Frontier orbital theory

On the other hand, the negative overlap in the region of one of the newly created bonds in the 2s + 2s dimerization of ethene is the indication of the forbiddeness of the process. 

In connection with cycloaddition reactions it is convenient to mention yet another interesting possibility of the exploitation of the Fukui s approach. This possibility concerns the rationalization of the so-called endo addition in Diels-Alder reactions. In order to demonstrate the preference of this specific reaction mode let us assume a simple addition of two butadiene molecules resulting in the formation of vinylcyclohexene. For this reaction there are two alternative 4s + 2s reaction paths differing in the stereochemical arrangement of the corresponding products. One of these products is of the so-called exo type, whereas for the other the name endo is reserved. 

If we now visualize the nodal structure of the HOMO and LUMO orbitals of individual fragments, the final picture results. 

As can be seen from this scheme, the [1,3] rearrangement is thermally allowed as antarafacial process, whereas for the [1,5] rearrangement, the suprafacial reaction mechanism is preferred. Similarly as in the case of 2s + 2a addition, the considerable steric strain accompanying the antarafacial [1,3] rearrangement makes this reaction unfavorable. Nevertheless for larger, more flexible systems, the antara cial rearrangements are observed. An example in this respect is the [1,7] rearrangement. 

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Frontier Orbital theory supplies an additional assumption to this calculation. It considers only the interactions between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO). These orbitals have the smallest energy separation, leading to a small denominator in the Klopman-Salem equation. The Frontier orbitals are generally diffuse, so the numerator in the equation has large terms. 

Frontier Orbital theory is qualitative, so there is no need for great accuracy in the calculation as long as it produces the approximate form of the orbitals. 

Btamp/e Another example of frontier orbital theory uses the reaction of phenyl-butadiene with phenylethylene. This reaction is a [4 + 2] pericyclic addition to form a six-membered ring. It could proceed with the two phenyl rings close to each other (head to head) or further away from each other (head to tail). 

This example uses AMI for optimization and orbital calculations. For more examples of Frontier Orbital theory, see Fleming sbook. ... 

Frontier orbital theory predicts that electrophilic substitution of pyrroles with soft electrophiles will be frontier controlled and occur at the 2-position, whereas electrophilic substitution with hard electrophiles will be charge controlled and occur at the 3-position. These predictions may be illustrated by the substitution behaviour of 1-benzenesulfonylpyr-role. Nitration and Friedel-Crafts acylation of this substrate occurs at the 3-position, whereas the softer electrophiles generated in the Mannich reaction (R2N=CH2), in formylation under Vilsmeier conditions (R2N=CHC1) or in formylation with dichloromethyl methyl ether and aluminum chloride (MeO=CHCl) effect substitution mainly in the 2-position (81TL4899, 81TL4901). Formylation of 2-methoxycarbonyl-l-methylpyrrole with... 

The LUMO, which is the frontier orbital in reactions with nucleophiles, has a larger coefficient on the /3-carbon atom, whereas the two occupied orbitals are distorted in such a way as to have larger coefficients on oxygen. The overall effect is that the LUMO is relatively low-lying and has a high coefficient on the /3-carbon atom. The frontier orbital theory therefore predicts that nucleophiles will react preferentially at the /3-carbon atom. 

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. 

Both the reactivity data in Tables 11.3 and 11.4 and the regiochemical relationships in Scheme 11.3 ean be understood on the basis of frontier orbital theory. In reactions of types A and B illustrated in Seheme 11.3, the frontier orbitals will be the diene HOMO and the dienophile LUMO. This is illustrated in Fig. 11.12. This will be the strongest interaction because the donor substituent on the diene will raise the diene orbitals in energy whereas the acceptor substituent will lower the dienophile orbitals. The strongest interaction will be between j/2 and jc. In reactions of types C and D, the pairing of diene LUMO and dienophile HOMO will be expected to be the strongest interaction because of the substituent effects, as illustrated in Fig. 11.12. 

Reactivity Patterns The Role of Frontier Orbital Theory... 

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... 

How can we predict whether a given cycloaddition reaction will occur with suprafacial or with antarafacial geometry According to frontier orbital theory, a cycloaddition reaction takes place when a bonding interaction occurs between the HOMO of one reactant and the LUMO of the other. An intuitive explanation of this rule is to imagine that one reactant donates electrons to the other. As with elec-trocyclic reactions, it s the electrons in the HOMO of the first reactant that are least tightly held and most likely to be donated. But when the second reactant accepts those electrons, they must go into a vacant, unoccupied orbital—the LUMO. 

