  Semiclassical electrodynamics is an appealing approach for studying
light-matter interactions, especially for realistic molecular systems. However,
there is no unique semiclassical scheme. On the one hand, intermolecular
interactions can be described instantaneously by static two-body interactions
connecting different molecules plus a classical transverse E-field; we will
call this Hamiltonian #I. On the other hand, intermolecular interactions can
also be described as effects that are mediated exclusively through a classical
one-body E-field without any quantum effects at all (assuming we ignore
electronic exchange); we will call this Hamiltonian #II. Moreover, one can also
mix these two Hamiltonians into a third, hybrid Hamiltonian, which preserves
quantum electron-electron correlations for lower excitations but describes
higher excitations in a mean-field way. To investigate which semiclassical
scheme is most reliable for practical use, here we study the real-time dynamics
of a pair of identical two-level systems (TLSs) undergoing either resonance
energy transfer (RET) or collectively driven dynamics. While all approaches
perform reasonably well when there is no strong external excitation, we find
that no single approach is perfect for all conditions. Each method has its own
distinct problems: Hamiltonian #I performs best for RET but behaves in a
complicated manner for driven dynamics. Hamiltonian #II is always stable, but
obviously fails for RET at short distances. One key finding is that, under
externally driving, a full configuration interaction description of Hamiltonian
#I strongly overestimates the long-time electronic energy, highlighting the not
obvious fact that, if one plans to merge quantum molecules with classical
light, a full, exact treatment of electron-electron correlations can actually
lead to worse results than a simple mean-field treatment.
