  The fundamental physical mechanisms of energy transfer in photosynthetic
complexes is not yet fully understood. In particular, the degree of efficiency
or sensitivity of these systems for energy transfer is not known given their
non-perturbative and non-Markovian interactions with proteins backbone and
surrounding photonic and phononic environments. One major problem in studying
light-harvesting complexes has been the lack of an efficient method for
simulation of their dynamics in biological environments. To this end, here we
revisit the second-order time-convolution (TC2) master equation and examine its
reliability beyond extreme Markovian and perturbative limits. In particular, we
present a derivation of TC2 without making the usual weak system-bath coupling
assumption. Using this equation, we explore the long time behaviour of exciton
dynamics of Fenna-Matthews-Olson (FMO) protein complex. Moreover, we introduce
a constructive error analysis to estimate the accuracy of TC2 equation in
calculating energy transfer efficiency, exhibiting reliable performance for
environments with weak and intermediate memory and strength. Furthermore, we
numerically show that energy transfer efficiency is optimal and robust for the
FMO protein complex of green sulphur bacteria with respect to variations in
reorganization energy and bath correlation time-scales.
