LUMO coefficients

Figure 15.2 AMI LUMO coefficients for acrolein with net charges in parenthesis...

The authors justified their result considering that the bond index [Br = (coefficient r LUMO) (coefficient s LUMO) ] on the LUMO accounted for the formation of the Dewar isomer on the central ring of the trithiazole. By contrast, calculations show that the Dewar isomer should be formed on the third ring of the trithiazole (Fig. 17) (99MI233). 

The coordination of the dienophile to a Lewis acid (in the calculations a proton was used as the Lewis acid) leads also to an increase in regioselectivity. The re-gioselectivity of reactions of electron-rich, or conjugated dienes, with electron-deficient dienophiles is also controlled hy the diene HOMO-dienophile LUMO interaction. From Fig. 8.2 it appears that the difference in magnitudes of the LUMO coefficients at carhon atoms 1 and 2 of acrolein (Ci -C2 = 0.20) is smaller than the same difference for protonated acrolein (Ci -C2 = 0.30-0.43) so that the reaction of the latter should he considerable more regioselective than the former in accordance with the experimental results [3]. 

Lewis-acid-catalyzed cycloadditions of dienophiles, such as a,/l-unsaturated carbonyl compounds, with open-chain carbon-dienes, are generally highly ortho-para regioselective because the oxygen complexation increases the difference of LUMO coefficients of the alkene moiety. 

LUMO Atom coefficients Atom LUMO coefficients... 

Species LUMO energy (eV) LUMO coefficient on reacting atom Total charge on reacting atom"... 

The regioselectivity in radical addition reactions to alkenes in general has successfully been interpreted by a combination of steric and electronic effects1815,47. In the absence of steric effects, regiochemical preferences can readily be explained with FMO theory. The most relevant polyene orbital for the addition of nucleophilic radicals to polyenes will be the LUMO for the addition of electrophilic orbitals it will be the HOMO. Table 10 lists the HOMO and LUMO coefficients (without the phase sign) for the first three members of the polyene family together with those for ethylene as calculated from Hiickel theory and with the AMI semiempirical method48. 

The orbital coefficients obtained from Hiickel calculations predict the terminal position to be the most reactive one, while the AMI model predicts the Cl and C3 positions to be competitive. In polyenes, this is true for the addition of nucleophilic as well as electrophilic radicals, as HOMO and LUMO coefficients are basically identical. Both theoretical methods agree, however, in predicting the Cl position to be considerably more reactive as compared to the C2 position. It must be remembered in this context that FMO-based reactivity predictions are only relevant in kinetically controlled reactions. Under thermodynamic control, the most stable adduct will be formed which, for the case of polyenyl radicals, will most likely be the radical obtained by addition to the C1 position. 

TABLE 10. HOMO and LUMO coefficients for ethylene and selected polyenes... 

The observed preferential electrophilic attack on carbon D of C70 under Friedel-Crafts conditions (CHC13/A1C13) is consistent with the large HOMO coefficient of this carbon (Figure 13). This is in contrast to the fact that nucleophilic addition (7,35-38) and cycloaddition (38-40) to C70 favor carbons A and B, which are most pyramidalized and have large LUMO coefficients (Figure 13). 

Allenes participate in the Diels-Alder-type [4+2]-cycloaddition mostly as an electron-deficient dienophile. The LUMO energy level of an allene is lowered by the introduction of an electron-withdrawing unsaturated substituent. The largest LUMO coefficient locates on the central carbon (C2) and the next largest on the substituted carbon (Cl). Thus, [4 + 2]-cycloadditions of activated allenes take place at the internal C=C bond of the allene. 

Theoretical calculations have been an important means of rationalizing the electronic course of hetero-Diels-Alder and related pericylic reactions for the formation of 1,2-thiazines 25 and 26. MOP AC 93 PM3 calculations have been used to deduce the regioselectivity of [4-1-2] cycloaddition reactions involving thiazinylium perchlorate 27 (Scheme 1) <1999TL1505>. Due to the higher lowest unoccupied molecular orbital (LUMO) coefficient at C-6 compared to N-2, the C-6 and S-1 behave preferentially as the dienophile double bond in cycloaddition reactions of this substrate with butadienes 28. 

The exceptions to the general rule of preference for para-attack are cases in which, according to calculations, the para-product is destabilized relative to the observed ort/ro-product (85f) by at least 35 kcal/mol, or the observed conjugated product of attack on the S-carbon of a 4-stilbenyl ion (44k,1) is stabilized by ca. 5 kcal/mol relative to the product of para-attack. In the latter case calculations at the RHF/6-31G //3-21G level suggest that attack of H2O on the /S-carbon may be facilitated by the large magnitude of the LUMO coefficient at that carbon. ... 

Attempts to rationalize the regioselectivity of attack of nucleophiles on the aryl rings of nitrenium ions in terms of calculated properties of the ions (LUMO coefficients, localization energies, etc.) have been moderately successful. An adequate explanation of electrophilic reactivity of nitrenium ions at N with certain nucleophiles such as glutathione, C-8 of d-G, and other carbon nucleophiles has not yet appeared. ... 

The preference for bridging at the meso positions is dictated by HOMO-LUMO coefficients in the exciplex. At high arene concentrations, the stereochemical preference is diminished. In general, however, the local symmetry of the frontier orbitals determines implicitly the favorable pathway for cycloadditions involving significant charge transfer but without the intervention of radical ions (55). 

More precisely, a nucleophile will attack the site having the highest LUMO coefficient whereas an electrophile will attack the site having the highest HOMO coefficient. 

The nonsubstituted carbon atom has the highest HOMO coefficent in donor-substituted dienophiles and highest LUMO coefficient in acceptor-substituted dienophiles... 

The highest LUMO coefficient in a diene will also be localized on position 4 if an acceptor substituent is present at Q, but will be on position 1 for an acceptor at C2. 

Check that the rule (the nonsubstituted atom has the highest HOMO coefficient in electron-rich and the highest LUMO coefficient in electron-poor dienophiles) is general, using examples in the MO Catalog in the Appendix (enol, propene, acrolein, styrene, acrylonitrile). 

In CH2=S, the LUMO coefficient at S is smaller than that at C. In Me-CH=S, this difference increases slightly, but in 0=CH—CH=S, the S coefficient is larger. Can you predict these changes, without any numerical calculations ... 

The reagent, being an electron-rich diene, will react through Q where its HOMO is most heavily localized. Hence, the first bond will form between Q and the site of highest LUMO coefficient in the reaction partner S for 0=CH—CH=S and C in CH2=S and Me-CH=S. The major products will be 1, 2 and 3. 

Methoxybutadiene can be used to model the diene in a qualitative treatment. AMI calculations give very similar S and C LUMO coefficients for 0=CH—CH=S however, the difference is more pronounced in STO-3G and 3-21G calculations. Note that even with AMI calculations (C coefficient = —0.64 S coefficient = 0.65), a preference is still expected for attack at sulfur, as sulfur orbitals are much more diffuse than carbon orbitals (covalent radii 1.02 and 0.77 A respectively). 

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