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QMC Methods for Calculating Excitation Energies

Two separate methods for calculating excited states within QMC, namely the addition and subtraction of electrons from the bulk solid and the promotion of individual electrons to the conduction band, have been applied to bulk silicon in the diamond structure. The following sections describe the technical details of implementing these techniques within both the variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC) frameworks. Both methods are effectively ` tex2html_wrap_inline7951 ' techniques, i.e. the change in the energy due to the excitation is inversely proportional to the number of electrons in the simulation cell. The calculations therefore have to be of sufficient accuracy to resolve this energy change amid the statistical noise produced by all N electrons. This is in contrast to the ground state calculations described in chapters gif and gif where one is interested in the total energy per atom averaged over all the atoms in the simulation cell. The increased accuracy required in these excitation energy calculations makes them especially demanding and we must be careful to use high quality trial/guiding wavefunctions and to correct for the finite size effects. Hence, the progress made in these areas that has already been described in chapters gif and gif is directly applicable to the techniques described here.

Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996