Diamond to $\beta$-tin phase transition in Si within diffusion quantum Monte Carlo

We have studied the diamond to $\beta$-tin phase transition in Si using diffusion quantum Monte Carlo (DMC) methods. Slater-Jastrow-backflow trial wave functions give lower DMC energies than Slater-Jastrow ones, and backflow slightly favors the $\beta$-tin phase with respect to the diamond phase. We have investigated the changes in the equation of state that result from the use of different pseudopotentials, the inclusion of either zero-point motion or finite-temperature vibrations, and the application of corrections for finite-size effects. Our tests indicate that the choice of pseudopotential can significantly affect the equation of state. Using a Dirac-Fock pseudopotential leads to an overestimation of the transition pressure but an empirical pseudopotential designed for use in correlated calculations gives a transition pressure in quite good agreement with experiment.

Figure 1

(Color online) Difference between the SJ and SJB DMC energies for the diamond and $\beta$-tin phases. The diamond- and $\beta$-tin-structure calculations were performed at the $L$ and $M$ points in the Brillouin zone, respectively.

Figure 2

(Color online) Variation in the free energy with volume for the diamond and $\beta$-tin phases of Si calculated within DMC and with corrections for the vibrational energy from PBE-DFT. Static lattice, $T=0$ and $T=300\text{K}$ results are shown, and the zero of free energy is taken to be the DMC results including vibrational effects at 300 K. The common tangents labeled “Tang.” join the coexistence points. Filled symbols denote that the structures were found to be dynamically stable within the DFT phonon calculations. The statistical error bars on the DMC energies are in the range 0.00005–0.00007 a.u./atom in all cases.