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Variance Minimisation with Non-Local Pseudopotentials

In the following chapter, results are presented for calculations performed on solid silicon in the diamond structure. The variance minimisation process for silicon is very similar to that for germanium except that a non-local pseudopotential is used in the silicon calculations. The inclusion of a non-local pseudopotential complicates the optimisation process somewhat because its expectation value depends of the value of the wavefunction throughout all space. This means that the value of the non-local potential energy cannot be stored as a constant during the optimisation procedure in the same way as the local potential energy. Any change in the values of the variational parameters in the wavefunction will effect the value of the non-local energy. This change then requires a full 3N-dimensional integral to be evaluated for each change in the parameters. Several different techniques have been experimented with to try and deal with the non-local pseudopotential.

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996