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.().
