It is well known that many-body correlations have a significant impact on important band structure features such as band gaps, band widths and other excitation energies. One of the advantages of the quantum Monte Carlo (QMC) method over other electronic structure techniques is that it can include these correlation effects. In this chapter two separate methods for using QMC to calculate excitation energies are described. These are the addition and subtraction of electrons from the bulk solid and the promotion of electrons from the valence band into the conduction band. Results are presented for the band gaps of silicon in the diamond structure obtained using both methods. Silicon was chosen to serve as a useful test material for experimenting with the different methods of calculating excitation energies using QMC. There is a wealth of both experimental and theoretical electronic structure results for excitation energies in silicon that can be used as a measure of the relative successes of the techniques described in this chapter.
The efficiency and accuracy of the two QMC methods are compared and contrasted with recent QMC results published by the Illinois group, and with other electronic structure techniques. Finally, some alternative techniques for calculating excitation energies within QMC are discussed.