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Optimising Wavefunctions for Atoms

The energy calculated within a VMC framework is an upper bound to the true energy of the system. When calculating energy differences it is important to use wavefunctions of similar quality for the different systems so that there is a strong cancellation of errors. This feature is common to many electronic structure methods, for instance in bandstructure methods the errors due to incomplete basis sets are often large, but if sufficient care is taken it is often possible to calculate energy differences with high precision. A severe test of such cancellation is provided by the cohesive energy of a solid, which is the difference in energy between the solid and its constituent atoms. This section describes calculations performed for the ground-state energy of the germanium pseudo-atom using the same pseudopotential as for our solid calculations, and using a wavefunction of, as near as possible, the same quality as in the solid calculations. This allows us to test the extent to which the remaining errors/omissions in the trial/guiding wavefunction cancel between atomic and solid germanium.

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