Calculation of chromophore excited state energy shifts in response to molecular dynamics of pigment-protein complexes

The absorption and energy transfer properties of photosynthetic pigments are strongly influenced by their local environment or "site.'' Local electrostatic fields vary in time with protein and chromophore molecular movement and thus transiently influence the excited state transition properties of individual chromophores. Site-specific information is experimentally inaccessible in many light-harvesting pigment-proteins due to multiple chromophores with overlapping spectra. Full quantum mechanical calculations of each chromophores excited state properties are too computationally demanding to efficiently calculate the changing excitation energies along a molecular dynamics trajectory in a pigment-protein complex. A simplified calculation of electrostatic interactions with each chromophores ground to excited state transition, the so-called charge density coupling (CDC) for site energy, CDC, has previously been developed to address this problem. We compared CDC to more rigorous quantum chemical calculations to determine its accuracy in computing excited state energy shifts and their fluctuations within a molecular dynamics simulation of the bacteriochlorophyll containing light-harvesting Fenna-Mathews-Olson (FMO) protein. In most cases CDC calculations differed from quantum mechanical (QM) calculations in predicting both excited state energy and its fluctuations. The discrepancies arose from the inability of CDC to account for the differing effects of charge on ground and excited state electron orbitals. Results of our study show that QM calculations are indispensible for site energy computations and the quantification of contributions from different parts of the system to the overall site energy shift. We suggest an extension of QM/MM methodology of site energy shift calculations capable of accounting for long-range electrostatic potential contributions from the whole system, including solvent and ions.