Melting Si: Beyond Density Functional Theory

The melting point of silicon in the cubic diamond phase is calculated using the random phase approximation (RPA). The RPA includes exact exchange as well as an approximate treatment of local as well as nonlocal many body correlation effects of the electrons. We predict a melting temperature of about 1735 and 1640 K without and with core polarization effects, respectively. Both values are within 3% of the experimental melting temperature of 1687 K. In comparison, the commonly used gradient approximation to density functional theory predicts a melting point that is 200 K too low, and hybrid functionals overestimate the melting point by 150 K. We correlate the predicted melting point with the energy difference between cubic diamond and the beta-tin phase of silicon, establishing that this energy difference is an important benchmark for the development of approximate functionals. The current results demonstrate that the RPA can be used to predict accurate finite temperature properties and underlines the excellent predictive properties of the RPA for condensed matter.

Figure 1

Variance of the energy difference between the RPA and hybrid functional calculations ${\sigma }^2=\text{Var}(U_{\mathrm{RPA}}-U_{\mathrm{DFT}})$ as a function of the amount $\alpha$ of exact exchange. The ensembles were created using the corresponding hybrid functional. The variance was calculated for 200 configurations picked from the MD trajectory.

Figure 2

Integrand of the TI from the ideal gas to liquid Si using SCAN as a function of $\lambda$ and, after the transformation, as a function $x$ for $k=0.8$. The inset in the right panel shows a zoom in for negative $x$. The smooth curve indicates the absence of any phase transitions.

Figure 3

Energy versus volume curves for cubic diamond Si and Si in the $\beta$-tin structure for various functionals. For each functional the curves were shifted vertically to align at zero for the cubic diamond phase.