New Mechanism for Autocatalytic Decomposition of H2CO3 in the

Mar 11, 2014 - The present study suggests that this new decomposition mechanism is effectively a near-barrierless process at room temperature and make...
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New Mechanism for Autocatalytic Decomposition of H2CO3 in the Vapor Phase Sourav Ghoshal and Montu K. Hazra* Chemical Sciences Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Kolkata 700064, India S Supporting Information *

ABSTRACT: In this article, we present high level ab initio calculations investigating the energetics of a new autocatalytic decomposition mechanism for carbonic acid (H2CO3) in the vapor phase. The calculation have been performed at the MP2 level of theory in conjunction with aug-cc-pVDZ, aug-ccpVTZ, and 6-311++G(3df,3pd) basis sets as well as at the CCSD(T)/aug-cc-pVTZ level. The present study suggests that this new decomposition mechanism is effectively a nearbarrierless process at room temperature and makes vapor phase of H2CO3 unstable even in the absence of water molecules. Our calculation at the MP2/aug-cc-pVTZ level predicts that the effective barrier, defined as the difference between the zero-point vibrational energy (ZPE) corrected energy of the transition state and the total energy of the isolated starting reactants in terms of bimolecular encounters, is nearly zero for the autocatalytic decomposition mechanism. The results at the CCSD(T)/aug-cc-pVTZ level of calculations suggest that the effective barrier, as defined above, is sensitive to some extent to the levels of calculations used, nevertheless, we find that the effective barrier height predicted at the CCSD(T)/aug-cc-pVTZ level is very small or in other words the autocatalytic decomposition mechanism presented in this work is a near-barrierless process as mentioned above. Thus, we suggest that this new autocatalytic decomposition mechanism has to be considered as the primary mechanism for the decomposition of carbonic acid, especially at its source, where the vapor phase concentration of H2CO3 molecules reaches its highest levels.

I. 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 among several ubiquitous molecules of huge fundamental importance in many fields including astrophysics, marine-chemistry, geochemistry, and medicine.1−36 Carbonic acid was long believed to be an unstable and elusive species as it decomposes rapidly into CO2 and H2O molecules.9−11 In aqueous solution, its detection for formation and/or decomposition has been possible only by using fast and ultrafast spectroscopic techniques.12,13 In the past, it had also been believed that isolated H2CO3 cannot exist in the free sate.9,10 In 1987, Terlouw et al.11 were the first to detect the free H2CO3 molecule in gas phase from the thermolysis of ammonium bicarbonate (NH4HCO3) via mass spectrometry, and hence, thereafter, the evidence for the possible existence of H2CO3 in gas phase was established. Subsequently in the next two and half decades the α- and β-carbonic acid, which are known to date as the two distinct polymorphs of H2CO3,6,14−20 have been synthesized by acid−base chemistry at cryogenic temperatures in many occasions.4,6,14−18,20 In the gas phase, the rotationally resolved spectra for the two most stable conformers of H2CO3, as shown in the Figure 1, have been measured recently by Mori et al.21,22 in the cold supersonic jet environment. Furthermore © 2014 American Chemical Society

Figure 1. Two most stable conformers of H2CO3.31 Geometries have been optimized at the MP2/aug-cc-pVTZ level of calculations.

and more importantly, the β-polymorphs, which are formed in outer space,20,32,33 have also been synthesized by using highenergy proton (H), helium (He), and UV irradiations of CO2/ H2O ice mixture2,23−28 as well as by H implantation of pure CO2 ice under the cold cryogenic environment similar to those encountered in the extraterrestrial space25,29 and also by the surface reaction of CO molecules with nonenergetic OH radical at 10−40 K.30 Thus, the H2CO3 molecule has profound astrophysical as well as environmental significance as both H2O and CO2 coexists in various astrophysical environments such as ice grain mantles in interstellar medium.1−36 It is also believed to be present in cirrus clouds in the Earth’s atmosphere, on Received: December 14, 2013 Revised: March 5, 2014 Published: March 11, 2014 2385

