Allyl cation, radical, anion

Unfortunately, while it is clear that the allyl cation, radical, and anion all enjoy some degree of resonance stabilization, neither experiment, in the form of measured rotational barriers, nor higher levels of theory support the notion that in all three cases the magnitude is the same (see, for instance, Gobbi and Frenking 1994 Mo el al. 1996). So, what aspects of Hiickel theory render it incapable of accurately distinguishing between these three allyl systems ... 

Calculate the difference in energy between localized and delocalized forms for allyl cation, radical and anion. Does it increase, decrease or remain approximately the same with increasing number of n electrons Rationalize your result. 

Q Show how to construct the molecular orbitals of ethylene, butadiene, and the allylic Problems 15-35 and 36 system. Show the electronic configurations of ethylene, butadiene, and the allyl cation, radical, and anion. 

The allyl cation, radical and anion have the same a framework 1.7, with 14 bonding molecular orbitals filled with 28 electrons made by mixing the Is orbitals of the five hydrogen atoms either with the sp2 hybrids or with the 2s, 2px and 2py orbitals of the three carbon atoms. The allyl systems are bent not linear, but we shall treat them as linear to simplify the discussion. The x, y and z coordinates have to be redefined as local x, y and z coordinates, different at each atom, in order to make this simplification, but this leads to no complications in the general story. 

Finally, Gobbi and Frenking analyzed the allyl cation, radical, and anion. They stated that their results show that jr-electron delocalization is a stabilizing factor operative in the symmetric (C2O and bond alternating (Cs) forms of the planar compounds. Delocalization resists the rotation of the methylene groups but not necessarily bond alternation. Subsequently. they analyzed the distortion energy for the three allyl systems. They partitioned the total energy in three parts... 

Equation 4.52 can be used to calculate the charge density for each position of the allyl cation, radical, and anion, and the results are shown in Table 4.1. These values are comforting, because they agree with our chemical experience with allylic systems. The resonance description of the allyl cation and radical (Figure 4.13) suggests that exactly half of the charge or unpaired electron density is associated with each of the terminal carbon atoms, and the HMO result is the same. 

The TT molecular orbitals of allyl cation, radical, and anion. Allyl cation has two tt electrons, allyl radical has three, and allyl anion has four. 

The greater Sn2 reactivity of allylic halides results from a combination of two effects steric and electronic. Sterically, a CH2CI group is less crowded and more reactive when it is attached to the 5p -hybridized carbon of an allylic halide compared with the sp -hybridized carbon of an alkyl halide. Electronically, the tt-electron MO approximation doesn t apply because the reactant is allyl chloride, not an allyl cation, radical, or anion. Higher level MO treatments such as seen earlier for the Sn2 mechanism in Section 8.3 are readily adapted to allyl chloride, however. According to that picture, electrons flow from the nucleophile to the LUMO of the alkyl halide. 

The ground-state tt-electron configuration of the allyl system is built up by putting electrons in pairs into the MOs, starting with those of lowest energy. Thus far, we have been describing our system as the allyl radical. However, since we have as yet made no use of the number of tt electrons in the system, our results so far apply equally well for the allyl cation, radical, or anion. 

Figure 14-3 The Aufbau principle is used to fill up the tt molecular orbitals of 2-propenyl (allyl) cation, radical, and anion. In each case, the total energy of the TT electrons is lower than that of three noninteracting p orbitals. Partial cation, radical, or anion character is present at the end carbons in these systems, a result of the location of the lobes in the 772 molecular orbital.

Are the carbon-carbon bond distances in allyl cation, allyl radical allyl anion all similar, or are they significantly... 

Allyl cation, allyl radical and allyl anion differ in the number of electrons contained in a nonbonding 7i-type orbital, the LUMO in the cation and the HOMO in the radical and anion. 

