Prediction of structures and magnetic orientations in solidα− and β−O2

A quasiharmonic-lattice-dynamics method coupled with a pattern-recognition optimization scheme is used to determine the minimum energy structures and magnetic orientations of solid oxygen. It is shown that the magnetic interaction is responsible for the stability of $\alpha -{\mathrm{O}}_2$ with respect to $\beta -{\mathrm{O}}_2$ at zero temperature and pressure. The calculated $\alpha -{\mathrm{O}}_2$ lattice parameters, magnetic orientations, and sublimation energy are in good agreement with experiment. Phonon dispersion curves are calculated at $\overrightarrow{\mathrm{k}}\ne 0$ and the acoustic sound velocities are determined. The root-mean-square translational and orientational fluctuations from equilibrium are also calculated. The $\beta -{\mathrm{O}}_2$ phase is described by constraining the magnetic moments so that the magnetic Hamiltonian preserves the hexagonal symmetry of the crystal. The calculated lattice parameters are in good agreement with experiment and a three-sublattice, quasihelical magnetic orientation is predicted from structural and energetic considerations.