Modelling excited states by random walks in biomolecules of increasing complexity

Abstract

The development of theoretical methods in quantum chemistry has targeted for a long time the description of ground-state properties and, only recently, the attention has moved to the evaluation of excited states. Here, we develop novel theoretical tools and provide in-depth insight on the simulation of structural relaxation in the excited state also beyond the gas phase, and on the description of the coupling of the active site with its surroundings in the computation of the absorption energies of a realistic photobiological system. We first investigate the excited-state geometry optimization in the gas phase of small molecules using quantum Monte Carlo (QMC), which turns out to be a robust approach when compared with other correlated methods or with the time-dependent density functional theory (TDDFT). Strong of these findings, we combine QMC with the polarizable continuum model (PCM) to perform excited-state geometry optimization in solution finding that all the investigated TDDFT functionals overestimate the excited-state geometrical response to the presence of a solvent. Then, we model the absorption properties of solvated molecules using a discrete representation of the environment. We introduce a quantum-in-classical multiscale scheme combining QMC with classical polarizable dipoles. The comparison with supermolecular calculations reveals that the use of two sets of state-specific dipoles, separately equilibrated with the states involved in the electronic transition, leads to superior results than the use of a frozen environment. Finally, this approach is used in the study of the light absorption of retinal in rhodopsin, inducing the dipoles also within linear-response theory. The differential polarization effects recovered with the state-specific embedding ameliorate the agreement with absorption experiments with respect to the use of point charges but do not account for the full description of the chromophore-protein coupling. The use of dipoles obtained within linear-response theory has also a large impact on the excitation, indicating that non-classical, resonant interactions between retinal and the protein environment are also important. When this effect is accounted for together with the electrostatic response of the environment to the electronic transition, we obtain excitation energies in good agreement with the experimental absorption maximum of rhodopsin.