Diffusion quantum Monte Carlo calculations of the excited states of silicon

The band structure of silicon is calculated at the $\Gamma$, $X$, and $L$ wave vectors using diffusion quantum Monte Carlo (DMC) methods. Excited states are formed by promoting an electron from the valence band into the conduction band. We obtain good agreement with experiment for states around the gap region, and demonstrate that the method works equally well for direct and indirect excitations, and that one can calculate many excited states at each wave vector. This work establishes the fixed-node DMC approach as an accurate method for calculating the energies of low-lying excitations in solids.