The calculation of harmonic frequencies raises the problem of
solvation in the COSMO framework, because the molecular vibrations
are on a time scale that do not allow a re-orientation
of the solvent molecules.
Therefore, the total response of the continuum is split into a
described by the electronic polarization, and a slow term related to the
orientational relaxation. As can be shown  the dielectric energy for the
disturbed state can be written as
Eddiel = f ()()() + f (n2)()() + f ()()(),
denotes the density difference between the distorted state and the initial state with density
The interaction is composed of three contributions: the initial state
the interaction of the potential difference with the initial state
charges, and the
electronic screening energy that results from the density difference.
The energy expression can be used to derive the correspondent gradients, which can be applied in
a numerical frequency calculation.
Because the COSMO cavity changes for every distorted geometry the initial state
potential has to be mapped onto the new cavity in every step.
The mapped potential of a segment of the new cavity is calculated from the
potentials of all segments of the old cavity that fulfill
a certain distance criterion. The mapped initial state screening charges are
re-calculated from the new potential.
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