Holomorphic Density Functional Theory

TL;DR

This paper introduces holomorphic DFT, a complex-analytic extension of density functional theory, enabling continuous tracking of multiple SCF solutions across molecular structures and functionals, revealing their coalescence and disappearance.

Contribution

It develops a novel holomorphic DFT framework that allows analytical continuation of SCF solutions, bridging the gap between HF and KS-DFT methods.

Findings

Multiple solutions can coalesce and vanish during functional changes.

Holomorphic DFT enables continuous tracking of all SCF solutions.

The approach provides new insights into the solution landscape of DFT.

Abstract

Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham Density Functional Theory (KS-DFT) both have the potential to yield multiple solutions. However, the formal relationship between multiple solutions identified using HF or KS-DFT remains generally unknown. We investigate the connection between multiple SCF solutions for HF or KS-DFT by introducing a parametrised functional that scales between the two representations. Using the hydrogen molecule and a model of electron transfer, we continuously map multiple solutions from the HF potential to a KS-DFT description. We discover that multiple solutions can coalesce and vanish as the functional changes, forming a direct analogy with the disappearance of real HF solutions along a change in molecular structure. To overcome this disappearance of solutions, we develop a complex-analytic extension of DFT - the "holomorphic DFT" approach - that allows every SCF stationary state to be analytically continued across all molecular structures and exchange-correlation functionals.