Casimir-Polder size consistency -- a constraint violated by some dispersion theories

TL;DR

This paper introduces the concept of Casimir-Polder size consistency in quantum chemistry, highlighting how certain local approximations in dispersion energy calculations violate this principle due to incorrect non-local physics treatment.

Contribution

It formulates Casimir-Polder size consistency and demonstrates its violation in local TDDFT dispersion calculations, revealing a fundamental limitation in current methods.

Findings

Local TDDFT dispersion calculations violate size consistency by up to 10%

Incorrect treatment of non-local xc kernel physics causes the violation

Highlights the need for non-local approaches in dispersion energy computations

Abstract

A key goal in quantum chemistry methods, whether ab initio or otherwise, is to achieve size consistency. In this manuscript we formulate the related idea of "Casimir-Polder size consistency" that manifests in long-range dispersion energetics. We show that local approximations in time-dependent density functional theory dispersion energy calculations violate the consistency condition because of incorrect treatment of highly non-local "xc kernel" physics, by up to 10% in our tests on closed-shell atoms.