Quadrupole Arrangements and the Ground State of Solid Hydrogen

TL;DR

This study uses classical quadrupole models and simulations to analyze the role of quadrupole interactions in the phase transitions and symmetry breaking of solid hydrogen, revealing that these interactions dominate Phase II behavior.

Contribution

It provides the first detailed simulation-based analysis of quadrupole arrangements in solid hydrogen, clarifying their role in phase transitions and symmetry breaking.

Findings

Quadrupole interactions cause first-order phase transitions in classical lattices.

Cooling fcc leads to P$a3$ structure, hcp results are inconsistent.

Quadrupole interactions are not responsible for Phase II's hcp structure.

Abstract

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 of fcc and hcp quadrupolar 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 P$a3$ structure, whereas cooling hcp gave inconsistent, frustrated and $c/a$-ratio-dependent broken symmetry states. Analysing the lowest-energy hcp states using simulated annealing, we found P$6_3/m$ and P$ca2_1$ 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.