Natural spin density

In natural population analysis (NPA) of open-shell species (see, for example, 1/0-3.10), the natural spin density is evaluated for each NAO, then summed over NAOs on each atom to give and finally over all atoms to give net overall spin density of the species (as measured hy ESR spectroscopy see Chapter 7). This provides a very detailed picture of spin charge and spin polarization distributions throughout the molecule, allowing one to quantify (or rationally design) specific magnetic properties of interest. 

However, the final natural spin density column reveals the striking spin polarization in ozone, with ca. 0.5e excess (3 spin on 0(1) and compensating excess a-spin on 0(3), corresponding to significant singlet diradical character. 

Although Tempone is often depicted as having the unpaired electron localized on the nitroxide oxygen atom, the calculated natural spin density (NSD) distribution presents a more complex picture, as summarized in Table 7.3. 

Table 7.3 Calculated natural spin density (NSD) distribution for tempone spin label, showing total atomic spin density at each atomic center (cf. 1/0-7.6). ...

Lowdin, P.-O., Phys. Rev. 97, 1474, 1490, 1509, Quantum theory of many-particle systems. I. Physical interpretations by means of density matrices, natural spin-orbitals and convergence problems in the method of configuration interaction. II. Study of the ordinary Hartree-Fock approximation. III. Extension of the Har-tree-Fock scheme to include degenerate systems and correlation effects. ... 

Levy, M., 1979, Universal Variational Functionals of Electron Densities, First Order Density Matrices, and Natural Spin Orbitals and Solution of the v-Representability Problem , Proc. Natl. Acad. Sci. USA, 16, 6062. 

The dimerisation energy for derivatives of 2 (ca. 35 kJ mol-1) is considerable, particularly in relation to the strength of intermolecular forces and some persistence is required in order to isolate derivatives of 2 which do not form 7T —7r dimers in the solid state. A survey of the monomeric derivatives has been published recently.26 Since the spin density distribution in 2 is rather insensitive to chemical tuning, approaches to inhibit dimerisation rely exclusively on structural modifications, which affect the nature of the intermolecular forces. Inclusion of sterically demanding groups, such as 13, 14 and 15 has proved partially successful (in the case of the diradical 14 one ring is involved in formation of a dimer, while the other retains its open shell character). 

Despite the enormous importance of dienes as monomers in the polymer field, the use of radical addition reactions to dienes for synthetic purposes has been rather limited. This is in contrast to the significant advances radical based synthetic methodology has witnessed in recent years. The major problems with the synthetic use of radical addition reactions to polyenes are a consequence of the nature of radical processes in general. Most synthetically useful radical reactions are chain reactions. In its most simple form, the radical chain consists of only two chain-carrying steps as shown in Scheme 1 for the addition of reagent R—X to a substituted polyene. In the first of these steps, addition of radical R. (1) to the polyene results in the formation of adduct polyenyl radical 2, in which the unpaired spin density is delocalized over several centers. In the second step, reaction of 2 with reagent R—X leads to the regeneration of radical 1 and the formation of addition products 3a and 3b. Radical 2 can also react with a second molecule of diene which leads to the formation of polyene telomers. 

Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction. 

The radical anions of various phenyldiphosphaalkenes (Scheme 11) were studied by EPR. Their reduction is easier than that of monophosphaalkenes and is dependent on the nature of the isomer. Both EPR spectra and DFT calculations showed that in the radical anion the unpaired electron belongs to a Jt orbital and that its delocalization is dependent on the relative position of the two phos-phaalkene moieties and on the nature of the bridging group. The spin density on the phosphaalkene carbon is higher for the meta compound than for the ortho and para compounds. 

Naturally, the cation-radical of diphenylamine is characterized with an analogous positive-charge delocalization (Liu and Lund 2005). The A,A -diphenyl-p-phenylenediamine cation-radical is almost planar and the spin density intrudes outer phenyls. When the outer phenyls contain two methyl groups in ortho positions, the molecule loses planarity. As a result, the spin density concentrates within the inner ring and its adjacent two nitrogen atoms (Nishiumi et al. 2004). 

Any molecular entity possessing an unpaired electron. The modifier unpaired is preferred over free in this context. The term free radical is to be restricted to those radicals which do not form parts of radical pairs. Further distinctions are often made, either by the nature of the central atom having the unpaired electron (or atom of highest electron spin density) such as a carbon radical (e.g., -CHs) or whether the unpaired electron is in an orbital having more s character (thus, radical molecular entity in a manuscript, the structure should always be written with a superscript dot or, preferably, a center-spaced bullet (e.g., -OH, -CHs, CF). 

While the nuclei of the aromatic segments show the identical signal directions, the cyclopropane protons show characteristic differences. This suggests significantly different spin-density distributions for the cyclopropane moieties of the two species and, thus, different structures. Like the norcaradiene HOMO, the styrene HOMO is antisymmetric at the positions of attachment, suggesting preferred interaction with the antisymmetric cyclopropane HOMO. In the norcaradiene system, the natural structure ( Aj) of the cyclopropane radical cation is altered by the interaction with the diolefin entity. 

M. Levy, Universal variational functionals of electron-densities, Ist-order density-matrices, and natural spin-orbitals and solution of the v-representability problem. Pmc. Natl. Acad. Sci. U.S.A. 76(12), 6062-6065 (1979). 

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