Vibrational analysis frequency

Molecular descriptors must then be computed. Any numerical value that describes the molecule could be used. Many descriptors are obtained from molecular mechanics or semiempirical calculations. Energies, population analysis, and vibrational frequency analysis with its associated thermodynamic quantities are often obtained this way. Ah initio results can be used reliably, but are often avoided due to the large amount of computation necessary. The largest percentage of descriptors are easily determined values, such as molecular weights, topological indexes, moments of inertia, and so on. Table 30.1 lists some of the descriptors that have been found to be useful in previous studies. These are discussed in more detail in the review articles listed in the bibliography. 

Figure 4.8 Free amino acid ligands, gly and met, which will be useful in the vibrational frequency analysis.

The dispersion correction energy, its gradient and second derivative were implemented in the deMon2K program [29], allowing geometry optimization, Bom-Oppenheimer molecular dynamics, and vibrational frequency analysis. We used a nonscaled empirical dispersion term, unlike previously mentioned DFT-D calculations [62, 63]. 

The experimental IR spectrum for the mixture glycine-KI-l2 is provided in [21]. For the la and 11a structures of their vibrational spectra are predicted at the DFT-B3PW91/midi level. The possibility of the presence of small amounts of water molecules in the structure of solid amino acids is established by IR spectroscopy [43]. Following this suggestion when calculating the vibrational frequencies the water molecules were not eliminated from the computational models of la and Ila structures. The details of vibrational frequency analysis for the la complex are provided in [21]. 

Free Energy Gradient Method and Its Recent Related Developments Free Energy Optimization and Vibrational Frequency Analysis in Solution... 

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. 

For an application to the vibrational spectroscopy analysis, we took an H2O molecule in liquid water [42]. Initially, the structure of the H2O molecule in water was optimized by the standard FEG method for the H2O geometry to satisfy the zero-FEG condition (cf. Eq. (8.19)) using the FE-Hessian matrix (cf. Eq. 8.10). Then, to estimate INM-Hessian matrices for the vibrational frequency analysis (VFA) at the optimized stmcture q on FES, we executed ab initio QM/MM-MD simulation to apply the dual VFA (cf. Sect. 8.2.2.3) approach to the present H2O system. 

---