Stabilizing the Exotic Carbonic Acid by Bisulfate Ion

Carbonic acid is an important species in a variety of fields and has long been regarded to be non-existing in isolated state, as it is thermodynamically favorable to decompose into water and carbon dioxide. In this work, we systematically studied a novel ionic complex [H2CO3·HSO4]− using density functional theory calculations, molecular dynamics simulations, and topological analysis to investigate if the exotic H2CO3 molecule could be stabilized by bisulfate ion, which is a ubiquitous ion in various environments. We found that bisulfate ion could efficiently stabilize all the three conformers of H2CO3 and reduce the energy differences of isomers with H2CO3 in three different conformations compared to the isolated H2CO3 molecule. Calculated isomerization pathways and ab initio molecular dynamics simulations suggest that all the optimized isomers of the complex have good thermal stability and could exist at finite temperatures. We also explored the hydrogen bonding properties in this interesting complex and simulated their harmonic infrared spectra to aid future infrared spectroscopic experiments. This work could be potentially important to understand the fate of carbonic acid in certain complex environments, such as in environments where both sulfuric acid (or rather bisulfate ion) and carbonic acid (or rather carbonic dioxide and water) exist.


Introduction
Carbonic acid, H 2 CO 3 , is a diprotic oxyacid and has long been considered as nonexisting in isolated state [1]. Its importance in a range of fields, including astrophysics, astrobiology, astrochemistry, geography, and biochemistry, has been well-recognized [2][3][4][5][6][7]. It is of great significance in regulating blood pH, in adjusting ocean acidification, and in the dissolution of carbonate minerals [8]. In recent years, its potential as an interstellar molecule on the Martian surface, comets, and icy grain mantles has also attracted a lot of attention since both decomposition components of carbonic acid (i.e., carbon dioxide and water) have been discovered in those environments [4,5,9].
The non-existence of carbonic acid in isolated state was thought to be due to the fact that it is thermodynamically favorable to decompose into water and carbon dioxide, although theoretical calculations indicated that it might be kinetically trapped by a potential well [10,11]. The decomposition of carbonic acid could be efficiently promoted by a variety of species, such as water, ammonia, sulfuric acid, organics, and cloud particle surfaces. That could be one reason why isolated H 2 CO 3 has escaped direct detection for a long time [11][12][13][14][15][16][17]. In 1987, Schwarz and co-workers reported the first observation of isolated H 2 CO 3 via neutralization-reionization mass spectrometry of heated ammonium bicarbonate (NH 4 HCO 3 ) vapor [1]. More than 20 years later, Endo and co-workers first spectroscopically detected both the cis-trans H 2 CO 3 molecule in 2009 and the cis-cis H 2 CO 3 molecule in 2011 using Fourier-transform microwave spectroscopy; the two H 2 CO 3 isomers were produced via supersonic expansion and pulsed electric discharge of a carbon dioxide and water mixture [18,19]. In 2011, Bernard et al. also detected the two isomers of H 2 CO 3 with the cis-trans isomer being less stable than the cis-cis one by about 4 kJ/mol and showed that H 2 CO 3 is stable at temperatures above 200 K [20]. Later in 2014, Schreiner and coworkers reported a novel and general approach to prepare H 2 CO 3 and its monomethyl ester (CH 3 OCO 2 H) through gas-phase pyrolysis of di-tert-butyl and tert-butyl methyl carbonate, respectively [21]. Furthermore, they verified that the previously thought polymorph of solid carbonic acid α-H 2 CO 3 actually belongs to the carbonic acid monomethyl ester, and the β-polymorph is true H 2 CO 3 . Very recently, Ioppolo et al. provided evidence that β-H 2 CO 3 should be ubiquitously present in space on the surface of CO 2 -and H 2 O-rich ices. They also observed unique spectral features of γ-H 2 CO 3 , deserving future search in the coldest regions of the interstellar medium [22]. Moreover, Wang et al. found that carbonic acid can even be formed from CO 2 on ice in the absence of high-energy irradiation and without protonation by strong acids, implying its potential role in the upper troposphere in cirrus clouds [23].