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aug-cc-pVDZ level that at least three water molecules are required to come closer to experimental decomposition rate with the decomposition reaction mechanism involving one water molecule actively and the remaining two water molecules as passively to stabilize the TS with respect to reactants. However, the characterization of both the crystalline α- and βcarbonic acid by means of infrared spectroscopy as well as Raman spectroscopy6,14−18,20 in the cold environment (80−250 K) shows that the α-polymorphs17 sublime without decomposition up to at least 200 K and that the β-polymorphs20 sublime without decomposition up to at least 230 K. It is important to note here that during the course of the measurement of infrared and Raman spectra of both the αand β-polymorphs of H2CO3, synthesized by acid−base chemistry at cryogenic temperatures as mentioned above, the excess reactant solvents including acid as well as the traces of ice and/or air moisture accumulated on the windows have been removed as much as possible by heating the samples in vacuum.6,14−18,20 Therefore, it is natural to inquire how the pure and isolated H2CO3 decomposes in the water restricted environment and what could be the mechanism for its rapid decomposition when the concentration of H2CO3 in vapor phase is high such as that occurs during the sublimation of the α- or β-polymorphs of H2CO3. We note that decomposition of the isolated cis−trans H2CO3 occurs via the transfer of a hydrogen atom from an OH group to the oxygen atom of another OH group as shown in Figure 2. The water molecule because of its simultaneous hydrogen donor and acceptor capability promotes this hydrogen transfer process.35,36 Therefore, various acids those have both the hydrogen donor and acceptor functional groups, such as those present in formic acid (HCOOH), should facilitate the above said hydrogen atom transfer process similar to that of a water molecule. Given that there are several possibilities in the presence of various acids, we focus here upon the investigation of energitics for the autocatalytic decomposition mechanism of the cis−trans conformer of H2CO3, as the H2CO3 molecule itself has both the hydrogen donor and acceptor units to promote the hydrogen transfer process required for its decomposition. Second, we note that the autocatalytic decomposition mechanism of H2CO3 molecule may also provide a clear idea to space scientists toward the possible detection of H2CO3 molecule in its source points at Earth’s surface as well as in the outer space, where the concentrations of H2CO3 are expected to be high. We note that the autocatalytic decomposition of H2CO3 has been investigated recently37 and that the mechanism which has been considered is not effective like what we present below.

Venus and Martian surfaces, as well as in Comets and the Galilean satellites.6,15−20,34 Indeed, as noted by Kohl et al.,16 a comparison of the spectra of carbonic acid on Mars with the IR spectrum of β-H2CO3 suggests that the β-H2CO3 is present on the Martian surface.5 Given that the isolated H2CO3 monomer has been detected in various experimental conditions in laboratory similar to those encountered in the extraterrestrial space, it is surprising that it has not been detected yet in interstellar clouds or at its source points either in the solid or in the gas phase.20,30,34 We note, what already had been emphasized by Hudson et al.7 and Huber et al.,34 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. It is only hoped that one day, in the near future, it will be detected as scientists get success in measuring the infrared spectra of the vapor phase H2CO3 resulted from the sublimations of both of its α- and βpolymorphs at cryogenic temperatures.17,20 From the results of high levels of theoretical calculations, it is seen that the H2CO3 monomer has three conformers, and among these three conformers, cis−cis and cis−trans conformers (Figure 1) are respectively the global minimum and the second most stable one.31 Experimentally, the noble gas matrix isolated infrared spectroscopy of both the α- and β-carbonic acid vapors,17,20 produced respectively from the sublimations of crystalline α- and β-carbonic acids, show that the population of the cis−trans conformer with respect to the cis−cis conformer in case of α-carbonic acid is 10% at 210 K, and for β-carbonic acid, it varies from 10% to 20% at 250 K. It is worth noting here that the cis−trans conformer, which is slightly energetically disfavored over the cis−cis conformer, has been considered as a starting point for the decomposition of H2CO3 into CO2 and H2O molecules.35,36 Furthermore, we note that though the population of the cis−trans conformer with respect to the cis− cis conformer in the matrix isolated experiments is only ∼10 to 20%; nevertheless, the cis−trans conformer may be the major component under different conditions in nature such as under the influence of UV/Vis radiation, as the cis−trans conformer is formed at the cost of cis−cis conformer upon the UV irradiation of both α- and β-H2CO3 trapped in the noble gas matrixes.17,20 Theoretical calculation also predicts that the isolated cis−trans H2CO3 is kinetically very stable due to high barrier height (∼37 kcal/mol, Figure 2) associated with its unimolecular decomposition reaction, and the calculated half-life of the cis−trans H2CO3 is estimated to be ∼0.18 million years at room temperature.35,36 In aqueous phase, it is found from the polarized continuum model (PCM) calculation36 at the MP2/aug-cc-pVDZ//MP2/

