Point-Group Selection Rules and Polarization for an Alternative Singlet—Triplet Transition Mechanism

Abstract

A radiative transition mechanism which involves the direct interaction between the electron spin and the radiation field is studied in detail in the limit of small spin—orbit coupling. In this mechanism, the odd-parity, spin-dependent multipoles of the lowest order, the spin—electric dipole and the spin—magnetic quadrupole, are considered as alternative operators for the usual spin—orbit assisted electric-dipole operator in singlet—triplet transitions. It is shown that, although these two spin-dependent spherical operators transform very differently in the three-dimensional rotation group, they contribute comparably to the radiative transition and they must be considered together to preserve the transverse nature of light. For applications to (plane) polarized light spectroscopy in oriented molecular crystals, expressions of these spin-dependent spherical operators are found in terms of the quadratic products of the Cartesian coordinates x, y, and z with the spin components Sx, Sy, and Sz. The explicit forms of the transition operators for propagation of light and polarization along x, y, or z directions are tabulated. The selection rules of the coordinate part of these operators are illustrated for the D6 point group. The selection rules of the spin part are given for the ``uncoupled'' spin quantized with respect to the principal molecular axis or with respect to an external magnetic field. General formulas for deriving the angular distribution of intensity are given in terms of rotation matrices. Specific formulas for the angular dependence and polarization of the ``direct'' phosphorescence from each and all of the three triplet components via this mechanism are derived. These are expressed in terms of the cosine of Euler angles [open phi] and ψ and functions of reduced rotation matrices. The explicit values of these functions of reduced rotation matrices in terms of the Euler angle θ are tabulated. The tabulation is extended for possible use in transitions involving symmetry-adapted spin wavefunctions and transitions in systems with any (lower than axial) point-group symmetry.