Range separation of the Coulomb hole

TL;DR

This paper introduces a range-separated approach to analyze the Coulomb hole, distinguishing between short- and long-range electron correlation components to improve understanding and modeling of electron correlation in molecules.

Contribution

It provides a detailed analysis of the Coulomb hole components, linking them to correlation regimes and proposing their use in developing more efficient electronic structure methods.

Findings

hcI identifies molecules with nondynamic correlation

hcI retrieves long-range electron correlation

Coulomb hole components distinguish different correlation regimes

Abstract

A range-separation of the Coulomb hole into two components, one of them being predominant at long interelectronic separations (hcI ) and the other at short distances (hcII ), is exhaustively analyzed throughout various examples that put forward the most relevant features of this approach and how they can be used to develop efficient ways to capture electron correlation. We show that hcI , which only depends on the first-order reduced density matrix, can be used to identify molecules with a predominant nondynamic correlation regime and differentiate between two types of nondynamic correlation, types A and B. Through the asymptotic properties of the hole components, we explain how hcI can retrieve the long-range part of electron correlation. We perform an exhaustive analysis of the hydrogen molecule in a minimal basis set, dissecting the hole contributions into spin components. We also analyze the simplest molecule presenting a dispersion interaction and how hcII helps identify it. The study of several atoms in different spin states reveals that the Coulomb hole components distinguish correlation regimes that are not apparent from the entire hole. The results of this work hold the promise to aid in developing new electronic structure methods that efficiently capture electron correlation.