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amplitude of a normal mode. To each "eigenvector" there belongs an "eigenvalue" representing the characteristic frequency of this normal mode. Six of the 3n frequencies are zero, corresponding to the 3 translations and 3 rotations of the molecule,and the remaining 3n~6 are the molecular harmonic frequencies. Once the eigenvectors are derived in Cartesian coordinates, they can be transformed to internal coordinates where the symmetry prOperties of the normal modes are easily recognized. This formalism for calculating vibrational normal modes is particularly Suitable for large computers. It requires one and the same program for any molecule, provided sufficient computer space and time are available. It is, however, much more than a convenient formalism. Its main innovation is that it links together the calculation of the static properties — the equilibrium energy and the equilibrium structure, and the dynamic properties — the vibrational modes, and brings out their intrinsic interdependence. Melecular vibrations contain much information about the molecular energy surface in the whole vicinity.of the equilibrium conformation, since they depend on the curvature of the energy surface around equilibrium. Therefore, the representation of Vtotal as a sum of functions of single variables, as given by Equation (17), must be supplemented for the calCulation of vibra- tional Spectra by functionS'of adjacent internal coordinates. Such functions could not be deduced by theory, therefore simple guess—functions have been introduced, Such as the bi—linear function Kbe{b—b0)(B—BO) which couples bond stretching and angle bending. These are called "cross terms” or "interaction terms", and are reduced to the bare minimum required to fit experimental data, but they still increase the number of functions and adaptable para— meters more than necessary for calculations of molecular structure alone. However, it shOuld be noted that if cross terms are omitted from Vtotal, then the coefficients of the single~variable functions cannot be transfered from spectroscopy. we discussed hitherto the variables of single molecules. By extending the potential energy Vtotal to include the lattice energy of molecular crystals,the vibrations of molecules in a lattice are obtained‘l. The 6 degrees of freedom of molecular translations and rotations in the gas phase are replaced in condensed phases by lattice vibrations and molecular librations. Further, some molecular vibrations are modified by interactions with neighbour molecules, and frequencies of degenerate modes are split.by the asymmetric environment of the molecules in the crystal.

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