  We investigate two key representative semiclassical approaches for
propagating resonant energy transfer 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
F\"orster 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.

Chemical Physics