  We explore excitonic energy transfer dynamics in a molecular dimer system
coupled to both structured and unstructured oscillator environments. By
extending the reaction coordinate master equation technique developed in [J.
Iles-Smith, N. Lambert, and A. Nazir, Phys. Rev. A 90, 032114 (2014)], we go
beyond the commonly used Born-Markov approximations to incorporate
system-environment correlations and the resultant non-Markovian dynamical
effects. We obtain energy transfer dynamics for both underdamped and overdamped
oscillator environments that are in perfect agreement with the numerical
hierarchical equations of motion over a wide range of parameters. Furthermore,
we show that the Zusman equations, which may be obtained in a semiclassical
limit of the reaction coordinate model, are often incapable of describing the
correct dynamical behaviour. This demonstrates the necessity of properly
accounting for quantum correlations generated between the system and its
environment when the Born-Markov approximations no longer hold. Finally, we
apply the reaction coordinate formalism to the case of a structured environment
comprising of both underdamped (i.e. sharply peaked) and overdamped (broad)
components simultaneously. We find that though an enhancement of the dimer
energy transfer rate can be obtained when compared to an unstructured
environment, its magnitude is rather sensitive to both the dimer-peak resonance
conditions and the relative strengths of the underdamped and overdamped
contributions.
