Quadrupole Arrangements in Solid Hydrogen and Nitrogen

A group-theoretical classification of all possible quadrupole arrangements in a crystal is carried out following the method of Opechowski and Guccione for the classification of spin arrangements in magnetic crystals. The method is applied to find possible quadrupole arrangements in the various phases of solid orthohydrogen and solid nitrogen. It turns out that the quadrupole arrangement in the cubic phase is Tₕ⁶ with axially symmetric quadrupoles. In the hexagonal phase there are two possible arrangements with very low energy. One is C_6ν³, where none of the quadrupoles are axially symmetric, and the other is C₆ₕ², where some are and some are not. The quadrupole arrangement of lowest energy in the tetragonal phase of solid nitrogen is D₄ₕ¹⁴ with non-axial-symmetric quadrupoles.