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Concept
Selection rule
Summary
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 and are the wave functions of the two states, "state 1" and "state 2", involved in the transition, and μ is the transition moment operator. This integral represents the propagator (and thus the probability) of the transition between states 1 and 2; if the value of this integral is zero then the transition is "forbidden".
In practice, to determine a selection rule the integral itself does not need to be calculated: It is sufficient to determine the symmetry of the transition moment function
If the transition moment function is symmetric over all of the totally symmetric representation of the point group to which the atom or molecule belongs, then the integral's value is (in general) not zero and the transition is allowed. Otherwise, the transition is "forbidden".
The transition moment integral is zero if the transition moment function, is anti-symmetric or odd, i.e. holds. The symmetry of the transition moment function is the direct product of the parities of its three components. The symmetry characteristics of each component can be obtained from standard character tables. Rules for obtaining the symmetries of a direct product can be found in texts on character tables.
The Laporte rule is a selection rule formally stated as follows: In a centrosymmetric environment, transitions between like atomic orbitals such as s-s, p-p, d-d, or f-f, transitions are forbidden.
Official source
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