Including protein density relaxation effects in first-principles embedding calculations of cofactor excitation energies

The Three-Partition Frozen Density Embedding (3-FDE) method is applied to the photosynthetic Fenna-Matthews-Olson (FMO) complex of green sulphur bacteria in order to determine cofactor excitation energies. We present a sophisticated multi-layer embedding protocol, which allows to choose fragments of arbitrary size. This is useful in order to limit the total number of calculations, which can create a significant overhead. The approach allows to determine fully polarised densities for realistic proteins in this framework for the first time. A solvent shell around the total system is described in terms of the LoCOSMO algorithm, which tremendously simplifies the computational effort of a continuum description around a system of this size. The solvent response to the excitation is incorporated by a new extension of the LoCOSMO scheme to time-dependent density functional theory. Excitation energies for the chromophores are calculated under the influence of density-based embedding potentials obtained with different technical settings. It is found that protein density relaxation in this particular example hardly influences the transitions, indicating that embedding of the pigments in the initial protein density is sufficient to determine site energy modulations with our approach.