Theory of Singlet-Triplet Transitions in Cyclic Tetramers: Applications to Tetraphenyl Group IV Compounds
A description of singlet-triplet transitions in cyclic molecules is presented such that the selection rules take full advantage of the cyclic symmetry. It is found that unlike singlet-singlet transitions, all component triplet states of a cyclic tetramer have allowed transitions to the ground state in electric dipole radiation. The relative intensities of transitions to the various excitonlike states is determined by the geometrical transformation involved in switching the axis of spin quantization from the monometer to the cyclic tetramer basis. The theoretical predictions are convincingly exemplified by the T1 ← S0 low-temperature absorption spectra of crystals of the tetraphenyl Group IV (C, Si, Ge, Sn, and Pb) compounds, all of which have S4 symmetry. The absorption spectra of the singlet states of neat crystals of these materials is also presented and these also demonstrate the cyclic exciton selection rules but in this case only two of the four states are seen as predicted. The tetraphenyl-X triplets all show four excitonlike states—3A, 3B, and3E: The total splittings are: X = Si, 3E - 3B = 1.1 cm-1; X = Ge, 3E - 3B = 2.8 cm-1; X = Sn, 3E - 3A = 7.4 cm-1; X = Pb, 3E - 3A = 6.6 cm-1. The 3E state is always at highest energy. In the singlet states only the E and B states are seen and the splittings are: X = Ge, 3B - 3E = 11 cm-1; X = Sn, 3B - 3E = 10 cm-1; and X = Si, 3B - 3E = 6 cm-1. The spectra in high magnetic fields (Zeeman effect) confirm the detailed assignments and the theoretical model. In addition we have seen the spin-orbit interaction between different monomer based triplet states.