Radiationless processes in transition-metal complexes

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Abstract
This work applies recent theories of radiationless relaxation processes to the case of transition-metal complexes. Existing theories developed for understanding radiationless transitions in organic molecules separate coupling terms into electronic and vibrational factors. In this work the symmetry based selection rules on the coupling terms are examined since the high symmetry of many transition-metal complexes offers the possibility that strict selection rules will operate. First, the theoretical expressions have been extended to include the spin-orbit coupling operator in the zeroth order hamiltonian. This then allows application of the final expressions to transition metal ions of any atomic number and also permits derivation of selection rules for relaxation processes between spinor states. Secondly, the application of the vibrational factor, which is a product of a promoting term and an overlap factor or accepting term, to a series of octahedral and pseudooctahedral Cr(III) complexes, studied by Forster and co-workers, is described. It is shown that there is a good linear correlation between the radiationless transition rate 2 Eg ↭4 A2g and the number of active hydrogen atoms on the ligands. It is concluded that the highest frequency internal ligand modes are acting as promoting modes. This can be understood by examination of the selection rules on the electronic factors which show that, for the 2 Eg ↭4 A 2g process in Cr(III), there are no vibrations of the metal-ligand framework likely to be efficient as promoting modes. Finally, the selection rules are given for the electronic coupling factors between the lowest excited and ground states of all the d configurations of both tetrahedral and octahedral complexes of the first row of transition metal ions. A comparison of these rules with available experimental data shows there is some correlation between the occurrence of emission and the absence of a promoting mode among the skeletal vibrations of the complex considered.