F\"orster resonance energy transfer, absorption and emission spectra in multichromophoric systems: I. Cumulant expansions

We study the F\"orster resonant energy transfer (FRET) rate in multichromophoric systems. The multichromophoric FRET rate is determined by the overlap integral of the donor's emission and acceptor's absorption spectra, which are obtained via 2nd-order cumulant expansion techniques developed in this work. We calculate the spectra and multichromophoric FRET rate for both localized and delocalized systems. (i) The role of the initial entanglement between the donor and its bath is found to be crucial in both the emission spectrum and the multichromophoric FRET rate. (ii) The absorption spectra obtained by the cumulant expansion method are quite close to the exact one for both localized and delocalized systems, even when the system-bath coupling is far from the perturbative regime. (iii) For the emission spectra, the cumulant expansion can give very good results for the localized system, but fail to obtain reliable spectra of the high excitations of a delocalized system, when the system-bath coupling is large and the thermal energy is small. (iv) Even though, the multichromophoric FRET rate is good enough since it is determined by the overlap integral of the spectra.