Frontier orbital symmetries

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

According to one classification (15,16), symmetrical dinuclear PMDs can be divided into two classes, A and B, with respect to the symmetry of the frontier molecular orbital (MO). Thus, the lowest unoccupied MO (LUMO) of class-A dyes is antisymmetrical and the highest occupied MO (HOMO) is symmetrical, and the TT-system contains an odd number of TT-electron pairs. On the other hand, the frontier MO symmetry of class-B dyes is the opposite, and the molecule has an even number of TT-electron pairs. 

Frontier orbital theory also provides the basic framework for analysis of the effect that the symmetiy of orbitals has upon reactivity. One of the basic tenets of MO theory is that the symmetries of two orbitals must match to permit a strong interaction between them. This symmetry requirement, when used in the context of frontier orbital theory, can be a very powerful tool for predicting reactivity. As an example, let us examine the approach of an allyl cation and an ethylene molecule and ask whether the following reaction is likely to occur. 

The positively charged allyl cation would be expected to be the electron acceptor in any initial interaction with ethylene. Therefore, to consider this reaction in terms of frontier orbital theory, the question we need to answer is, do the ethylene HOMO and allyl cation LUMO interact favorably as the reactants approach one another The orbitals that are involved are shown in Fig. 1.27. If we analyze a symmetrical approach, which would be necessary for the simultaneous formation of the two new bonds, we see that the symmetries of the two orbitals do not match. Any bonding interaction developing at one end would be canceled by an antibonding interaction at the other end. The conclusion that is drawn from this analysis is that this particular reaction process is not favorable. We would need to consider other modes of approach to analyze the problem more thoroughly, but this analysis indicates that simultaneous (concerted) bond formation between ethylene and an allyl cation to form a cyclopentyl cation is not possible. 

A complete mechanistic description of these reactions must explain not only their high degree of stereospecificity, but also why four-ir-electron systems undergo conrotatory reactions whereas six-Ji-electron systems undergo disrotatory reactions. Woodward and Hoifinann proposed that the stereochemistry of the reactions is controlled by the symmetry properties of the HOMO of the reacting system. The idea that the HOMO should control the course of the reaction is an example of frontier orbital theory, which holds that it is the electrons of highest energy, i.e., those in the HOMO, that are of prime importance. The symmetry characteristics of the occupied orbitals of 1,3-butadiene are shown in Fig. 11.1. 

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. 

Orbital symmetry control of subsequent ring opening could account for isomerization at only one of the double bonds. Taking ij/ as the controlling frontier orbital, it can be seen that a concerted return to ip2 to rotation at only one terminus of the diene ... 

Cycloaddition reactions also have important applications for acyclic chalcogen-nitrogen species. Extensive studies have been carried out on the cycloaddition chemistry of [NSa]" which, unlike [NOa]", undergoes quantitative, cycloaddition reactions with unsaturated molecules such as alkenes, alkynes and nitriles (Section 5.3.2). ° The frontier orbital interactions involved in the cycloaddition of [NSa]" and alkynes are illustrated in Fig. 4.13. The HOMO ( Tn) and LUMO ( r ) of the sulfur-nitrogen species are of the correct symmetry to interact with the LUMO (tt ) and HOMO (tt) of a typical alkyne, respectively. Although both... 

See, e.g. (a) Woodward, R. B. Hoffmann, R. The Conservation of Orbital Symmetry, Verlag Chemie 1970 (b) Flfm-ING, L. Frontier Orbitals and Organic Chemical Reactions, John Wiley and Sons, London, 1977. 

Mechanistically the 1,3-dipolar cycloaddition reaction very likely is a concerted one-step process via a cyclic transition state. The transition state is less symmetric and more polar as for a Diels-Alder reaction however the symmetry of the frontier orbitals is similar. In order to describe the bonding of the 1,3-dipolar compound, e.g. diazomethane 4, several Lewis structures can be drawn that are resonance structures ... 

How can we predict whether conrotatory or disrotatory motion will occur in a given case According to frontier orbital theory, the stereochemistry of an electro-cyclic reaction is determined by the symmetry of the polyene HOMO. The electrons in the HOMO are the highest-energy, most loosely held electrons, and are therefore most easily moved during reaction. For thermal reactions, the ground-state... 

Thermal and photochemical electrocyclic reactions always take place with opposite stereochemistry because the symmetries of the frontier orbitals are always different. Table 30.1 gives some simple rules that make it possible to predict the stereochemistry of electrocyclic reactions. 

The last decade has witnessed an unprecedented strengthening of the bone between theory and experiment in organic chemistry. Much of this success may be credited to the development of widely applicable, unifying concepts, such as the symmetry rules of Woodward and Hoffmann, and the frontier orbital thee>ry of Eukui. Whereas the the ore tical emphasis had historically been on detailed structure and spectroscopy, the new methods are de signe d to solve pre)blems e>f special importance to organic chemists reactivity, stereochemistry, and mechanisms. 

In any given sigmatropic rearrangement, only one of the two pathways is allowed by the orbital-symmetry rules the other is forbidden. To analyze this situation we first use a modified frontier-orbital approach. We will imagine that in the transition state the migrating H atom breaks away from the rest of the system, which we may treat as if it were a free radical. 

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

Scheme 24 The symmetry-allowed frontier orbital interaction for the Diels-Alder reactions...

Scheme 25a,b The symmetry-forbidden (a) and -free (b) frontier orbital interactions for the dimerization of ethylenes... 

The frontier orbital interaction is forbidden by the symmetry for the dimerization of ethylenes throngh the rectangular transition state. The HOMO is symmetric and the LUMO is antisymmetric (Scheme 25a). The overlap integrals have the opposite signs at the reaction sites. The overlap between the frontier orbitals is zero even if each overlap between the atomic p-orbitals increases. It follows that the dimerization cannot occur throngh the fonr-membered ring transition states in a concerted and stereospecfic manner. 

The frontier orbital interaction can be free from the symmetry restriction. A pair of the reaction sites is close to each other while the other pair of the sites is far from each other (Scheme 25b). This is the geometry of the transition state leading to diradical intermediates. 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

Frontier orbital approaches are not yet implemented in EROS. Nor does EROS take account of the features of reactivity which are controlled by orbital symmetries. This will follow the current work on stereochemistry and conformation. 

---