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
` 
' 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 
and 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
and is directly applicable to the techniques
described here.