To illustrate the effectiveness of the new electron-electron interaction the set of VMC calculations for the silicon simulation cells shown in figure were repeated using the new interaction energy expression of Eq.( ). The wavefunctions were optimised using Hamiltonians based on both the Ewald interaction and with the new interaction, but even for the smallest simulation cells the wavefunctions obtained were virtually identical. This shows that properties other than the energy are not significantly affected by the change in the interaction term. The sensitivity to the input charge density used in Eq. () was tested using the charge densities obtained from an n=2 LDA calculation and from a fully converged LDA calculation. This made no detectable difference to the calculated energies. Figure shows the energy per atom obtained from VMC calculations using the new interaction and the Ewald interaction. It is clear that the use of the new interaction greatly reduces the CFSE.
Figure: The energy per atom in diamond-structure silicon as a function of simulation cell size, from VMC calculations using the Ewald electron-electron interaction and the new interaction. The statistical error bars are smaller than the size of the symbols.