The diffusion quantum Monte Carlo (DMC) method can be applied to excited states as well as ground states (see here for more on this). Williamson et al. calculated the bandstructures of silicon using the DMC method, while Towler et al. used a similar approach for diamond. We normally prepare the wave functions for the excited states by removing an occupied orbital from the determinant and replacing it by an unoccupied one. (Where necessary, we make proper singlet and triplet excited states.) For both silicon and diamond the results are excellent for low-energy excited states, but there is a tendency for the energies of the higher excited states to be overestimated. We hope to improve the energies of the higher excited states using more sophisticated wave functions.

Drummond et al. used DMC to study the optical gaps of diamondoids (hydrogen terminated carbon nanoparticles), while Porter et al. studied small hydrogen terminated silicon nanoparticles within DMC. Hood et al. used DMC to calculate the excited state energies of the neutral vacancy in diamond, which form a multiplet structure and require a multi-determinant description. The calculated energy of the lowest dipole allowed transition is consistent with the experimentally observed GR1 band, which has long been identified with the neutral vacancy in diamond, although there had been no previous first-principles calculation of this transition energy.