First-Principles Models for Biological Light-Harvesting: Phycobiliprotein Complexes from Cryptophyte Algae

There have been numerous efforts, both experimental and theoretical, that have attempted to parametrize model Hamiltonians to describe excited state energy transfer in photosynthetic light harvesting systems. The Frenkel exciton model, with its set of electronically coupled two level chromophores that are each linearly coupled to dissipative baths of harmonic oscillators, has become the workhorse of this field. The challenges to parametrizing such Hamiltonians have been their uniqueness, and physical interpretation. Here we present a computational approach that uses accurate first-principles electronic structure methods to compute unique model parameters for a collection of local minima that are sampled with molecular dynamics and QM geometry optimization enabling the construction of an ensemble of local models that captures fluctuations as these systems move between local basins of inherent structure. The accuracy, robustness, and reliability of the approach is demonstrated in an application to the phycobiliprotein light harvesting complexes from cryptophyte algae. Our computed Hamiltonian ensemble provides a first-principles description of inhomogeneous broadening processes, and a standard approximate non-Markovian reduced density matrix dynamics description is used to estimate lifetime broadening contributions to the spectral line shape arising from electronic-vibrational coupling. Despite the overbroadening arising from this approximate line shape theory, we demonstrate that our model Hamiltonian ensemble approach is able to provide a reliable fully first-principles method for computation of spectra and can distinguish the influence of different chromophore protonation states in experimental results. A key feature in the dynamics of these systems is the excitation of intrachromophore vibrations upon electronic excitation and energy transfer. We demonstrate that the Hamiltonian ensemble approach provides a reliable first-principles description of these contributions that have been detailed in recent broad-band pump-probe and two-dimensional electronic spectroscopy experiments.