HOMO-LUMO reaction

FMO theory requires that a HOMO of one reactant has to be correlated with the LUMO of the other reactant. The decision between the two alternatives - i.e., from which reactant the HOMO should be taken - is made on the basis of which is the smaller energy difference in our case the HOMO of the electron rich diene, 3.1, has to be correlated with the LUMO of the electron-poor dienophile, 3.2. The smaller this HOMO-LUMO gap, the higher the reactivity will be. With the HOMO and LUMO fixed, the orbital coefficients of these two orbitals can explain the regios-electivity of the reaction, which strongly favors the formation of 3.3 over 3.4. 

Hydrogen bonding of water to the activating group of (for normal-electron demand Diels-Alder reactions) the dienophile constitutes the second important effect". Hydrogen bonds strengthen the electron-withdrawing capacity of this functionality and thereby decrease the HOMO-LUMO gap... 

Lithium aluminum hydride reduction of 2,3,4-triphenylisoxazolin-5-one yielded 1,2,3-triphenylaziridine and dibenzylaniline. The reaction was considered to proceed by a concerted [l,3]-sigmatropic migration of the N to a C atom. HOMO-LUMO calculations show this type of concerted reaction is possible (Scheme 68) (80JA1372). 

Since the optical transitions near the HOMO-LUMO gap are symmetry-forbidden for electric dipole transitions, and their absorption strengths are consequently very low, study of the absorption edge in Ceo is difficult from both an experimental and theoretical standpoint. To add to this difficulty, Ceo is strongly photosensitive, so that unless measurements arc made under low light intensities, photo-induced chemical reactions take place, in some cases giving rise to irreversible structural changes and polymerization of the... 

The same conclusions are drawn by analysis of the frontier orbitals involved in cycloadditions. For the most common case of the Diels-Alder reaction, which involves dienophiles with electron-attracting substituents, the frontier orbitals are l/2 of the diene (which is the HOMO) and n of the dienophile (which is the LUMO). Reaction occurs by interaction of the HOMO and LUMO, which can be seen from the illustration below to be allowed. 

When both the 1,3-dipoIe and the dipolarophile are unsymmetrical, there are two possible orientations for addition. Both steric and electronic factors play a role in determining the regioselectivity of the addition. The most generally satisfactory interpretation of the regiochemistry of dipolar cycloadditions is based on frontier orbital concepts. As with the Diels-Alder reaction, the most favorable orientation is that which involves complementary interaction between the frontier orbitals of the 1,3-dipole and the dipolarophile. Although most dipolar cycloadditions are of the type in which the LUMO of the dipolarophile interacts with the HOMO of the 1,3-dipole, there are a significant number of systems in which the relationship is reversed. There are also some in which the two possible HOMO-LUMO interactions are of comparable magnitude. 

According to Frontier Molecular Orbital (FMO) theory, Diels-Alder reaction between an electron-rich diene and an electron-poor dienophile involves interaction between the highest-occupied molecular orbital (HOMO) on the diene and the lowest-unoccupied molecular orbital (LUMO) on the dienophile. The better the HOMO/LUMO overlap and the smaller their energy difference, the more favorable the interaction and the faster the reaction. 

Lewis acids catalyze Diels-Alder reactions. Do they enhance overlap between diene and dienophile orbitals and/ or do they reduce the HOMO/LUMO energy difference ... 

In a photochemical cycloaddition, one component is electronically excited as a consequence of the promotion of one electron from the HOMO to the LUMO. The HOMO -LUMO of the component in the excited state interact with the HOMO-LUMO orbitals of the other component in the ground state. These interactions are bonding in [2+2] cycloadditions, giving an intermediate called exciplex, but are antibonding at one end in the [,i4j + 2j] Diels-Alder reaction (Scheme 1.17) therefore this type of cycloaddition cannot be concerted and any stereospecificity can be lost. According to the Woodward-Hoffmann rules [65], a concerted Diels-Alder reaction is thermally allowed but photochemically forbidden. 

Since the reactivity depends on the lowest HOMO-LUMO energy separation that can be achieved by the reacting partners, all the factors, steric and electronic, that lower the HOMO-LUMO distance increase the reaction rate and, as a consequence, allow the reactions to be carried out under mild conditions. Thus the normal electron-demand Diels-Alder reaction between 1,4-benzoquinone and 1,3-butadiene (Equation 2.2) proceeds at 35 °C almost quantitatively. 

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. ... 

