In an attempt to improve on the VMC results from section a selected set of the VMC calculations were repeated within DMC. As described in chapter , the DMC algorithm requires not only an energy expression but also the associated Hamiltonian. The Hamiltonian corresponding to the new electron-electron energy expression designed to remove the long range finite size effects introduced by the periodic boundary conditions acting on the additional electron is
The Hamiltonian is physically very reasonable. It describes each electron `feeling' the full 1/r interaction with all the other X electrons within a Wigner-Seitz cell centred on the electron and the Hartree interaction with a charge density due to N electrons outside the Wigner-Seitz cell.
The total electron-electron energy, , in DMC is then
The second term in Eq.() can be accumulated during a ground state, N electron, DMC calculation and then just subtracted from the energies calculated with electrons.
In the following DMC calculations each of the , and calculations use the VMC trial wavefunction as the guiding wavefunction, , optimised for that system using the Hamiltonian of Eq.().