Cohesion and excitations of diamond-structure silicon by quantum Monte Carlo: Benchmarks and control of systematic biases

TL;DR

This study uses quantum Monte Carlo methods to accurately analyze silicon's electronic structure, achieving high precision in energies, band gaps, and excitations, while systematically controlling biases and errors.

Contribution

It provides benchmark QMC calculations for silicon, demonstrating minimal systematic biases and high accuracy in energies and electronic properties compared to experiments.

Findings

Supercell sizes of 64 and 216 atoms yield consistent energies.

Ground state cohesion energy with errors below 0.05 eV.

Band gaps differ from experiments by about 0.2 eV, mainly due to residual errors.

Abstract

We have carried out quantum Monte Carlo (QMC) calculations of silicon crystal focusing on the accuracy and systematic biases that affect the electronic structure characteristics. The results 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 $\textit{systematic and statistical errors}$ below $\approx$0.05 eV. The ground state exhibits a fixed-node error of only $1.3(2)\%$ 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 quasiparticle 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. This difference is assigned 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.