Embedding non-rigid solutes in an averaged environment: a case study on rhodopsins

Many simulation methods concerning solvated molecules are based on the assumption that the solvated species and the solvent can be characterized by some representative structure of the solute and some embedding potential corresponding to this structure. This assumption is re-examined and generalized for conformationally flexible solutes. In the proposed and investigated generalization, the solute is characterized by a set of representative structures and the corresponding embedding potentials. The representative structures are identified by means of subdividing the statistical ensemble, which in this work is generated by a constant-temperature molecular dynamics simulation. The embedding potential defined in Frozen-Density Embedding Theory is used to characterize the average effect of the solvent in each subensemble. The numerical examples concern vertical excitation energies of protonated retinal Schiff bases in protein environments. It is comprehensively shown that subensemble averaging leads to huge computational savings compared to explicit averaging of the excitation energies in the whole ensemble while introducing only minor errors.