Optimized Effective Potentials in Finite Basis Sets

Abstract

The finite basis optimized effective potential (OEP) method within density functional theory is examined as an ill-posed problem. It is shown that the generation of nonphysical potentials is a controllable manifestation of the use of unbalanced, and thus unsuitable, basis sets. A modified functional incorporating a regularizing smoothness measure of the OEP is introduced. This provides a condition on balanced basis sets for the potential, as well as a method to determine the most appropriate OEP and energy from calculations performed with any finite basis set.

Nonanalyticity of the optimized effective potential with finite basis sets

“…In general, the problem of how to separate the singular (g ν ) from the nonsingular (g α ) eigenvalues of A kn is considered not straightforward and ill-posed [20,27]. We focus on this problem in a forthcoming publication [28], where we follow Ref.…”

“…Several attempts have been made to overcome these issues [13][14][15][16][17][18][19][20] but with limited success so far. As a result and despite promise, interest in OEP has diminished.…”

Reply to “Comment on ‘Nonanalyticity of the optimized effective potential with finite basis sets’ ”

“…Understanding this pathological behavior is the aim of our paper [1] that is criticized in the Comment by Friedrich et al [2]. This pathological behavior was demonstrated by several authors in the past [3][4][5][6][7][8].…”

Exchange-only optimized-effective-potential calculations using Slater-type basis functions: Atoms and diatomic molecules

“…The xOEP equations in a basis-set representation are obtained from the minimization of the total energy presented in Eq. (2) with respect to the local potential V σ (r) [25,29], this minimization being equivalent to the minimization with respect to the density by virtue of the Sham-Schlüter condition [7] and the Hohenberg-Kohn theorems [1].…”

“…An expansion of the exchange part of the local potential is assumed in terms of an appropriate set of functions [20,22,24,25,29,30],…”