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Adding a new Function to Chi

In an attempt to further improve the quality of the trial wavefunction, it was proposed to add an extra function to ţo increase the variational freedom available to the optimisation procedure. A spherically symmetric function centred on each of the ionic cores was chosen as this was simple to implement while still adding considerable extra variational freedom. The new function was designed to add some extra atomic quality to the trial wavefunction is these regions.

The requirements for the new function are only that it should be well behaved as an electron moves through the ionic core, i.e. there should be no cusp in as tex2html_wrap_inline7103 .

Subject to these constraints, the most general polynomial function,


was chosen. In Eq.({gif), L is the range of the function, r' is a rescaled r,


and the tex2html_wrap_inline7111 are coefficients. Chebyshev polynomials, tex2html_wrap_inline6255 , were chosen because they exhibit good numerical stability during the fitting procedure.

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