Louisa Fraser performed a series of VMC calculations[3] for
systems with 
equal to 1 and 3. For comparison, the average
value of in silicon is approximately 2.6. A series of system
sizes containing 18 to 614 electrons were used to examine the finite
size scaling. In figure 
the results of these
calculations are shown using the old electron-electron interaction in
the Hamiltonian which is based on the Ewald interaction. The energy
at each system size has been ``corrected'' using the LDA finite size
errors to remove the IPFSE. It can then be seen quite clearly that
there is a residual CFSE that appears to decay approximately as 1/N.
Figure: VMC results corrected using finite size errors from LDA
calculations. Results are for densities corresponding to = 1 and
= 3 and systems containing 18 to 614 electrons.
The calculations of figure were then repeated using
the new energy expression described by Eq.(). The
results are shown in figure . They show that the
CFSE has been dramatically reduced and it is no longer possible to
detect a trend in the remaining finite size effects.
Figure: VMC
results using the new electron-electron potential. Results have been
corrected using finite size errors from LDA calculations. Results are
for densities corresponding to = 1 and = 3 and systems
containing 18 to 614 electrons.