Optimized Effective Potential Method in Current-Spin Density Functional Theory

TL;DR

This paper extends the Optimized Effective Potential method to current-spin density functional theory, enabling better modeling of magnetic systems with explicit orbital dependence and analyzing its impact on atomic energies.

Contribution

It generalizes the OEP method to CSDFT with orbital-dependent functionals and introduces a simplifying approximation for practical calculations.

Findings

Small energy lowering for current-carrying states in zero magnetic field

CSDFT results match spin DFT for non-current states

Numerical results obtained for open-shell atoms

Abstract

Current-spin density functional theory (CSDFT) provides a framework to describe interacting many-electron systems in a magnetic field which couples to both spin- and orbital-degrees of freedom. Unlike in usual (spin-) density functional theory, approximations to the exchange-correlation energy based on the model of the uniform electron gas face problems in practical applications. In this work, explicitly orbital-dependent functionals are used and a generalization of the Optimized Effective Potential (OEP) method to the CSDFT framework is presented. A simplifying approximation to the resulting integral equations for the exchange-correlation potentials is suggested. A detailed analysis of these equations is carried out for the case of open-shell atoms and numerical results are given using the exact-exchange energy functional. For zero external magnetic field, a small systematic lowering of the total energy for current-carrying states is observed due to the inclusion of the current in the Kohn-Sham scheme. For states without current, CSDFT results coincide with those of spin density functional theory.