Quadrupole arrangements and the ground state of solid hydrogen

The electric quadrupole-quadrupole $({\mathcal{E}}_qq)$ interaction is believed to play an important role in the broken symmetry transition from phase I to II in solid hydrogen. To evaluate this, we study structures adopted by purely classical quadrupoles using Markov chain Monte Carlo simulations on face centered cubic (fcc) and hexagonal close packed (hcp) lattices. Both undergo first-order phase transitions from rotationally ordered to disordered structures, as indicated by a discontinuity in both quadrupole interaction energy $({\mathcal{E}}_qq)$ and its heat capacity. Cooling fcc reliably induced a transition to the $Pa3$ structure, whereas cooling hcp gave inconsistent, frustrated, and $c/a$-ratio-dependent broken symmetry states. Analyzing the lowest-energy hcp states using simulated annealing, we found $P{6}₃/m$ and $Pca{2}₁$ structures found previously as minimum-energy structures in full electronic-structure calculations. The candidate structures for hydrogen phases III--V were not observed. This demonstrates that ${\mathcal{E}}_qq$ is the dominant interaction determining the symmetry breaking in phase II. The disorder transition occurs at significantly lower temperature in hcp than fcc, showing that the ${\mathcal{E}}_qq$ cannot be responsible for hydrogen phase II being based on hcp.