Spin density distributions

Figure 5 shows the spin density distribution of the low-spin form of C54. It is interesting to note that also here the spin density is almost entirely localized on the cartx>n atom that would carry the dangling bond in a simple valence orbital picture. 

Figure 5. Spin density distribution in the low-spin form of C...

Just as we obtain the spin density distribution q(i), and hence the projection of the investigated object, in phase encoded imaging, we can reconstruct P(R, A) by... 

Fig. 3.3.8 Two-dimensional cross section through the fixed-bed reactor (upper) and radial spin-density distribution obtained from the images (lower) for (a) spherical glass beads of 2 mm in diameter and (b) cylindrical pellets with average equivalent diameter of 2.2 mm.

Thus, for paramagnetic complexes the reactivity patterns promoted either by the metal center or by the ligand (equivalent to an inner- vs. an outer-sphere pathway), are essentially triggered by the spin density distribution. 

The spin density distribution within the [Ni3c-0]8 moiety (43% on Ni and 57% on O), being distinctly shifted towards the oxygen, renders this terminal atom a preferred site for subsequent NO attack to produce Ni-bound N02... 

Pietrzyk, P., Piskorz, W., Sojka, Z. et al. (2003) Molecular structure, spin density distribution, and hyperfine coupling constants of the i7l CuNO n adduct in the ZSM-5 zeolite DFT calculations and comparison with EPR data, J. Phys. Chem. B., 107, 6105. 

The detection of zero-field splitting for dianions of [18] or [21] is very important it reveals not only the existence of a triplet state, but it also provides information on the mode of spin density distribution. Even more... 

While the rate of an electron-transfer process and thus the mode of the resulting spin-density distribution can be controlled by the length and the conformation of the spacer groups, the ion pairing creates an additional factor that can serve as some external control even for a given choice of subunits and spacers. 

The same control mechanism can be put to work for the doubly layered electrophores [14]. From esr measurements it appears that a change only of the ion pairing brings about a different hopping rate and creates a different spin-density distribution within the timescale of the experiment. 

The rate of degenerate intramolecular electron-transfer processes in biselectrophoric redox systems, and the observed spin-density distribution over one or two units depend upon the overall reorganization energy and thus upon... 

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). 

An experimental determination of the spin density distribution in these complexes was recently reported, based on EPR data on 77Se-enriched (at 100%) diselenolene analogs where the 77Se coupling constants and g tensors could be determined from frozen solutions spectra [60]. A 14% spin density was determined on each Se atom in 77Se-enriched [CpNi(bds)] while a larger 16% spin density on... 

Fig. 7 Spin density distribution in CpNi(dddt) (left) and CpNi(bdt) (right) (taken from [59], with authorization of the American Chemical Society)...

Table 3 Spin density distribution on the metal atom and summed over all atoms of each of the three ligands in [Cp M(dmit)2], M = Mo, W [43]...

Considering a five-point spin density distribution (central ion and four nitrogens) for the determination of the dipolar proton hfs tensors in Ag(TPP) (5.5), the computed ADD principal values are found to be close to the experimental results. It should be noted that in Ag(TPP) the Mulliken population, UN, on the nitrogen nearest to the pyrrole proton provides a larger contribution to ADD along the Ag-H direction than the population UAg. 

The positional selectivity on formation of the cydoadducts from 221 is less pronounced than that of the isobenzene 162, but it is the conjugated double of the allene moiety as well that predominantly undergoes the reaction. As demonstrated by the thermolysis of several products, these are formed from 221 under kinetic control. For example, on heating, the styrene adduct 240 and the furan adduct 231 rearranged virtually completely to 241 and 232, which are formally the cycloadducts to the non-conjugated double bond of the allene subunit of 221 [92, 137]. The cause of the selectivity may be the spin-density distribution in the phenylallyl radical entity of the diradical intermediates. 

Esr spectroscopy has been used extensively in connection with the problem of radical stabilization. Two properties of the radicals are analysed to obtain information on their stability spin-density distribution and lifetime. The former has a solid physical basis in hyperfine splitting and the universally accepted hypothesis that spin delocalization accords stability to a free radical (for a discussion, see Walton, 1984). The more the unpaired spin density is delocalized, the higher is, supposedly, the stability of the radical. This argument, as we shall see, is mainly used on a qualitative basis (see. 

Spin-density distributions obtained from the analysis of esr spectra can be taken to establish a scale for the radical-stabilizing power of substituents. 

Arnold s o -scaIe (Arnold, 1986 Dust and Arnold, 1983 Wayner and Arnold, 1984), which reflects the spin-density distribution in meta- and para-substituted benzylic radicals and leads to parameters similar to those derived from other sources (Jackson, 1986), provide a good example. Arnold s scheme is based on the hypothesis that hyperfine coupling constants of the a-hydrogen in substituted benzylic radicals give information regarding the effect of substituents on the distribution of spin throughout the radical and that this is connected with the stability of the benzylic radical. 

Arnold s scale is derived for the action of a single substituent on the benzylic 7c-system. It cannot be used to estimate the influence of several substituents on the system under consideration. In this way it is, therefore, not possible to gain insight into the problem of captodative stabilization of a radical centre. The investigation of the spin-density distribution in benzylic radicals has been extended (Korth et al., 1987) to include multiple substitution patterns. Three types of benzylic radicals were considered a,p-disubsti-tuted a-methylbenzyl radicals [17], a-substituted p-methylbenzyl radicals [18] and a-substituted benzyl radicals [19]. In [17] and [18] the hyperfine coupling constants of the methyl hydrogens were used to determine the spin-density... 

Spin-density distributions are inherent features of free radicals. Esr experiments take place when the radical is in its electronic ground state and the measurement of the spin distribution constitutes only a minute perturbation of the system. This feature and the fact that esr hyperfine splitting can be measured with high precision makes the esr method ideally suited for the study of substituent effects. Therefore, if spin delocalization is accepted as a measure of stabilization, the data in Table 6 provide quantitative information. However, these are percentage values and not energies of stabiliza-... 

Fig. 19 n-Spin-density distribution in diphenylcarbene [15 m= ] determined by ENDOR experiments and MO calculations. The o-spin density at the divalent carbon is in parentheses. 

A) BLYP/DZVP optimized cluster model of the active centre of D. gigas [NiFe] hydrogenase and (B) contour plot at 0.005 e/a.u. of the unpaired spin density distribution in the active centre of D. gigas [NiFe] hydrogenase... 

---