Odd Alternant Hydrocarbon Radicals

During the past few years, the ionization potentials of a number of organic radicals have become available primarily in the laboratories of F. P. Lossing, using the electron impact method. Values by this method are used almost exclusively in this section. 

In the simple Hiickel MO (HMO) method, the odd electron in radicals of odd alternant hydrocarbons such as methyl, allyl, benzyl and benzhydryl, pertains to a nonbonding MO hence, these radicals should have the same ionization potentials. Actually, the ionization potentials vary over more than a 2-e.v. range (Table I). The 

In comparing the /-values for methyl and allyl radicals, it is not enough to consider the resonance energy of allyl cations alone. Allylic resonance applies to both allyl radical and allyl cation  

Similarly, in a common application of resonance structures, charge dispersal increases in the order benzyl j8-naphthylmethyl -naphthylmethyl and the ionization potentials decrease in the same order. As expected, I for benzhydryl radical is substantially lower than I for benzyl in the cation, positive charge is distributed over two rings instead of one. The effect of the second phenyl group is much less than that of the first perhaps because noncoplanarity of the benzhydryl systems prevents complete conjugation. 

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A +E substituent R and a — E substituent T can conjugate mutually through an odd alternant hydrocarbon radical S if R, T are both attached to active atoms in S. 

Figure 2.23. Odd alternant hydrocarbon radicals a) Schematic representation of the frontier orbital energy levels and of the various configurations that are obtained by single excitations from the ground configuration o. (It should be remembered that spin eigenstates cannot be represented correctly in these diagrams.) b) Energies of these configurations and effect of first-order configuration interaction.

Odd-Alternate Polynuclear Aromatic Hydrocarbon Radicals. Substantial evidence supports the contention that the stable free radicals formed during the pyrolysis of polynuclear aromatic compounds are odd-alternate hydrocarbon radicals. As an example, the phenalenyl radical (5) is formed during pyrolysis of a number of organic compounds including acenaphthylene (3) and dihydronaphthalene (4) (24) (see Scheme III). The... 

The latter case is particularly important because all odd alternant hydrocarbon radicals turn out to have a nonbonding molecular orbital. 

Large amounts of spin polarization are expected in radicals where (1) the SOMO has nodes at some nuclei and (2) some of the formally paired electrons occupy subjacent bonding MOs of relatively high energy (e.g., k MOs) that are easily polarized. Good examples of this combination of features are odd-alternant hydrocarbon radicals (e.g., allyl and benzyl) where (1) the SOMOs have nodes at every other carbon atom and (2) electrons in subjacent n MOs, whose spin is opposite to that of the electron in the SOMO, can relatively easily be confined at these nodal carbons. 

Since (S ) is close to 1 in allyl, has an uncomfortably high level of spin contamination. If one compares the observed hyperfin. couplings in allyl radical to those computed from a UHF wavefunction, one finds that spin contamination causes the amount of spin polarization to be exaggerated. In longer odd-alternant hydrocarbon radicals, spin contamination can become quite spectacular As shown in Figure 3, (S ) for the UHF wavefunctions of odd-alternant polyenyl radicals increases by 0.38 units for every pair of CH groups added, instead of remaining constant at (S ) = 0.75, as it would for a pure doublet wavefunction. 

By an odd-alternant hydrocarbon is usually meant a free radical, such as the benzyl radical (Fig. 6-3). In this example there are seven carbon-atoms, hence seven atomic-orbitals and seven molecular-orbitals which must accommodate the seven jt-electrons. Of the seven energy-levels, six of them will occur quite naturally in pairs, according to the Theorem we have just proved, as shown schematically in Fig. 6-4. How can the seventh be... 

The fourth approach is to use derivatives of odd-alternant hydrocarbons, such as the phenalenium radical, in which the Hiickel resonance energy is the same for the anion, the radical, and the cation, because the HOMO is a non-bonding MO [43,44]. However, the radicals seem too reactive. 

Use the properties of odd alternant hydrocarbons to determine the impaired electron density at the exocyclic carbon in the radical 31. Is this result surprising to you Show how resonance theory can easily rationalize the result. 

As an illustration of the points just discussed, consider the allyl radical, the simplest odd-alternant hydrocarbon. By symmetry, the SOMO, 2, has equal coefficients on the two terminal C atoms and a node through the central one. Thus, the [3 electron in the subjacent bonding MO, Tti, can avoid the a electron by occupying an MO with a large coefficient at the central carbon. Since the paired a electron in can never appear simultaneously in the same AO as... 

As a general treatment of the problem of substitution, Wheland s method has the disadvantage of not being very easy to apply. For one class of aromatic substances, namely the alternant hydrocarbons and heterocyclic compounds isoaromatic with them, a comprehensive and rapid treatment has been developed. Alternant hydrocarbons have no odd-numbered rings. They have the property that the constituent carbon atoms fall into two sets distinguished as starred and unstarred, such that no atom of one set is adjacent to another of the same set. Odd alternant hydrocarbons are radicals or ions. As an... 

For an even alternate hydrocarbon such as benzene the cyclization of hexa-triene could be considered. However, it turns out to be much simpler to compare the energy of formation of the linear and cycUc structure from the union of two odd alternate hydrocarbons (Fig, 2.4b and c). For this purpose the methyl radical is regarded as a simple odd alternant hydrocarbon. 

The properties of the minors of the secular determinant of an alternant hydrocarbon may again be used to show that the integrals for which the index is even in (44) and odd in (45) and (46) are zero. It follows that the finite change Aq is an odd function, of Sa, while AFg and Apgt are even. Any inequalities between values of any index for two different positions u), as defined in equations (31) to (34) which arise as first terms of the corresponding infinite series in (44) to (46), persist term-by-term in the expression for the exact finite changes (Baba, 1957). In consequence, the broad agreement with experiment found earlier in the description of ionic and radical reactions by the approximate method carries over to the exact form. 

Radicals with an odd number of electrons can be either uncharged odd hydrocarbons or radical ions of even hydrocarbons or systems derived from such hydrocarbons. Of special interest are the relationships that exist for radicals and radical ions of alternant hydrocarbons. 

Figure 2.24. Orbital energy levels of alternant hydrocarbon ions a) anions and cations of odd-alternant systems, and b) radical anions and radical cations of even-alternant systems in the HMO approximation and c) in the PPP approximation.

We introduce here for the conjugated hydrocarbon radicals the same classification which we used for the closed-shell hydrocarbons 55). We divide the hydrocarbons into two large groups alternant and nonalternant. Further classification concerns the even and odd systems, and the presence of cycles in the skeleton. The phenyl substituents are... 

We know (see p. 60) that an alternant hydrocarbon (AH) has a self-consistent field so that = 0 at all atoms therefore if we remove an electron from the NBMO to get a benzyl cation, the pasitive charge will be distributed sole over those atoms whose orbital coefficients are not zero for the NBMO. The same will be true if we add an electron to the radical and make the benzyl anion. The NBMO coefficients are clearly of signal importance since their values determine the calculated distribution of the odd electron in the radical and the charges in the cation and anion. For the benzyl radical the NBMO may be rendered schematically as follows ... 

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