Calculations of Reduced Partition Function Ratios of Monomeric and Dimeric Boric Acids and Borates by the ab initio Molecular Orbital Theory

Abstract

With the final goal to elucidate boron isotope fractionation observed experimentally, molecular orbital calculations were performed on boric acid and borate monomers and dimers. The geometries of B(OH)3 and B(OH)4 − were first optimized and their vibrational frequencies were calculated at their optimized structures. The estimated 11B-to-10B isotopic reduced partition function ratios (RPFRs) of B(OH)3 and B(OH)4 − and the calculated equilibrium constant of the boron isotope exchange reaction between the two boron species revealed that a more advanced molecular orbital theory with a higher level basis set did not necessarily yield better results. It was concluded that HF/6-31G(d) calculations were most appropriate for the present purpose. The RPFRs of the dimers, H4B2O5, H5B2O6AJA- and H6B2AJA-, estimated from the RPFRs of the monomers by the use of additivity of the logarithm of RPFRs agreed with those calculated using the frequencies of the dimers within a margin of 1%. This error corresponded to the error of 5% on In(RPFR). The equilibrium constant of boron isotope exchange reaction between two boron species among the monomer and dimers at 25°C varied from 1.0207 to 1.0360, indicating the importance of accurate estimation of the RPFRs of polyboric acids and polyborates in real systems.