Orbitals Hiickel type

Hiickel-type systems (such as Hilcfcel pericyclic reactions and suprafacial sigmatropic shifts) obey the same rules as for sigma electron. The rationale for this observation is clear If the overlap between adjacent p-electron orbitals is positive along the reaction coordinate, only the peraiutational mechanism can... 

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. 

Similar considerations apply to the thiirene oxide system (18), since in this case too the sulfur s 3d-orbitals have the potential of interacting with the 2p-orbitals of both the adjacent carbon and oxygen atoms. Such an interaction should facilitate some kind of conjugation of the carbon-carbon double-bond -electrons with the formally unoccupied 3d-orbitals, which in turn would give rise to Hiickel-type stabilization associated with cyclic array of 4n + 2 (n = 0) 7t-electrons. 

Conjugation of the 7t-electrons of the carbon-carbon double bond with the LUMO sulfur 3d-orbitals would be expected to stabilize the Hiickel 4n -I- 2 (n = 0) array of n-electrons in the thiirene dioxide system. No wonder, therefore, that the successful synthesis of the first member in this series (e.g. 19b) has initiated and stimulated several studies , the main objective of which was to determine whether or not thiirene dioxides should be considered to be aromatic (or pseudo-aromatic ) and/or to what extent conjugation effects, which require some sort of n-d bonding in the conjugatively unsaturated sulfones, are operative within these systems. The fact that the sulfur-oxygen bond lengths in thiirene dioxides were found to be similar to those of other 802-containing compounds, does not corroborate a Hiickel-type jr-delocalization... 

In the potentially homoantiaromatic molecules of Figure 11, electron delocalization occurs along the periphery of a bicyclic system, involving in this way Aq + 2 rather than 4 q electrons. Since, however, the corresponding orbital system is of Mobius rather than Hiickel type (Figure 9), delocalization of 4q + 2 electrons leads to overall destabilization rather than stabilization. 

The next step in the analysis is to provide an unambiguous method of recognizing systems of the Hiickel or anti-Hiickel type. We introduce first the idea of a phase inversion.3 In the orbital interaction diagram, each interaction joining lobes of opposite sign constitutes a phase inversion. A change of sign within an orbital does not constitute a phase inversion. In 42, for example, there... 

Denotes a spin—orbital in a Slater determinant with spin (3, where the identity of the spin is indicated by the bar over the orbital symbol. The lack of the bar indicates a spin orbital with spin a. Denotes the reduced matrix element, for example, (3afo = hab — 0.5(haa + hbb)Sab. This reduced matrix element is equivalent to the resonance integral of the Hiickel type. 

The Mobius-Huckel concept was introduced by Zimmerman in 1966 35). It was suggested that each cyclic array of orbitals in a reacting system may be categorized as a Hiickel type or a Mobius type , depending on the number of plus-minus overlaps between adjacent orbitals. With zero or an even number of such sign inversions, the system is a Hiickel variety array while with one or some other odd number the system is a Mobius system. 

In a pericyclic reaction the array of basis orbitals of the reacting molecule is cyclic halfway along the reaction coordinate. The array will either be of the Mobius or the Hiickel type. Since the circle mnemonics give the distribution of MO energies... 

Tihis study was initiated to determine to what extent empirical molecu-lar orbital (MO) theories of the Hiickel type can provide information on the thermodynamic stability of a hypothetical unknown compound. The test, of course, has to be made on known compounds. Our interests have centered on compounds involving atoms such as N, O, F, and Cl, but compounds with C and H have also been included. The results thus far have been encouraging. 

The reaction of 1,3-butadiene with ethylene to give cyclohexene is an allowed reaction if the ethylene fragment approaches the butadiene fragment from one face, preserving a plane of symmetry as indicated in 4. The Hiickel-type arrangement of the p-orbitals shown in 4 involves six electrons and so should express some aromatic stabilization. 

This difference between the a - and rf -P-containing rings may be rationalized by the nature of the orbitals involved in 7t-delocalization. In diphosphirenylium ions I with dicoordinate phosphorus atoms, these are one 2p(C) and two 3p(P) orbitals. In ions of type IV one 2p(C), one 3p(P), and one a (PX) orbital have to be considered for the cyclic dilocalization of two 7t-electrons. It is obvious that the Hiickel-type three-orbital two-electron interaction typical for the cyclopropenium cation is more favored in diphosphirenylium ions I than in the related diphosphir-enium systems IV. 

TT-Electron calculations. Hiickel-type molecular orbital (HMO) method Bases—first calculations Base pairs—first calculations 56CR(243)380 59BBA(36)343... 

The pseudosecular equation for the corresponding bond orbital in a one-electron Hiickel-type approximation including overlap can then be written as ... 

Now the pattern has changed drastically relative to Fig. 9. Practically all the systems containing one d-orbital center are below the limit of aromaticity except the Mobius-type eight- and twelve-membered ring compounds, for which no examples of chemical compounds are known (compare Fig. 1 the phos-phonitrilic compounds 16a and 16b are of the unfavourable Hiickel type and already ruled out by consideration of the idealized systems). 

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