Aromaticity Woodward-Hoffmann rule

A part of the chemical consequences of the cyclic orbital interactions in the cyclic conjngation is well known as the Hueckel rule for aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions [14]. In this section, we describe the basis for the rnles very briefly and other rules derived from or related to the orbital phase theory. The rules include kinetic stability (electron-donating and accepting abilities) of cyclic conjugate molecules (Sect. 2.2.2) and discontinnity of cyclic conjngation or inapplicability of the Hueckel rule to a certain class of conjngate molecnles (Sect. 2.2.3). Further applications are described in Sect. 4. 

The orbital phase theory can be applied to cyclically interacting systems which may be molecules at the equilibrium geometries or transition structures of reactions. The orbital phase continuity underlies the Hueckel rule for the aromaticity and the Woodward-Hoffmann rule for the stereoselection of organic reactions. 

Orbitals interact in cyclic manners in cyclic molecules and at cyclic transition structures of chemical reactions. The orbital phase theory is readily seen to contain the Hueckel 4n h- 2 ti electron rule for aromaticity and the Woodward-Hof nann mle for the pericyclic reactions. Both rules have been well documented. Here we review the advances in the cyclic conjugation, which cannot be made either by the Hueckel rule or by the Woodward-Hoffmann rule but only by the orbital phase theory. 

Besides the applications of the electrophilicity index mentioned in the review article [40], following recent applications and developments have been observed, including relationship between basicity and nucleophilicity [64], 3D-quantitative structure activity analysis [65], Quantitative Structure-Toxicity Relationship (QSTR) [66], redox potential [67,68], Woodward-Hoffmann rules [69], Michael-type reactions [70], Sn2 reactions [71], multiphilic descriptions [72], etc. Molecular systems include silylenes [73], heterocyclohexanones [74], pyrido-di-indoles [65], bipyridine [75], aromatic and heterocyclic sulfonamides [76], substituted nitrenes and phosphi-nidenes [77], first-row transition metal ions [67], triruthenium ring core structures [78], benzhydryl derivatives [79], multivalent superatoms [80], nitrobenzodifuroxan [70], dialkylpyridinium ions [81], dioxins [82], arsenosugars and thioarsenicals [83], dynamic properties of clusters and nanostructures [84], porphyrin compounds [85-87], and so on. 

Day21 has given a careful account of the relationship between the Woodward-Hoffmann rules and Mobius/Hiickel aromaticity, and has defined the terms supra-facial and antarafacial in terms of the nodal structure of the atomic basis functions. His approach makes quite explicit the assumption that the transition state involves a cyclic array of basis functions. Thus the interconversion of prismane (10) and benzene, apparently an allowed (n2s+ 2S+ 2S) process, is in fact forbidden because there are additional unfavourable overlaps across the ring.2... 

The so-called aromaticity rules are chosen for comparison, as they provide a beautiful correspondence with the symmetry-based Woodward-Hoffmann rules. A detailed analysis [92] showed the equivalence of the generalized Woodward-Hoffmann selection rules and the aromaticity-based selection rules for pericyclic reactions. Zimmermann [93] and Dewar [94] have made especially important contributions in this field. 

Three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

All the reactions we have looked at so far involve only the geometrically easy, and hence commonly observed, suprafacial processes. If we restrict ourselves to all-suprafacial processes, we may note that the allowed reactions involve an aromatic (4n + 2) number of electrons, and the forbidden reactions an antiaromatic (4n) number of electrons. (The number of electrons involved is easily counted it is twice the number of curly arrows.) This is the simplest version of the Woodward-Hoffmann rules it was first pointed out by Evans126 in 1939 and recalled many years later by Dewar.127... 

A simple consequence of the Woodward—Hoffmann rules is that cycloadditions involving a total (4n + 2) electrons, if they are all suprafacial, are always allowed they must always involve an odd number of (4q + 2)s components. Such reactions are often referred to as having aromatic transition states because of the obvious link with the aromatic requirement for (4n + 2) electrons. Six is the most common (4n + 2) number, but there are also a few cycloadditions involving ten electrons. These are mostly diene + triene, that is,, 4, +, 6j cycloadditions. Here are a couple of examples. 

Another important electronic structure principle is the maximum hardness principle " (MHP) which may be stated as, There seems to be a rule of nature that molecules arrange themselves to be as hard as possible . Numerical verification of this principle has been made in several physico-chemical problems such as molecular vibrations , internal rotations , chemical reactions" , isomer stability , pericyclic reactions and Woodward-Hoffmann rules , stability of magic clusters , stability of super atoms ", atomic shell structure" , aromaticity , electronic excitations , chaotic ionization, time-dependent problems like ion-atom collision and atom-field interaction " etc. 

