THE ROLE OF d-$\pi$ ORBITALS IN SPIN-ORBIT COUPLING

Abstract

Spin-orbit coupling in p-$\pi$ aromatic molecules is known to be extremely small. Transitions between the lowest $\pi, \pi^{*}$ triplet state and the ground state (T $<->$ $S_{\eta}$) are found to be very weak and largely polarized out of plane despite selection rules that would allow in-plane polarized intensity. Within the framework of LCAO-MO approximations it has been shown by $McClure^{1}$ that the smallness of the spin-orbit interaction arises from the vanishing (by symmetry) of one- and two-center spin-orbit coupling integrals that mix singlet $\pi, \pi^{*}$ and triplet $\pi, \pi^{*}$ states. This leaves only small three and four center terms to provide in-plane polarized intensity. It is found, however, that some of these one- and two-center integrals do not vanish for molecules containing atoms with d-$\pi$ orbitals. These terms are calculated for thiophene ($C_{4} H_{4}S$), and are found to make a significant contribution to spin-orbit coupling beyond that usually associated with heavy atom substitution. This contribution should introduce appreciable in-plane polarized intensity into the T $<->$ $S_{\eta}$ transition of thiophene. The implications of these ideas for the increased spin-orbit coupling in halogen (and other heavy atom) substituted aromatic molecules, and in paired spin poryphyrins is also considered.