symmetryforbidden

Symmetryforbidden refers to a transition between quantum states that is not allowed by symmetry for a given interaction, such as the electric dipole interaction, due to the transformation properties of the states and the transition operator. In practice, the transition moment integral vanishes when the initial and final state wavefunctions transform according to irreducible representations that do not couple to the operator responsible for the transition. This kind of restriction is central to selection rules in quantum mechanics and underpins the classification of transitions as allowed or forbidden.

In atomic and molecular spectroscopy, symmetryforbidden transitions are common when the simplest coupling is considered. For electronic transitions in atoms, standard selection rules include changes in orbital angular momentum (for example, Δl = ±1) and, in many cases, a conserved spin (ΔS = 0). If these conditions are not met, the transition is symmetryforbidden under the dominant interaction. However, forbidden transitions can occur via higher-order processes or when additional couplings are present, such as spin-orbit interaction, magnetic dipole, or electric quadrupole effects.

In molecules, symmetryforbidden behavior often arises from vibrational or rotational states. For example, in homonuclear diatomic molecules, vibrational transitions may be infrared inactive because there is no permanent dipole moment change, even though Raman activity may be allowed due to changes in polarizability. The apparent prohibition can also be lifted by vibronic coupling (Herzberg–Teller effects) or by external perturbations that break the strict symmetry.

Symmetryforbidden transitions are typically much weaker than allowed ones, but they can still be observable under certain conditions, such as low-density astrophysical environments where long-lived states permit weak transitions to be detected.