First-principles studies of the metallization and the equation of state of solid helium

The insulator-to-metal transition in hcp solid helium at high pressure is studied with first-principles simulations. Diffusion quantum Monte Carlo (DMC) calculations predict that the band gap closes at a density of 21.3 g/cm;{3} and a pressure of 25.7 terapascals, which is 20% higher in density and 40% higher in pressure than predicted by density functional calculations based on the generalized gradient approximation (GGA). The metallization density derived from GW calculations is found to be in very close agreement with DMC predictions. The zero point motion of the nuclei had no effect on the metallization density within the accuracy of the calculation. Finally, fit functions for the equation of state are presented, and the magnitude of the electronic correlation effects left out of the GGA approximation are discussed.