Dual VFA approach

To investigate vibrational properties of solute molecules in solution, we have proposed a new theoretical method as a direct extension of the FEG one, i.e., the dual approach to the vibrational frequency analysis (VFA) [31]. By employing the dual VFA approach, we can simultaneously obtain the effective vibrational normal modes and the vibrational spectra in solution, which uses complementarily two kinds of Hessian matrices obtained by the equilibrium QM/MM-MD trajectories, that is, a unique Hessian on the FES (i.e., the FE-Hessian) and a sequence of instantaneous ones (i.e., the instantaneous normal mode Hessians INM-Hessians). Figure 8.1 shows a schematic chart of the dual VFA approach. First, we execute the QM/MM-MD simulation and collect many solvent conformations around the solute molecule being fixed at q, sequentially numbered. Second, we obtain an FE-Hessian as the average of instantaneous Hessian matrices at those conformations and then, by diagonalizing the FE-Hessian (cf. Eq. (8.11 a)), we can obtain a set of FE normal coordinates Qi and FE vibrational frequencies coi of the solute molecule in solution. 

Finally, as for the third issue (iii), the dual VFA approach [31] proposed in Sect. S.2.2.3, is one possible solution and some examples are discussed in the following sections. 

We applied the dual VFA approach to a neutral form (NF) glycine molecule in aqueous solution and compared the calculation results with those estimated by the conductor-like polarizable continuum model (CPCM) method in order to extract the explicit solvation effects. Table 8.1 shows a triple of typical vibrational frequencies (cugas, cocpcMi coee) of glycine molecule in the isolated state and in aqueous solution with their vibrational frequency shifts, (AcocpcM) Acofe). evaluated by two types of solute-solvent interactions, i.e., the CPCM and QM/MM method, scaled by the recommended factor of 0.9418 [43]. In addition, they were compared with the experimental values Acoexp obtained by the Fourier transform infrared (FT-IR)... 

---