Geometry Dependence of Spin-Orbit Coupling in Complexes of Molecular Oxygen with Atoms, H₂, or Organic Molecules

Studies of the interactions between molecular oxygen and a perturbing species, such as an organic solvent, have been an active research area for at least 70 years. In particular, interaction with a neighboring molecule or atom may perturb the electronic states of oxygen to such an extent that the O₂(a¹Δ_g) → O₂(X³Σ_g^-) transition, formally forbidden as an electric dipole process, achieves significant transition probability. We present a computational study of how the geometry of complexes consisting of molecular oxygen and different perturbing species influences the magnitude of spin-orbit coupling that facilitates the O₂(a¹Δ_g) → O₂(X³Σ_g^-) transition. We rationalize our results using a model based on orbital interactions: a non-zero spin-orbit coupling matrix element results from asymmetric transfer of charge to or from the 1π_g orbitals on oxygen. Our results indicate that the atoms in a perturbing species closest to oxygen are responsible for the majority of the spin-orbit interactions, suggesting that large systems can be simplified appreciably. Furthermore, we infer and confirm that an estimate of the spin-orbit coupling matrix element can be obtained from the magnitude of the induced energy splitting of oxygen's 1π_g orbitals. These results should provide further momentum in the long-standing issue of understanding phenomena that influence the O₂(a¹Δ_g) → O₂(X³Σ_g^-) transition.