Transition states aromaticity indices

Table 23 Transition state aromaticity indices for the reactions of 61H-0 and 61H-S with carbanions in the gas phase3... 

The aromaticities of symmetry-allowed and -forbidden transition states for electrocyclic reactions and sigmatropic rearrangements involving two, four, and six r-electrons, and Diels-Alder cycloadditions, have been investigated by ab initio CASSCF calculations and analysis based on an index of deviation from aromaticity. The order of the aromaticity levels was found to correspond to the energy barriers for some of the reactions studied, and also to the allowed or forbidden nature of the transition states.2 The uses of catalytic metal vinylidene complexes in electrocycliza-tion, [l,5]-hydrogen shift reactions, and 2 + 2-cycloadditions, and the mechanisms of these transformations, have been reviewed.3... 

If only the electron density of the highest occupied molecular orbital (HOMO) is taken into account, an electrophilic attack is said to be regulated by the frontier electron density index (54JCP1433 79FCF1). In nucleophilic substitutions, the aromatic substrate tends to accept an electron pair in the transition state, and so the frontier orbital is taken as the lowest unoccupied molecular orbital (LUMO). In this case, the frontier electron density is assumed to be as the electron distribution that would be present in the LUMO if it were occupied by two electrons. In contrast to arguments based on the charge or 7c-electron densities, both nucleophilic and electrophilic substitution occur preferentially at the atom with the highest electron density within the appropriate frontier orbital, i.e., LUMO or HOMO, respectively. 

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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