II. COMPUTATIONAL METHODS Gaussian09 suite of program with “opt=tight” convergence criteria has been used to carry out all the quantum chemistry calculations presented here.38 Both the geometry optimizations and frequency calculations have been performed using the second order Møller−Plesset (MP2) perturbation theory in conjunction with aug-cc-pVDZ, aug-cc-pVTZ, and 6-311+ +G(3df,3pd) basis sets. It is worthwhile to note that geometry optimizations using the larger basis set are required to reduce basis set superposition error (BSSE), even though full (100%) counterpoise corrections often underestimate binding energies of dimeric complexes.39−42 Transition states (TS) have been located using the QST2/QST3 routines as implemented in the Gaussian09 program. Furthermore, intrinsic reaction coordi-

Figure 2. Potential energy profile for the gas phase decomposition of isolated H2CO3. The energy profile has been calculated at the MP2/ aug-cc-pVTZ level of theory with zero-point vibration energy (ZPE) corrections. 2386

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Table 1. Zero-Point Vibrational Energy (ZPE) Corrected Binding Energies (kcal/mol) of All the Hydrogen-Bonded (HBonded) Complexes at the MP2 Level of Theory in Conjunction with the aug-cc-pVDZ, aug-cc-pVTZ, and 6-311++G(3df,3pd) Basis Sets As Well As at the CCSD(T)/aug-cc-pVTZ Level of Calculationsa complexes

MP2/aug-cc-pVDZ

CO2···H2O cis−trans H2CO3···cis−cis H2CO3 cis−trans H2CO3···cis−trans H2CO3 CO2···H2O···cis−trans H2CO3 CO2···H2O···cis−cis H2CO3 cis−trans H2CO3···H2O (H2O)2 (H2O)3 (H2O)4 cis−trans H2CO3···H2O···(H2O)2 CO2···(H2O)4 cis−trans H2CO3···cis−trans H2CO3 CO2···H2O···CO2···H2O

12.01 12.30 11.05 10.58

MP2/aug-cc-pVTZ

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

CCSD(T)/aug-cc-pVTZ

12.04 12.34 10.71 10.32

12.23 12.46 11.35 10.89

2.04 12.19 12.47 10.89 10.43 7.25 3.08 10.86 20.30 13.20b (12.66)c 3.07d 8.05e 9.98f (5.89)g

a

Except other than those labeled below, the binding energies for a particular binary, ternary, and quaternary H-bonded complexes have been calculated by subtracting the total electronic energies of monomers forming the complex from the calculated energy of that complex. 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 ZPE correction in the case of the CCSD(T)/aug-cc-pVTZ level of calculations has been done from the MP2/aug-cc-pVTZ level predicted ZPE correction. bBinding energy for the cis−trans H2CO3···H2O···(H2O)2 complex, when it is formed from the cis−trans H2CO3···H2O + (H2O)2 reactants. cBinding energy for the cis−trans H2CO3···H2O···(H2O)2 complex when it is formed from the cis−trans H2CO3 + (H2O)3 reactants. dBinding energy for the CO2···(H2O)4 complex when it is formed from the CO2 + (H2O)4 reactants. e Binding energy for the cis−trans H2CO3···cis−trans H2CO3 complex according to ref 37 (see Figure 5). fBinding energy for the CO2···H2O···CO2··· H2O complex, when it forms from two CO2 and two H2O molecules via quaternary collision. gBinding energy for the CO2···H2O···CO2···H2O complex, when it forms from two CO2···H2O complexes.

