Dewar-Evans rule

Sigmatropic shifts represent another important class of pericyclic reactions to which the Woodward-Hoffmann rules apply. The selection rules for these reactions are best discussed by means of the Dewar-Evans-Zimmerman rules. It is then easy to see that a suprafacial [1,3]-hydrogen shift is forbidden in the ground state but allowed in the excited state, since the transition state is isoelectronic with an antiaromatic 4N-HQckel system (with n = 1), in which the signs of the 4N AOs can be chosen such that all overlaps are positive. The antarafacial reaction, on the other hand, is thermally allowed, inasmuch as the transition state may be considered as a Mobius system with just one change in phase. 

This is a natural generalization of the Woodward-Hoffmann (W-H) rules 155,158) A similar approach was also discussed by Salem 157>. The extraordinary success of the W-H rules shows that in some cases purely topological factors govern the course of chemical reactions 158>. An interesting approach was also developed by Dewar and advocated by him for twenty years 159>. He established the following set of rules, now known as the Dewar-Evans (D-E) rules 160> ... 

Euler-Lagrange equations, electron nuclear dynamics (END), time-dependent variational principle (TDVP) basic ansatz, 330-333 free electrons, 333-334 Evans-Dewar-Zimmerman approach, phase-change rule, 435... 

Dewar [note 28(b), p. 603] refers to this rule as the Evans principle. 

The reactants cannot retain their coplanarity during cycloaddition, but -as M.G. Evans pointed out over half a century ago - the transition state of the Diels-Alder reaction nevertheless reduces to a six-electron problem [26] in which the mobile electrons. .. simulate their behaviour in a benzene molecule [27]. Following this line of reasoning, Dewar [28] extended to non-planar systems, like those illustrated in (b) and (c) of Fig. 1.1, the scope of the familiar Hiickel Rule [29], according to which planar monocyclic molecules with 4N -f 2 mobile electrons have aromatic stability. It follows that [ 4 2]-cycloaddition, which has an aromatic transition state, is allowed, whereas [ 2 2]-cycloaddition is... 

The basis of this concept [32] is a simple parallel intuitively felt by Evans [154], between the ease of certain reactions and the arrangement of corresponding transition states. Thus, e.g., the ease of a majority of Diels-Alder reactions is related to the fact that transient structure created by approaching the diene and dienophilic components is isoconjugated, or in other words, topologically equivalent, with the aromatic benzene and as a such should be therefore stabilized, at least in part, as the benzene itself. This simple idea was revived by Dewar [32] who also generalized it into the form of simple rule that (thermally) allowed reactions proceed via aromatic transition states. The proposed theoretical justification of the above criterion arises from a simple idea of direct quantitative evaluation of the resemblance of electron structure of expected transition states with the appropriate aromatic standards. The quantitative measure of this resemblance is the similarily index (102), where Q and ref represent the density matrices of the expected transition state and the appropriate reference standard respectively. 

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