### 13.3 Vibrational frequencies with fixed atoms using NumForce

The NumForce script provides with the option -frznuclei a possibility to do a
vibrational analysis with fixed atoms. The atoms for which the cartesian coordinates
should frozen have to be marked in $coord with a "f" behind the atom type.
The frozen coordinates will be skipped during the numerical evaluation of the
force constant matrix; instead all off-diagonal elements of the force constant
matrix which refer to one or two frozen coordinates will be set to zero, while the
diagonale elements for the frozen coordinates will be set to an arbitrarly chosen large
value.

This feature is mainly intended to allow for a vibrational analysis in embbeded cluster
calculations e.g. for defects in ionic crystals. The vibrational analysis uses a kind of
“frozen phonon” approximation which corresponds to setting the masses of the fixed atoms
to infinity, i.e. decoupling the fixed atoms mechanically from the “mechanically active”
subsystem. The resulting vibrational frequencies will thus only provide good
approximations to the true (harmonic) frequencies for such modes for which the
mechanical coupling to the embedding environment is negligible. In particular the
frequencies of stretch modes which involve bonds between the “mechanically active”
subsystem and atoms with frozen coordinates will be strongly affected by this
approximation.

Note:

- The -frznuclei is not compatible with the polyhedral difference algorithm.
It can only be used with central differences which should be enforced with the
-central option.
- If the option -frznuclei is switched on, the program assumes that the
constraints enforced by fixing coordinates remove the six external degrees of
freedom for on overall rotation or translation of the system and therefore the
hessian matrix is not projected onto the subspace of internal coordinates. Fixing
the coordinates of only one or two atoms might does lead to some artifical
small, but non-zero frequencies.
- Zero-point vibrational energies calculated with the -frznuclei option are only
meaningful for comparison of systems with the same mechanically active atoms
and similar embedding, as the contributions from the frozen coordinates are
not included.