Correlation diagrams general principles

Correlation diagrams general principles, 196-197 orbital, 196-203 state, 203-208... 

We have now considered three viewpoints from which thermal electrocyclic processes can be analyzed symmetry characteristics of the frontier orbitals, orbital correlation diagrams, and transition-state aromaticity. All arrive at the same conclusions about stereochemistiy of electrocyclic reactions. Reactions involving 4n + 2 electrons will be disrotatory and involve a Hiickel-type transition state, whereas those involving 4n electrons will be conrotatory and the orbital array will be of the Mobius type. These general principles serve to explain and correlate many specific experimental observations made both before and after the orbital symmetry mles were formulated. We will discuss a few representative examples in the following paragraphs. 

We have emphasized that the Diels-Alder reaction generally takes place rapidly and conveniently. In sharp contrast, the apparently similar dimerization of olefins to cyclobutanes (5-49) gives very poor results in most cases, except when photochemically induced. Fukui, Woodward, and Hoffmann have shown that these contrasting results can be explained by the principle of conservation of orbital symmetry,895 which predicts that certain reactions are allowed and others forbidden. The orbital-symmetry rules (also called the Woodward-Hoffmann rules) apply only to concerted reactions, e.g., mechanism a, and are based on the principle that reactions take place in such a way as to maintain maximum bonding throughout the course of the reaction. There are several ways of applying the orbital-symmetry principle to cycloaddition reactions, three of which are used more frequently than others.896 Of these three we will discuss two the frontier-orbital method and the Mobius-Huckel method. The third, called the correlation diagram method,897 is less convenient to apply than the other two. 

Contents Molecular Orbitals. - Chemical Reactivity Theory. - Interaction of Two Reacting Species. - Principles Governing the Reaction Pathway. - General Orientation Rule. - Reactivity Indices. - Various Examples. -Singlet-Triplet Selectivity. - Pseudoexcitation. -Three-species Interaction. - Orbital Catalysis. -Thermolytic Generation of Excited States. - Reaction Coordinate Formalism. - Correlation Diagram Approach. 

In constructing correlation diagrams in more complicated cases it is important to bear in mind the non-crossing m(e, which is an important general principle in quantum mechanics. This states that electronic potential energy-curves corresponding to orbitals or states (see Section 1.8) with the same symmetry do not cross. 

Of course, the Fourier transforms of the correlation functions are calculated by applying the same principles. Moreover, the generalization to the polydis-perse case is trivial. Finally, we recall that 2 (9 NxS) can be easily expressed as a sum of contributions associated with anchored diagrams. 

The areas sp are subjected to constraints. First, the sum of the areas of the segments constituting a polymer a is equal to the area Sm of this polymer. Secondly, if there are correlation points on a polymer, these correlations points determine polymer sections having well-defined areas, and one must write that the sum of the areas of the segments constituting a polymer section is equal to the area of the section. To simplify, in what follows we consider only diagrams which have no correlation points in the middle of a chain, and we admit that the principles developed in this simple case are actually quite general. 

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