Nonanalyticity of the optimized effective potential with finite basis sets

TL;DR

This paper reveals singular behavior in finite-basis optimized effective potential equations and proposes a new analytic approach to ensure well-behaved solutions for large basis sets.

Contribution

It introduces a novel finite-basis-set OEP formulation that addresses singularities and provides an analytic solution method.

Findings

Identification of singular behavior in finite-basis OEP equations

Development of a new well-behaved OEP equation formulation

Analytic solution via matrix inversion for large basis sets

Abstract

We show that the finite-basis optimized effective potential (OEP) equations exhibit previously unknown singular behavior.Imposing continuity, we derive new well-behaved finite-basis-set OEP equations that determine OEP for any orbital and any large enough potential basis sets and which adopt an analytic solution via matrix-inversion.