Dependence of response functions and orbital functionals on occupation numbers

TL;DR

This paper examines how the dependence of response functions and orbital functionals on occupation numbers affects the calculation of exchange-correlation potentials in density functional theory, highlighting when variations in occupation numbers are justified.

Contribution

It clarifies the conditions under which the variation of occupation numbers can be included in the OEP method for orbital-dependent functionals.

Findings

Identifies circumstances justifying occupation number variations

Analyzes the impact on exchange-correlation potential calculations

Provides guidelines for orbital-dependent functional approximations

Abstract

Explicitly orbital-dependent approximations to the exchange-correlation energy functional of density functional theory typically not only depend on the single-particle Kohn-Sham orbitals but also on their occupation numbers in the ground state Slater determinant. The variational calculation of the corresponding exchange-correlation potentials with the Optimized Effective Potential (OEP) method therefore also requires a variation of the occupation numbers with respect to a variation in the effective single-particle potential, which is usually not taken into account. Here it is shown under which circumstances this procedure is justified.