Diamond andβ-tin structures of Si studied with quantum Monte Carlo calculations

We have used diffusion quantum Monte Carlo (DMC) calculations to study the pressure-induced phase transition from the diamond to β-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 10.3em0exGPa in the transition pressure the noncanceling errors in the energies of the two structures must be reduced to 300.3em0exmeV∕atom. Extensive tests on system size errors, nonlocal 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 300.3em0exmeV∕atom. The calculated DMC transition pressure is about 3--40.3em0exGPa 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.