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 . The function was hard wired to use those parameters. It was intended that if the inclusion of 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 and functions.
Only the and orders of the Chebyshev expansion were used in Eq.(). This gave a total of 12 parameters to be optimised (6 for the parallel and 6 the for anti-parallel functions). Four separate optimisations were performed for values of the range of , L=3.0, 3.5, 4.0, 5.0. These correspond to an average number of electron pairs around each ion contributing to of 3, 5.5, 7, 12 respectively.
The overall size of 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.