Table 2. Zero-Point Vibrational Energy (ZPE) Corrected Barrier Heights (kcal/mol) for the Various Unimolecular Isomerization Reactions at the MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ, and MP2/6-311++G(3df,3pd) Level of Calculations As Well As at the CCSD(T)/aug-cc-pVTZ Level of Calculationsa unimolecular isomerization steps cis−trans cis−trans cis−trans cis−trans cis−trans

H2CO3 → CO2···H2O H2CO3···cis−cis H2CO3 → CO2···H2O···cis−trans H2CO3 H2CO3···cis−trans H2CO3 → CO2···H2O···cis−cis H2CO3 H2CO3···H2O···(H2O)2 → CO2···(H2O)4 H2CO3···cis−trans H2CO3 → CO2···H2O··· CO2···H2O

MP2/aug-ccpVDZ 12.07 (+0.06) 10.93 (−1.37)

MP2/aug-ccpVTZ 36.78 11.97 10.75 16.84 22.59

(−0.22) (−1.72) (+3.64) (+14.54)

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

CCSD(T)/aug-ccpVTZ

12.17 (+0.13) 10.95 (−1.39)

14.02 (+1.79) 12.83 (+0.37)

a The values in parentheses are the relative energies of the transition states (TSs) with respect to those reactants involved in bimolecular encounters as discussed in the text. For an example, in case of cis-trans H2CO3···H2O···(H2O)2 → CO2···(H2O)4 unimolecular isomerization, the MP2/aug-ccpVTZ level of calculation incorporating ZPE correction predict that TS is being 3.64 kcal/mol higher in energy (indicated by positive sign) than the total energy of the cis-trans H2CO3···H2O + (H2O)2 reactants. Normal mode vibrational frequency calculations at the MP2/aug-cc-pVDZ, MP2/augcc-pVTZ, and MP2/6-311++G(3df,3pd) levels have been performed to estimate the respective zero-point energy (ZPE) corrections. The ZPE correction in the case of the CCSD(T)/aug-cc-pVTZ level of calculations has been done from the MP2/aug-cc-pVTZ level predicted ZPE correction.

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).

nate (IRC) calculations were performed at the same level of theories to unambiguously verify that the transition states found connect with the desired reactants and products. In order to improve our estimates of the reaction energetics, we have carried out single-point energy calculations at the CCSD(T)/ aug-cc-pVTZ level using the MP2/aug-cc-pVTZ level optimized geometries. Normal-mode vibrational-frequencies predicted at MP2 level of theory in conjunction with aug-cc-pVDZ, aug-cc-pVTZ, and 6-311++G(3df,3pd) basis sets have been used to estimate the zero-point vibration energy (ZPE) corrections for the reactants, products, and TS. In case of CCSD(T)/aug-cc-pVTZ level of calculations, ZPE corrections have been done with the aid of MP2/aug-cc-pVTZ level predicted vibrational frequencies. The computed total electronic energies (Etotal) along with the ZPE corrected electronic energies [Etotal(ZPE)] of the monomers, complexes, and the transition states are given in Table S1, Supporting

III. RESULTS AND DISCUSSION The autocatalytic decomposition of H2CO3 into its constituent CO2 and H2O molecules can be explicitly written as follows: H 2CO3 + H 2CO3 ⇌ H 2CO3···H 2CO3 → CO2 ···H 2O···H 2CO3 ⇌ CO2 + H 2O + H 2CO3 (1)

In the above reaction, the H2CO3···H2CO3 species is the prereactive entrance channel complex that undergoes unimolecular isomerization via an eight-membered ring cyclic 2387

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transition state (TS) to form the CO2···H2O···H2CO3 complex in the exit channel. To the best of our knowledge, there have been no previous studies reported in the literature investigating autocatalytic decomposition of H2CO3 as represented by reaction 1. The calculated binding energies of various complexes as well as the barrier heights for the unimolecular isomerizations as discussed here have been given in Tables 1 and 2. From Tables 1 and 2, it is seen that the predicted binding energies as well as barrier heights at the MP2 level of calculations are consistent for the three different basis sets used. Therefore, to keep the discussion simple, we prefer only to highlight the results predicted at the MP2/aug-cc-pVTZ level of calculations including zero-point vibrational energy (ZPE) corrections. In Figure 3A & B, we present the potential energy

