Rules for Correlation of Electronic States

When the electronic states of both the reactants and products have been determined and characterized, a correlation diagram may be constructed by connecting the states according to the following rules  

As with orbital correlation diagrams, states are correlated from the lowest to the highest. 

Reactant states will only correlate with product states of the same spatial symmetry and spin multiplicity. 

Correlation lines define potential energy surfaces. Surfaces are allowed to cross (intersect) if the states involved are different in spatial symmetry or spin multiplicity but may not cross if both characteristics are the same. 

Inspection of the orbital make-up of reactant and product states may imply intended correlations which would lead to state crossings. If the states involved may not cross by rule 3, an avoided crossing occurs. The intention to cross is often depicted by dashed lines. 

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Chapter 14 deals with orbital correlation diagrams following Woodward and Hoffmann [3]. State wave functions and properties of electronic states are deduced from the orbital picture, and rules for state correlation diagrams are reviewed, as a prelude to an introduction to the field of organic photochemistry in Chapter 15. 

Correlation rules relate the symmetry of reactants to the symmetry of products. More precisely, they give the symmetry of the fragments which can result when a molecule or transition state is distorted in the direction of reactants or products32,33. A familiar example is the correlation of the states of a diatomic molecule with those of its constituent atoms. Within the Bom-Oppenheimer separation we can deal with strictly electronic correlation rules, valid when there is negligible coupling between electronic and vibrational wave functions. When such coupling is important, correlations forbidden on a strictly electronic basis may be allowed, so the validity of purely electronic correlation rules is hard to assess for polyatomic molecules with strongly excited vibration. 

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. 

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. 

Valuable insight, particularly with regard to the effects of electronic excitation on reaction cross sections and reaction dynamics, has also been achieved without accurate knowledge of the actual potential surfaces, through the use of molecular-orbital correlation diagrams. Adiabatic correlation rules for neutral reactions involving polyatomic intermediates were developed by Shuler 478 These were adapted and extended for ion-neutral interactions by Mahan and co-workers.192,45 479,480 Electronic-state correlation diagrams have been used to deduce the qualitative nature of the potential surfaces that control ion-neutral reaction dynamics. The dynamics of the reaction N+(H2,H)NH+ and in particular the different behavior of the N + (3P) and N + ( Z)) states,123 for example, have been rationalized from such considerations (see Fig. 62). In this case the... 

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