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

Abstract

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 O 2 (a 1 Δ g ) → O 2 (X 3 Σ 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 O 2 (a 1 Δ g ) → O 2 (X 3 Σ 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 O 2 (a 1 Δ g ) → O 2 (X 3 Σ g − ) transition.

The oxygen–organic molecule photosystem: revisiting the past, recalibrating the present, and redefining the future

“…One parameter that we have, thus far, not explicitly included in the PaAD model is the matrix element for spin-orbit coupling between the O 2 (a 1 Δ g ) and O 2 (X 3 Σ g − ) states as influenced by M. In the isolated O 2 system, the matrix element for spin-orbit coupling is zero. In a recent study, we examined how the magnitude of this matrix element depends on the geometry of the M-O 2 complex using a variety of different M's [52]. Our results demonstrate that a non-zero spin-orbit coupling matrix element is the result of an M-dependent disruption of oxygen's cylindrical symmetry through an asymmetric transfer of electrons to and/or from oxygen's 1π g antibonding orbitals (Fig.…”

“…This observation has been interpreted to reflect a mechanism in which the O 2 (a 1 Δ g ) → O 2 (X 3 Σ g − ) transition borrows intensity from the spinallowed O 2 (b 1 Σ g + ) → O 2 (a 1 Δ g ) transition and, from this perspective, a computed prediction of 4.5 × 10 -4 for the ratio of radiative rate constants is consistent with experimental data [51,53]. A corollary to this observation is that the magnitude of the radiative rate constant for the O 2 (a 1 Δ g ) → O 2 (X 3 Σ g − ) transition does not depend as much on the magnitude of the matrix element for solventinduced spin-orbit coupling in oxygen as does the magnitude of the non-radiative rate constant for the O 2 (a 1 Δ g ) → O 2 (X 3 Σ g − ) transition [52].…”

“…) and M-O 2 (a 1 Δ g ) states facilitates appreciable coupling between O 2 (X 3 Σ g − ) and O 2 (a 1 Δ g ) [1,32,39,52]. Such state mixing is another way to describe our model of asymmetric M-induced perturbation of oxygen's 1π g antibonding orbitals (Fig.…”

“…transition more allowed [1,51,52]. Furthermore, polyatomic collision partners provide vibrational modes that can readily accept the excitation energy of O 2 (a 1 Δ g ).…”

“…Such state mixing is another way to describe our model of asymmetric M-induced perturbation of oxygen's 1π g antibonding orbitals (Fig. 4) [52].…”