Separation of Dynamic and Nondynamic Correlation

TL;DR

This paper introduces a physically-sound matrix-based method to separate dynamic and nondynamic electron correlation using natural orbital occupancies, applicable to various systems, and simplifies the analysis of electron correlation regimes.

Contribution

It proposes a novel matrix formulation that separates dynamic and nondynamic correlation solely based on natural orbital occupancies, enabling local and orbital-resolved analysis.

Findings

Method effectively distinguishes correlation types in diverse systems

The correlation index depends only on natural orbitals and occupancies

The approach provides a local and orbital-resolved correlation separation

Abstract

The account of electron correlation and its efficient separation into dynamic and nondynamic parts plays a key role in the development of computational methods. In this paper we suggest a physically-sound matrix formulation to split electron correlation into dynamic and nondynamic parts using the two-particle cumulant matrix and a measure of the deviation from idempotency of the first-order density matrix. These matrices are applied to a two-electron model, giving rise to a simplified electron correlation index that ($i$) depends only on natural orbitals and their occupancies, ($ii$) can be straightforwardly decomposed into orbital contributions and ($iii$) splits into dynamic and nondynamic correlation parts that ($iv$) admit a local version. These expressions are shown to account for dynamic and nondynamic correlation in a variety of systems containing different electron correlation regimes, thus providing the first separation of dynamic and nondynamic correlation using solely natural orbital occupancies.