Allyl radical negative spin density

The second set of illustrations show the spin density plotted on the electron density isosurface the spin density provides the shading for the isodensity surface dark areas indicate positive (excess a) spin density and light areas indicate negative (excess P) spin density. For example, in the allyl radical, the spin density is concentrated around the two terminal carbons (and away from the central carbon). In the Be form, it is concentrated around the substituent, and in acetyl radical, it is centered around the C2 carbon atom. 

In contrast, CIDNP results indicate that the radical cations of barbaralane (157, X = C = 0) and semibullvalene (157, X = —) correspond to the elusive structure type with a single minimum [391, 424]. The spin density resides primarily on the termini (C-2,4,6,8) of the twin allyl moieties, whereas the remaining (internal) carbons of the 5 jr-electron perimeter have negative spin density. This spin density distribution reflects the coefficients of orbital 158, the HOMO of a bis-homoaromatic structure (Fig. 32) [424], More recently, ESR results have confirmed this assignment [392, 393],... 

SAD Spin-alternant determinant. The VB determinant with one electron per site and with alternating spins. Other terms describing the same determinant are the quasiclassical (QC) state, and the antiferromagnetic (AF) state. In nonalternant hydrocarbons, where compete spin alternation is impossible, the determinant is called MS AD, namely, the maximum spin-alternating determinant. The SAD MSAD are the leading terms in the wave function of molecules with one electron per site, for example, conjugated hydrocarbons. In radicals (e.g., allyl radical) the SAD is the root cause of spin polarization (i.e., negative spin densities flanked by positive ones). See Chapters 7 and 8. 

The electron spin resonance of certain paramagnetic compounds e. g., diphenyl picryl hydrosil (DPPH) and the allyl radical are said to exhibit negative spin density. The negative spin density is determined by the freeon unpaired... 

An analysis of the NBMO of allyl nicely ties together the valence bond concept of resonance (see Chapter 1) with the MO concepts presented in this chapter. The NBMO only has coefficients on the end carbons, meaning that allyl radical does not have radical character on the central carbon at this level of theory. (See, however, the discussion of negative spin density in Section 17.3.2.) This is exactly what the resonance structures for allyl radical tell us. 

The second effect that stabilizes the singlet, relative to the triplet, is interaction between the negative spin densities in the p- r AOs at the central carbons of the two allylic radicals... 

Repeat your analysis for localized and delocalized allyl radical and allyl anion. Focus on location of the spin density in the former and on the negative charge in the latter. 

As the MSADs have the largest coefficients in the ground-state wave function, one may expect that for alternant free radicals or polyradicals, the dominant positive spin density will be largest on the atoms that bear an alpha spin in the MSAD. An example that was analyzed in Chapter 7 is the allyl radical, where the MSAD predicts positive spin densities at positions 1, 3 and a negative density at position 2. Similarly, the MSAD of benzyl radical predicts positive spin densities on the benzylic carbon and on the ortho and para positions. 

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