Hydrogen bonding is an effective way to stabilize otherwise unstable and uncommon structures [24][25][26][27][28][29][30][31][32][33][34]. For example, Hou et al. have performed a series of studies on bisulfate ion-containing complexes, showing that hydrogen bonding interactions can alter the protonation pattern in the complex, which violates the gas-phase proton affinity prediction [24,27,[35][36][37][38]. This motivated us to wonder whether an appropriate partner such as bisulfate ion could also stabilize the exotic conformers of H 2 CO 3 molecule. In fact, Thomas et al. has recently measured the infrared spectrum of the carbonic acid-fluoride complex anion in helium nanodroplets and found remarkable stability of F − (H 2 CO 3 ) with carbonic acid in a trans-trans conformation [39]. Similar work on the whole series of carbonic acid-halide complexes, X -(H 2 CO 3 ) (X = F, Cl, Br, and I), has been followed by Zhang et al. through joint photoelectron spectroscopy and ab initio calculations [40]. Here in this work, we theoretically studied the carbonic acid-bisulfate ion complex by using density functional theory (DFT) calculations and molecular dynamics simulations. The stability and bonding property of the complex have been explored.

Theoretical Methods
Geometry optimizations of all minima and transition states on the potential energy surface of the anionic molecular complex [H 2 CO 3 ·HSO 4 ] − were performed by using DFT calculations. Specifically, M06-2X functional and aug-cc-pVTZ basis set were employed, as previous studies showed that this combination could provide reliable results for hydrogen bonded, bisulfate ion-containing complexes [24,27,35,36]. Harmonic frequency analysis was conducted at the same level of theory. All the quantum chemical calculations were performed with Gaussian09 program [41]. The natural bond orbital (NBO) analyses were carried out at M06-2X/aug-cc-pVTZ level using NBO 3.1 as implemented in Gaussian09. Ab initio molecular dynamics (AIMD) simulations using the Nosé-Hoover heat bath scheme with the average temperature of the system at 300, 400, 500, and 1000 K were performed for the most stable isomer, and an average temperature of 300 K for the second most stable isomer, with the Vienna ab initio simulation package (VASP) [42][43][44]. The PBE functional was used for the exchange-correlation functional [45]. A unit cell of 30 × 30 × 30 Å has been employed to avoid spurious interaction in space and the reciprocal space was represented by the Gamma point. The plane wave cut-off energy in the wave vector K space was 520 eV with the convergence criteria for the energy as 1 × 10 −4 eV. Quantum theory of atoms in molecules (QTAIM) [46] analyses were also performed with Mutiwfn software [47] to gain insights into the H-bonding interactions in [H 2 CO 3 ·HSO 4 ] − . provide the optimized three conformers of carbonic acid, bisulfate ion, and sulfuric acid in Figure S1. It can be seen that the optimized structures of the three conformers are in good agreement with previous studies, and their relative stabilities are also consistent with previous calculations at a higher level of theory CCSD(T)/cc-pVQZ [10,11,18], verifying the reliability of the theoretical method utilized in the current work. For [H 2 CO 3 ·HSO 4 ] − , we have obtained six stable isomers, among which isomers 2a and 2b could be considered as enantiomers, and isomers 3a and 3b could also be considered as enantiomers. While isomers 1, 3, and 4 may be regarded as HSO4 -·H 2 CO 3 , isomer 2 is better recognized as H 2 SO4·HCO 3 − , which is only about 2 kJ/mol higher in energy than isomer 1. Isomer 2 is unexpected solely from gas-phase proton affinity prediction and its stability can be attributed to the formation of two strong hydrogen bonds and highly delocalized extra electrons according to previous findings by Hou et al. [24,27,[36][37][38]. Such electron delocalization can be partly reflected by the highest occupied molecular orbitals (HOMOs) as presented in Figure S2. Since we are mainly interested in understanding if bisulfate ion could stabilize carbonic acid molecule, in the following we will focus on isomers 1, 3, and 4.  