Diamond and $\beta$-tin structures of Si studied with quantum Monte Carlo calculations

Abstract

We have used diffusion quantum Monte Carlo (DMC) calculations to study the pressure-induced phase transition from the diamond to $\beta$-tin structure in silicon. The calculations employ the pseudopotential technique and systematically improvable B-spline basis sets. We show that in order to achieve a precision of 1 GPa in the transition pressure the non-cancelling errors in the energies of the two structures must be reduced to 30 meV/atom. Extensive tests on system size errors, non-local pseudopotential errors, basis-set incompleteness errors, and other sources of error, performed on periodically repeated systems of up to 432 atoms, show that all these errors together can be reduced to well below 30 meV/atom. The calculated DMC transition pressure is about 3-4 GPa higher than the accepted experimental range of values, and we argue that the discrepancy may be due to the fixed-node error inherent in DMC techniques.

10 pages, 4 figures

References in corpus (1)

• An efficient localized basis set for quantum Monte Carlo calculations on condensed matter

Cited by in corpus (15)

• Electrically Tunable Band Gap in Silicene
• Applications of quantum Monte Carlo methods in condensed systems
• Quantum Monte Carlo applied to solids
• Phase transformation in Si from semiconducting diamond to metallic beta-Sn phase in QMC and DFT under hydrostatic and anisotropic stress
• Pressure-induced diamond to beta-tin transition in bulk silicon: a near-exact quantum Monte Carlo study
• Phase diagram of silicon from atomistic simulations
• Accuracy of Quantum Monte Carlo Methods for Point Defects in Solids
• Effective Hamiltonians for the study of real metals using quantum chemical theories
• Ab-initio calculations for the beta-tin diamond transition in Silicon: comparing theories with experiments
• Diamond -> beta-tin phase transition in Si within diffusion quantum Monte Carlo
• Cohesion and excitations of diamond-structure silicon by quantum Monte Carlo: Benchmarks and control of systematic biases
• Exact special twist method for quantum Monte Carlo simulations
• Equations of state and stability of MgSiO${}_3$ perovskite and post-perovskite phases from quantum Monte Carlo simulations
• Point defect formation energies in graphene from diffusion quantum Monte Carlo and density functional theory
• Development of Path Integral Monte Carlo Simulations with Localized Nodal Surfaces for Second-Row Elements