<i>Ab Initio</i>Calculation of the Heisenberg Exchange Interaction between<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">O</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>Molecules

The exchange interaction between ${^{3}\ensuremath{\Sigma}_{\mathrm{g}}}^{\ensuremath{-}}$ ${\mathrm{O}}_{2}$ 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 ${\mathrm{\AA{}}}^{\ensuremath{-}1}$ 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 $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ ${\mathrm{O}}_{2}$ solids, which determine their magnetic order and properties, have been evaluated.

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