Relativistic kinetic energies and massndash;velocity corrections in diatomic molecules

摘要

Expectation values of various operators with respect to nonrelativistic, selfhyphen;consistenthyphen;field wave functions of good quality for 46 diatomic molecules are computed to examine the differences between the relativistic kinetic energy lang;Hrrang; and the quasirelativistic kinetic energy lang;Tnrrang;+lang;Hmvrang; in which lang;Tnrrang; is the nonrelativistic kinetic energy and lang;Hmvrang; is the massndash;velocity correction. Then lang;Hrcrang;=lang;Hrrang;minus;lang;Tnrrang;=lang;Hmvrang;+lang;dgr;Erang; is the full relativistic correction to the kinetic energy. lang;Hrcrang; can differ appreciably from lang;Hmvrang; for molecules containing at least one atom with a moderately large atomic numberZ. These differences are greatly amplified when the relativistic corrections to dissociation energies are considered; the massndash;velocity contribution to the binding energy is found to be inaccurate even for moderate values ofZ. Great care is necessary to ensure that the molecular and atomic calculations are of comparable accuracy. A qualitative argument is provided to explain why lang;Hmvrang; can provide a reasonable approximation to lang;Hrcrang; for small enoughZdespite the fact that the two operators are inequivalent for agr;pge;1 where agr; is the fine structure constant andpis the momentum. Finally the asymptotic behavior of the pertinent integrands is used to show why the numerical evaluation, in momentum space, of lang;Hrcrang; is easier than that of lang;Hmvrang;.