Relativistic kinetic energies and mass–velocity corrections in diatomic molecules

Abstract

Expectation values of various operators with respect to nonrelativistic, self-consistent-field wave functions of good quality for 46 diatomic molecules are computed to examine the differences between the relativistic kinetic energy 〈Hr〉 and the quasirelativistic kinetic energy 〈Tnr〉+〈Hmv〉 in which 〈Tnr〉 is the nonrelativistic kinetic energy and 〈Hmv〉 is the mass–velocity correction. Then 〈Hrc〉=〈Hr〉−〈Tnr〉=〈H mv〉+〈δE〉 is the full relativistic correction to the kinetic energy. 〈Hrc〉 can differ appreciably from 〈Hmv〉 for molecules containing at least one atom with a moderately large atomic number Z. These differences are greatly amplified when the relativistic corrections to dissociation energies are considered; the mass–velocity contribution to the binding energy is found to be inaccurate even for moderate values of Z. Great care is necessary to ensure that the molecular and atomic calculations are of comparable accuracy. A qualitative argument is provided to explain why 〈Hmv〉 can provide a reasonable approximation to 〈Hrc〉 for small enough Z despite the fact that the two operators are inequivalent for αp≥1 where α is the fine structure constant and p is the momentum. Finally the asymptotic behavior of the pertinent integrands is used to show why the numerical evaluation, in momentum space, of 〈Hrc〉 is easier than that of 〈Hmv〉.