Cohesion and excitations of diamond structure silicon by quantum Monte Carlo: benchmarks and control of systematic biases.

We have carried out quantum Monte Carlo (QMC) calculations of silicon crystal focusing on the accuracy and systematic biases that affect electronic structure characteristics. We show that 64 and 216 atom supercells provide an excellent consistency for extrapolated energies per atom in the thermodynamic limit for ground, excited, and ionized states. We have calculated the ground state cohesion energy with both systematic and statistical errors below $\approx$ 0.05 eV. The ground state exhibits a fixed-node error of only $\approx 1.3$% of the correlation energy, suggesting an unusually high accuracy of the corresponding single-reference trial wave function. We obtain a very good agreement between optical and quasi-particle gaps that affirms the marginal impact of excitonic effects. Our most accurate results for band gaps differ from the experiments by about 0.2 eV. We assign this difference to a combination of residual finite-size and fixed-node errors. We have estimated the crystal Fermi level referenced to vacuum that enabled us to calculate the edges of valence and conduction bands in agreement with experiments.