The number of applications of QMC to solid systems is relatively
small. The most noteworthy to date are the original Ceperley and
Alder calculations of the total energy of the Homogeneous Electron
Gas (HEG) [25, 43] and the HEG surface
[44, 45], calculations for different phases of hydrogen
[46, 47] and pseudopotential studies of heavier atoms
such as carbon[48, 26], silicon[26, 49],
germanium[50, 33] and
nitrogen[51]. The reasons for the slow adoption of
QMC as a tool for studying the electronic structure of solids is the
intrinsic scaling of the algorithms with the fifth or sixth power of
the atomic number and the large finite size effects present in
traditional solid QMC calculations[3]. It was only with the
introduction of pseudopotentials into QMC
calculations[48, 26], that the study of solids with
atoms heavier than lithium became feasible with current computing
power. Even with this advance there are still several problems
involved with performing solid calculations that are unique to QMC
because of the real-space representation of the electrons as delta
functions. The most severe of these is how to deal with the Coulomb
interactions between particles. The traditional Ewald method for
treating these interactions is described in section 
.