  In this paper we work out a parameterization of the environment noise within
the Haken-Strobl-Reinenker (HSR) model for the PE545 light-harvesting complex
based on atomic-level quantum mechanics/molecular mechanics (QM/MM)
simulations. We use this approach to investigate the role of different auto-
and cross-correlations in the HSR noise tensor, confirming that site-energy
autocorrelations (pure dephasing) terms dominate the noise-induced exciton
mobility enhancement, followed by site energy-coupling cross-correlations for
specific triplets of pigments. Interestingly, several cross-correlations of the
latter kind, together with coupling-coupling cross-correlations, display clear
low-frequency signatures in their spectral densities in the region 30-70
inverse centimeters. These slow components lie at the limits of validity of the
HSR approach, requiring that environmental fluctuations be faster than typical
exciton transfer time scales. We show that a simple coarse-grained
elastic-network-model (ENM) analysis of the PE545 protein naturally spotlights
collective normal modes in this frequency range, that represent specific
concerted motions of the subnetwork of cysteines that are covalenty linked to
the pigments. This analysis strongly suggests that protein scaffolds in
light-harvesting complexes are able to express specific collective,
low-frequency normal modes providing a fold-rooted blueprint of exciton
transport pathways. We speculate that ENM-based mixed quantum classical
methods, such as Ehrenfest dynamics, might be promising tools to disentangle
the fundamental designing principles of these dynamical processes in natural
and artificial light-harvesting structures.
