Effect of spin orbit interactions on the dipolar nature of the radiative microwave zero-field transitions in aromatic molecules

Abstract

In the absence of spin orbit interaction, each of the zero-field (zf) transitions of a triplet state of a polyatomic molecule is magnetic dipole allowed, with a magnetic dipole moment of two Bohr magnetons resulting from the change of the spin motion from one quantization direction in the molecule to the other. By the introduction of spin orbit perturbations, the radiative transition probability of a zf transition can be altered in the following manner. (1) Additional transition probability could be ``borrowed'' from (orbital type) magnetic dipole allowed triplet-triplet and singlet-singlet transitions. (2) Additional transition probability could be ``borrowed'' from the spin zf magnetic dipole allowed transitions of other triplet states. (3) Transition probability can be ``borrowed'' from (orbital type) electric-dipole allowed triplet-triplet and singlet-singlet transitions. (4) Contributions 1 and 2 above are shown not to alter the polarization of the zf transition, but contribution 3 could, for some Cs or C2v type molecules, cause the electric moment to be in a different direction from that for the magnetic moment resulting from contributions 1 and 2. (5) In contributions 1 and 3, triplet-triplet transitions between the state under examination and other triplet states are found to be more important than singlet-singlet transitions, whose contributions appear in second order in the spin orbit mixing coefficient. (6) Because of the symmetry of the spin orbit and the electric dipole operators, the zf transitions of molecules having a center of inversion are found to be totally magnetic allowed in nature (i.e., contribution 3 vanishes). A rough estimate of the spin orbit mixing coefficient required to make the transition probability for the electric dipole allowed part of the zf transition comparable to that for the magnetic dipole allowed part shows it to be within the value expected in some molecules with strong spin orbit perturbation, e.g., out of plane distorted haloaromatics, N-heterocyclic or carbonyl molecules. This analysis leads to the important conclusion that some of the zf transitions of some low symmetry molecules with large spin orbit interactions could possess a magnetic and an electric transition moment parallel to one another and should thus show natural circular dichroism in the microwave region.