Electronic structure of semiconductor nanoparticles from stochastic evaluation of imaginary-time path integral: nonrelativistic U(1) lattice gauge theory in the Kohn-Sham basis

In the Kohn-Sham orbital basis imaginary-time path integral for electrons in a semiconductor nanoparticle has a mild fermion sign problem and is, therefore, amenable to evaluation by the standard stochastic methods. Utilizing output from the density functional theory simulations with Perdew, Burke and Ernzerhof exchange-correlation functional we compute imaginary-time electron propagators in several silicon hydrogen-passivated nanocrystals, such as Si₃₅H₃₆, Si₈₇H₇₆ and Si₁₄₇H₁₀₀, and extract energies of low-lying electron and hole levels. Our quasiparticle gap predictions agree with the results of recent G₀W₀ calculations from M. Govoni, G. Galli, “Large Scale GW Calculations", J. Chem. Theory Comp., 11 (2015).