Thermal dimerization of ethylene to cyclobutane is forbidden by orbital symmetry (Sect 3.5 in Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). The activation barrier is high E =44 kcal mof ) [9]. Cyclobutane cannot be prepared on a preparative scale by the dimerization of ethylenes despite a favorable reaction enthalpy (AH = -19 kcal mol" ). Thermal reactions between alkenes usually proceed via diradical intermediates [10-12]. The process of the diradical formation is the most favored by the HOMO-LUMO interaction (Scheme 25b in chapter Elements of a Chemical Orbital Theory ). The intervention of the diradical intermediates impfies loss of stereochemical integrity. This is a characteric feature of the thermal reactions between alkenes in the delocalization band of the mechanistic spectrum. 

Benzyne shares a feature with A in the [2+2] cycloaddition reactions. The HOMO-LUMO interaction prefers the three-centered interaction (Scheme 4) [115]. This is in agreement with the calculated reaction path [116]. 

Khanna et al. [136] proposed a mechanism of the reactions of aluminum based clusters with O, which lends a physical interpretation as to why the HOMO-LUMO gap of the clusters successfully predicts the oxygen etching behaviors. The importance of the HOMO-LUMO gap strongly suggests that the reactions of the metal clusters belong to the pseudoexcitation band. 

Metal surfaces and clusters are readily pseudoexcited. The band gaps of the surface states and the HOMO-LUMO gaps of metal clusters will be found to be important for more and more reactions in future. 

Fig. 6.2. HOMO-LUMO interactions rationalize regioselectivity of Diels-Alder reactions.

Interestingly, the reactions were modestly slower in the presence of the Lewis acid. It is suggested that the catalyst inverts the HOMO-LUMO relationships, making the complexed nitrone the electrophilic reactant. In agreement with this interpretation, the reaction is favored by EWGs on the aromatic ring. 

Jason Green has successfully applied the Selenski method to the synthesis of (+ )-bromoheliane (79, Fig. 4.38).34 In this example, two equivalents of the chiral enol ether are added to the benzaldehyde 77 in diethyl ether (0.1 M) and cooled to —78 °C. Methyl Grignard is then added. The cycloaddition occurs while the reaction warms to room temperature. The benzopyran adduct 78 forms in 80% yield with 50 1 diaster-eoselectivity. DFT calculations and experiments suggest that the diastereoselectivity depends on the magnitude of the HOMO-LUMO band gap. In this instance, the LUMO of the supposed o-QM intermediate is computed to be —2.6 eV, whereas the HOMO of the enol ether is —5.9 eV. A 50 1 selectivity is recorded for resulting 3.3 eV gap. For reactions of 2,5-bis-OBoc-4-methyl-benzaldehyde, where the HOMO-LUMO gap is larger (3.6 eV), a 20 1 ratio of diastereomers is observed. 

An intermolecular 1,3-dipolar cycloaddition of diazocarbonyl compounds with alkynes was developed by using an InCl3-catalyzed cycloaddition in water. The reaction was found to proceed by a domino 1,3-dipolar cycloaddition-hydrogen (alkyl or aryl) migration (Eq. 12.68).146 The reaction is applicable to various a-diazocarbonyl compounds and alkynes with a carbonyl group at the neighboring position, and the success of the reaction was rationalized by decreasing the HOMO-LUMO of the reaction. 

AMI semi-empirical and B3LYP/6-31G(d)/AMl density functional theory (DFT) computational studies were performed with the purpose of determining which variously substituted 1,3,4-oxadiazoles would participate in Diels-Alder reactions as dienes and under what conditions. Also, bond orders for 1,3,4-oxadiazole and its 2,5-diacetyl, 2,5-dimethyl, 2,5-di(trifluoromethyl), and 2,5-di(methoxycarbonyl) derivatives were calculated <1998JMT153>. The AMI method was also used to evaluate the electronic properties of 2,5-bis[5-(4,5,6,7-tetrahydrobenzo[A thien-2-yl)thien-2-yl]-l,3,4-oxadiazole 8. The experimentally determined redox potentials were compared with the calculated highest occupied molecular orbital/lowest unoccupied molecular orbital (HOMO/LUMO) energies. The performance of the available parameters from AMI was verified with other semi-empirical calculations (PM3, MNDO) as well as by ab initio methods <1998CEJ2211>. 

Scheme 3 HOMO-LUMO interaction schemes for concerted four-centered carbometallation reactions.

Now let us take the case of a reaction between ethylene and an allyl anion. In both cases the HOMO-LUMO interaction leads to bonding at both terminals. 

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