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

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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, H5B2O6− and H6B2O72−, 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 ln(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.
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