Hiickel MO theory

One criterion of aromaticity is the ring current, which is indicated by a chemical shift difference between protons, in the plane of the conjugated system and those above or below the plane. The chemical shifts of two isomeric hydrocarbons are given below. In qualitative terms, which appears to be more aromatic (Because the chemical shift depends on the geometric relationship to the ring current, a quantitative calculation would be necessary to confirm the correctness of this qualitative impression.) Does Hiickel MO theory predict a difference in the aromaticity of these two compounds ... 

Such cross-conjugation (where two of the vinyls are conjugated with each other through boron but not simultaneously with the third vinyl35) always lowers the total delocalization energy (DE) of the conjugated atomic set In simple Hiickel MO theory, for example, ( )-l,3,5-hexatriene (37) has a DE of 0.988/3, while 2-vinyl-1,3-butadiene (38) yields a DE of 0.900/3. 

MO) with the protons in the nodal plane. The mechanism of coupling (discussed below) requires contact between the unpaired electron and the proton, an apparent impossibility for n electrons that have a nodal plane at the position of an attached proton. A third, pleasant, surprise was the ratio of the magnitudes of the two couplings, 5.01 G/1.79 G = 2.80. This ratio is remarkably close to the ratio of spin densities at the a and (3 positions, 2.62, predicted by simple Hiickel MO theory for an electron placed in the lowest unoccupied MO (LUMO) of naphthalene (see Table 2.1). This result led to Hiickel MO theory being used extensively in the semi-quantitative interpretation of ESR spectra of aromatic hydrocarbon anion and cation radicals. 

For aromatic hydrocarbon radical anions, this approach works pretty well. Figure 2.7 shows a correlation plot of observed hyperfine splitting versus the spin density calculated from Hiickel MO theory. It also correctly predicts the negative sign of aH for protons attached to n systems. 

One of the most used approaches for predicting homoaromaticity has been the perturbational molecular orbital (PMO) theory of Dewar (1969) as developed by Haddon (1975). This method is based on perturbations in the Hiickel MO theory based on reducing the resonance integral (/3) of one bond. This bond represents the homoaromatic linkage. The main advantage of this method is its simplicity. PMO theory predicted many potential homoaromatic species and gave rise to several experimental investigations. 

Nitrenium ions are isoelectronic to carbenes [177]. They contain a dicoordinated nitrogen atom formally with two valence electrons. The possible electronic structures of the parent nitrenium ion NHj are shown in Figure 7.9. On the basis of Hiickel MO theory one would expect that the lowest energy configuration, that is, the electronic ground... 

Let us now apply Hiickel MO theory to the particular case of the allyl system, C3H3, as illustrated in Figure 4.2. Because we have three carbon atoms, our basis set is determined from convention (a) and will consist of 3 carbon 2p orbitals, one centered on each atom. We will arbitrarily number them 1, 2, 3, from left to right for bookkeeping purposes. 

We now consider some applications of the McConnell equation (8.126), using Hiickel MO theory to estimate pw C. For the methyl radical, pw>c l, and aH is predicted to be - 23 G, in agreement with the observed proton coupling constant (Fig. 8.15). 

For the naphthalene negative ion, Hiickel MO theory puts the unpaired electron in the lowest unoccupied MO of the neutral naphthalene molecule this MO is (Levine, Section 15.8)... 

REACTIONS OF AROMATIC COMPOUNDS Cyclic 7r Systems by Simple Hiickel MO Theory... 

C (Table 5). These measurements can be related to the approach adopted by Duben29 who used the Hiickel MO theory to compare the reactivity of five-and six-membered ring products containing S or N. Six-membered rings, such as pyridine, produced a different distribution of 7r-molecular orbitals from that produced by five-membered rings, such as thiophene or pyrrole, in adsorbed states this factor could be the most important one when comparing the catalytic activities of different compounds. 

H is an effective hamiltonian for a single electron, i and j label the molecular orbitals, and r and s label the atomic orbitals. In Hiickel MO theory Hrs is taken to be non-zero only for bonded pairs of atoms r and s, and all Srs are assumed to be zero for r s. 

However, QMe (or B) may vary with type of radical, especially charge type, and also with the nature of the a-atom. Thus, methyl hyperfine splittings in alternant hydrocarbon anion- and cation-radicals, for which Hiickel MO theory predicts identical spin populations at the methylated positions, typically differ by a factor of at least two.15... 

Hiickel MO theory with the AO overlap integral Sab included generates an instability for the (homonuclear) three-electron bond when Sab exceeds 0.3 [33], and heteronuclear three-electron bonds are also overlap destabilized under compression. The following speculation, which utilizes the overlap instability of three-electron bonds, may have relevance for the provision of a VB formulation for aspects of the mechanism for electron conduction in the high Tc superconductor YBa2Cu3C>7. 

The major importance of the Hiickel rule is that its predictions can be experimentally checked and hence the predictive power of the Hiickel MO theory (i. e. topological MO theory) can be critically evaluated. The efforts made to prove or disprove the Hiickel rule strongly influenced the development of annulene chemistry 141.142),... 

Bicyclo[3.3.0]octa-l,3,5,7-tetraene, trivially called pentalene (2) (Fig. 1) [28] is the second member in the series of fully unsaturated oligoquinanes. Hiickel-MO theory predicts that this planar hydrocarbon with its 8n -electron system should be an antiaromatic species [3]. The 2-methylpentalene 36 could be generated by a retro-Diels-Alder reaction and deposited as a film at -196 °C on an NaCl or quartz plate to be characterized spectroscopically. It rapidly dimerized upon... 

Table 11.2. The potentials correlate with the energy of the LUMO as calculated by simple Hiickel MO theory. Note that polycyclic aromatics are easier both to reduce and to oxidize than benzene. This is because the HOMO-LUMO gap decreases with...

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