Selection rule

In physics and chemistry, a selection rule, or transition rule, formally constrains the possible transitions of a system from one quantum state to another. Selection rules have been derived for electromagnetic transitions in molecules, in atoms, in atomic nuclei, and so on. The selection rules may differ according to the technique used to observe the transition. The selection rule also plays a role in chemical reactions, where some are formally spin forbidden reactions, that is, reactions where the spin state changes at least once from reactants to products.

In the following, mainly atomic and molecular transitions are considered.

In quantum mechanics the basis for a spectroscopic selection rule is the value of the transition moment integral

where ${\displaystyle \psi _{1}}$ and ${\displaystyle \psi _{2}}$ are the wave functions of the two states involved in the transition and µ is the transition moment operator. If the value of this integral is zero the transition is forbidden. In practice, the integral itself does not need to be calculated to determine a selection rule. It is sufficient to determine the symmetry of transition moment function, ${\displaystyle \psi _{1}^{*}\mu \psi _{2}}$. If the symmetry of this function spans the totally symmetric representation of the point group to which the atom or molecule belongs then its value is (in general) not zero and the transition is allowed. Otherwise, the transition is forbidden.

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