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

B(OH)(3) and CO2 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 pK(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, pKa values are calculated quantum mechanically for the oxyacids B(OH)(3), H2CO3 and HNO3, which have experimental first pK(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 pK(a) values of 21.6, 3.8 to 2.2 and -0.8 for the three oxyacids mentioned above, closely matching experiment only for HNO3. The discrepancies with experiment arise from the more complex nature of the acid dissociation process for B(OH)(3), which involves the addition of H2O to B(OH)3 and formation of the B(OH)(4) anion, and from the instability of hypothetical H2CO3 compared to the proper hydrated reactant complex CO2... H2O. When the proper microscopic description of the reactants and products is used the calculated pKa values for the three acids become 11.1, 7.2 and -0.8, in considerably better agreement with experiment for B(OH)(3) and CO2... H2O. Thus pKa 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. B-11 and C-13-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 C-13-NMR chemical shift has never been measured for an actual H,CO3 molecule in solution, consistent with its thermodynamic and kinetic instability with respect to CO2 + H2O. 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 H2CO3 and its H-bonded dimer support the idea that spectra previously assigned to condensed phase or surface H2CO3 are better interpreted as arising from some type of H-bonded H2CO3 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 C-13 and C-12 between CO2(aq) and HCO3- is considerably different from the fractionation between hypothetical H2CO3 and HCO3-. We find a much better match to the experimental CO2(g) vs. HCO3- (aq) C-13,C-12 fractionation if the bicarbonate cluster model includes a counter ion, such as Na+. The B-11,B-10 fractionation between B(OH)(3) and the van der Waals complex B(OH)(3)... H2O is quite small, while that between gas-phase B(OH)(3) and B(OH)(4) is on the order of 30 parts per thousand, in qualitative agreement with more rigorous values recently obtained from supermolecule or water-droplet calculations.Copyright (c) 2005 Elsevier Ltd.