Figure 1 presents the optimized low-lying isomers of [H2CO3·HSO4] -. To better understand the changes of each component in [H2CO3·HSO4] -upon complexation, we provide the optimized three conformers of carbonic acid, bisulfate ion, and sulfuric acid in Figure S1. It can be seen that the optimized structures of the three conformers are in good agreement with previous studies, and their relative stabilities are also consistent with previous calculations at a higher level of theory CCSD(T)/cc-pVQZ [10,11,18], verifying the reliability of the theoretical method utilized in the current work. For [H2CO3·HSO4] -, we have obtained six stable isomers, among which isomers 2a and 2b could be considered as enantiomers, and isomers 3a and 3b could also be considered as enantiomers. While isomers 1, 3, and 4 may be regarded as HSO4 -·H2CO3, isomer 2 is better recognized as H2SO4·HCO3 − , which is only about 2 kJ/mol higher in energy than isomer 1. Isomer 2 is unexpected solely from gas-phase proton affinity prediction and its stability can be attributed to the formation of two strong hydrogen bonds and highly delocalized extra electrons according to previous findings by Hou et al. [24,27,[36][37][38]. Such electron delocalization can be partly reflected by the highest occupied molecular orbitals (HOMOs) as presented in Figure S2. Since we are mainly interested in understanding if bisulfate ion could stabilize carbonic acid molecule, in the following we will focus on isomers 1, 3, and 4. It is interesting to note that in isomers 1, 3a, 3b, and 4, carbonic acid moiety is in the form of trans-trans, cis-trans, cis-cis, and cis-trans, respectively. For bare carbonic acid, ciscis conformer is the most stable one, and cis-trans and trans-trans are higher in energy by 6.1 and 41.2 kJ/mol, respectively. Upon complexation with bisulfate ion, the isomer with carbonic acid moiety in trans-trans becomes to be the most stable one, which could be due to the formation of two equivalent hydrogen bonds. The energy differences of isomers with carbonic acid moiety in cis-trans and cis-cis relative to the most stable trans-trans one are much smaller compared in the bare case, suggesting the efficient stabilization of carbonic acid molecule by bisulfate ion. The smaller energy difference implies that these isomers may convert to each other upon gaining sufficient perturbation (for example, by thermionic heating or photoabsorption).

Results and Discussion
In Figure 2, we present the isomerization pathways between the different isomers of [H2CO3·HSO4] -and the energy barriers needed to be overcome. The calculations show that the isomerization between isomers 2a and 2b, isomers 3a and 3b involves the rotation of −OH group in bicarbonate or carbonic acid, and the barriers are almost equal to be 45.4 It is interesting to note that in isomers 1, 3a, 3b, and 4, carbonic acid moiety is in the form of trans-trans, cis-trans, cis-cis, and cis-trans, respectively. For bare carbonic acid, cis-cis conformer is the most stable one, and cis-trans and trans-trans are higher in energy by 6.1 and 41.2 kJ/mol, respectively. Upon complexation with bisulfate ion, the isomer with carbonic acid moiety in trans-trans becomes to be the most stable one, which could be due to the formation of two equivalent hydrogen bonds. The energy differences of isomers with carbonic acid moiety in cis-trans and cis-cis relative to the most stable trans-trans one are much smaller compared in the bare case, suggesting the efficient stabilization of carbonic acid molecule by bisulfate ion. The smaller energy difference implies that these isomers may convert to each other upon gaining sufficient perturbation (for example, by thermionic heating or photoabsorption).
In Figure 2, we present the isomerization pathways between the different isomers of [H 2 CO 3 ·HSO 4 ] − and the energy barriers needed to be overcome. The calculations show that the isomerization between isomers 2a and 2b, isomers 3a and 3b involves the rotation of −OH group in bicarbonate or carbonic acid, and the barriers are almost equal to be 45.4 and 46.4 kJ/mol, respectively. Such relatively high energy barriers may preclude the isomerization between the enantiomers of 2 and 3, and they may all exist at finite temperatures. Isomerization between isomers 2a and 3a, isomers 2b and 3b has low barriers of only about 8 kJ/mol, indicating that the proton translocation between the two negatively charged oxygen atoms should not be difficult, as found in HCOO − ·H + ·HSO 4 - [36,48].