The frontier orbital theory [7-9] assumes that the stabihzation by the electron delocalization could control chemical reactions. The stabilization comes from the interactions between the occupied molecular orbitals of one molecule and the unoccupied molecular orbitals of another (Sect. 1.4). The strong interaction occurs when the energy gap is small (Sect. 1.3). The HOMO and the LUMO are the closest in energy to each other. The HOMO-LUMO interaction, especially the interaction between the HOMO of electron donors and the LUMO of electron acceptors, controls the chemical reactions (Scheme 20). The HOMO and the LUMO are termed the frontier orbitals. ... 

Naphthalene undergoes electrophihc substitutions at the a rather than p position. The Hueckel molecular orbital calculations show that all the carbons have the same jt electron density 1.0. This is not in agreement with the theory of organic reactions based on the Coulombic interaction that electrophilic attack occurs on the most negatively charged atom. Fukui [7] proposed the frontier orbital theory for the discrepancy between the theory and the experimental observation. The importance of... 

Molecules have some occupied and some unoccupied orbitals. There occur diverse interactions (Scheme 1) when molecules undergo reactions. According to the frontier orbital theory (Sect 3 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume), the HOMO d) of an electron donor (D) and the LUMO (fl ) of an electron acceptor (A) play a predominant role in the chemical reactions (delocalization band in Scheme 2). The electron configuration D A where one electron transfers from dio a significantly mixes into the ground configuration DA where... 

According to the calculations at high levels of theory, the [4+2] cycloaddition reactions of dienes with the singlet ( A oxygen follow stepwise pathways [37, 38], These results, which were unexpected from the Woodward-Hoffmann rule and the frontier orbital theory, suggest that the [4+2] cycloadditions of the singlet ( A oxygen could be the reactions in the pseudoexcitation band. 

The frontier orbital theory was developed for electrophilic aromatic substitution (Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). Application is successful to the ortho-para orientation (Scheme 23a) for the benzenes substituted with electron donating groups. The ortho and para positions have larger HOMO amplitudes. The meta orientation (Scheme 23b) for the electron accepting groups is under control of both HOMO and the next HOMO [25]. 

Frontier orbital theory can also explain the regioselectivity observed when both the diene and alkene are unsymmetrically substituted.4 Generally, there is a preference... 

The actual rates of thermally-allowed pericyclic reactions vary vastly, and frontier-orbital theory (14, 15, 16) has proven to be the primary basis for quantitative understanding and correlation of the factors responsible. It is therefore of interest to find the dominant frontier orbital interactions for the group transfer reactions hypothesized to occur. 

Thus the reactivity of transition metal-carbene complexes, that is, whether they behave as electrophiles or nucleophiles, is well explained on the basis of the frontier orbital theory. Studies of carbene complexes of ruthenium and osmium, by providing examples with the metal in either of two oxidation states [Ru(II), Os(II) Ru(0), Os(O)], help clarify this picture, and further illustrations of this will be found in the following sections. 

A local frontier orbital (LFO) study involving the variational method to analytically find appropriate combinations of valence atomic orbitals giving the maximum and minimum energies of the occupied and unoccupied LFOs, respectively, was employed to find the acidities of the conjugate cation of 1,2,5-thiadiazole 1 <1997PCA5593>. A later study adopted a projected reactive orbital (PRO) approach, which describes local reactivity better than frontier orbital theory in high-symmetry systems to predict the basicity of 1,2,5-thiadiazole 1 <2005PCA7642>. 

The above selection rules can also be derived from frontier orbital theory. 

The effect of cryptands on the reduction of ketones and aldehydes by metal hydrides has also been studied by Loupy et al. (1976). Their results showed that, whereas cryptating the lithium cation in LiAlH4 completely inhibited the reduction of isobutyraldehyde, it merely reduced the rate of reduction of aromatic aldehydes and ketones. The authors rationalized the difference between the results obtained with aliphatic and aromatic compounds in terms of frontier orbital theory, which gave the following reactivity sequence Li+-co-ordinated aliphatic C=0 x Li+-co-ordinated aromatic C=0 > non-co-ordinated aromatic C=0 > non-co-ordinated aliphatic C=0. By increasing the reaction time, Loupy and Seyden-Penne (1978) showed that cyclohexenone [197] was reduced by LiAlH4 and LiBH4, even in the presence of [2.1.1]-cryptand, albeit much more slowly. In diethyl ether in the absence of... 

S (3p), and Cu (3d) orbit, respectively. According to the frontier orbital theory, the electrons in the highest occupied state are most easily bound and have an imexpectedly great significance for the chemical reactivity of materials. It indicates that the different reduction or oxidation would happen on the three mineral surfaces in the pulp during flotation system. 

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