energetically favorable to some extent over the other mechanism. However, as the infrared (IR) and Raman spectroscopy of the crystalline H2CO3 polymorphs12,16,19,27-29 suggest that the most possible basic building blocks of the H2CO3 polymorphs consist of only and exclusively the (cc)– conformers and also, as the (cc)–conformer exists as the major species in vapor phase during the sublimation of these polymorphs, we conclude that the autocatalytic isomerization of the (cc)–conformer to its (ct)–conformer in presence of another (cc)–conformer via double hydrogen transfer within the eight-membered cyclic doubly H-bonded homodimer formed between two (cc)–conformers of H2CO3 is ACS Paragon Plus Environment

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ultimately the starting mechanism that occurs during the sublimation of H2CO3 polymorphs. It is also worthwhile to note that these autocatalytic mechanisms are not expected to be the primary mechanisms in the Earth’s atmosphere or in the surroundings away from the source points of H2CO3. This follows as concentrations of both the conformers of H2CO3 or the probability of bimolecular collisions between two H2CO3 molecules is expected to significantly fall off due to dilution of carbonic acid concentration resulting in presence of other various species in earth atmosphere.

Acknowledgement: Financial support from the BARD project (PIC No: 12-R&D-SIN-5.04-0103), Department of Atomic Energy, Government of India, is gratefully acknowledged.

Supporting Information Available: The computed total electronic energies (Etotal), ZPE corrected electronic energies [Etotal(ZPE)], relative energies, free energies, enthalpies, entropies, barrier heights associated with the isomerization of the (cc)–conformer to its (ct)–conformer via the rotation of OH functional group, imaginary frequencies of various Transition states (TS) as well as the rotational constants of the homodimers at the MP2 level of calculations as mentioned in the text. This material is available free of charge via the Internet at http://pubs.acs.org.


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A Polymorph of Carbonic Acid and Its Possible

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32. Moore, M. H.; Khanna, R. K. Infrared and Mass Spectral Studies of Proton Irradiated H2O + CO2 Ice: Evidence for Carbonic Acid. Spectrochim. Acta, Part A 1991, 47A, 255-262. 33. Brucato, J. R.; Palumbo, M. E.; Strazzulla, G.

Carbonic Acid by Ion Implantation in

Water/Carbon Dioxide Ice Mixtures. Icarus 1997, 125, 135-144. 34. Strazzulla, G.; Leto, G.; Spinella, F.; Gomis, O. Production of Oxidants by Ion Irradiation of Water/Carbon Dioxide Frozen Mixtures. Astrobiology 2005, 5, 612-621. 35. Gerakines, P. A.; Moore, M. H.; Hudson, R. L. Carbonic Acid Production in H2O:CO2 Ices. UV Photolysis vs. Proton Bombardment. Astron. Astrophys. 2000, 357, 793-800. 36. Wu, C. Y. R.; Judge, D. L.; Cheng, B.-M.; Yih, T.-S.; Lee, C. S.; Ip, W. H. Extreme Ultraviolet Photolysis of CO2 - H2O Mixed Ices at 10 K . J. Geophys. Res. [Planets] 2003, 108, 5032. 37. Garozzo, M.; Fulvio, D.; Gomis, O.; Palumbo, M. E.; Strazzulla, G. H-Implantation in SO2 and CO2 Ices. Planet. Space Sci. 2008, 56, 1300-1308. 38. Oba, Y.; Watanabe, N.; Kouchi, A.; Hama, T.; Pirronello, V. Formation of Carbonic Acid (H2CO3) by Surface Reactions of Non-Energetic OH Radicals with CO Molecules at Low Temperatures. Astrophys. J. 2010, 722, 1598-1606. 39. Mori, T.; Suma, K.; Sumiyoshi, Y.; Endo, Y. Spectroscopic Detection of Isolated Carbonic Acid. J. Chem. Phys. 2009, 130, 204308. 40. Loerting, T.; Bernard, J. Aqueous Carbonic Acid (H2CO3). ChemPhysChem 2010, 11, 23052309. 41. Mori, T.; Suma, K.; Sumiyoshi, Y.; Endo, Y. Spectroscopic Detection of the Most Stable Carbonic Acid, cis-cis H2CO3. J. Chem. Phys. 2011, 134, 044319. 42. Kumar, P. P.; Kalinichev, A. G.; Kirkpatrick, R. J. Dissociation of Carbonic acid: Gas Phase Energetics and Mechanism From ab initio Metadynamics Simulations. J. Chem. Phys. 2007, 126, 204315.


