Hyper-Raman Spectra in Solution Based on the Reference Interaction Site Model Self-Consistent Field Method Coupled with the Constrained Spatial Electron Density Distribution and Vibrational Quasi-Degenerate Perturbation Theory

We present a new approach for calculating hyper-Raman (HR) spectra of molecules in solution, combining the reference interaction site model self-consistent field method coupled with the constrained spatial electron density distribution (RISM-SCF-cSED) and second-order vibrational quasi-degenerate perturbation theory (VQDPT2). With solvents described using the integral equation theory and anharmonic vibrations modeled with VQDPT2, this method enables the efficient computation of HR spectra in solution with a low computational cost. We demonstrate its application to water, neat <i>N</i>-methylacetamide (NMA), and acetonitrile solutions, showing that the peak positions and shifts in the HR spectra of NMA in solution are predicted with high accuracy. Furthermore, the calculated depolarization ratios for each vibronic mode showed a strong agreement with experimental results. The proposed method serves as a powerful theoretical framework for calculating molecular structures and solvation effects, such as those in biomolecules and peptide bonds, in the context of HR spectra in solution.