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Quantum Monte Carlo Calculations on Solids


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 gif.

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