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Results of Optimising the new Jastrow Factor

For a first test, the optimisation procedure was set up using 10,000 configurations generated by a VMC calculation, using the best parameters so far obtained for tex2html_wrap_inline6237 . The function was hard wired to use those parameters. It was intended that if the inclusion of tex2html_wrap_inline7145 produced a large change in the wavefunction and therefore the charge density, would also have to be included in the optimisation to allow it to adjust to these changes as there could be significant coupling between the tex2html_wrap_inline7145 and functions.

Only the tex2html_wrap_inline7287 and tex2html_wrap_inline7289 orders of the Chebyshev expansion were used in Eq.(gif). This gave a total of 12 parameters to be optimised (6 for the parallel and 6 the for anti-parallel tex2html_wrap_inline7145 functions). Four separate optimisations were performed for values of the range of tex2html_wrap_inline7145 , L=3.0, 3.5, 4.0, 5.0. These correspond to an average number of electron pairs around each ion contributing to tex2html_wrap_inline7145 of 3, 5.5, 7, 12 respectively.

The overall size of tex2html_wrap_inline7145 naturally increased with L as more electron pairs were included, but the optimised parameters were still very small compared to the original part of the u function. The result with the lowest variance of the local energy was achieved by choosing L=4.0 (larger values lead to instabilities in the optimisation procedure.) This produced a lowering of the energy beyond the optimised energy of about 0.01eV per atom. As with the optimisation of , the variance again showed little change.

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