Spin distribution

The ESR spectra of a large variety of sulfonyl radicals have been obtained photolytically in liquid phase over a wide range of temperature. Some selected data are summarized in Table 2. The magnitudes of hyperfine splittings and the observations of line broadening resulting from restricted rotation about the C—S bond have been used successfully in conjunction with INDO SCF MO calculations to elucidate both structure and conformational properties. Thus the spin distribution in these species is typical of (T-radicals with a pyramidal center at sulfur and in accord with the solid-state ESR data. 

The effect can be applied, for example, to estimate a bond length or atomic spacing, to observe valence electron spin distribution around a specific atom and to derive information of the nearest neighbor atom distribution in a disordered system such as amorphous, under an expansion of the theory. 

FIGURE 9.4 Unpaired spin distribution for zeaxanthin (left) and violaxanthin (right) radicals. From up to down Zea-+, Zea (4), Zea (5) and Vio +, Vio (4), Vio (5), respectively. The black represents excess a and the dark gray excess 3 unpaired spin density. (Adapted from Focsan, A.L. et al., J. Phys. Chem. B, 112, 1806, 2008. With permission.)... 

Let us first consider the charge and spin distributions for atoms and ions of the first transition series (M = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn). The neutral ground-state TM electron configurations are of generic form s2d , except at n = 4 (Cr sM5) and n = 9 (Cu s d1") where the well-known anomalies associated with the special stability of half-filled and filled d shells are manifested. The simplest picture of ionic bonding therefore involves metal ionization from an s orbital to give the... 

Let us first consider the charge and spin distributions in TM monofluorides MF for the first transition series. Calculated geometrical and energetic properties of these species are summarized in Table 2.3. 

In a similar fashion the bonding in H2 might be formally regarded as a complementary pair of one-electron donor-acceptor interactions, one in the ot (spin up ) and the other in the 3 (spin down ) spin set.8 In the long-range diradical or spin-polarized portion of the potential-energy curve, the electrons of ot and (3 spin are localized on opposite atoms (say, at on HA and 3 on HB), in accordance with the asymptotic dissociation into neutral atoms. However as R diminishes, the ot electron begins to delocalize into the vacant lsB(a) spin-orbital on HB, while (3 simultaneously delocalizes into Isa on HA, until the ot and (3 occupancies on each atom become equalized near R = 1.4 A, as shown in Fig. 3.3. These one-electron delocalizations are formally very similar to the two-electron ( dative ) delocalizations discussed in Chapter 2, and they culminate as before (cf. Fig. 2.9) in an ionic-covalent transition to a completely delocalized two-center spin distribution at... 

In a basic pulsed NMR experiment (for I = 1/2), when a sample is placed in the applied magnetic field (B0), the nuclear spins distribute themselves between parallel and antiparallel positions, according to Boltzmann distribution [Eq. (11)] (Figure 21 A). The number of spins in the parallel position is slightly greater than that in the antiparallel position. At equilibrium, the spins are processing randomly (i.e., lack phase coherence). The populations... 

The Arrhenius parameters for the reaction of the persistent (CF3)2NO-radical with n-Bu3SiH also were determined by ESR spectroscopy (Table V).72 It has been suggested that the unusually low preexponential factor is due to geometric constraints on the transition state. The similar reactivities of (CF3)2NO- and PhCMe200- radicals toward n-Bu3SiH and Ph3SiH, respectively, are expected because both the thermochemistries and spin distributions for these two radicals are rather similar.72,73... 

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-... 

The spin distribution in the lower homologue [15 w = 2] was most elegantly studied by Takui et al. (1989) by means of a combination of ENDOR experiments and theoretical calculations within the framework of a generalized UHF Hubbard model (Teki et al., 1987a) and a Heisenberg model (Teki et al., 1987b). The spin distribution obtained is just as expected qualitatively in Fig. 7. 

In [16e-h] it appears that, since the spin delocalization is considerable, the radicals must be kinetically less stable at sites other than the original radical centre where there is no steric protection. Therefore, it was difficult to obtain samples that contain satisfactory spin concentrations. In [16j] and [16k], by contrast, the spin distribution seems not to be extensive and so the kinetic stability of the radical centres must be well protected. 

The effect of the sulfone dipole on the ESR spectrum of the dibenzothiophene 5,5-dioxide anion has been examined, modified Hiickel calculations which ignored d-orbital conjugation predicting spin distributions which agreed with experimental data. Proton hyperfine splitting constants have also been obtained for the sulfone. Correlation with MO calculations shows that the sulfone group contributes a vacant symmetric orbital to the conjugated system. ... 

---