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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 the asymmetric
environment of the molecules in the crystal.

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