Boric acid, “carbonic” acid, and N-containing oxyacids in aqueous solution: Ab initio studies of structure, p Ka, NMR shifts, and isotopic fractionations

Abstract

B(OH) 3 and CO 2 are acidic species of considerable geochemical importance, yet the microscopic nature of the acid dissociation reactions for these B and C species is not well understood. Quantum mechanical methods have recently been applied to the direct ab initio calculation of p K a values for many organic and inorganic weak acids, but the B and C acids have not yet been considered in detail. In the present study, p K a values are calculated quantum mechanically for the oxyacids B(OH) 3, H 2CO 3 and HNO 3, which have experimental first p K a values of 9.2, 6.4 and −1.3, respectively. We calculate the gas-phase reaction free energies at the highly accurate CBS-QB3 ab initio quantum mechanical level and reaction free energies of hydration using a polarizable continuum method. Using a thermodynamic cycle corresponding to the simple dissociation process HA A − + H +, in aqueous solution, we calculate p K a values of 21.6, 3.8 to 2.2 and −0.8 for the three oxyacids mentioned above, closely matching experiment only for HNO 3. The discrepancies with experiment arise from the more complex nature of the acid dissociation process for B(OH) 3, which involves the addition of H 2O to B(OH) 3 and formation of the B(OH) 4 − anion, and from the instability of hypothetical H 2CO 3 compared to the proper hydrated reactant complex CO 2. . . H 2O. When the proper microscopic description of the reactants and products is used the calculated p K a values for the three acids become 11.1, 7.2 and −0.8, in considerably better agreement with experiment for B(OH) 3 and CO 2. . . H 2O. Thus p K a calculations using this approach are accurate enough to give information on the actual acid species present in solution and the details of their acid dissociation processes at the microscopic level. 11B and 13C-NMR chemical shifts are also calculated for the various species and compared to experiment. By comparison of our calculations with experiment it is apparent that the 13C-NMR chemical shift has never been measured for an actual H 2CO 3 molecule in solution, consistent with its thermodynamic and kinetic instability with respect to CO 2 + H 2O. By contrast, the good agreement of calculated and experimental NMR shifts for the species B(OH) 3 and B(OH) 4 − support their existence in solution. Calculations of the IR spectra of H 2CO 3 and its H-bonded dimer support the idea that spectra previously assigned to condensed phase or surface H 2CO 3 are better interpreted as arising from some type of H-bonded H 2CO 3 oligomer, rather than the monomer. Calculations of the relative free energy for different isotopomers of the B and C oxyacids establish that the partitioning of 13C and 12C between CO 2(aq) and HCO 3 − is considerably different from the fractionation between hypothetical H 2CO 3 and HCO 3 −. We find a much better match to the experimental CO 2(g) vs. HCO 3 −(aq) 13,12C fractionation if the bicarbonate cluster model includes a counter ion, such as Na +. The 11,10B fractionation between B(OH) 3 and the van der Waals complex B(OH) 3. . . H 2O is quite small, while that between gas-phase B(OH) 3 and B(OH) 4 − is on the order of 30‰, in qualitative agreement with more rigorous values recently obtained from supermolecule or “water-droplet” calculations.