Transitions between energy levels in a quantum-mechanical system that are not allowed to take place because of selection rules. In practice, forbidden transitions can occur, but they do so with much lower probability than allowed transitions; this means that their intensities are much weaker than allowed transitions. There are three reasons why forbidden transitions may occur:

1. (1) the selection rule that is violated is only an approximate rule. An example is provided by those selection rules that are only exact in the absence of spin–orbit coupling. When spin–orbit coupling is taken into account, the forbidden transitions become allowed—their strength increasing with the size of the spin–orbit coupling;

2. (2) the selection rule is valid for dipole radiation, i.e. in the interaction between a quantum-mechanical system, such as an atom, and an electromagnetic field, only the (variable) electric dipole moment is considered. Actual transitions may involve magnetic dipole radiation or quadrupole radiation;

3. (3) the selection rule only applies for an atom, molecule, etc., in isolation and does not necessarily apply if external fields, collisions, etc., are taken into account.

See also Laporte selection rule.