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

TL;DR

This study uses diffusion quantum Monte Carlo calculations to accurately determine the pressure-induced phase transition in silicon from diamond to β-tin structure, highlighting the importance of error reduction for precision.

Contribution

The paper demonstrates systematic error control in DMC calculations for phase transition pressures in silicon, achieving high precision and discussing fixed-node errors.

Findings

Calculated transition pressure is 3-4 GPa higher than experimental values.

Errors in energy calculations can be reduced below 30 meV/atom.

System size and pseudopotential errors are systematically minimized.

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.