Spin distance dependence

In a second attempt to obtain more insight into the binding location of the dienophile and now also the diene, we have made use of the influence of paramagnetic ions on the spin-lattice relaxation rates of species in their proximity. Qose to these ions the spin-lattice relaxation rate is dramatically enhanced. This effect is highly distance-dependent as is expressed by Equation 5.7, describing the spin-lattice... 

In an isolated two-spin system, the NOE (or, more accurately, the slope of its buildup) depends simply on where d is the distance between two protons. The difficulties in the interpretation of the NOE originate in deviations from this simple distance dependence of the NOE buildup (due to spin diffusion caused by other nearby protons, and internal dynamics) and from possible ambiguities in its assignment to a specific proton pair. Mofec-ufar modeling methods to deaf with these difficulties are discussed further below. 

Depending on experimental parameters, NOE intensities will be affected by spin diffusion (Eig. 8). Magnetization can be transferred between two protons via third protons such that the NOE between the two protons is increased and may be observed even when the distance between the two protons is above the usual experimental limit. This is a consequence of the distance dependence of the NOE. Depending on the conformation, it can be more efficient to move magnetization over intennediate protons than directly. The treatment of spin diffusion during structure refinement is reviewed in more detail in Refs. 31, and 71-73. 

The [Ni(NCS)f,]4 ion is almost perfectly octahedral, with Ni—N distances of around 209.5 pm and N—Ni—N angles around 89.5°. The Ni—N—C and N—C—S entities are practically linear.438,439 In [Ni(NCS)2L2] where L is a R-substituted pyridine, stereochemistry and spin state depend on the type and positions of R.431 While for 2-Me- and 2-Et-pyridine square planar complexes are observed, other pyridins lead to coordination polymers with pseudo-octahedral Ni11 due to N,S-bridging thiocyanate. Ni11 thiocyanato complexes have been studied quite intensively as hosts for inclusion compounds.440"442... 

In the absence of an endogenous centre, the specificity of relaxation data can be improved by introducing in known positions paramagnetic probes. The unpaired electron spin enhances the relaxation rate of the surrounding nuclei in a distance-dependent fashion. In this way, it is possible to evaluate specific interaction sites between a marked polymer and the small molecules. 

The magnitude of the paramagnetic relaxation enhancement (PRE) caused by dipolar interactions depends on the square of the gyromagnetic ratios of both involved spins, the inverse sixth power of the inter-spin distance, and the correlation time rc of the vector connecting the two spins. For the transverse relaxation rate enhancement, R2para of a spin I,... 

Since dipolar interaction is a distance-dependent interaction, the heteronuclear interaction between spins 1 and S can be exploited to get information about the distance between these nuclei. Heteronuclear dipolar interactions that are averaged by magic angle spiiming can be reintroduced by suitable dephasing pulses that are synchronized with the sample spinning. It is a difference spectroscopy... 

This is plotted in the right-hand panel of Fig. 3.8 as a function of I/2 h. Remembering that h(R) - 0 as R - oo, we see that it shows the same square root distance-dependence as that displayed by the numerical self-consistent solution of the local spin density functional Schrddinger equation in Fig. 3.6. Thus, as the hydrogen molecule is pulled apart, it moves from the singlet state S = 0 at equilibrium to the isolated free atoms in doublet states with S = 2-... 

H is particularly important in NMR experiments because of its high sensitivity and natural abundance. For macromolecules, 1H NMR spectra can become quite complicated. Even a small protein has hundreds of 1H atoms, typically resulting in a one-dimensional NMR spectrum too complex for analysis. Structural analysis of proteins became possible with the advent of two-dimensional NMR techniques (Fig. 3). These methods allow measurement of distance-dependent coupling of nuclear spins in nearby atoms through space (the nuclear Overhauser effect (NOE), in a method dubbed NOESY) or the coupling of nuclear spins in atoms connected by covalent bonds (total correlation spectroscopy, or TOCSY). 

Loss of airflow through a finned tube air cooler bundle is a universal problem. The effect is to reduce the exchanger s cooling efficiency. To restore cooling, you might wish to try the Norm Lieberman method, which consists of reversing the polarity of the fan motor electric leads. The fan will now spin backward. Depending on the nature of the deposits, a portion of the accumulated dirt will be blown off the tubes— but all over the unit. Personnel observe this procedure from a safe distance. 

When tr is unknown, it can be adjusted together with re and r by using non-linear least-squares fits of eqs. (15), (16) as similarly described for the treatment of NMRD profiles (Bertini et al., 1995 Ruloff et al., 1998 Toth et al., 1998), but a much simpler approach considers that both dipolar and Curie-spin contribution depend on r 6. When a nucleus for which the / -nucleus distance rref can be estimated either from crystal structure or gas-phase modeling is used as a reference, eq. (15) reduces to its simplest form (eq. (18)) and relative /Gnucleus i distances are accessible without estimations of re and rr (Barry et al., 1971 ... 

Where the Schrodinger or Dirac equations apply, quantization will appear from sundry mathematical conditions on the existence of physically meaningful solutions to these differential equations. However, in nonrela-tivistic terms, spin does not come from a differential equation It comes from the assumptions of spin matrices, or from "necessity" (the Dirac equation does yield spin = 1/2 solutions, but not for higher spin). So we must posit quantum numbers (see Section 2.12) even when there are no differential equations in the back to "comfort us." This is especially true for the weak and strong forces, where no distance-dependent potential energy functions have been developed. 

Recently many modifications of pulse ESR have been designed that allow to improve the distances measurement accuracy and to expand range of distance available for ESR spectroscopy (Eaton et al., 2000 Eaton et al., 2000 Freed, 2000 (Milov et al., 1998) Maret, 1993 and references herein). The principle advances of such the pulse methods is the direct determination of spin-relaxation parameters which, in turn, directly related to spin-spin interactions depending on distances. 

The geminal H-Si-N spin-spin interaction depends also on Si-N distance the ionization process discussed above (Eq. 17) causes bond shortening. Scheme 3 demonstrates the effect of ionization (and resulting... 

In general. Tie > T2e and the line width depends mainly on spin-spin interactions. T2e increases on decreasing the spin concentration, that is, the spin-spin distance in the system. On the other hand when Tie becomes very short, below roughly 10 sec, its effect on the lifetime of a species in a given energy level makes an important contribution to the linewidth. In some cases the EPR lines are broadened beyond detection. 

Early studies of the distance dependence of ET dynamics focused on intramolecular electron-spin transfer in radical anions containing two equivalent Ti-moieties separated by a hydrocarbon bridge (Figure 8). One of these moieties, which houses the unpaired electron, functions as the donor, while the other (neutral) is an acceptor. ESR studies of the radieal anions of a, ct -diarylalkanes, Ar-(CH2) -Ar 1( ) and re-... 

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