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43. Ballone, P.; Montanari, B.; Jones, R. O. Density Functional Study of Carbonic Acid Clusters. J. Chem. Phys. 2000, 112, 6571-6575. 44. de Marothy, S. A. Autocatalytic Decomposition of Carbonic Acid. Int. J. Quant. Chem. 2013, 113, 2306-2311. 45. Loerting, T.; Tautermann, C.; Kroemer, R. T.; Kohl, I.; Hallbrucker, A.; Mayer, E.; Liedl, K. R. On the Surprising Kinetic Stability of Carbonic Acid (H2CO3). Angew. Chem. Int. Ed. 2000, 39, 891-894. 46. Tautermann, C. S.; Voegele, A. F.; Loerting, T.; Kohl, I.; Hallbrucker, A.; Mayer, E.; Liedl, K. R. Towards the Experimental Decomposition Rate of Carbonic Acid (H2CO3) in Aqueous Solution. Chem. Eur. J. 2002, 8, 66-73. 47. Ghoshal, S.; Hazra, M. K. New Mechanism for Autocatalytic Decomposition of H2CO3 in the Vapor Phase J. Phys. Chem. A. 2014, 118, 2385-2392. 48. Schwerdtfeger, C. A.; Mazziotti, D. A. Population of Carbonic Acid Isomers at 210 K from a Fast Two-electron Reduced-Density Matrix Theory. J. Phys. Chem. A. 2011, 115, 12011-12016. 49. Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A. et al. Gaussian 09, Revision B.01, Gaussian, Inc., Wallingford, CT, 2010. 50. Galano, A.; Alvarez-Idaboy, J. R. A New Approach to Counterpoise Correction to BSSE. J. Comput. Chem. 2006, 27, 1203-1210. 51. Alvarez-Idaboy, J. R.; Galano, A. Counterpoise Corrected Interaction Energies are not Systematically Better than Uncorrected Ones: Comparison with CCSD(T) CBS Extrapolated Values. Theor. Chem. Acc. 2010, 126, 75-85. 52. Liedl, K. R.; Sekusak, S.; Mayer, E. Has the Dimer of Carbonic Acid a Lower Energy Than Its Constituents Water and Carbon Dioxide? J. Am. Chem. Soc. 1997, 119, 3782-3784.


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53. Reimann, B.; Buchhold, K.; H.-D. Barth, H.-D.; Brutschy, B.; Tarakeshwar, P.; Kim, K. S. Anisole-(H2O)n (n = 1–3) Complexes: An Experimental and Theoretical Investigation of the Modulation of Optimal Structures, Binding Energies, and Vibrational Spectra in Both the Ground and First Excited States. J. Chem. Phys. 2002, 117, 8805-8822. 54. Hazra, M. K.; Sinha, A. Formic Acid Catalyzed Hydrolysis of SO3 in the Gas Phase: A Barrierless Mechanism for Sulfuric Acid Production of Potential Atmospheric Importance. J. Am. Chem. Soc. 2011, 133, 17444-17453. 55. Long, B.; Long, Z-w.; Wang, Y-b.; Tan, X-f.; Han, Y-h.; Long, C-y.; Qin, S-j.; Zhang, W-j. Formic Acid Catalyzed Gas-Phase Reaction of H2O with SO3 and the Reverse Reaction: A Theoretical Study. Chem.Phys.Chem. 2011, 13, 323-329. 56. Buszek, R. J.; Sinha, A.; Francisco, J. S. The Isomerization of Methoxy Radical: Intramolecular Hydrogen Atom Transfer Mediated through Acid Catalysis. J. Am. Chem. Soc. 2011, 133, 20132015. 57. Hazra, M. K.; Francisco, J. S.; Sinha, A. Computational Study of Hydrogen-bonded Complexes of HOCO with Acids: HOCO· · ·HCOOH, HOCO· · ·H2SO4, and HOCO· · ·H2CO3. J. Chem. Phys. 2012, 137, 064319. 58. da Silva, G. Carboxylic Acid Catalyzed Keto-Enol Tautomerizations in the Gas Phase. Angew. Chem. Int. Ed. 2010, 49, 7523-7525. 59. Hazra, M. K.; Chakraborty, T. Formamide Tautomerization: Catalytic Role of Formic Acid. J. Phys. Chem. A 2005, 109, 7621-7625. 60. Hazra, M. K.; Chakraborty, T. 2-Hydroxypyridine ↔ 2-Pyridone Tautomerization: Catalytic Influence of Formic Acid. J. Phys. Chem. A 2006, 110, 9130-9136; 61. Khanna, A.; Kurtzman, N. A. Metabolic Alkalosis. J. Nephrol. 2006, 19, 86-96. 62. Swietach, P.; Vaughan-Jones, R. D.; Harris, A. L. Regulation of Tumor pH and the Role of Carbonic Anhydrase 9. Cancer Metast. Rev. 2007, 26, 299-310. ACS Paragon Plus Environment

