Wigner-Witmer rule

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. 

The chemical reaction is the most chemical event. The first application of symmetry considerations to chemical reactions can be attributed to Wigner and Witmer [2], The Wigner-Witmer rules are concerned with the conservation of spin and orbital angular momentum in the reaction of diatomic molecules. Although symmetry is not explicitly mentioned, it is present implicitly in the principle of conservation of orbital angular momentum. It was Emmy Noether (1882-1935), a German mathematician, who established that there was a one-to-one correspondence between symmetry and the different conservation laws [3, 4],... 

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. 

In contrast to the well-known Wigner-Witmer rule [24] that multiplicity is retained during a chemical reaction, the origin of the spin exclusion principle is both the retention and the distortion of symmetry. The fact is that from the viewpoint of rigorous invariance the initially singlet system cannot spontaneously pass into the triplet state. Spin-orbital and spin-lattice interactions probably play the main role in this transition. 

Such reactions are indeed relatively free of orbital symmetry restrictions, but not entirely so. The electrons of a bond that is broken must still end up somewhere. The above rule says that they must end up in orbitals of the same S5unmetry as the bond that they originated from. For example, as HCl dissociaties into atoms, the electrons of the a bond must remain in atomic orbitals of a S3munetry. Essentially this restriction, plus the spin conservation rule, is the basis of the Wigner-Witmer rules. ) In the same way, a bond that is formed must conserve the symmetry of the original orbitals of the constituent electrons. Additionally, bonding can only occur by the combination of atomic orbitals of the same synunetry (net positive overlap). 

The adiabatic behaviour for chemical reactions provides some sort of selection rules for some classes of chemical reactions. One of the simplest is the Wigner-Witmer rule concerning the conservation of spin. This rule is based upon the evidence that coupling of the electron spin to other types of motion (e.g. translational motion) is very small and, consequently, can be neglected. As a result, the spin angular momentum is considered constant, i.e. AS = 0. An example of a chemical reaction in which the spin is not conserved is CO oxidation ... 

The states that can he formed from two atoms in a given state are enumerated hy the Wigner-Witmer rules (Herzheig, 1950 Zaie, 1988). See also P. Pechukas and R. N. Zare, Am. J. Phys. 40, 1687 (1972). 

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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