Wigner's Spin Conservation Rule
The Wigner spin conservation rule states that in any allowed electronic energy transfer process, the overall spin angular momentum of the system should not change. The rule is applicable whether the transfer occurs between an excited atom or a molecule and another molecule in its ground state or in the excited state. In an electronic transition between the energy states of the same molecule also, spin is necessarily conserved. But the phenomenon is governed by rules for dipole-dipole interaction.
Wigner's spin conservation rule requires that there must be correlation of spins between the reactants and the products. The possible spin of the transition state for reactants A and B with spins SA, and SB can be obtained by vector addition rule as |SA + SB|, |SA + SA - 1|,..., |SA - SA|. In order that there is smooth correlation with the products X and Y, the transition state formed by the products must also have total spin magnitude which belongs to one of the above values. This situation allows the reactants and the products to lie on the same potential energy surface. Such reactions whether physical or chemical, are known as adiabatic.
In these reactions a close approach of two reacting partners is necessary. Essentially, Wigner's rule states that the total spins of the α type (↑) and the β type (↓) in the combined initial and final state of the system remains the same, no matter how we combine them in the final state.
Thus, for example, in a singlet-singlet, triplet-triplet and triplet-singlet transfer of energy by exchange mechanism, the following combinations are possible-
These rules also predict the nature of photoproducts expected in a metal- sensitized reactions. From the restrictions imposed by conservation of spin, we expect different products for singlet-sensitized and triplet-sensitized reactions. The Wigner spin rule is utilized to predict the outcome of photophysical processes such as, allowed electronic states of triplet-triplet annihilation processes, quenching by paramagnetic ions, electronic energy transfer by exchange mechanism and also in a variety of photochemical primary processes leading to reactant-product correlation.
Limitations of Wigner's Spin Conservation Rule
The Wigner's spin conservation rule may break down when the total angular momentum quantum number is no longer a good quantum number, such as in strong magnetic fields, where spin mixing can occur. The propensity for spin conservation can be influenced by the mechanisms of the reactions involved. For particular reactions, especially those involving complex systems or high energy states, the conservation rule may not strictly apply.
Source: Fundamentals of Photochemistry by K.K.Rohatgi-Mukherjee