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63. Vaughan-Jones, R. D.; Spitzer, K. W.; Swietach, P. Intracellular pH Regulation in Heart. J. Mol. Cell. Cardiol. 2009, 46, 318-331. 64. Liamis, G.; Milionis, H. J.; Elisaf, M. Pharmacologically-Induced Metabolic Acidosis: A Review. Drug Saf. 2010, 33, 371-391.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 1: Optimized bond lengths (Å), angles (Degrees) and rotational constants (MHz) of the two most stable conformers of carbonic acid as shown in Figure 1. The values have been computed at the MP2 level in conjunction with aug-cc-pVDZ, aug-cc-pVTZ and 6311++G(3df,3pd) basis sets. For comparison, we have also included the corresponding experimental values from Ref. 39 and 41.

Geometrical Parameters C1—O2 C1—O3 C1—O4 O3—H5 O4—H6 O2—C1—O3 O2—C1—O4 C1—O3—H5 C1—O4—H6 A B C

MP2/augcc-pVDZ 1.218 1.351 1.351 0.971 0.971 126.1 126.1 105.5 105.5 11651.79 11215.96 5714.86

(cc)–H2CO3 MP2/aug- MP2/6-311+ cc-pVTZ +G(3df,3pd) 1.208 1.205 1.340 1.336 1.340 1.336 0.967 0.964 0.967 0.964 125.9 125.9 125.9 125.9 105.6 105.6 105.6 105.6 11879.01 11954.25 11360.53 11398.68 5806.99 5834.93

Experimental Values 1.202 1.340 1.340 0.968 0.968 125.7 125.7 105.7 105.7 11997.055 11308.380 5813.828

MP2/augcc-pVDZ 1.209 1.369 1.350 0.971 0.970 125.5 124.1 105.8 108.4 11559.32 11217.38 5692.89


(ct)–H2CO3 MP2/aug- MP2/6-311+ cc-pVTZ +G(3df,3pd) 1.199 1.196 1.357 1.354 1.339 1.336 0.967 0.964 0.966 0.963 125.4 125.3 124.2 124.2 106.0 106.0 108.5 108.6 11756.09 11815.57 11389.10 11441.29 5784.84 5812.71

Experimental Values 1.187 1.344 1.356 0.968 0.968 126.78 122.94 106.1 108.6 11778.680 11423.134 5792.074

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Page 28 of 40

Table 2: Zero point vibrational energy (ZPE) corrected binding energies of all the hydrogen-bonded homodimers of H2CO3 associated with the Mechanism-1, 2 & 3, as mentioned in the text, at the MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ, MP2/6-311++G(3df,3pd) level of calculations. Binding energies of the homodimers have been calculated by subtracting the total electronic energies of monomers forming the homodimers from the calculated energies of the homodimers. Normal mode vibrational frequency calculations at the MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ and MP2/6-311++G(3df,3pd) level have been performed to estimate the respective zero point energy (ZPE) corrections. The values have been given in kcal/mol.

