The nomenclature of quantum mechanics is rather funny. We speak of allowed and forbidden transitions. Yet, forbidden transitions are not really forbidden. They are usually observed, but they are just weak compard to the allowed transitions. What makes the forbidden transition allowed? We say that there is a higher order effect. A Franck-Condon transition is allowed because the totally symmetric modes permit overkap of the initial and final state. Of course, the strength of a FC transition depends on the magnitude of the transition dipole moment. A FC transition can still be weak because the transition dipole moment is small. However, a vibronic transition is only allowed because of distortions of the molecule that lower its symmetry. Those distortions permit state mixing that cannot occur in the equilibrium geometry. The mathematical description of that mixing is based on two theories known as Herzberg-Teller coupling (interstate mixing) and Jahn-Teller coupling (intrastate mixing).
The role of symmetry in predicting electronic transitions
Symmetry is an extremely powerful tool that can be used to determine whether a transition is allowed or forbidden. For molecules that belong to a point group we can determine the linear combination of atomic orbitals that correspond to the HOMO, LUMO and other frontier orbitals. We can predict which transitions are allowed based a simple rule that the direct product of the ground and excited state should be equal to the irreducible representation of the x, y or z, corresponding to the three possible polarizations of electromagnetic radiation. A transition that meets these criteria is allowed. An allowed transition is coupled only to totally symmetry modes (Franck-Condon active). Other transitions are forbidden. Symmetry can help us to determine, which vibrational normal modes can couple two states in a transition that is nominally forbidden. In the presentation on vibronic coupling the use of product tables is demonstrated. Using product tables one can rapidly scan the available vibrational modes and find those that meet the criteria that the direct product of the ground state, excited state and the vibration should be equal to the irrep of x, y or z.
Examples of vibronic coupling
The presentations show several specific examples where vibronic coupling is required to explain the spectroscopy. Formaldehyde, benzene and porphyrin are three very different molecules that provide various perspectives on vibronic coupling. Formaldehyde has a n - pi* transition that is vibronically coupled by an out-of-plane bending mode. By contrast benzene has a vibronic pi-pi* transition that is part of a set of two transitions, the B and Q bands where one is very intense and allowed while the other is forbidden. This pattern is observed in all aromatic molecules (including porphyrin) so it is of great utility to study it here.
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