Since (I-A) is a measure of hardness according to the maximum hardness principle, the stability of a system or the favorable direction of a physicochemical process is often dictated by this quantity. Because aromatic systems are much less reactive, especially toward addition reactions, I -A may be considered to be a proper diagnostic of aromaticity. Moreover, (/ - A) has been used in different other contexts, such as stability of magic clusters, chemical periodicity, molecular vibrations and internal rotations, chemical reactions, electronic excitations, confinement, solvation, dynamics in the presence of external field, atomic and molecular collisions, toxicity and biological activity, chaotic ionization, and Woodward-Hoffmann rules. The concept of absolute hardness as a unifying concept for identifying shells and subshells in nuclei, atoms, molecules, and metallic clusters has also been discussed by Parr and Zhou. ... 

According to the Woodward-Hoffmann rules for electrocychc reactions, a 6k electrocychzation is thermally allowed in a disrotatory manner and photochemically allowed in a conrotatory manner. However, in the present context of synthesis of aromatic compounds as final products, which are devoid of any stereocenters, the stereochemical aspects of the substituents in the intermediate dihydroaromatic compound should not matter. The photochemical 6x electrocychzation of c/s-stilbene derivatives followed by oxidation of the dihydroaromatic intermediate provides access to angularly fused polycyclic aromatic compounds (Scheme 16.2) [4]. 

The thermal Diels-Alder reaction of electron-rich 1,3-dienes with electron-deficient alkynes affords the corresponding cyclohexa-1,4-dienes, aromatization of which gives the corresponding benzenes. As the thermal Diels-Alder reaction proceeds in a concerted fashion that is best described by the Woodward-Hoffmann rules, it is difficult to use electronically neutral substrates. On the other hand, as the transition metal-catalyzed Diels-Alder reaction may proceed in a stepwise fashion, electronically neutral substrates can be employed. For the transition metal-catalyzed Diels-Alder reaction, cobalt-based complexes are the most frequently employed catalysts [38], although some rhodium-based complexes have also been used [39]. 

The parallelism between Clar s intuitive notion of aromatic sextets, migrating sextets, and anpty (of sextets) rings and the relative magnitudes of the numerical ring bond orders is so complete that there is not a single exception. So, in this respect, this theory is comparable with the Woodward-Hoffmann rules [28-31] initially formulated to explain the impressive stereospecificity of electrocyclic reactions under thermal and photochemical control. One lengthy review article on Woodward-Hoffmann rules ends with Exceptions None." The same is the case with our numerical characterization of k aromatic sextets with RBO. 

It is therefore inaccurate and misleading to talk about allowed and forbidden pericyclic reactions. The terms aromatic and antiaromatic pericyclic reaction are much more appropriate. It is also clear that the distinction between them has nothing to do with symmetry. It depends on the topology of overlap of the AOs in pericyclic transition states, not on the symmetries of MOs. If symmetry were involved, the distinction between allowed and forbidden reactions would be attenuated as symmetry was lost. This is not the case. The Woodward-Hoffmann rules, or the equivalent statement embodied in Evans principle, hold just as strongly in systems lacking symmetry as in symmetric systems. Indeed, if this were not the case, they would be far less useful and important. 

Electrocyclization provides an efficient way to synthesize a large variety of heterocyclic compounds. Among the many photocyclization reactions of aromatic compounds, electrocyclization is among the most frequently studied. An example of this is that illustrated in Scheme 1. This involves cyclization between the arene moieties of the protonated azobenzene 1, which reacts from the jtJt state reaction and is controlled by the Woodward-Hoffmann rules. Six rr-electrons are involved in the conrotatory cyclization. The reaction was not observed when unprotonated azobenzene was irradiated because in this case, the ntt state is populated. Since the photochemical electrocyclization is reversible, a consecutive trapping reaction is needed to obtain the final products in good yields. In the present case, as in many other reactions, a rearomatization step via oxidation took place to afford the final product 2. In the same way, the imine 3 can be cyclized to the phenanthridine derivative 4. In this case, the oxidation of the... 

The aromatic-antiaromatic transition state rules are. another formulation of the Woodward-Hoffmann type rules (Table 8.3). 

No more than a hydroboration is The transition state for a Woodward-Hoffmann-allowed reaction is aromatic in character, whereas a forbidden one is antiaromatic. However, the rules of aromaticity only apply when each atom of the annulene uses one, and only one, AO to bind to its neighbors. This is not the case here each fluorine atom uses two AOs, one for bonding to the other F atom and one for the incipient bond to C. 

The Woodward-Hoffmann orbital symmetry rules are not limited in application to the neutral polyene systems that have been discussed up to this point. They also apply to charged systems, just as the Htickel aromaticity rule can be applied to charged ring systems. The conversion of a cyclopropyl cation to an allyl cation is the simplest... 

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