Positive spin densities

In Fig. 3 the number of possible classical structures arising from the spin being localised at each carbon atom (top half) is compared to the UHFAA spin density results (lower half). Note that the number of classical structures when the unpaired electron is at sites 2, 5 and 6 is the same as for the double bonds involving atoms 1 and 2, 1 and 5 or 1 and 6 in Ceo- The correlation between the number of classical structures and the spin density is excellent. With only one exception all centres with the number of classical structures larger than 2200 show positive spin density and all those less than 2200 show negative spin density. This anticipated correlation can be further quantified. 

Figure 1. Induced spin density map for MnCu(pba)(H20)j. 2H20 at 10K under 5 T in projection along the perpendicular to the basal plane. Solid and dashed lines are used respectively for negative and positive spin densities. Contour steps are 5 mpB/A2. The spin delocalisation is more pronounced toward the N atom than the O atoms.

Related research has been reported by Elder and Worley (39), in which MNDO was used to examine the structure of coniferyl alcohol, and its corresponding phenolate anion and free radical. This method represents an improvement over the PPP method, in that MNDO is an all-electron technique, and performs geometry optimizations. It was found that the calculated spin densities and charge values for the reactive sites did not correlate quantitatively with observed bond frequency, but it was observed that positions with partial negative charge and positive spin densities are the positions through which the polymerization has been found to occur. 

Proton-magnetic-resonance shifts have been reported on solid samples of dicyclopentadienyl nickel (97), vanadium (98), and chromium (98). For the nickel compound, a shift to higher fields was observed in contrast to shifts to lower fields for vanadium and chromium. It was suggested that charge-transfer effects give a positive spin density to the carbon atoms in the nickel compound and a negative spin density to the carbon atoms in other cases, but the reason for this difference is not clear from molecular-orbital theory. 

Proton magnetic resonance studies131 of V(C H6) and Cr(C H )2 show negative electron spin densities of —0.06 and —0.12, respectively, on the carbon atoms. These negative spin densities probably arise in a different way from the positive spin density in Ni(C6H5)s, discussed above. The unpaired electrons in 3d orbitals are restricted to the metal atom. They interact with the shared electron pairs of the M—C bonds in such a way as to make the distribution of the electrons of the shared pair unsymmetrical the electron with spin parallel tn those of the unshared electrons on the metal tends to remain on the metal and the other one on the carbon atom. The observed negative spin densities can be accounted for in this way, with the values of the 3d — 3d... 

If the spin delocalization mechanism on the pyridine ring were a solely, substitution of y-H with Y-CH3 would produce almost zero spin density on the y-CH3 protons. On the contrary (Table 2.3 and Fig. 2.11), some upheld (negative) shift is observed [22,23]. Spin polarization, from e.g. positive spin density on the pz orbital of an sp2 carbon, produces negative spin density on the attached proton (Fig. 2.12), and positive spin density again on the protons of an attached CH3 moiety (see also Section 2.4). Therefore, if the y-CH3 protons experience upheld... 

HMO) formalism, because its singly occupied molecular orbital (SOMO) is constrained by symmetry to be on those atoms. More sophisticated molecular orbital analysis finds not only equal, positive spin densities on the end carbons but also a small negative 7T-spin density on the central carbon due to spin polarization. At the UB3LYP/6-31G level, the spin density p ) - p(C3) = +0.700, mostly from 7T-spin contributions, and p(C2) = -0.275.27 The experimental numbers estimated for TT-spin density (not overall spin density) are p(C ) = p(C3) = +0.582 and p(C2) = -0.164 from electron paramagnetic resonance (EPR) studies of 13C hyperfine coupling (hfc).28... 

The distribution of the total spin density in radicals was calculated using the UB3LYP16-31g method. In systems 1, 3, 4, and 8-11, the spin density is localized on the -S-N-S- fragment with minor spin distribution onto the Jt-framework, presumably through a spin polarization mechanism. For instance, in 1,3,2-dithiazolyl 1, virtually all positive spin density is localized on the -S-N-S- array due to the two polar resonance structures shown in Equation (2). A very similar spin distribution is observed in ring-fused derivatives 3, 4 and 9-11 <2001PCA7615>. 

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. 

Ab initio (B3LYP/6-31G or UHF/6-31G ) quantum-chemical calculations of spin density distribution in nitroazole radical anions (Scheme 3.29) are in a good agreement with experimental data (Scheme 3.28, Figs. 3.2 and 3.3) and show that the largest positive spin density is located at the carbon atom of azole ring, where the vicarious C-amination is realized [277]. 

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