Exactly factorized molecular Kohn-Sham density functional theory

TL;DR

This paper introduces a novel exact factorization approach to molecular Kohn-Sham density functional theory, enabling a more detailed treatment of electron-nuclear interactions beyond the Born-Oppenheimer approximation.

Contribution

It applies the exact factorization formalism to the molecular KS wavefunction, resulting in coupled marginal and conditional KS equations that extend traditional KS-DFT.

Findings

New coupled KS equations derived from exact factorization

Potential for practical extension beyond Born-Oppenheimer approximation

Discussion on correlations induced by second-order derivatives

Abstract

Fromager and Lasorne [Electron. Struct. 6 025002 (2024)] have recently derived an in-principle exact Kohn-Sham density functional theory (KS-DFT) of electrons and nuclei, where the nuclear density and the (so-called conditional) electronic density are mapped onto a fictitious electronically non-interacting KS molecule. In this work, we apply the exact factorization formalism to the molecular KS wavefunction, thus leading to disentangled (but coupled) marginal and conditional KS equations. We show that, while being equivalent to the original theory, these equations open new perspectives in the practical extension of regular (electronic) KS-DFT beyond the Born-Oppenheimer approximation. The importance and treatment of correlations induced in this context by second-order geometrical derivatives is also discussed.