An <i>ab initio</i> molecular orbital study of the nuclear volume effects in uranium isotope fractionations

Abstract

This paper discusses the nuclear volume dependence of uranium isotope fractionations in the U(3+)-U(4+) and U(4+)-UO(2) (2+) systems by reference to a series of ab initio molecular orbital calculations. Nuclear volume-dependent terms ( identical withln K(nv)) in isotope fractionation coefficients ( identical withepsilon) are calculated from the energetic balance of the isotopomers involved in the systems. We used the Dirac-Coulomb Hartree-Fock (DCHF) method with the Gaussian-type finite-nucleus model. We employed three types of generally contracted Gaussian basis sets to check the basis set dependences. In the U(3+)-U(4+) system, the present values of ln K(nv) for uranium, other than those with the smallest double-zeta basis set, are in good agreement with previous values of ln K(nv) obtained from a numerical atomic multiconfigurational DCHF method with the Fermi-type finite-nucleus model. The present calculations reasonably reproduce the experimental value of epsilon in the U(3+)-U(4+) system, and the value of ln K(nv) in the U(4+)-UO(2) (2+) system, obtained empirically by temperature-dependent fitting of the experimental epsilon values. For instance, in the U(4+)-UO(2) (2+) system, the present ab initio ln K(nv) value for a (235)U-(238)U isotope pair is 0.002 09 using the largest basis set, while the experimental value is 0.002 24. This paper also shows that nuclear volume effects are negligibly small on the U-O bond length and two force constants of UO(2) (2+). Hence, the molecular vibrational terms of the isotope fractionation coefficients mainly depend on the nuclear mass rather than the nuclear volume.