Ab InitioCalculation of the Heisenberg Exchange Interaction betweenO2Molecules

The exchange interaction between ${{}_{}{}^3{}_{}{}^{}\Sigma _{\mathrm{g}}^{}{}_{}{}^{}}^{-}$ ${\mathrm{O}}_2$ molecules, as obtained from ab initio calculations for a singlet, triplet, and quintet dimer, can be well represented by the Heisenberg Hamiltonian. The coupling parameter $J$ depends exponentially on the ${\mathrm{O}}_2$-${\mathrm{O}}_2$ distance, with exponents ranging from 3.6 to 4.2 ${\mathrm{\AA }}^{-1\mathrm{}}$ for different ${\mathrm{O}}_2$ orientations. For most orientations the coupling is antiferromagnetic, but for a few $J$ is positive. The different neighbor interactions in $\alpha$ and $\beta$ ${\mathrm{O}}_2$ solids, which determine their magnetic order and properties, have been evaluated.