Visually, it seems isomerization between isomer 4 and isomer 3b is more likely due to the fact that they have same hydrogen bond pattern between the two partners. However, due to the low energy barrier of proton translocation, our calculations show that isomerization happens between isomers 4 and 2b via a transition state ts42b in which a proton translocates to bisulfate ion moiety simultaneously with the H transfer. This isomerization process has a large barrier of about 140 kJ/mol which is likely mainly resulted from the H transfer, making the isomerization between isomers 4 and 2b not likely under ambient conditions. Conversion between isomers 1 and 4 is a stepwise process via an intermediate state in14. The first step is the H transfer from the −SOH moiety to the O of HSO 4 that connects to the H 2 CO 3 via a OH-O hydrogen bond; this step has a high energy barrier of~125 kJ/mol. The second step is the swing of the H of one −OH of the H 2 CO 3 with a comparably lower barrier of about 56 kJ/mol. This stepwise process has been confirmed by intrinsic reaction coordinate (IRC) scan ( Figure S3 in the Supplementary Material). The large barrier of the first step renders the isomerization to be only possible at elevated temperatures or heating conditions. and 46.4 kJ/mol, respectively. Such relatively high energy barriers may preclude the isomerization between the enantiomers of 2 and 3, and they may all exist at finite temperatures. Isomerization between isomers 2a and 3a, isomers 2b and 3b has low barriers of only about 8 kJ/mol, indicating that the proton translocation between the two negatively charged oxygen atoms should not be difficult, as found in HCOO − ·H + ·HSO4 - [36,48]. Visually, it seems isomerization between isomer 4 and isomer 3b is more likely due to the fact that they have same hydrogen bond pattern between the two partners. However, due to the low energy barrier of proton translocation, our calculations show that isomerization happens between isomers 4 and 2b via a transition state ts42b in which a proton translocates to bisulfate ion moiety simultaneously with the H transfer. This isomerization process has a large barrier of about 140 kJ/mol which is likely mainly resulted from the H transfer, making the isomerization between isomers 4 and 2b not likely under ambient conditions. Conversion between isomers 1 and 4 is a stepwise process via an intermediate state in14. The first step is the H transfer from the −SOH moiety to the O of HSO4 -that connects to the H2CO3 via a OˑˑˑH-O hydrogen bond; this step has a high energy barrier of ~125 kJ/mol. The second step is the swing of the H of one −OH of the H2CO3 with a comparably lower barrier of about 56 kJ/mol. This stepwise process has been confirmed by intrinsic reaction coordinate (IRC) scan ( Figure S3 in the Supplementary Material). The large barrier of the first step renders the isomerization to be only possible at elevated temperatures or heating conditions. To further evaluate the thermodynamical stability of the different isomers of [H2CO3·HSO4] -, we performed AIMD simulations for isomers 1 and 2a, as presented in Figure 3. It can be seen that after 10,000 simulation steps (10 picoseconds), the structures of both isomers only show slight deformation compared to the ground state at 0 K, suggesting their high thermodynamic stability. Temperature and energy fluctuate over time in a steady-state, and the difference of the maximum and the minimum energies (ΔE) of isomer 1 and isomer 2a are only about 0.5 eV, confirming their high-temperature stability [49,50]. We further simulated isomer 1 at higher temperatures of 400, 500, and 1000 K, all presenting its good stability (see animations in Figure S4). To further evaluate the thermodynamical stability of the different isomers of [H 2 CO 3 ·HSO 4 ] − , we performed AIMD simulations for isomers 1 and 2a, as presented in Figure 3. It can be seen that after 10,000 simulation steps (10 picoseconds), the structures of both isomers only show slight deformation compared to the ground state at 0 K, suggesting their high thermodynamic stability. Temperature and energy fluctuate over time in a steady-state, and the difference of the maximum and the minimum energies (∆E) of isomer 1 and isomer 2a are only about 0.5 eV, confirming their high-temperature stability [49,50]. We further