The way we tackle this problem is using the Musgrave-Pople interatomic potential to model the vibrational properties of those bulk atoms for which we do not calculate the energetic double derivatives directly. This can be used in conjunction with the AIMPRO double derivative data for the core defect atoms.

In order to parameterise the potential it is necessary to calculate
the double derivatives for a small group of core atoms in a cluster of
pure bulk material, and the parameters are then fitted to these
derivatives. The Musgrave-Pople potential parameters are calculated
from a least-squares fit to the *ab initio* energy double
derivatives, calculated for the core of a fully relaxed bulk cluster.
For example, the InP potential parameters given in
Section 4.3 were determined using an 86 atom C_{3v}
cluster . This was relaxed using AIMPRO, and
then the energy double derivatives were calculated for the inner eight
atoms, four of each chemical species. This leads to 156 double
derivative terms which produces a very accurate fit.

Examples of the application of the MP potential to defect problems is given in Chapter 4, the parameters used for Si are given in Reference [35].