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.().

Tue Nov 19 17:11:34 GMT 1996