Convergence of environment polarization effects in multiscale modeling of excitation energies

We present a systematic investigation of the influence of polarization effects from a surrounding medium on the excitation energies of a chromophore. We use a combined molecular dynamics and polarizable embedding time-dependent density functional theory (PE-TD-DFT) approach for chromophores in proteins and in homogeneous solvents. The mutual polarization between the chromophore and its surroundings is included in the PE-TD-DFT approach through the use of induced dipoles, placed on all atoms in the classical region, and self-consistent optimization of the quantum and classical polarizable regions. By varying the subset of sites in the environment for which atomic polarizabilities are included, we investigate to what distance from the quantum region explicit polarization effects need to be taken into account in order to provide converged excitation energies. Our study gives new insight into the range of polarization interactions for chromophores in different chemical environments. We find that the rate of convergence of excitation energies with respect to polarization cut-off is much slower for chromophores in an ordered environment such as a protein than for chromophores in a homogeneous medium such as a solvent. We show that this in part is related to the (partial) charges in the protein. Our results provide insight into how to define a representation of complex environments of different kinds in an accurate and affordable way.