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

TL;DR

This paper extends Coulomb interaction models in density functional theory to include spin-orbit coupling in the $jm_j$ basis, improving accuracy for $f$-state elements like plutonium by considering full Coulomb matrices and spin-flip terms.

Contribution

It generalizes the Coulomb interaction treatment to the $jm_j$ basis with spin-orbit coupling, including spin-flip terms, for better modeling of complex $f$-electron systems.

Findings

$jm_j$ basis yields accurate Coulomb matrix approximations.

Density-density approximation is effective in the $jm_j$ basis.

Results improve modeling of plutonium's electronic structure.

Abstract

Attempts to go beyond the local density approximation (LDA) of Density Functional Theory (DFT) have been increasingly based on the incorporation of more realistic Coulomb interactions. In their earliest implementations, methods like LDA+$U$, LDA + DMFT (Dynamical Mean Field Theory), and LDA+Gutzwiller used a simple model interaction $U$. In this article we generalize the solution of the full Coulomb matrix involving $F^{(0)}$ to $F^{(6)}$ parameters, which is usually presented in terms of an $\ell m_\ell$ basis, into a $jm_{j}$ 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 like plutonium, which we use as an example of our theory. Close attention will be paid to spin-flip terms, which are important in multiplet theory but that have been usually neglected in these kinds of studies. We find that, in a density-density approximation, the $jm_j$ basis results provide a very good approximation to the full Coulomb matrix result, in contrast to the much less accurate results for the more conventional $\ell m_\ell$ basis.