### 14.3 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.