Analytical derivatives of molecular vibrational frequencies with respect to coordinates and model potential parameters

Derivatives of vibrational frequencies are calculated with respect to molecular mechanics force field parameters and with respect to atomic Cartesian coordinate displacements. In the former case the implicit dependence of the minimum-energy configuration upon the parameters is accounted for. The frequency derivatives require the availability of third derivatives of the force field with respect to atomic Cartesian coordinates, and these have been obtained analytically. Application is made to a small and a moderate sized molecule as illustrations of the frequency derivative capability. A principal component analysis is performed for each structure and for each type of derivative, thereby identifying the most important parameters and atomic displacements. The results are interpreted in terms of molecular size, the localized nature of specific vibrational modes, and interactions known to be important in producing realistic molecular force fields. Implications of the findings for molecular mechanics and vibrational spectroscopy are discussed.