Analysis of multi-configuration Kohn-Sham methods

TL;DR

This paper extends Kohn-Sham density functional theory to multiconfiguration wavefunctions, deriving new equations and analyzing conditions under which wavefunctions collapse to single determinants at the ground state.

Contribution

It introduces a rigorous multiconfiguration Kohn-Sham framework, deriving energy functionals and equations, and clarifies the collapse behavior of wavefunctions at the ground state.

Findings

Multiconfiguration wavefunctions collapse to single determinants at ground state.

Derived proper energy functionals for multiconfiguration Kohn-Sham methods.

Discussed non-collapse scenarios in partially interacting auxiliary systems.

Abstract

We consider the extension of the standard single-determinant Kohn-Sham method to the case of a multiconfiguration trial wavefunction. By applying the rigorous Kohn-Sham method to this case, we construct the proper interacting and non-interacting energy functionals. Following the Hohenberg-Kohn theorem for both energy functionals, we derive the corre-sponding multiconfiguration Kohn-Sham equations. At the end of the analysis we show that, at the ground state, the multiconfiguration wavefunction must collapse into a single-determinant wavefunction, equal to the regular KS wavefunction. We also discuss the non-collapse of the wavefunction in other multiconfiguration density functional theory methods where the auxiliary system is partially interacting.