collision, are nearly zero. Our calculations at the MP2/aug-ccpVTZ level show that the ZPE corrected energy difference between the cis−trans H2CO3 + cis−cis H2CO3 reactants and the corresponding TS, associated with the H2CO3···H2CO3 → CO2···H2O···H2CO3 unimolecular isomerization step (Figure 3A), is ∼0.2 kcal/mol with the TS being at lower energy. Similarly, in case of cis−trans H2CO3 + cis−trans H2CO3 reactants channel (Figure 3B), this energy difference becomes much more prominent, and the value is ∼1.7 kcal/mol with the TS being at lower energy (Table 2). It has been mentioned before that we have also carried out single-point energy calculations at the CCSD(T)/aug-cc-pVTZ level using the MP2/aug-cc-pVTZ level optimized geometries in order to improve our estimates of the reaction energetics. From the calculations at the CCSD(T)/aug-cc-pVTZ level including ZPE corrections of the MP2/aug-cc-pVTZ level, it is seen that the energy difference between the cis−trans H2CO3 + cis−cis H2CO3 reactants and the corresponding TS is only ∼1.8 kcal/ mol with the TS being at higher energy. Similarly, as expected, the energy difference between the cis−trans H2CO3 + cis−trans H2CO3 reactants and the corresponding TS is only ∼0.4 kcal/ mol with the TS being at higher energy. Therefore, even though the results shown above suggest that the energy difference between the TS and the reactants is sensitive to some extent to the levels of calculations used, nevertheless, we find that effective barrier heights are very small for the two channels of the autocatalytic reaction mechanism presented here. Thus, our calculations suggest that, while the decomposition of isolated H2CO3 is forbidden in gas phase, the decomposition of H2CO3 is effectively allowed at room temperature with its autocatalytic decomposition mechanism. It is also worthwhile to note that energetics of the potential energy diagram as revealed by the theoretical calculations presented here is consistent with experimental observation noted by Bernard et al.17,20 in the matrix isolated infrared spectroscopy of the H2CO3 molecule. In their experiments, it is observed from the measured infrared spectra that the vapors of H2CO3, formed via the sublimation of the β-polymorph, decomposes into CO2 and H2O at 230 K. We also note that the bimolecular collision between two cis− cis conformers of H2CO3 is another possibility that may result in the decomposition of H2CO3 molecule into its constituent CO2 and H2O molecules. However, it is important to note that the direct decomposition of the isolated cis−cis conformer is forbidden in vapor phase and also that the cis−trans conformer, which is different from the cis−cis conformer with respect to the orientation of two OH functional groups present in the H2CO3 molecule, has been considered as a starting point for the decomposition of H 2 CO 3 into CO 2 and H 2 O molecules.21,22,35−37 Moreover, it is also worthwhile to note here that the currently accepted mechanism for the isomerization of the cis−cis conformer of H2CO3 to its cis−trans conformer is the rotation of one of the two indistinguishable OH functional groups present in the cis−cis conformer and that the barrier height for this isomerization process at the CCSD(T)/aug-ccpVTZ level of calculation including ZPE correction is 9.3 kcal/ mol.37 Therefore, for the decomposition of the cis−cis conformer in the presence of another cis−cis conformer, we find that one of the two cis−cis conformers involved in the bimolecular collision requires a conformational change before its decomposition to occur via either one of the two pathways associated with the autocatalytic decomposition mechanism discussed above.

Figure 3. Potential energy profiles for the autocatalytic decomposition of cis−trans H2CO3 in the presence of both the cis−cis (A) and cis− trans (B) conformers (Figure 1). The energy profiles have been calculated at the MP2/aug-cc-pVTZ level of theory with ZPE corrections.

