Strong Electron Correlation from Partition Density Functional Theory

TL;DR

This paper introduces a simple approximation within partition density functional theory that significantly improves the accuracy of modeling strongly-correlated systems, especially hydrogen chains, by reducing errors of traditional local density approximations.

Contribution

The paper presents the generalized overlap approximation (GOA) for the partition energy in PDFT, enhancing the accuracy of LDA in strongly-correlated systems without breaking spin symmetry.

Findings

GOA improves LDA dissociation curves for hydrogen chains.

GOA produces results comparable to spin-unrestricted LDA.

Additional corrections yield dissociation energies matching DMRG calculations.

Abstract

Standard approximations for the exchange-correlation (XC) functional in Kohn-Sham density functional theory (KS-DFT) typically lead to unacceptably large errors when applied to strongly-correlated electronic systems. Partition-DFT (PDFT) is a formally exact reformulation of KS-DFT in which the ground-state density and energy of a system are obtained through self-consistent calculations on isolated fragments, with a partition energy representing the \textit{inter}-fragment interactions. Here we show how typical errors of the local density approximation (LDA) in KS-DFT can be largely suppressed through a simple approximation, the generalized overlap approximation (GOA), for the partition energy in PDFT. Our method is illustrated on simple models of one-dimensional strongly-correlated linear hydrogen chains. The GOA, when used in combination with the LDA for the fragments, improves the LDA dissociation curves of hydrogen chains and produces results that are comparable to those of spin-unrestricted LDA, but without breaking the spin symmetry. GOA also induces a correction to the LDA electron density that partially captures the correct density dimerization in strongly-correlated hydrogen chains. Moreover, with an additional correction to the partition energy, the approximation is shown to produce dissociation energies in quantitative agreement to calculations based on the Density Matrix Renormalization Group method.