In the following calculations it has been assumed that the addition (removal) of a single electron does not significantly affect the overall shape of the exchange correlation hole and so the same Jastrow correlation function that was introduced in chapter has again been used. It was also assumed that although the addition(removal) of a single electron will reduce the symmetry of the charge density, this will not be a strong effect. The same form of the 1-body function, grouped into stars according to the higher point group symmetry of the crystal in its ground state as described in section , should therefore still be applicable. The validity of these approximations in the trial wavefunction is tested in section , where the calculations are repeated in DMC. The value of the energy calculated in DMC is independent of the quality of the u and parts of the trial wavefunction. Therefore, if the quality of the u and parts of the trial wavefunction is much lower for the calculations where an electron has been added or removed, one would expect to see a bigger reduction in the energy when moving from VMC to DMC.
The trial wavefunctions for each of the , and systems were individually optimised using the variance minimisation techniques described in chapter . Six stars of vectors were used to describe the functions and 22 parameters were used to describe the u functions, as in chapter . Large ensembles of up to 1 million electron configurations were used in each iteration of the optimisation procedure and 3-5 iterations were performed to obtain ground state wavefunctions with an accuracy of approximately 0.01eV per atom within the parameter space of the optimisation. This is equivalent to an accuracy of approximately 0.3eV in the energy of the gap as given by Eq.().