Diels-Alder reactions coefficients

As an example, we shall discuss the Diels-Alder reaction of 2-methoxybuta-l,3-diene with acrylonitrile. Figure 3-7 gives the reaction equation, the correlation diagram of the HOMOs and LUMOs, and the orbital coefficients of the correlated HOMO and LUMO. 

The regioselectivity benefits from the increased polarisation of the alkene moiety, reflected in the increased difference in the orbital coefficients on carbon 1 and 2. The increase in endo-exo selectivity is a result of an increased secondary orbital interaction that can be attributed to the increased orbital coefficient on the carbonyl carbon ". Also increased dipolar interactions, as a result of an increased polarisation, will contribute. Interestingly, Yamamoto has demonstrated that by usirg a very bulky catalyst the endo-pathway can be blocked and an excess of exo product can be obtained The increased di as tereo facial selectivity has been attributed to a more compact transition state for the catalysed reaction as a result of more efficient primary and secondary orbital interactions as well as conformational changes in the complexed dienophile" . Calculations show that, with the polarisation of the dienophile, the extent of asynchronicity in the activated complex increases . Some authors even report a zwitteriorric character of the activated complex of the Lewis-acid catalysed reaction " . Currently, Lewis-acid catalysis of Diels-Alder reactions is everyday practice in synthetic organic chemistry. 

Table 5.2. Analysis using the pseudophase model partition coefficients for 5.2 over CTAB or SDS micelles and water and second-order rate constants for the Diels-Alder reaction of 5.If and 5.1g with 5.2 in CTAB and SDS micelles at 25 C.

In contrast to SDS, CTAB and C12E7, CufDSjz micelles catalyse the Diels-Alder reaction between 1 and 2 with enzyme-like efficiency, leading to rate enhancements up to 1.8-10 compared to the reaction in acetonitrile. This results primarily from the essentially complete complexation off to the copper ions at the micellar surface. Comparison of the partition coefficients of 2 over the water phase and the micellar pseudophase, as derived from kinetic analysis using the pseudophase model, reveals a higher affinity of 2 for Cu(DS)2 than for SDS and CTAB. The inhibitory effect resulting from spatial separation of la-g and 2 is likely to be at least less pronoimced for Cu(DS)2 than for the other surfactants. 

This regioselectivity was originally one of the greatest unsolved problems in Diels-Alder reaction but with the application of FMO theory, it has now been solved satisfactorily. Calculations made on systems containing heteroatoms give a set of coefficients which account for the observed orientation. 

In the [4 + 2] cycloadditions discussed so far, the enol ether double bond of alkoxyallenes is exclusively attacked by the heterodienes, resulting in products bearing the alkoxy group at C-6of the heterocycles. This regioselective behavior is expected for [4+2] cycloadditions with inverse electron demand considering the HOMO coefficients of methoxyallene 145 [100]. In contrast, all known intramolecular Diels-Alder reactions of allenyl ether intermediates occur at the terminal C=C bond [101], most probably because of geometric restrictions. 

The explanation of the regiospecificity of Diels-Alder reactions requires knowledge of the effect of substituents on the coefficients of the HOMO and LUMO orbitals. In the case of normal electron demand, the important orbitals are the HOMO on the diene and the LUMO on the dienophile. It has been shown that the reaction occurs in a way which bonds together the terminal atoms with the coefficients of greatest magnitude and those with the coefficients of smaller magnitude [18]. The additions are almost exclusively cis and with only a few exceptions, the relative configurations of substituents in the components is kept in the products [19]. 

In a Diels-Alder reaction, when both n systems are polarized, the more favorable overlap, and therefore the stronger interaction, occurs when the ends with the larger coefficients get together and the smaller coefficients get together. Predict the major product of each of the following cycloaddition reactions ... 

One can compute, for example, the stabilizations AETS for the transition states of the para - and meta -selective cycloadditions, respectively, of acrylonitrile and isoprene according to Equation 15.2 with the data provided in Figure 15.26 (HOMO/LUMO gaps, LCAO coefficients at the centers that interact with each other). The result for the Diels-Alder reaction of Figure 15.25 is shown in Equations 15.4 and 15.5 ... 

Fig. 15.26. Frontier orbital coefficients and energy difference of the H0M0-LUM0 gaps in orientation-selective Diels— Alder reactions (cf. Figure 15.25, X = H).

What has just been stated regarding the LCAO coefficients of the dienophile LUMO combined with the rules for the regioselectivity of any one-step cycloaddition leads to the following consequences for the Diels-Alder reactions of isoprene ... 

Calculations performed at the HF/3-21G level indicated smaller energy gaps between the HOMOs of the aforementioned electron-rich dienophiles and the LUMOs of the quinone ketals, as can be expected for inverse electron-demand Diels-Alder reactions under FMO control [141]. Regiochemical controls observed with quinone ketals such as 76a were well corroborated by the relative magnitudes of the atomic coefficients of the frontier orbitals. The highest coefficients at C-5 of the quinone ketal LUMO and at C-2 of the electron-rich alkenes would indeed promote bond formation between these centers. The results of calculations on other quinone ketals were, however, rather vague [141]. 

The increase in orientation selectivity of Diels-Alder reactions upon addition of Lewis acid has a second cause aside from the one which was just mentioned.The reaction conditions described in Figure 12.27 indicate that A1C13 increases the rate of cycloaddition. The same effect also was seen in the cycloaddition depicted in Figure 12.20. In both instances, the effect is the consequence of the lowering of the LUMO level of the dienophile. According to Equation 12.2, this means that the magnitude of the denominator of the first term decreases and the first term therefore becomes larger than the second term. II) in addition, the numerators of these terms differ by a certain amount for the para and meta transition states (as determined by the combinations of the LCAO coefficients), the effect is further enhanced. This also increases the para selectivity. 

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