Homodimers (cc)–H2CO3…(cc)–H2CO3 (ct)–H2CO3…(ct)–H2CO3 [(cc)–H2CO3…(cc)–H2CO3] a [(ct)–H2CO3…(ct)–H2CO3] a (cc)–H2CO3…(ct)–H2CO3

MP2/aug-cc-pVDZ 17.07 18.71 8.59 9.64 17.80

MP2/aug-cc-pVTZ 17.52 19.21 8.60 9.74 18.27

MP2/6-311++G (3df,3pd) 17.41 19.17 8.46 9.58 18.19

The binding energies for the (cc)–H2CO3…(cc)–H2CO3 reactant homodimer and the exit channel (ct)–H2CO3…(ct)–H2CO3 product homodimer associated with the Mechanism-2, as mentioned in the text.

a


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


Table 3: Zero point vibrational energy (ZPE) corrected barrier heights for the (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 and (cc)–H2CO3…(ct)–H2CO3 → (ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization steps associated with the Mechanism-1, 2 & 3 at the MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ, MP2/6-311++G(3df,3pd) level of calculations, as mentioned in the text. The values have been given in kcal/mol and normal mode vibrational frequency calculations at the MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ and MP2/6-311++G(3df,3pd) levels have been performed to estimate the respective zero point energy (ZPE) corrections. The values in parenthesis are the relative energies of the transition states (TSs) with respect to reactants those are involved in bimolecular collision as discussed in the text. For an example, the MP2/ aug-cc-pVTZ level of calculation incorporating ZPE correction predict that the TS associated with the (cc)–H2CO3…(ct)–H2CO3 → (ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization step is being 16.68 kcal/mol lower in energy (indicated by negative sign) than the total energy of the isolated (cc)–H2CO3 + (ct)–H2CO3 reactants.

Unimolecular Isomerization Steps

MP2/aug-cc-pVDZ

MP2/aug-cc-pVTZ

MP2/6-311++G(3df,3pd)

(cc)–H2CO3…(cc)-H2CO3 → (ct)–H2CO3…(ct)–H2CO3

3.09 (-13.98)

2.38 (-15.14)

2.48 (-14.93)

[(cc)–H2CO3…(cc)-H2CO3 → (ct)–H2CO3…(ct)–H2CO3] a

12.52 (+3.93)

10.56 (+1.96)

10.76 (+2.3)

(cc)–H2CO3…(ct)-H2CO3 → (ct)–H2CO3…(cc)–H2CO3

2.33 (-15.47)

1.59 (-16.68)

1.70 (-16.49)

The barrier heights for the (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step associated with the Mechanism-2, as mentioned in the text.

a


29


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Page 30 of 40

Figure captions: Figure 1: Two most stable conformers of H2CO3. Geometries have been optimized at the MP2/aug-ccpVTZ level of calculations. Figure 2: Visualization of the two most possible basic building blocks of the two distinct α– and β– polymorphs of H2CO3. (Ref: 16 & 19) Figure 3: Potential energy profile for the isomerization of the cis–cis conformer of H2CO3 [(cc)–H2CO3] to its cis–trans conformer [(ct)–H2CO3] via the rotation of one of the two indistinguishable OH functional groups presents in the (cc)–H2CO3 conformer. The energy profile has been calculated at the MP2/aug-cc-pVTZ level of theory with zero point vibration energy (ZPE) corrections. Figure 4: Visualization of the isomerization of the cis–cis conformer of H2CO3 [(cc)–H2CO3] to its cis– trans conformer [(ct)–H2CO3] via the intramolecular hydrogen atom transfer from either one of the two OH functional groups to the oxygen atom of the C=O functional group present within the (cc)–H2CO3. Figure 5: (A) The MP2/aug-cc-pVTZ level optimized geometries of the starting eight-membered cyclic (cc)–H2CO3…(cc)–H2CO3 reactant homodimer, the exit channel eight-membered cyclic (ct)– H2CO3…(ct)–H2CO3 product homodimer and the eight-membered cyclic ring TS associated with the (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step via the double hydrogen transfer (Mechanism-1 via Reaction-1). (B) The MP2/aug-cc-pVTZ level optimized geometries of the starting six-membered cyclic (cc)–H2CO3…(cc)–H2CO3 reactant homodimer, the exit channel six-membered cyclic (ct)–H2CO3…(ct)–H2CO3 product homodimer and the six-membered cyclic ring TS associated with the (cc)–H2CO3…(cc)–H2CO3 → (ct)–H2CO3…(ct)–H2CO3 unimolecular isomerization step via the double hydrogen transfer (Mechanism-2 via Reaction-1). (C) The MP2/augcc-pVTZ level optimized geometries of the starting eight-membered cyclic (cc)–H2CO3…(ct)–H2CO3 reactant homodimer, the exit channel eight-membered cyclic (ct)–H2CO3…(cc)–H2CO3 product homodimer and the eight-membered cyclic ring TS associated with the (cc)–H2CO3…(ct)–H2CO3 → (ct)–H2CO3…(cc)–H2CO3 unimolecular isomerization step via the double hydrogen transfer (Mechanism3 via Reaction-2). Figure 6: Potential energy profile for the autocatalytic isomerization of the (cc)–conformer of H2CO3 in presence of another (cc)–conformer via double hydrogen transfer within the eight-membered doubly Hbonded ring interface (Mechanism-1), which result two (ct)–conformers of H2CO3 together from the


