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.().