diagrams for the decomposition of H2CO3 into its constituents (CO2 and H2O) in the presence of both the conformers of H2CO3 (Figure 1). The MP2/aug-cc-pVTZ level optimized geometries of the starting H2CO3···H2CO3 complexes, the exit channel CO2···H2O···H2CO3 product complexes, and transition states associated with the H2CO3···H2CO3 → CO2···H2O··· H2CO3 unimolecular isomerizations with respect to both the conformers of H2CO3 are also shown in Figure 3A & B. From the Figure 3A & B, it is seen that the barrier heights for the unimolecular isomezation steps, which are the rate limiting steps for the autocatalytic decomposition reaction mechanism, are respectively only 12 and 10.7 kcal/mol including ZPE corrections. These values are substantially lower than the ∼37 kcal/mol barrier height associated with the unimolecular decomposition of isolated H2CO3 (Figure 2). Furthermore, inspection of the potential energy diagrams in Figure 3A & B shows that the effective barriers, defined as the difference between the ZPE corrected energy of the TS and the total energy of the isolated starting reactants in terms of bimolecular 2388

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bimolecular encounters between H2CO3···H2O complex and (H2O)2 dimer reactants. In Figure 4, we also present the MP2/ aug-cc-pVTZ level optimized geometries of the starting H2CO3···H2O···(H2O)2 preassociation complex, the exit channel CO2···(H2O)4 product complex, and TS associated with the H2CO3···H2O···(H2O)2 → CO2···(H2O)4 unimolecular isomerization. From our calculations at the MP2/aug-ccpVTZ level in the case of the H2CO3 decomposition reaction involving three water molecules with the mechanism as discussed above, it is seen that the effective barrier, defined as the difference between the ZPE corrected energy of the TS and the total energy of the isolated starting reactants in terms of bimolecular collision, is 3.6 kcal/mol. Furthermore, even if the H2CO3···H2O···(H2O)2 preassociation complex (Figure 4) is considered to form from the H2CO3 + (H2O)3 reactants channel with the mechanism where only one water subunit of among the three water subunits present in the water trimer [(H2O)3] participate actively, the effective barrier is 4.2 kcal/ mol. Therefore, we find that the gas phase decomposition of isolated H2CO3 in the presence of water molecules is most likely a hindered process at room temperature and that this mechanism is not expected to be competitive with the autocatalytic decomposition as discussed above. Another very important aspect of the autocatalytic decomposition reaction mechanism, as presented in the Figure 3A & B, is that the decomposition of the cis−trans conformer of H2CO3 occurs simultaneously with the isomerization of the other conformer of H2CO3 involved in the reaction. For example, the bimolecular collision between cis−trans H2CO3 and cis−cis H2CO3 (Figure 3A) results in the decomposition of the cis−trans conformer of H2CO3 along with the isomerization of the cis−cis conformer of H2CO3 to its cis−trans conformer. Similarly, the bimolecular collision between cis−trans H2CO3 and cis−trans H2CO3 (Figure 3B) results in the decomposition of the cis−trans conformer of H2CO3 along with the isomerization of the cis−trans conformer of H2CO3 to its cis− cis conformer. Therefore, it is important to note here that though the autocatalytic decomposition via the cis−trans H2CO3 + cis−trans H2CO3 reactants (Figure 3B) is energetically favorable over the cis−trans H2CO3 + cis−cis H2CO3 reactants (Figure 3A), nevertheless, the reaction channel for its decomposition is expected to start with the cis−trans H2CO3 + cis−cis H2CO3 reactants, as the population of the cis−cis conformer in the cold environment (210−250 K) has been found to be higher than the population to cis−trans conformer.17,20 However, as the reverse process, the conversion of the cis−trans conformer to the cis−cis conformer during its autocatalytic decomposition (Figure 3B), is also present, there will be an equilibrium between the cis−trans and cis−cis conformers in terms of their populations, and the autocatalytic decomposition of H2CO3 counting the interconversion of its two most stable conformers is expected to be the primary mechanism for its dissociation. It is worthwhile to note that in the case of water-assisted decomposition mechanism as discussed above the decomposition of H2CO3 in vapor phase, if there is any, is hindered not only because of ∼4 kcal/mol effective barrier but also because of less population of the cis− trans H2CO3 over the most stable cis−cis H2CO3. Moreover, it has been mentioned before that autocatalytic decomposition of H2CO3 has been investigated recently,37 and the mechanism that has been considered in terms of bimolecular collision between two cis−trans conformers of H2CO3 can be written as follows:

