Band gaps and excitons in quantum Monte Carlo

Using the fixed-node approximation, quantum Monte Carlo (QMC) allows for calculations of both ground and excited energy levels with explicit electron correlations. For example, in periodic systems, one can estimate band gaps by promoting an electron from the valence to conduction band or alternatively from the ionization potential and electron affinity. Since fixed-node QMC's accuracy depends on the quality of trial functions this tacitly assumes that the relevant states are close to single reference states and well represented by single orbital promotions in the Slater determinant. However, this becomes more challenging for excitations that appear in the gap and are not representative of typical conduction states such as significantly localized excitonic states, impurity or defect levels that are not captured by ordinary band theories. Here the construction of the corresponding trial functions requires more elaborate schemes that might involve multi-reference forms, geometry relaxation and/or additional considerations depending on experiment that one compares with such as optical, conductivity or photoemission measurements. We study a few such cases, eg, benzene molecule and crystal and other systems to capture and illustrate these effects using QMC calculations.