Reactivity HOMO-LUMO gaps

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. 

The numerical value of hardness obtained by MNDO-level calculations correlates with the stability of aromatic compounds. The correlation can be extended to a wider range of compounds, including heterocyclic compounds, when hardness is determined experimentally on the basis of molar reffactivity. The relatively large HOMO-LUMO gap also indicates the absence of relatively high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds toward electrophilic reagents. 

These results led to a separation of the observed Diels-Alder reactivities into three categories (a) increase of the rate constants on increasing the Lewis acid character of the solvent as quantified by the AN parameter this behaviour reflects the interactions between the LUMO of the solvent and the HOMO of the reactants and is similar to Lewis acid catalysis (vide supra) (b) reaction retardation by electron donation, as quantified by the D-ji parameter the HOMOsoivent-LUMOreactant interactions are held responsible for this effect, representing an anti-Lewis acid interaction which increases the HOMO-LUMO gap and hence hampers the reaction (c) the Diels-Alder reactions show very small solvent effects and are relatively insensitive to specific reactant-solvent interactions, and... 

Compounds with a narrow HOMO-LUMO gap (Figure 5.5d) are kinetically reactive and subject to dimerization (e.g., cyclopentadiene) or reaction with Lewis acids or bases. Polyenes are the dominant organic examples of this group. The difficulty in isolation of cyclobutadiene lies not with any intrinsic instability of the molecule but with the self-reactivity which arises from an extremely narrow HOMO-LUMO gap. A second class of compounds also falls in this category, coordinatively unsaturated transition metal complexes. In transition metals, the atomic n d orbital set may be partially occupied and/or nearly degenerate with the partially occupied n + 1 spn set. Such a configuration permits exceptional reactivity, even toward C—H and C—C bonds. These systems are treated separately in Chapter 13. 

The HOMO of hexasilabenzene is by ca 2 eV higher than in benzene, while the HOMO-LUMO gap is much smaller in 31 than in benzene60. This suggest that hexasilabenzene should be more reactive than benzene towards both electrophiles and nucleophiles. 

The hexasila-Dewar benzene 13 is thermally stable at —150 °C, but it gradually reverted to the hexasilaprismane 1243. The half-life is 11/2 = 0.52 min at 0 °C in 3-methylpentane. The activation parameters for the isomerization of 13 to 12 are a = 13.7 kcalmol-1, A= 13.2 kcalmol-1 and A= — 17.8 cal K-1 mol-1. The small Ea value is consistent with the high reactivity of Si=Si double bonds. Most probably, the small HOMO-LUMO gap of 13 makes it possible that the Si=Si double bonds undergo a formally symmetry forbidden [2 + 2] thermal reaction. Hexasila-Dewar benzene is a key... 

Analogous calculations give a + 0.549)8and a — 0.494)8for 2-azabutadiene. Since the HOMO-LUMO gap is smaller in the latter case, 2-azabutadiene is more reactive. The reactivity difference will be accentuated in reactions with electron-poor dienophiles. 

Their calculations show that the LUMO energy level of the free alkene and the HOMO-LUMO energy gaps mirror the observed reactivity in the PK reaction. In a comparison between cyclohexene, cyclopentene and norbornene, cyclohexene has the largest HOMO-LUMO gap, the highest... 

LUMO energy and is the least reactive substrate while norbornene has the smallest HOMO-LUMO gap, the lowest LUMO energy and is the most reactive. They note that the LUMO energy level of an alkene is a useful approximation of its reactivity. They also note a correlation between a smaller C=C C bond angle and a lowering of the LUMO energy level - a link with Pericas theory of strain driving the reaction.12... 

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