Louisa Fraser performed a series of VMC calculations 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.