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Variance Minimisation with the New Interaction

In section gif results are presented for VMC calculations performed using both the Ewald interaction and the new interaction. To provide the fairest possible comparison of the two interactions, the trial wavefunctions for each calculation were optimised, using the variance minimisation technique described in chapter gif, with respect to the Hamiltonian to be used in the subsequent VMC calculation. This enables both calculations to be performed using the optimal values of the variational parameters in the wavefunction for the given Hamiltonian. The standard expression for the intrinsic variance


was used. The form of tex2html_wrap_inline5881 was chosen to match the form to be used in the VMC calculation. For the calculations using the Ewald interaction, tex2html_wrap_inline7883 was chosen to be


For the calculations using the new electron-electron interaction, tex2html_wrap_inline7883 was chosen to be


In both cases, the electron configurations are still fixed throughout the optimisation process. Therefore the total electron-electron energy for each configuration is still just calculated once and stored throughout the optimisation procedure.

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