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We investigate two key representative semiclassical approaches forpropagating resonant energy transfer between a pair of electronic two-levelsystems (donor and acceptor) with coupled Maxwell-Liouville equations. On theone hand, when the electromagnetic (EM) field is treated classically andCoulomb interactions are treated quantum-mechanically, we find that aquantum-classical mismatch leads to a violation of causality, i.e., theacceptor can be excited before the retarded EM field arrives. On the otherhand, if we invoke a classical intermolecular Coulomb operator, we find thatthe energy transfer in the near field loses quantitative accuracy compared withF\"orster theory, even though causality is strictly obeyed. Thus, our workraises a fundamental paradox when choosing a semiclassical electrodynamicsalgorithm. Namely, which is more important: Accurate short range interactionsor long range causality? Apparently, one cannot have one's cake and eat it too.

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