Casimir–Polder Size Consistency: A Constraint Violated by Some Dispersion Theories

A key goal in quantum chemistry methods, whether ab initio or otherwise, is to achieve size consistency. In this work 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 nonlocal “xc kernel” physics, by up to 10% in our tests on closed-shell atoms.