Spectra and Dynamics in the B800 Antenna: Comparing Hierarchical Equations, Redfield and Forster Theories

We model the spectra (absorption and circular dichroism) and excitation dynamics in the B800 ring of the LH2 antenna complex from Rs. molischianum using different theoretical approaches, i.e., Forster theory, standard and modified versions of the Redfield theory, and the more versatile nonperturbative approach based on hierarchically coupled equations for the reduced density operator. We demonstrate that, although excitations in the B800 ring are localized due to disorder, thermal effects, and phonons, there are still sizable excitonic effects producing shift, narrowing, and asymmetry of the spectra. Moreover, the excitation dynamics reveals the presence of long-lived (up to 1 ps) non-oscillatory coherences between the exciton states maintained due to nonsecular population-to-coherence transfers. The sub-ps decay of the coherences is followed by slow motion of the excitation around the ring, producing equilibration of the site populations with a time constant of about 3-4 ps, which is slower than the B800 -> B850 transfer. The exact solution obtained with the hierarchical equations is compared with other approaches, thus illustrating limitations of the Forster and Redfield pictures.