Frustrated supermolecules: The high-pressure phases of crystalline methane

Methane is the simplest hydrocarbon, yet it exhibits an extraordinarily complicated series of crystal phases. Notably, the non-plastic phases have large unit cells with nearly, but not quite, cubic symmetry. Furthermore, although non-polar molecules interact very weakly, their reorganization across phase transitions is very sluggish. Here, we demonstrate that these complex structures can be understood as a simple packing of near-spherical supermolecular clusters of methane molecules: the departure from cubic symmetry arising from the non-spherical nature of the molecules. We use molecular dynamics based on density functional theory calculations to simulate the finite-temperature crystal structures of methane, finding that the complex phase A is based around a 13-molecule regular icosahedron, with 8 additional molecules forming the 21-molecule unit cell. Similarly, phase B is based on a body-centered cubic (bcc) packing of 17-molecule Z16 polyhedra, with the remaining 12 molecules per cell in tetrahedral interstices. We demonstrate that the favored intermolecular separation depends sensitively on molecular orientation, leading to hindered rotation and suppressed entropy. The structures are determined by a trade-off between efficient packing and entropy.