An Exchange-Based Diagnostic for Static Correlation

TL;DR

This paper introduces a DFT-based diagnostic for static correlation that effectively measures the difference between DFT and HF exchange energies, providing a cost-effective way to assess static correlation importance.

Contribution

It presents a new, intuitive diagnostic based on exchange energy differences and analyzes the main factors explaining static correlation variation.

Findings

The diagnostic correlates well with existing measures of static correlation.

Principal component analysis reveals four main factors explaining variation.

The diagnostic is computationally efficient and intuitive.

Abstract

We propose here a DFT-based diagnostic for static correlation %TAEX[TPSS@HF - HF] which effectively measures how different the DFT and HF exchange energies for a given HF density are. This and %TAEcorr[TPSS] are two cost-effective a priori estimates for the adequacy of the importance of static correlation. %TAEX[TPSS@HF - HF] contains nearly the same information as the earlier A diagnostic, but may be more intuitive to understand. Principal component and variable clustering analysis of a large number of static correlation diagnostics reveals much of the variation is explained by just two components, and almost all of it by four; these are blocked by four variable clusters (single excitations; correlation entropy; double excitations; pragmatic energetics).