simulated isomer 1 at higher temperatures of 400, 500, and 1000 K, all presenting its good stability (see animations in Figure S4). Molecules 2021, 26, x FOR PEER REVIEW As stated above, the high stability of those isomers comes from hydrogen bon mation and extra electron delocalization. The electron delocalization could partly flected by the HOMOs as shown in Figure S2 and partly by the charge distributi summarized in Table S1. QTAIM is a useful approach to evaluate the nature of hyd bond and its strength in addition to the geometrical analysis [37,46]. According to B theory, the critical points (3,−3) are the nuclear positions where the charge density maximum in all directions, and the BCPs (3,−1) correspond to the second-order points, for which two eigenvalues of the charge density Hessian matrix are negati one is positive. The BCPs and the nuclei are connected by the maximum charge d paths. Figure S5 presents the molecular graphs showing all the BCPs. The electron d (ρ) and its Laplacian (∇ 2 ρ) at BCP are closely related to bonding strength and bo type, respectively; the potential energy density (V(r)), gradient kinetic energy d (G(r)), and electronic energy density (K(r)) are highly correlated with the hydrogen energies. These values are summarized in Table 1. Table 1. Electron density (ρ), Laplacian (∇ 2 ρ), potential energy density (V(r)), gradient kinetic energy density (G(r)), an electronic energy density (K(r)) at BCPs of the hydrogen bonds in the different isomeric structures of [H2CO3·HSO4] -. A units are in a.u, except that EHB is in kcal/mol.  II  I  II  I  II  I  II  I  II Figure S5 for the notation of hydrogen bonds I and II in each isomer. As stated above, the high stability of those isomers comes from hydrogen bond formation and extra electron delocalization. The electron delocalization could partly be reflected by the HOMOs as shown in Figure S2 and partly by the charge distributions as summarized in Table S1. QTAIM is a useful approach to evaluate the nature of hydrogen bond and its strength in addition to the geometrical analysis [37,46]. According to Bader's theory, the critical points (3,−3) are the nuclear positions where the charge density is local maximum in all directions, and the BCPs (3,−1) correspond to the second-order saddle points, for which two eigenvalues of the charge density Hessian matrix are negative and one is positive. The BCPs and the nuclei are connected by the maximum charge density paths. Figure S5 presents the molecular graphs showing all the BCPs. The electron density (ρ) and its Laplacian (∇ 2 ρ) at BCP are closely related to bonding strength and bonding type, respectively; the potential energy density (V(r)), gradient kinetic energy density (G(r)), and electronic energy density (K(r)) are highly correlated with the hydrogen bond energies. These values are summarized in Table 1. Table 1. Electron density (ρ), Laplacian (∇ 2 ρ), potential energy density (V(r)), gradient kinetic energy density (G(r)), and electronic energy density (K(r)) at BCPs of the hydrogen bonds in the different isomeric structures of [H 2 CO 3 ·HSO 4 ] − . All units are in a.u, except that E HB is in kcal/mol.  II  I  II  I  II  I  II  I  II  I [51]. b See Figure S5 for the notation of hydrogen bonds I and II in each isomer. From Table 1, it can be seen that the electron density distribution (ρ) and its Laplacian (∇ 2 ρ) at BCPs of the two hydrogen bonds of isomers 1 and 2 are almost identical, while those of isomers 3 and 4 differ a lot, consistent with the structural analyses. Such difference can also be seen from the values of electronic energy density K(r), whose magnitude is related to the hydrogen bond strength. In 2019, Emamian et al. investigated a series of hydrogen bonded complexes and fitted an equation E HB = −332.34 × ρ BCP − 1.0661 to estimate the hydrogen bond energy (E HB ) for hydrogen bonded ionic complexes. This equation gives a mean absolute percentage error (MAPE, in kcal/mol) of 10.0%, and ρ BCP is the electron density at the BCP of hydrogen bonds in a.u., and E HB is in kcal/mol [52]. The hydrogen bond energies estimated in this way are summarized in Table 1, and it is shown clearly that the calculated hydrogen bond strengths are consistent with the optimized geometric structures (i.e., the shorter O-HO distance, the higher hydrogen bond energy).
