Enhancing Density Functional Theory for Static Correlation in Large Molecules

TL;DR

This paper improves density functional theory (DFT) for large molecules by renormalizing a key matrix, enhancing its ability to accurately handle static electron correlation without increasing computational cost.

Contribution

The authors introduce a renormalization technique for a generalized DFT that improves static correlation treatment in large molecules while maintaining $O(N^3)$ scaling.

Findings

Accurately predicts static correlation in large molecules.

Retains computational efficiency of $O(N^3)$.

Successfully applied to hydrogen chains and acenes.

Abstract

A critical challenge for density functional theory (DFT) in practice is its limited ability to treat static electron correlation, leading to errors in its prediction of charges, multiradicals, and reaction barriers. Recently, we combined one- and two-electron reduced density matrix theories with DFT to obtain a universal $O(N^3)$ generalization of DFT for static correlation. In this Letter, we enhance the theory's treatment of large molecules by renormalizing the trace of the two-electron identity matrix in the correction using Cauchy-Schwarz inequalities of the electron-electron repulsion matrix. We apply the resulting functional theory to linear hydrogen chains as well as the prediction of the singlet-triplet gap and equilibrium geometries of a series of acenes. This renormalization of the generalized DFT retains the $O(N^{3})$ computational scaling of DFT while enabling the accurate treatment of static correlation for a broad range of molecules and materials.