  Shock compression of silicon (Si) under extremely high pressures (>100 Mbar)
was investigated by using two first-principles methods of orbital-free
molecular dynamics (OFMD) and path integral Monte Carlo (PIMC). While pressures
from the two methods agree very well, PIMC predicts a second compression
maximum because of 1s electron ionization that is absent in OFMD calculations
since Thomas-Fermi-based theories lack shell structure. The Kohn-Sham density
functional theory is used to calculate the equation of state (EOS) of warm
dense silicon for low-pressure loadings (P < 100 Mbar). Combining these
first-principles EOS results, the principal shock Hugoniot curve of silicon for
pressures varying from 1 Mbar to above 10 Gbar was derived. We find that
silicon is 20% or more softer than what was predicted by widely-used EOS
models. Existing high-pressure experimental data (P = 1 - 2 Mbar) seem to
indicate this softening behavior of Si, which calls for future strong-shock
experiments (P > 10 Mbar) to benchmark our results.
