A Necessary Trade-off for Semiclassical Electrodynamics: Accurate Short-Range Coulomb Interactions versus the Enforcement of Causality?

J Phys Chem Lett. 2018 Oct 18;9(20):5955-5961. doi: 10.1021/acs.jpclett.8b02309. Epub 2018 Oct 2.

Abstract

We investigate two key representative semiclassical approaches for propagating resonant energy transfer (RET) between a pair of electronic two-level systems (donor and acceptor) with coupled Maxwell-Liouville equations. On the one hand, when the electromagnetic (EM) field is treated classically and Coulomb interactions are treated quantum-mechanically, we find that a quantum-classical mismatch leads to a violation of causality, i.e., the acceptor can be excited before the retarded EM field arrives. On the other hand, if we invoke a classical intermolecular Coulomb operator, we find that the energy transfer in the near field loses quantitative accuracy compared with Förster theory, even though causality is strictly obeyed. Thus, our work raises a fundamental paradox when choosing a semiclassical electrodynamics algorithm. Namely, which is more important: Accurate short-range interactions or long-range causality? Apparently, one cannot have one's cake and eat it too.