Given that the autocatalytic decomposition of H2CO3 via either one of the two paths as presented in Figure 3 is effectively a near-barrierless process at room temperature, it will also produce water molecules continuously during its decomposition, and there may be an impact of the bimolecular collisions between H2CO3···H2O complex and (H2O)2 dimer in its decomposition, in particular when the concentration of the water molecules becomes high over the concentration of H2CO3. It is important to note here that the currently accepted mechanism for its decomposition in aqueous phase is the path where H2CO3 involves one water molecule actively and the remaining two water molecules as passively to stabilize the TS with respect to the reactants.36 Thus, in order to compare the energetics of the autocatalytic decomposition of H2CO3 and water-assisted decomposition reactions on an equal footing, we have also performed similar calculations at the MP2/aug-ccpVTZ level for the H2CO3 decomposition reaction involving three water molecules with the mechanism where H2CO3 involves one water molecule actively in presence of water dimer [(H2O)2] that stabilizes the TS with respect to H2CO3··· H2O + (H2O)2 reactants. The decomposition of H2CO3 in the scenario of bimolecular encounters between the H2CO3···H2O complex and (H2O)2 dimer reactants can be explicitly written as follows: H 2CO3···H 2O + (H 2O)2 ⇌ H 2CO3···H 2O···(H 2O)2 → CO2 ···(H 2O)4 ⇌ CO2 + (H 2O)4

(2)

Similar to the autocatalytic decomposition of H2CO3, the H2CO3···H2O···(H2O)2 species in the above reaction is the prereactive entrance channel complex that undergoes unimolecular isomerization via an six-membered ring cyclic transition state (TS) to form the CO2···(H2O)4 complex in the exit channel. It is important to note here that though the decomposition of H2CO3 in aqueous phase can occur in presence of many water molecules as required, the probability for the formation of H2CO3···H2O···(H2O)2 preassociation complex (Figure 4) in vapor phase via the ternary or quaternary collisions involving H2CO3 and H2O molecules is expected to be very low. In Figure 4, we present the potential energy diagram for the decomposition of H2CO3 with respect to

Figure 4. Potential energy profile for the decomposition of the cis− trans H2CO3 in the presence of three water molecules with the mechanism where H2CO3 involves one water molecule actively in the presence of water dimer [(H2O)2] that stabilizes the TS with respect to H2CO3···H2O + (H2O)2 reactants. The energy profile has been calculated at the MP2/aug-cc-pVTZ level of theory with ZPE corrections. 2389

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H2CO3···H2CO3 → CO2···H2O···CO2···H2O unimolecular isomerization step (Figure 5), is ∼14.5 kcal/mol with the TS being at higher energy. This value is substantially higher than the values associated with our new autocatalytic decomposition mechanism presented above. Therefore, we conclude that reaction 3, which eventually represents the simultaneous decomposition of two cis−trans conformers of H2CO3 into two CO2 and two H2O molecules, is not the effective one and a hindered process in vapor phase in compared to the new mechanism, what we present here.

H 2CO3 + H 2CO3 ⇌ H 2CO3···H 2CO3 → CO2 ···H 2O···CO2 ···H 2O ⇌ 2CO2 + 2H 2O

(3)

Like before, in the above reaction, the H2CO3···H2CO3 species is the prereactive entrance channel complex that undergoes unimolecular isomerization via an eight-membered ring cyclic TS to form the CO2···H2O···CO2···H2O complex in the exit channel. Obviously, the difference between this mechanism (reaction 3) and the mechanism given by us (reaction 1) is that the bimolecular collision between two cis− trans conformers of H2CO3 in reaction 3 represents the simultaneous decomposition of both the H2CO3 molecules involved in the reaction, whereas the bimolecular collision between two cis−trans conformers of H2CO3 in reaction 1 represents the decomposition of only one H2CO3 molecule. Therefore, to compare the energetics of the cis−trans H2CO3 + cis−trans H2CO3 reactants channel of reaction 3 with our presented cis−trans H2CO3 + cis−trans H2CO3 reactants channel on equal footing, we have also performed the MP2/ aug-cc-pVTZ level of calculations to explore the energetics for simultaneous decomposition of both the H2CO3 molecules involved in reaction 3. In Figure 5, we present the computed

