We present a theoretical study of radiationless transitions in transition-metal ion systems, taking a coupling mechanism of the Herzberg-Teller type. The transition-metal complex is characterized by displaced potential hyper-surfaces involving frequency changes. The radiationless decay rate is expressed in terms of a weighted sum of line shape functions which involve both the intramolecular and intermolecular contributions of the relaxation processes. It is a new approach for the analysis and understanding of the radiationless decay of the2E state in transition-metal ion systems. © 1979 Taylor & Francis Group, LLC.