Spin density negative

Agreement with experiment is not particularly good, and the ROHF method cannot give regions of negative spin density, since the spin density is just the sum of the squares of the partially occupied orbitals in this model. Corresponding calculations with the UHF method give Table 18.4. 

These methods can give us useful information on radicals in a manner similar to that for closed-shell systems, provided the exploitation is correct. Of course, in expressions for total energy, bond orders, etc., a singly occupied orbital must be taken into account. One should be aware of areas where the simple methods give qualitatively incorrect pictures. The HMO method, for example, cannot estimate negative spin densities or disproportionation equilibria. On the other hand, esr spectra of thousands of radicals and radical ions have been interpreted successfully with HMO. On the basis of HMO orbital energies and MO symmetry... 

Fig.4 Spin density in the DPPH molecule projected onto a plane containing the two N-atoms of the hydrazyl group. Densities are given in units of e/X negative spin densities are indicated by broken lines.

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. 

Both objects are much less complicated than the total A -particle wavefunction itself, since they only depend on three spatial variables. The electron density is manifestly positive (or zero) everywhere in space while the spin-density can be positive or negative. If, by convention, there are more spin-up than spin-down electrons, the positive part of the spin-density will prevail and there will usually be only small regions of negative spin-density that arise from spin-polarization. This spin-polarization is physically important and is already included in the UHF method but not in the ROHF method that, by construction, can only describe the... 

The analysis by Munzarova et al. [88] suggests the following interpretation of these findings the polarization of the metal 2s shell is due to the enhanced exchange interaction with the singly occupied metal 3d orbitals and causes the spin-up 2s orbital to move closer to the metal 3d shell which leaves a net negative spin-density... 

Since the core polarization will give a negative spin density at the iron nucleus, it is expected that in the state the isotropic and dipolar contributions partially cancel each other along the Fe-O bond direction while they will reinforce each other along this direction in the state. 

Cluster calculations in general have found qualitative (but not quantitative) agreement with the experimental observations for spin densities around Mu Estreicher (1987) found a negative spin density at the bond center DeLeo et al. (1988) found 19% of the unpaired spin on the two Si neighbors, while Deak et al. (1988) found 90% for this value. 

Figure 6.10 In the absence of spin polarization, which corresponds to the ROHF picture, there is zero spin density in the plane containing the atoms of the methyl radical. Accounting for spin polarization, which corresponds to the UHF picture, results in a build-up of negative spin density (represented as a shaded region) in the same plane...

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... 

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