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concurrent isomerization of the two (cc)–conformers involved in the reaction in terms of bimolecular collision (Reaction-1). The energy profile has been calculated at the MP2/aug-cc-pVTZ level of theory with ZPE corrections. Figure 7: Potential energy profile for the autocatalytic isomerization of the (cc)–conformer of H2CO3 in presence of another (cc)–conformer via double hydrogen transfer within the six-membered doubly Hbonded ring interface (Mechanism-2), which result two (ct)–conformers of H2CO3 together from the concurrent isomerization of the two (cc)–conformers involved in the reaction in terms of bimolecular collision (Reaction-1). The energy profile has been calculated at the MP2/aug-cc-pVTZ level of theory with ZPE corrections. Figure 8: Potential energy profile for the autocatalytic isomerization of the (cc)–conformer of H2CO3 in presence of its (ct)–conformer (Mechanism-3) via the double hydrogen transfer within the eightmembered doubly H-bonded ring interface of the (cc)–H2CO3…(ct)–H2CO3 reactant homodimer (Reaction-2) . The energy profile has been calculated at the MP2/aug-cc-pVTZ level of theory with ZPE corrections.


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Figure 1:

6

2

2 4 1

4

1

6 3

3

5

(cc)–H2CO3

5

(ct)–H2CO3


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Figure 2:

α–H2CO3

β–H2CO3


33


Figure 3:

10

TS

8

6 9.6

4

(ct)–H2CO3

2

1.6

Relative Energy (Kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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(cc)–H2CO3

0


34

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Figure 4:

(cc)–H2CO3


(ct)–H2CO3

35


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Figure 5: (A)

(cc)–H2CO3…(cc)–H2CO3

TS

(ct)–H2CO3…(ct)–H2CO3

TS


(B)

(cc)–H2CO3…(cc)–H2CO3 (C)

(cc)–H2CO3…(ct)–H2CO3

TS


(ct)–H2CO3…(cc)–H2CO3

36

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Figure 6:

(cc)–H2CO3 + (cc)–H2CO3 → (ct)–H2CO3 + (ct)–H2CO3 [Mechanism-1] (ct)–H2CO3 + (ct)–H2CO3

2 0

3.2

4 (cc)–H2CO3 + (cc)–H2CO3

-2

-6 -8

19.2

-4 17.5


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-10 -12 -14

TS

-16 -18

2.4 (cc)–H2CO3

…(cc)–H

2CO3

1.5 (ct)–H2CO3


…(ct)–H

2CO3

37


Figure 7: (cc)–H2CO3 + (cc)–H2CO3 → (ct)–H2CO3 + (ct)–H2CO3 [Mechanism-2]

4

(ct)–H2CO3 + (ct)–H2CO3 TS (cc)–H2CO3 + (cc)–H2CO3

9.7

0

3.2

2

-4

10.6

-2 8.6

-6 2.1


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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-8



-10


38

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Figure 8: (cc)–H2CO3 + (ct)–H2CO3 → (ct)–H2CO3 + (cc)–H2CO3 [Mechanism-3]

0

(cc)–H2CO3 + (ct)–H2CO3

(ct)–H2CO3 + (cc)–H2CO3

-2 -4 -6

-10

18.3

-8 18.3


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


-12 -14 -16

TS

1.6

-18 -20

(cc)–H2CO3…(ct)–H2CO3

(ct)–H2CO3…(cc)–H2CO3


39


Graphical Abstract

(cc)–H2CO3 + (cc)–H2CO3 → (ct)–H2CO3 + (ct)–H2CO3 4


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(cc)–H2CO3 + (cc)–H2CO3

(ct)–H2CO3 + (ct)–H2CO3

0 -4 -8

-1 2

TS

-1 6 -2 0




40

Autocatalytic Isomerizations of the Two Most Stable Conformers of

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