Correlation effects on the different crystal structures of AO2 (A=Na, K, and Ba)

In alkali superoxide (A=Na, and K), the structural phase transition from high symmetry to low symmetry structures occurs upon cooling. On the other hand, in BaO$_2$ peroxide, the crystal structure is always the high symmetry tetragonal structure of KO$_2$, independent of temperature. To resolve these different crystal structures of AO$_2$ (A=Na, K, and Ba), we have calculated phonon dispersions of AO$_2$, assuming the high symmetry tetragonal structure of KO$_2$ with first-principle band structure method in the generalized gradient approximation (GGA) incorporating the Coulomb interaction U (GGA+U). From softened phonon modes, we have shown that, in KO$_2$ and NaO$_2$, the degeneracy of the incomplete pi anti-bonding level is lifted with the symmetry lowering such as Jahn-Teller effect with help of Coulomb correlation U. In contrast, in BaO$_2$, the pi anti-bonding level of the peroxide is completely filled without degeneracy. Thus, U is not effective on the phonon structure so that the structural instability does not occur in BaO$_2$.