Domain-averaged Fermi hole versus regional reduced density matrices: a critical comparison

TL;DR

This paper critically compares the domain-averaged Fermi hole method with regional reduced density matrices, clarifying conceptual differences and addressing recent proposals in electronic population analysis.

Contribution

It clarifies that the recent DAFH approximation is not a true approximation of the domain-averaged Fermi hole and relates it to existing reduced density matrix frameworks.

Findings

The proposed DAFH approximation is not conceptually equivalent to the domain-averaged Fermi hole.

Existing domain-restricted reduced density matrices encompass the proposed method.

The paper provides a critical analysis of the conceptual differences between the two approaches.

Abstract

In their recent work Cooper and Ponec [Phys. Chem. Chem. Phys., 2008, 10, 1319-1329] proposed a ``one-electron approximation to domain-averaged Fermi hole (DAFH)" used in electronic population studies. The goal of this comment is to note that the proposal had been already published within the framework of domain-restricted reduced density matrices ($\mathrm{\Omega}$-RDM) and to show that it cannot conceptually be considered as an approximation to DAFH as the authors invoke.