  Understanding the mechanisms of efficient and robust energy transfer in
light-harvesting systems provides new insights for the optimal design of
artificial systems. In this paper, we use the Fenna-Matthews-Olson (FMO)
protein complex and phycocyanin 645 (PC 645) to explore the general dependence
on physical parameters that help maximize the efficiency and maintain its
stability. With the Haken-Strobl model, the maximal energy transfer efficiency
(ETE) is achieved under an intermediate optimal value of dephasing rate. To
avoid the infinite temperature assumption in the Haken-Strobl model and the
failure of the Redfield equation in predicting the Forster rate behavior, we
use the generalized Bloch-Redfield (GBR) equation approach to correctly
describe dissipative exciton dynamics and find that maximal ETE can be achieved
under various physical conditions, including temperature, reorganization
energy, and spatial-temporal correlations in noise. We also identify regimes of
reorganization energy where the ETE changes monotonically with temperature or
spatial correlation and therefore cannot be optimized with respect to these two
variables.
