Evaluation of the equilibrium constant of boron isotope fractionation between boric acid and borate (k3−4) in water is of high geochemical importance, due to its contribution in reconstruction of ancient seawater pH and atmospheric CO2. As a result, precise evaluation of k3−4 has been the subject of numerous studies, yielding diverse and controversial results. In the present study, employing three different rigorous and high-precision theoretical approaches, we provide a reliable estimation of k3−4 which is a value between 1.028 to 1.030 for both pure and saline water. Within the context of present study, we also propose partial normal mode analysis, Boltzmann weighted averaging and a revision on the Bigeleisen and Mayer method which allow a more rigorous evaluation of isotope fraction in solution and can be used for studying other isotopic systems as well.

Evaluation of the equilibrium constant of boron isotope fractionation between boric acid and borate (k3−4) in water is of high geochemical importance, due to its contribution in reconstruction of ancient seawater pH and atmospheric CO2. As a result, precise evaluation of k3−4 has been the subject of numerous studies, yielding diverse and controversial results. In the present study, employing three different rigorous and high-precision theoretical approaches, we provide a reliable estimation of k3−4 which is a value between 1.028 to 1.030 for both pure and saline water. Within the context of present study, we also propose partial normal mode analysis, Boltzmann weighted averaging and a revision on the Bigeleisen and Mayer method which allow a more rigorous evaluation of isotope fraction in solution and can be used for studying other isotopic systems as well.