  We present a detailed theoretical study of the transfer of electronic
excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein
complex, using the new developed modified scaled hierarchical approach [Shi Q.
et al, J Chem Phys 2009, 130, 084105]. We show that this approach is
computationally more efficient than the original hierarchical approach. The
modified approach reduces the truncation levels of the auxiliary density
operators and the correlation function. We provide a systematic study of how
the number of auxiliary density operators and the higher-order correlation
functions affect the exciton dynamics. The time scales of the coherent beating
are consistent with experimental observations. Furthermore, our theoretical
results exhibit population beating at physiological temperature. Additionally,
the method does not require a low-temperature correction to obtain the correct
thermal equilibrium at long times.
