Polarizable continuum model with the fragment molecular orbital-based time-dependent density functional theory

The polarizable continuum model (PCM) for describing the solvent effect was combined with the fragment molecular orbital-based time-dependent density functional theory (TDDFT). Several levels of the many-body expansion were implemented, and the importance of the many-body contributions to the singlet-excited states was discussed. To calibrate the accuracy, we performed a number of the model calculations using our method and the regular TDDFT in solution, applying them to phenol and polypeptides at the long-range corrected BLYP/6-31G* level. It was found that for systems up to 192 atoms the largest error in the excitation energy was 0.006 eV (vs. the regular TDDFT/PCM of the full system). The solvent shifts and the conformer effects were discussed, and the scaling was found to be nearly linear. Finally, we applied our method to the lowest singlet excitation of the photoactive yellow protein (PYP) in aqueous solution and determined the excitation energy to be in reasonable agreement with experiment. The excitation energy analysis provided the contributions of individual residues, and the main factors as well as their solvent shifts were determined.