IV. SUMMARY AND CONCLUSIONS The quantum chemistry calculations at the MP2 level of theory in conjunction with aug-cc-pVDZ, aug-cc-pVTZ, and 6-311+ +G(3df,3pd) basis sets have been performed to explore the energetics of a new autocatalytic decomposition mechanism for carbonic acid (H2CO3). In our calculations, we have evaluated the energetics for the potential energy diagrams with respect to bimolecular encounters between cis−trans H2CO3 + cis−cis H2CO3 and between cis−trans H2CO3 + cis−trans H2CO3 conformers. From our calculations at the MP2/aug-cc-pVTZ level including ZPE corrections, it is seen that the effective barriers for the two autocatalytic decomposition reactions in terms of bimolecular encounters, as mentioned above, are respectively ∼0.2 and 1.7 kcal/mol with the corresponding TSs being at lower energies. In order to improve our estimates of the reaction energetics, we have also carried out single-point energy calculations at the CCSD(T)/aug-cc-pVTZ level using the MP2/aug-cc-pVTZ level optimized geometries. From the calculations at the CCSD(T)/aug-cc-pVTZ level including ZPE corrections of the MP2/aug-cc-pVTZ level, it is seen that these values are respectively ∼1.8 and 0.4 kcal/mol with the corresponding TSs being at higher energies. These values are substantially lower than the ∼37 kcal/mol barrier height associated with the unimolecular decomposition of isolated H2CO3. In conclusion, we find that vapor phase H2CO3 at its source point, where the concentration of H2CO3 is expected to be high, can result in the molecule being unstable due to the new autocatalytic decomposition mechanism presented above. The energetics of the potential energy surface, as revealed by the calculations presented here, is consistent with the experimental observations noted by Bernard et al.17,20 in their matrix isolated infrared spectroscopy of the H2CO3. Therefore, this new autocatalytic decomposition mechanism is expected to make it harder for detection of gas-phase carbonic acid at its source points present not only in the surface of Earth but also by extension, in outer spaces where the seasonal variations raise the temperature around 270 K. However, it is worthwhile to note that the present mechanism is not expected to be the primary decomposition mechanism in the Earth’s atmosphere or in the surroundings away from the source points of H2CO3. This follows as the probability of bimolecular collisions between two H2CO3 molecules is expected to significantly fall off due to dilution of carbonic acid concentration resulting from the presence of various other species away from the source.

Figure 5. Potential energy profile for the autocatalytic decomposition of cis−trans H2CO3 in the presence of another cis−trans conformer that represents the simultaneous decomposition of two cis−trans conformers of H2CO3 into two CO2 and two H2O molecules.37 The energy profile has been calculated at the MP2/aug-cc-pVTZ level of theory with ZPE corrections. In the figure, we have also shown the relative energy of 2CO2···H2O complexes with respect to the CO2··· H2O···CO2···H2O exit channel complex.

potential energy diagram associated with the simultaneous decompositions of both the two cis−trans conformers of H2CO3 into two CO2 and two H2O molecules (reaction 3). The MP2/aug-cc-pVTZ level optimized geometries of the starting H2CO3···H2CO3 complex, the exit channel CO2··· H2O···CO2···H2O product complex, and transition state associated with the H2CO3···H2CO3 → CO2···H2O···CO2··· H2O unimolecular isomerization step of reaction 3 are also shown in Figure 5. From Figure 5, it is seen that the barrier height for the H2CO3···H2CO3 → CO2···H2O···CO2···H2O unimolecular isomezation step, which is the rate limiting step for the simultaneous decomposition of both the two cis−trans conformers involved in reaction 3, is 22.6 kcal/mol. Moreover, the effective barrier as defined above, the ZPE corrected energy difference between the cis−trans H2CO3 + cis−cis H2CO3 reactants and the corresponding TS, associated with the

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ASSOCIATED CONTENT

S Supporting Information *

Computed total electronic energies (Etotal) along with the ZPE corrected electronic energies [Etotal(ZPE)] of the monomers, complexes, and the transition states (TSs) as well as the 2390

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imaginary frequencies of various TSs as discussed in the text at the MP2 and CCSD(T) levels of calculations. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*(M.K.H.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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

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