Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation

TL;DR

This paper transforms density functional theory into a one-electron reduced-density-matrix functional theory to better capture static correlation effects in strongly correlated systems, maintaining computational efficiency.

Contribution

It introduces a novel transformation of DFT into a 1-RDM functional theory with added quadratic terms, improving static correlation description while preserving $O(r^{3})$ scaling.

Findings

Enhanced accuracy in static correlation for chemical structures

Effective treatment of singlet biradicals and bond dissociations

Maintains computational efficiency comparable to traditional DFT

Abstract

Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically transformed into a one-electron reduced-density-matrix (1-RDM) functional theory, which can address the limitations of DFT while retaining favorable computational scaling compared to wavefunction-based approaches. In addition to relaxing the idempotency restriction on the 1-RDM in the kinetic energy term, we add a quadratic 1-RDM-based term to DFT's density-based exchange-correlation functional. Our approach, which we implement by quadratic semidefinite programming at DFT's computational scaling of $O(r^{3})$, yields substantial improvements over traditional DFT in the description of static correlation in chemical structures and processes such as singlet biradicals and bond dissociations.