Lagrangian of extended multiconfigurational self-consistent field second-order quasidegenerate perturbation theory combined with reference interaction site model self-consistent field constraint spatial electron density

Lagrangians of the SA multiconfigurational self-consistent field(SA-MCSCF) and multistate extended second-order quasidegenerate perturbation theory (MS-XMCQDPT2) coupled with the reference interaction site model self-consistent field constraint spatial electron density (RISM-SCF-cSED) are defined. In addition, variational equations were derived to calculate the excitation energies of target molecules dissolved in various solvents. The theory was applied to a phenol molecule in various solutions and the gradients and Hessian matrices were calculated to evaluate the absorption spectral lines including the broadening bandwidth. Numerical calculations revealed fine structures in any solvent surroundings. The main intramolecular vibrational modes related to such fine structures were stretching vibrations of the aromatic ring and the oxygen atom of the phenol molecule. The present theory plays an important role when predicting the structure of potential energy surfaces, such as Hessian matrices for various solvent types, during the photoexcitation process.