Quantum distribution of protons in solid molecular hydrogen at megabar pressures

Solid hydrogen, a simple system consisting only of protons and electrons, e xhibits a variety of structural phase transitions at high pressures. Experi mental studies' based on static compression up to about 230 GPa revealed th ree relevant phases of solid molecular hydrogen: phase I (high-temperature, low-pressure phase), phase II (low-temperature phase) and phase III (high- pressure phase). Spectroscopic data suggest that symmetry breaking; possibl y related to orientational ordering(1,2), accompanies the transition into p hases II and III. The boundaries dividing the three phases exhibit a strong isotope effect(3), indicating that the quantum-mechanical properties of hy drogen nuclei are important. Here we report the quantum distributions of pr otons in the three phases of solid hydrogen, obtained by a first-principles path-integral molecular dynamics method. We show that quantum fluctuations of protons effectively hinder molecular rotation-that is, a quantum locali zation occurs. The obtained crystal structures have entirely different symm etries from those predicted by the conventional simulations which treat pro tons classically.