Dienes LUMO energies

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. 

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 ... 

LUMO energy of the diene is lowered. However, for the eyeloaddition to oeeur, the dienophile is now the nueleophile and the diene is now the eleetrophile. Sinee the nature of the reaeting partners is inverted relative to the elassical ease, it is ealled an inverse eleetron demand Diels-Alder reaetion. Thus the Diels-Alder reaetion ean proeeed, in praetieal terms, in one of two eleetronie modes a) the normal mode whieh is HOMOdiene-eontrolled or b) the inverse eleetron demand or LUMOdiene-controlled process. 

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>. 

In contrast to allenyl sulfones, allenyl phenyl sulfoxide failed to react with the Danishefsky s diene even at an elevated temperature [116]. Introduction of an electron-withdrawing nitro group on the aromatic ring, however, lowered the LUMO energy level and facilitated the cycloaddition, providing phenol 134. 

Several quantitative descriptions of [4 + 2] cycloadditions have been reported applying equation 15 or derived equations. HOMO and LUMO energies can be calculated from ionization potentials or electron affinities. Orbital coefficients have been calculated for simple ethenes and dienes using various quantum mechanical methods, e.g. INDO, CNDO/2, AMI and STO-3G. These different methods may, however, lead to substantially different results54-56. 

While the reactivity is determined by the HOMO-LUMO energy separation, the selectivity is dominated by the orbital coefficients64. As a consequence, thekinetically controlled regioselectivity of the Diels-Alder ring closure, and thus the formation of the two new cr-bonds (between atoms 1,6 and 4,5 or between atoms 1,5 and 4,6 in Scheme 1), is determined by the FMO coefficients at the terminal carbon atoms of the diene and the dienophile. The FMO predictions boil down to the fact that the formation of cr-bonds between carbon atoms with similar orbital coefficients is preferred. The magnitudes of these coefficients... 

From work performed in 1983 by Burnier and Jorgensen [15], the following ab initio calculations for the HOMO and LUMO energies of the synthons were developed. The function n(x, parent) returns the number of atoms of type x in the parent. This function is abbreviated below as simply n(x) where the parent is understood. The symbols UU, O, N, S represent triple bonds, oxygen, nitrogen, and sulfer, respectively. The subscripts c and t denote central and terminal locations respectively in the parent for the elements which they modify. For brevity, the terms diene-synthon and dienophile-synthon will be replaced with diene and dienophile respectively. 

As we have already seen, delocalization of electrons by conjugation decreases the energy difference between the HOMO and LUMO energy levels, and this leads to a red shift. Alkyl substitution on a conjugated system also leads to a (smaller) red shift, due to the small interaction between the cr-bonded electrons of the alkyl group with the K-bond system. These effects are additive, and the empirical Woodward-Fieser rules were developed to predict the 2max values for dienes (and trienes). Similar sets of rules can be used to predict the A ax values for a,P-unsaturated aldehydes and ketones (enones) and the Amax values for aromatic carbonyl compounds. These rules are summarized in Table 2.4. 

According to the frontier orbital theory,525 electron-withdrawing substituents lower the energies of the lowest unoccupied molecular orbital (LUMO) of the di-enophile thereby decreasing the highets occupied molecular orbital (HOMO)-LUMO energy difference and the activation energy of the reaction. 1,3-Butadiene itself is sufficiently electron-rich to participate in cycloaddition. Other frequently used dienes are methyl-substituted butadienes, cyclopentadiene, 1,3-cyclohexa-diene, and 1,2-dimethylenecyclohexane. 

The essential features of the Diels-Alder reaction are a four-electron n system and a two-electron it system which interact by a HOMO-LUMO interaction. The Diels-Alder reaction uses a conjugated diene as the four-electron n system and a it bond between two elements as the two-electron component. However, other four-electron it systems could potentially interact widi olefins in a similar fashion to give cycloaddition products. For example, an allyl anion is a four-electron it system whose orbital diagram is shown below. The symmetry of the allyl anion nonbonding HOMO matches that of the olefin LUMO (as does the olefin HOMO and the allyl anion LUMO) thus effective overlap is possible and cycloaddition is allowed. The HOMO-LUMO energy gap determines the rate of reaction, which happens to be relatively slow in this case. 

Indole-3-carboxylic acids 325,326, and 327 afford the cycloadducts 328, 329, and 330 by intramolecular reactions. The conditions needed to effect cyclization were not especially mild (232°C, 8 hours for 2a 210°C, 7 hours for 2b refluxing nitrobenzene, 3 hours for 325), and yields were better in the case of the alkynes 326 and 327. The relative ease of reaction and greater yield for 326 and 327 were due to the smaller HOMO/LUMO energy gap between the relatively electron-rich 2-vinylindole diene and the relatively electron-poor alkyne (compared to an olefin) (90H993). 

This gives rise to 48 cases, all of the NED (Normal Electron Demand) type (i.e. where the diene is the electron donor and the dienophile is the electron acceptor), which was checked by inspecting the HOMO and LUMO energies of the sytems. 

Comparison of HOMO-LUMO energy differences. In buta- 1,3-diene, the 77 — 77 transition absorbs at a wavelength of 217 nm (540 kJ/mol) compared with 171 nm (686 kJ/mol) for ethylene. This longer wavelength (lower-energy) absorption results from a smaller energy difference between the HOMO and LUMO in butadiene than in ethylene. 

The dramatic effect observed on the reaction diastereoselectivity upon addition of a Lewis acid to 2H-azirine 127 was explained by a bidentate coordination of the Lewis acid to the 2H-azirine nitrogen and the carbonyl group. This chelation would lead to hindered rotation around the 2H-azirine carbonyl single bond and thus greater stereoselectivity. The increased reaction rate also indicates coordination of the Lewis acids to the 2H-azirine which leads to a lowering of the LUMO energy level and thus an increased reactivity toward the electron-rich diene (Scheme 32). 

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