Approximate two-electron spin-orbit coupling term for density-functional-theory DFT calculations using the Douglas-Kroll-Hess transformation

Abstract

A simple approximation is developed for the two-electron spin-orbit coupling terms generated by the Douglas-Kroll-Hess transformation, in the context of density-functional theory (DFT). For the special case of an isolated atom, the two-electron spin-orbit matrix element for each pair of basis functions of type l is replaced with the spin-orbit matrix element for a point charge $\ensuremath{-}Q(l)$ placed at the origin; where $Q(l)=0,2,10,28,\dots{}.$ Application of this screened-nuclear-spin-orbit (SNSO) approximation to linear combination of Gaussian-type orbital (LCGTO) DFT calculations on Ce, Ta, and Pu atoms yields spin-orbit splittings that agree with results from a numerical solution of the Dirac-Kohn-Sham equations to within about 6%. This is a marked improvement over the nuclear-only spin-orbit approximation, which systematically overestimates spin-orbit splittings; in some cases by as much as 100%. Crystalline LCGTO DFT calculations on the fcc phases of the light-actinide metals $\mathrm{Th}\ensuremath{\rightarrow}\mathrm{Pu},$ using a multiatom generalization of the SNSO approximation, yield atomic volumes that are in excellent agreement with results from full-potential linear-augmented-plane-wave calculations.