Coulomb correlation in the presence of spin-orbit coupling: Application to plutonium

Abstract

Attempts to go beyond the local density approximation (LDA) of the density functional theory (DFT) have been increasingly based on the incorporation of more realistic Coulomb interactions. In their earliest implementations, methods such as $\text{LDA}+U$, $\text{LDA}+\text{dynamical}$ mean-field theory, and $\text{LDA}+\text{Gutzwiller}$ used a simple model interaction $U$. In this paper, we generalize the solution of the full Coulomb matrix involving ${F}^{(0)}--{F}^{(6)}$ parameters, which is usually presented in terms of an $\ensuremath{\ell}{m}_{\ensuremath{\ell}}$ basis, into a $j{m}_{j}$ basis of the total angular momentum, where we also include spin-orbit coupling; this type of theory is needed for a reliable description of $f$-state elements such as plutonium, which we use as an example of our theory. Close attention will be paid to spin-flip terms, which are important in the multiplet theory but have been usually neglected in these kinds of studies. We find that, in a density-density approximation, the $j{m}_{j}$ basis results provide a very good approximation to the full Coulomb matrix result, which is in contrast to the much less accurate results for the more conventional $\ensuremath{\ell}{m}_{\ensuremath{\ell}}$ basis.