Wigner-Witmer correlation rules

The Woodward-Hoffmann rules have intellectual roots that can be traced back to Wigner-Witmer correlation rules (E. Wigner and E. E. Witmer, Z. Phys. 51 [1928], 859) and general correlation-diagram concepts (R. S. Mulliken, Rev. Mod. Phys. 4 [1932], 1) as employed, e.g., by K. F. Herzfeld, Rev. Mod. Phys. 41 (1949), 527. Alternative MO... 

The correlation between the electronic states of a polyatomic molecule and those of the separated atoms or molecular fragments can be derived from a generalization of the Wigner-Witmer correlation rules for diatomic molecules. 

Application of the correlation rules—The Wigner-Witruer correlation rules relate the nature of molecular states to the atomic states into which they may dissociate. The quantum-mechanical selection rules determine what electronic states may be excited by radiation, and with a knowledge of them it is often possible to deduce what type an electronic state is, and from this, using the Wigner-Witmer rules, to deduce what atomic states it may dissociate into. 

Silver8 adopted a similar approach, and proposed a further category of unfeasible reactions in which neither individual orbital correlation rules nor total symmetry correlation rules (Wigner-Witmer rules) were obeyed. Silver and Karplus87 have shown how to derive W-H symmetry rules using a simple valence-bond formalism. 

We have described the orbital approaches to the electron configurations of diatomic molecules, both the molecular orbital and the united atom models. We now turn to the question of what types of molecular states result from given states of the separate atoms. If Russell Saunders coupling is valid for the separate atoms, the correlation rules, due to Wigner and Witmer [16] provide a valid and complete summary of the molecular states. This information is extremely important for an understanding of both the formation and dissociation of diatomic molecules. 

The correlation rules for determining what types of molecular electronic states result from given electronic states of the separated atoms were derived quantum mechanically by Wigner and Witmer [1] and are discussed in great detail by Herzberg [2], These correlation rules hold for the adiabatic potential curves of the electronic states1 when Russell-Saunders coupling is valid for the separated atoms as well as the molecule. 

Operator equations have been employed by George and Ross (1971) to analyse symmetry in chemical reactions. In order to preserve the identity of electronic states of reactants and products, these authors worked within a quasi-adiabatic representation of electronic motions. By introducing a chain of approximations, going from separate conservation of total electronic spin to complete neglect of dynamics, they discussed the Wigner-Witmer angular momentum correlation rules, Shuler s rules for linear molecular conformations and the Woodward-Hoffmann rules. 

It is possible to correlate the molecular electronic states with the states of the separated atoms and independently, with the united atom having the same number of nucleons and electrons as the molecule. This correlation proceeds according to the Wigner-Witmer rules.and will be outlined in Appendix C. 

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