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A triple-layer QM/sQM/MM method was developed for accurately describing the excited-state molecular interactions between chromophore and the molecular environment (Hasegawa, J.; Yanai, K.; Ishimura, K. ChemPhysChem2015, 16, 305). A first-order-interaction space (FOIS) was defined for the interactions between QM and secondary QM (sQM) regions. Moreover, configuration interaction singles (CIS) and its second-order perturbation theory (PT2) calculations were performed within this space. In this study, numerical implementation of this FOISPT2 method significantly reduced the computing time, which realized application to solvatochromic systems, p-coumaric acid in neutral (p-CA) and anionic forms in aqueous solution, retinal Schiff base in methanol (MeOH) solution, and bacteriorhodopsin (bR). The results were consistent with the experimentally observed absorption spectra of the applied systems. The QM/sQM/MM result for the opsin shift was in better agreement to the experimental result than that of the ordinary QM/MM. A decomposition analysis was performed for the excited-state molecular interactions. Among the electronic interactions, charge-transfer (CT) effect, excitonic interaction, and dispersion interaction showed significant large contributions, while the electronic polarization effect presented only minor contribution. Furthermore, the result was analyzed to determine the contributions from each environmental molecule and was interpreted based on the distance of the molecules from the π system in the chromophores.

Electronic excitations of chromophores in proteins and solutions are associated with the electronic response of the molecular environment. The underlying interactions are important origins of solvatochromism. We performed large-scale configuration interaction singles (CIS) calculations (up to 1000 atoms) for retinal chromophores in proteins and methanol solution, in which one-electron processes (polarization and charge-transfer effects of the environment) are included. The present approach also improved the electrostatic potential, as compared to that described by a molecular mechanics (MM) force field. The CIS results were combined with the symmetry adapted cluster (SAC)-CI result using our own N-layer integrated molecular orbital molecular mechanics (ONIOM) method. As compared to the MM description, the CIS reduces the calculated excitation energy by 0.1–0.3 eV and also improves the relative excitation energies among retinal proteins. We applied our localized molecular orbital (LMO) transformation scheme to analyze the CI wave functions. The result clarified the contributions of the amino acids. In bacteriorhodopsin, Tyr185 contributes intermolecular CT excitations. The radial distribution of amino acids’ contributions to the CI wave function was also analyzed. The results of the analysis are useful not only for understanding the molecular interactions and the role of amino acids in color tuning, but also for providing insight into the structure of the excited-state wave function for the molecular environment. An excitation-energy decomposition analysis also supported the results of the excited-state wave functions.

The excited states of the three retinal proteins, bovine rhodopsin (Rh), bacteriorhodopsin (bR), and sensory rhodopsin II (sRII) were studied using the symmetry-adapted cluster-configuration interaction (SAC-CI) and combined quantum mechanical and molecular mechanical (QM/MM) methods. The computed absorption energies are in good agreement with the experimental ones for all three proteins. The spectral tuning mechanism was analyzed in terms of three contributions:  molecular structures of the chromophore in the binding pockets, electrostatic (ES) interaction of the chromophore with the surrounding protein environment, and quantum-mechanical effect between the chromophore and the counterion group. This analysis provided an insight into the mechanism of the large blue-shifts in the absorption peak position of Rh and sRII from that of bR. Protein ES effect is primarily important both in Rh and in sRII, and the structure effect is secondary important in Rh. The quantum-mechanical interaction between the chromophore and the counterion is very important for quantitative reproduction of the excitation energy. These results indicate that the present approach is useful for studying the absorption spectra and the mechanism of the color tuning in the retinal proteins.