Spin populations

One can note some interesting features from these trajectories. For example, the Mulliken population on the participating atoms in Figure 1 show that the departing deuterium canies a full electron. Also, the deuterium transferred to the NHj undergoes an initial substantial bond stretch with the up spin and down spin populations separating so that the system temporarily looks like a biradical before it settles into a normal closed-shell behavior. 

While the locations of the spins are not random - indeed, the spins populate sites of a regular lattice - the interactions themselves are completely random. Frustration, too, has been retained. Thus, arguably, two of the three fundamental properties of real spin glass systems are satisfied. What remains to be seen, of course, is the extent to which this simplified model retains the overall physics. 

Table 9. High-spin populations, rate constants fcm for the intersystem crossing in [Fe(acpa)2]BPh4-H20 according to a numerical simulation of the Mossbauer spectra"...

There is a second relaxation process, called spin-spin (or transverse) relaxation, at a rate controlled by the spin-spin relaxation time T2. It governs the evolution of the xy magnetisation toward its equilibrium value, which is zero. In the fluid state with fast motion and extreme narrowing 7) and T2 are equal in the solid state with slow motion and full line broadening T2 becomes much shorter than 7). The so-called 180° pulse which inverts the spin population present immediately prior to the pulse is important for the accurate determination of T and the true T2 value. The spin-spin relaxation time calculated from the experimental line widths is called T2 the ideal NMR line shape is Lorentzian and its FWHH is controlled by T2. Unlike chemical shifts and spin-spin coupling constants, relaxation times are not directly related to molecular structure, but depend on molecular mobility. 

Table 2. m-NPIN spin populations in the wave function modeling. 

An approach to solving the inverse Fourier problem is to reconstruct a parametrized spin density based on axially symmetrical p orbitals (pz orbitals) centered on all the atoms of the molecule (wave function modeling). In the model which was actually used, the spin populations of corresponding atoms of A and B were constrained to be equal. The averaged populations thus refined are displayed in Table 2. Most of the spin density lies on the 01, N1 and N2 atoms. However, the agreement obtained between observed and calculated data (x2 = 2.1) indicates that this model is not completely satisfactory. 

Supersilyl substituents also stabilize negative charges extremely well In the radical anion of 1,4-di(tris(trimethylsilyl)silyl)benzene - as proven by ESR/ENDOR coupling constants [5a,c] augmented by HMO estimates for the "blind" centers (2 O) [5a,c] - more than half of the it spin population p is located in its Si(SiR3)3 groups. 

The hexaphenyldilead radical anion almost certainly has a similar structure since the g values are all less than 2.0023. Calculation of the unpaired spin population in the lead 6s and 6p orbitals leads to values of 0.11 and 0.99. Once again the spin population is too large, especially for the 6p orbital. Nevertheless, the calculations do show that the spin density is probably entirely associated with the lead atoms. 

The earliest of the magnetization transfer experiments is the spin population inversion (SPI) experiment [27]. By selectively irradiating and inverting one of the 13C satellites of a proton resonance, the recorded proton spectrum is correspondingly perturbed and enhanced. Experiments of this type have been successfully utilized to solve complex structural assignments. They also form the basis for 2D-heteronuclear chemical shift correlation experiments that are discussed in more detail later in this chapter. 

Figure 10.2 Representation of excess spin population expressed as a bulk magnetization vector M ...

Methyl tricyclo[4.1.0.0 ]heptane-l-carboxylate gives a cation-radical in which the spin density is almost completely localized on C-1 while the positive charge is on C-7. The revealed structural feature of the intermediate cation-radical fairly explains the regioselectivity of N,N-dichlorobenzenesulfonamide addition to the molecular precursor of this cation-radical. In the reaction mentioned, the nucleophilic nitrogen atom of the reactant adds to electrophilic C-7, and the chlorine radical attacks C-1 whose spin population is maximal (Zverev and Vasin 1998, 2000). 

Both theory and experiment point to an almost perpendicular orientation of the two butadiene H2C=C(t-Bu) moieties (see Scheme 3.53). On passing from the neutral molecule to its anion-radical, this orthogonal orientation should flatten because the LUMO of 1,3-butadiene is bonding between C-2 and C-3. Therefore, C2-C3 bond should be considerably strengthened after the anion-radical formation. The anion-radical will acquire the cisoidal conformation. This conformation places two bulky tert-butyl substituents on one side of the molecule, so that the alkali metal counterion (M+) can approach the anion-radical from the other side. In this case, the cation will detain spin density in the localized part of the molecular skeleton. A direct transfer of the spin population from the SOMO of the anion-radical into the alkali cation has been proven (Gerson et al. 1998). 

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