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.