Temperature-controlled infrared spectroscopy is a useful experimental approach to probe the proton translocation dynamics as demonstrated by Johnson and co-workers [53,54] and very recently also by von Helden and co-workers [39,48]. To guide future infrared spectroscopic experiments, we simulated the harmonic vibrational spectra of the six isomers of [H 2 CO 3 ·HSO 4 ] − , as presented in Figure 4.
Molecules 2021, 26, x FOR PEER REVIEW 6 of 9 From Table 1, it can be seen that the electron density distribution (ρ) and its Laplacian (∇ 2 ρ) at BCPs of the two hydrogen bonds of isomers 1 and 2 are almost identical, while those of isomers 3 and 4 differ a lot, consistent with the structural analyses. Such difference can also be seen from the values of electronic energy density K(r), whose magnitude is related to the hydrogen bond strength. In 2019, Emamian et al. investigated a series of hydrogen bonded complexes and fitted an equation EHB = −332.34 × ρBCP − 1.0661 to estimate the hydrogen bond energy (EHB) for hydrogen bonded ionic complexes. This equation gives a mean absolute percentage error (MAPE, in kcal/mol) of 10.0%, and ρBCP is the electron density at the BCP of hydrogen bonds in a.u., and EHB is in kcal/mol [52]. The hydrogen bond energies estimated in this way are summarized in Table 1, and it is shown clearly that the calculated hydrogen bond strengths are consistent with the optimized geometric structures (i.e., the shorter O-HˑˑˑO distance, the higher hydrogen bond energy).
Temperature-controlled infrared spectroscopy is a useful experimental approach to probe the proton translocation dynamics as demonstrated by Johnson and co-workers [53,54] and very recently also by von Helden and co-workers [39,48]. To guide future infrared spectroscopic experiments, we simulated the harmonic vibrational spectra of the six isomers of [H2CO3·HSO4] -, as presented in Figure 4.    Figure S6 in the Supplementary Materials. It should be mentioned that more accurate description of the vibrations in those structures requires more advanced theoretical treatments including both anharmonic effects and nuclear quantum effects, and is beyond the scope of current study [48].

Conclusions
In summary, we theoretically explored the potential energy surface of the anionic [H 2 CO 3 ·HSO 4 ] − complex to investigate if bisulfate ion is capable to stabilize the exotic conformers of carbonic acid. Our results showed that compared to the bare H 2 CO 3 molecule, the energy differences between the different isomers of [H 2 CO 3 ·HSO 4 ] − complex with H 2 CO 3 moiety in the conformation of trans-trans, cis-trans, and cis-cis become smaller, suggesting that bisulfate ion can efficiently stabilize the three conformers of H 2 CO 3 . Notably, for bare H 2 CO 3 , the cis-cis conformer is the most stable, while in [H 2 CO 3 ·HSO 4 ] − the isomer with H 2 CO 3 in trans-trans becomes the most stable due to the formation of two strong hydrogen bonds. Combining quantum theory of atoms in molecules topological analysis and a fitted empirical equation, we estimated the strengths of the hydrogen bonds. The calculated isomerization pathways between the different isomers of [H 2 CO 3 ·HSO 4 ] − and also ab initio molecular dynamics simulations of the first two low-lying isomers revealed that these isomers could coexist at finite temperatures. We further simulated their harmonic infrared spectra to facilitate future infrared spectroscopic experiments to fully understand the proton translocation dynamics in this interesting complex.
Supplementary Materials: The following are available online. Figure S1: Three conformers of isolated carbonic acid molecule, bisulfate ion, and cis-cis sulfuric acid molecule; Figure S2