Frontier orbital analysis reactions

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

The modes of reaction of several 5-aminoimidazoles (96) with the reagents (135-142) are summarized in Table V. The variation of product structure with reagent is clearly discemable. The preference for C- or N-addition has been interpreted in terms of a frontier orbital analysis of the reactants [92JCS(P1)2779, 92JCS(P1)2789] (see Section VI,C). The... 

At first sight, radical reactions seem to be ideally adapted to frontier orbital analysis. They are usually exothermic, so their transition states resemble the reagents. Therefore, the starting material frontier orbitals should provide us with a very good approximation. Furthermore, radicals are soft reagents, whose reaction partners are often neutral molecules. Frontier control is dominant in such reactions. 

A frontier orbital analysis of the ene reaction is shown in Fig. 8.62. It displays many features of the [3,3]-sigmatropic shift. Thus, the hydrogen atom transfer from an allylic site to a double bond is seen to be symmetry allowed with respect to the HOMO of an... 

The frontier orbital analysis of electrocyclic reactions focuses on the HOMO of the open-chain polyene. 

In cycloaddition reactions, frontier orbital analysis considers the interaction of the HOMO of one component and the LUMO of the other. 

Because of the principle of microscopic reversibility it is appropriate to consider frontier orbital analysis of the reaction in either direction. The Hammond postulate dictates that the more exothermic the reaction the more the transition state will reflect the starting geometry, and frontier orbital analysis of reactant orbitals is expected to be a better predictor of relative transition state orbital interactions than for an endothermic or a less exothermic process. Conversely, frontier orbital analysis of product orbitals in exothermic reactions would be a poorer predictor of transition state energy. 

We have recently argued [39] that facial selectivity in the Diels-Alder reactions of 5-substituted cyclopenta-1,3-dienes is a reflection of hyperconjugative effects a frontier orbital analysis is shown in Fig. 6-10 [40], The molecule adopts a conformation where the better electron-donating group (C-Me rather than C-X) hinders approach of the dienophile from that face. Overlap of the C-C (T-bond (a better donor than C-X) increases the energy of the diene HOMO. Furthermore overlap of the C-C (T -orbital with the diene LUMO yP reduces the energy of the... 

For axial and equatorial nucleophilic addition to cyclohexanone, the principle of microscopic reversibility dictates that frontier orbital analysis can be considered for addition of the nucleophile to the carbonyl or loss of nucleophile from the product. Since the reaction is considered to be exothermic the frontier orbital interaction that should best represent the transition energy is the orbital interaction of the nucleophile HOMO with the ketone n (LUMO) (Fig. 6-11). 

The C-amino substituents possess reduced reactivity towards electrophiles in comparison with an. annular nitrogen. Reactions which result in exocyclic substitution may be a consequence of primary annular substitution followed by rearrangement (see CHEC-I). A frontier orbital analysis of elec-... 

Frontier orbital analysis of a [4 -I- 2] cycloaddition reaction shows that overlap of in-phase orbitals to form the two new a bonds requires suprafacial orbital overlap (Figure 29.5). This is tme whether we use the LUMO of the dienophile (a system with one TT bond Figure 29.1) and the HOMO of the diene (a system with two conjugated rr bonds Figure 29.2) or the HOMO of the dienophile and the LUMO of the diene. Now we can understand why Diels-Alder reactions occur with relative ease (Section 8.8). 

Orbital energies and approximate wavefunctions for the HOMO S of benzonor-bomadiene and 7-isopropylidenebenzonorbomadiene have been obtained from their p.e. spectra, and the differential reactivity of the systems in Diels-Alder reactions with inverse electron demand has been discussed in terms of frontier orbital analysis. Spectra for syn- and anti-7-norborneol show that in the sy -isomer the n-bond is ca. 0.2 eV more difficult to ionize, a result that is interpreted as arising from H-bond-induced stabilization of the tt-bond. Differential orbital interactions are ruled out by the finding that the n-n difference is the same for both of the analogous methyl ether derivatives. 

Frontier orbital analysis of some allowed perieyclic reactions... 

From the foregoing discussion it appears that the frontier orbital method is at once a simple, concise, and accurate method for assessing the stereochemical outcome of pericyclic reactions. Furthermore, it is a method that is equally applicable to symmetrical and to unsymmetrical systems. There are some disadvantages in the theory, however. Firstly, it is necessary to derive the general phase characteristics of the HOMO and LUMO levels. Hiickel molecular calculations can be used for tliis purpose, but there are available a number of approximate methods, for example the electron-in-a-box model, which are usually satisfactory even if they are more difficult to apply to more complex systems. Nevertheless, frontier orbital analysis is quicker and more simple than the formalized correlation diagram approach, and with a little practice one can intuitively arrive at the correct relative phase relationsliips in the HOMO and LUMO levels. 

Other reactions are controlled kinetically, and the most stable product is not the major one observed. In these cases, you must look at the reactant side of the reaction coordinate to discover factors determining the outcome. Klopman and Salem developed an analysis of reactivity in terms of two factors an electrostatic interaction approximated by atomic charges and a Frontier orbital interaction. Fleming s book provides an excellent introduction to these ideas. 

Another aspect of qualitative application of MO theory is the analysis of interactions of the orbitals in reacting molecules. As molecules approach one another and reaction proceeds, there is a mutual perturbation of the orbitals. This process continues until the reaction is complete and the new product (or intermediate in a multistep reaction) is formed. PMO theory incorporates the concept of frontier orbital control. This concept proposes that the most important interactions will be between a particular pair of orbitals. These orbitals are the highest filled oihital of one reactant (the HOMO, highest occupied molecular oihital) and the lowest unfilled (LUMO, lowest unoccupied molecular oihital) orbital of the other reactant. The basis for concentrating attention on these two orbitals is that they will be the closest in energy of the interacting orbitals. A basic postulate of PMO... 

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 more complete analysis of interacting molecules would examine all of the involved MOs in a similar wty. A correlation diagram would be constructed to determine which reactant orbital is transformed into wfiich product orbital. Reactions which permit smooth transformation of the reactant orbitals to product orbitals without intervention of high-energy transition states or intermediates can be identified in this way. If no such transformation is possible, a much higher activation energy is likely since the absence of a smooth transformation implies that bonds must be broken before they can be reformed. This treatment is more complete than the frontier orbital treatment because it focuses attention not only on the reactants but also on the products. We will describe this method of analysis in more detail in Chapter 11. The qualitative approach that has been described here is a useful and simple wty to apply MO theory to reactivity problems, and we will employ it in subsequent chapters to problems in reactivity that are best described in MO terms. I... 

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