Orbital coefficients Diels-Alder reaction

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. 

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]. 

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).

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]. 

These same features can ensure regioselective Diels-Alder reactions. The same orbital of the dienophile is used and, if the HOMO of the diene is also unsymmetrical, the regioselectivity of the reaction will be controlled by the two largest coefficients bonding together. 

Secondary orbital interactions have also been invoked to explain regiochemistry as well as stereochemistry. Whereas 1 -substituted dienes sometimes have only a small difference between the coefficients on C-l and C-4 in the HOMO, they can have a relatively large difference between the coefficients on C-2 and C-3. Noticing this pattern, Alston suggested that the regioselectivity in Diels-Alder reactions may be better attributed, not to the primary interactions of the frontier orbitals on C-l and C-4 that we have been using so far, but to a... 

The Site Selectivity of Diels-Alder Reactions. Site selectivity is another kind of regioselectivity, in which a reagent reacts at one site (or more) of a polyfunctional molecule when several sites are, in principle, available. Thus butadiene reacts faster with the quinone 6.209 at C-2 and C-3 than at C-5 and C-6. The cyano groups will lower the coefficients at C-2 and C-3 more than those at C-5 and C-6. The dimer of hexatriene is 6.210 and not 6.211, which we can similarly explain by looking at the coefficients of the frontier orbitals, essentially narrowing the problem down to assessing the Zc2 term in Equation 3.4. 

The regiochemistry of Diels-Alder reactions with 3.3.3-trifluoropropene (1) shows that the inductive effect of a trifluoromethyl group increases the magnitude of the molecular orbital coefficient of the unsubstituted terminus, but the effect is not great enough to achieve high regioselectivity with dienes other than l-methoxy-3-(trimethylsiloxy)buta-l,3-diene (Danishefsky s diene, 4) compare the reaction of 1 with 2, 3, and 4. ... 

MO calculations that give tt-orbital coefficients for dienes and dienophiles are beyond the scope of this book. However, there is a simple mnemonic trick that will predict regioselectivity in many cases. It involves drawing the four possible diradical intermediates that can be formed by homolytic bonding at one end of each reactant. Always remember, this is just a mnemonic trick most Diels-Alder reactions are concerted and do not proceed through a diradical intermediate. 

In frontier oibital terms, the regiochemistry is governed largely by the atomic orbital coefficients at the termini of the reaction pailners, which are tered by the substituents. Hence, in normal Diels-Alder reactions a diene substituent at C-1 has the tendency to direct the addition of a carbonyl-conjugated al-kene towards the ortho product (X), whereas a substituent at C-2 favors the para product (XI). The... 

FMO theory can also be used for explaining the stereochemistry of the Diels-Alder reaction. Consider the reaction between 2-methyl butadiene and cyanoethylene. These may react to give two different products, the para and/or meta isomer. The MO coefficients for the p-orbitals on the isoprene HOMO and cyanoethylene LUMO (taken from AMI calculations) are given in Figure 15.6. The FMO sum for the para isomer is (0.594 0.682 -I- 0.517 0.552) = 0.477, while the sum for the meta isomer is... 

Theoretical calculations have also permitted one to understand the simultaneous increase of reactivity and selectivity in Lewis acid catalyzed Diels-Alder reactions . This has been traditionally interpreted by frontier orbital considerations through the destabilization of the dienophile s LUMO and the increase in the asymmetry of molecular orbital coefficients produced by the catalyst. Birney and Houk have correctly reproduced, at the RHF/3-21G level, the lowering of the energy barrier and the increase in the endo selectivity for the reaction between acrolein and butadiene catalyzed by BH3. They have shown that the catalytic effect leads to a more asynchronous mechanism, in which the transition state stmcture presents a large zwitterionic character. Similar results have been recently obtained, at several ab initio levels, for the reaction between sulfur dioxide and isoprene. ... 

The regioselectivity of inverse electron-demand Diels-Alder reactions, 1,3-dipolar cycloadditions, and other cycloadditions can similarly be explained by resonance and orbital coefficient arguments. Determining which end of a 1,3-dipole is nucleophilic and which end is electrophilic can be dicey, though. In nitrones (R2C=NR-0), the O is the nucleophilic end, so it reacts with the electrophilic end of a dipolarophile. 

In order to answer the question first posed in Chapter 1 and repeated above, we begin by ignoring the substituents and counting only those parts of the conjugated system directly involved in the reaction. (We shall return to the crucial role of the substituents later in the chapter.) Thus the Diels-Alder reaction is simplified to that of butadiene reacting with ethylene the former component has four rc-electrons and the latter two, and these are the only electrons directly involved, as we can see from the curly arrows. Such a reaction is called a [4 + 2] cycloaddition. We now examine the signs of the coefficients of the frontier orbitals on the atoms which are to become bonded (Fig. 4-1). We are not yet concerned with the magnitude of the coefficients of the frontier orbitals, and therefore in this section all orbitals are drawn the same size, so as not to... 

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