A quantum Monte Carlo study of density-functional theory for a semiconducting wire

We use diffusion quantum Monte Carlo (DQMC) techniques to obtain accurate estimates of the components of the Kohn-Sham effective potential of density-functional theory for a model semiconductor, and the corresponding components of the energy functional, by determining the local potential which, when filled with noninteracting electrons, reproduces the DQMC electron density. The results are compared with the widely used local-density approximation. There is a large deviation in the exchange-correlation potential, a slight deviation in the electron density, but a very small deviation in the total energy and its components. We also use DQMC techniques to calculate the quasiparticle band gap, and hence the discontinuity Δ in the exchange-correlation potential on the addition of an electron.