Unity of Kohn-Sham Density Functional Theory and Reduced Density Matrix Functional Theory

TL;DR

This paper introduces a unified theoretical framework combining Kohn-Sham DFT and RDMFT through hypercomplex orbitals, enabling better treatment of strongly correlated systems and expanding the potential of density functional methods.

Contribution

It develops hypercomplex Kohn-Sham theory (HCKS) that unifies KS-DFT and RDMFT, allowing dynamic fractional occupations to address strong correlation.

Findings

HCKS captures multi-reference strong correlation effects.

HCKS outperforms traditional KS-DFT on transition metal systems.

HCKS provides a new pathway for DFT development.

Abstract

This work presents a theory to unify the two independent theoretical frameworks of Kohn-Sham (KS) density functional theory (DFT) and reduced density matrix functional theory (RDMFT). The generalization of the KS orbitals to hypercomplex number systems leads to the hypercomplex KS (HCKS) theory, which extends the search space for the density in KS-DFT to a space that is equivalent to natural spin orbitals with fractional occupations in RDMFT. Thereby, HCKS is able to capture the multi-reference nature of strong correlation by dynamically varying fractional occupations. Moreover, the potential of HCKS to overcome the fundamental limitations of KS is verified on systems with strong correlation, including atoms of transition metals. As a promising alternative to the realization of DFT, HCKS opens up new possibilities for the development and application of DFT in the future.