Allyl (27, 60, 119-125) and benzyl (26, 27, 60, 121, 125-133) radicals have been studied intensively. Other theoretical studies have concerned pentadienyl (60,124), triphenylmethyl-type radicals (27), odd polyenes and odd a,w-diphenylpolyenes (60), radicals of the benzyl and phenalenyl types (60), cyclohexadienyl and a-hydronaphthyl (134), radical ions of nonalternant hydrocarbons (11, 135), radical anions derived from nitroso- and nitrobenzene, benzonitrile, and four polycyanobenzenes (10), anilino and phenoxyl radicals (130), tetramethyl-p-phenylenediamine radical cation (56), tetracyanoquinodi-methane radical anion (62), perfluoro-2,l,3-benzoselenadiazole radical anion (136), 0-protonated neutral aromatic ketyl radicals (137), benzene cation (138), benzene anion (139-141), paracyclophane radical anion (141), sulfur-containing conjugated radicals (142), nitrogen-containing violenes (143), and p-semi-quinones (17, 144, 145). Some representative results are presented in Figure 12. 

In contrast to the allyl system, where the reduction of an isolated double bond is investigated, the reduction of extensively delocalized aromatic systems has been in the focus of interest for some time. Reduction of the systems with alkali metals in aprotic solvents under addition of effective cation-solvation agents affords initially radical anions that have found extensive use as reducing agents in synthetic chemistry. Further reduction is possible under formation of dianions, etc. Like many of the compounds mentioned in this article, the anions are extremely reactive, and their intensive studies were made possible by the advancement of low temperature X-ray crystallographic methods (including crystal mounting techniques) and advanced synthetic capabilities. 

For a linear system consisting of three carbon atoms (which includes the allyl radical and the cation and anion derived from it), the coulomb integrals will be identical ... 

The energy level diagram including electron populations for the allyl radical, cation, and anion can be shown as illustrated in Figure 5.16. The orbital diagram and energy levels for the allyl system is shown in Figure 5.17. 

I FIGURE 5.16 The energy level diagram for the allyl radical, cation, and anion species. 

Allyl cation, 10 Allyl radical Allyl anion, 11... 

The third intra-pair reaction to be discussed involves bond formation between radical anion and cation without intervening transfer both singlet and triplet radical ion pairs can couple. For example, the bifunctional radical cation 24 generates two chloranil adducts, most likely via zwitterions (e.g., 74 and 75 ), initiated by forming a C O bond. The CIDNP results indicate that 74 and 75 are formed from a singlet radical ion pair. Adduct 75 is a minor product, as the major spin density of 24 + is located in the allyl function which, therefore, is expected to be the principal site of coupling. 

Figure 4.2 Hiickel MOs for the allyl system. One pc orbital per atom defines the basis set. Combinations of these 3 AOs create the 3 MOs shown. The electron occupation illustrated corresponds to the allyl cation. One additional electron in

We may perform the same analysis for the allyl radical and the allyl anion, respectively, by adding the energy of 4>2 to the cation with each successive addition of an electron, i.e., H (allyl radical) = 2(a + V2/3) + a and Hn allyl anion) = 2(a + s/2f) + 2a. In the hypothetical fully 7T-localized non-interacting system, each new electron would go into the non-interacting p orbital, also contributing each time a factor of a to the energy (by definition of o ). Thus, the Hiickel resonance energies of the allyl radical and the allyl anion are the same as for the allyl cation, namely, 0.83/1. 

Are the carbon-carbon bond distances in allyl cation, allyl radical and allyl anion all similar, or are they significantly different The three molecules differ mainly in the number of electrons they assign to one particular molecular orbital. (This is the lowest-unoccupied molecular orbital (LUMO) in allyl cation, and the highest-occupied molecular orbital (HOMO) in allyl radical and allyl anion.) Examine the shape of this orbital. Are the changes in electron occupancy consistent with the changes in CC bond length Explain. 

The cation radical can undergo deprotonation to yield an allyl radical or nucleophilic attack by the solvent to produce a methoxyalkyl radical. Coupling of these radicals with the aromatic radical anion produces acyclic adducts. As an alternative, the anion radical can be protonated, ultimately giving reduction product. Thus, the degree of charge separation within the excited state complex dramatically influences the observable chemistry. 

Presumably the radical anion generated by the primary electron transfer fragments to a radical anion pair. Back electron transfer to the sensitizer cation radical generates the allyl cation from which geometric isomerization and structural rearrangement can be easily accomplished. 

---