Relaxation cross

Lightman A., Ben-Reuven A. Line mixing by collisions in the far-infrared spectrum of ammonia, J. Chem. Phys. 50, 351-3 (1969) Cross relaxation in the rotational inversion doublets of ammonia in the far infrared, J. Quant. Spectrosc. Radiat. Transfer 12, 449-54 (1972). 

The first example of chemically induced multiplet polarization was observed on treatment of a solution of n-butyl bromide and n-butyl lithium in hexane with a little ether to initiate reaction by depolymerizing the organometallic compound (Ward and Lawler, 1967). Polarization (E/A) of the protons on carbon atoms 1 and 2 in the 1-butene produced was observed and taken as evidence of the correctness of an earlier suggestion (Bryce-Smith, 1956) that radical intermediates are involved in this elimination. Similar observations were made in the reaction of t-butyl lithium with n-butyl bromide when both 1-butene and isobutene were found to be polarized. The observations were particularly significant because multiplet polarization could not be explained by the electron-nuclear cross-relaxation theory of CIDNP then being advanced to explain net polarization (Lawler, 1967 Bargon and Fischer, 1967). 

A single-quantum transition involves one spin only, whereas the zero- and doublequantum transitions involve two spins at the same time. The zero- and double-quantum transitions give rise to cross-relaxation pathways, which provide an efficient mechanism for dipole-dipole relaxation. 

Nevertheless, the overall structural problem can be solved from combined n.O.e. and single-selective relaxation-measurements through the evaluation of individual cross-relaxation terms, (Ty. According to Noggle and Shirmer, the n.O.e. value is a function of the cross-relaxation between spins i and j and the relaxation contributions of the neighboring protons to spin i, that is. 

According to these equations, the effect of selectively perturbing the spin states of spins i and j is to isolate the cross-relaxation paths common to these two spins. Combining Eqs. 15 and 19, the individual cross-relaxation terms are readily determined from single-selective and double-selective relaxation-rate measurements, that is. 

Because it is reasonable to expect that Eq. 11 holds true, a more realistic experimental measure of the cross-relaxation between spins i and J would be... 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

The relaxation data for the anomeric protons of the polysaccharides (see Table II) lack utility, inasmuch as the / ,(ns) values are identical within experimental error. Obviously, the distribution of correlation times associated with backbone and side-chain motions, complex patterns of intramolecular interaction, and significant cross-relaxation and cross-correlation effects dramatically lessen the diagnostic potential of these relaxation rates. 

While the final magnitude of nOe depends, as indicated earlier, on the relaxation pathways Wi, W, and W), the initial rate of buildup of nOe (transient nOe) depends only on the rate of cross-relaxation between the nuclei, and this can provide valuable information about the distance between the nuclei (r). This rate of buildup can be proportional to r" , where r is the distance between the nuclei. Thus, if the proportionality constant is determined, we can calculate an approximate distance between the two nuclei. The best results are obtained in rigid molecules when the nuclei are less than 3 A apart. If only direct nOe s are involved in a two-spin... 

The positive nOe observed in small molecules in nonviscous solution is mainly due to double-quantum relaxation, whereas the negative nOe observed for macromolecules in viscous solution is due to the predominance of the zero-quantum 1% cross-relaxation pathway. 

Transient nOe represents the rate of nOe buildup. The nOe effect (so-called equilibrium value) itself depends only on the competing balance between various complex relaxation pathways. But the initial rate at which the nOe grows (so-called transient nOe) depends only on the rate of cross-relaxation t, between the relevant dipolarly coupled nuclei, which in turn depends on their internuclear distance (r). 

Three-spin effects arise when the nonequilibrium population of an enhanced spin itself acts to disturb the equilibrium of other spins nearby. For example, in a three-spin system, saturation of spin A alters the population of spin B from its equilibrium value by cross-relaxation with A. This change in turn disturbs the whole balance of relaxation at B, including its cross-relaxation with C, so that its population disturbance is ultimately transmitted also to C. This is the basic mechanism of indirect nOe, or the three-spin effect. 

Cross-relaxation The mutual intermolecular or intramolecular relaxation of magnetically equivalent nuclei, e.g., through dipolar relaxation. This forms the basis of nOe experiments. 

Fig. 9.1 The internuclear transfer of magnetization via NOE cross-relaxation in an isolated spin-pair. (A) Build-up curves for the cross-peak intensity in a 2D NOESY experiment for various internuclear distances r. The dashed line indicates a typical mixing time tm = 300rns used for drug-like molecules.

For the simulation a correlation time 1 =0.1 ns is assumed for two protons at cOo=600MHz. (B) Maximum transfer efficiency for an isolated proton spin pair calculated using only dipolar relaxation processes. Note the sign change for the NOE cross-relaxation at cOo Uc=l -12. 

The accuracy of obtained cross-relaxation rates and therefore the derived distance restraints is influenced by many practical aspects. A critical point is the... 

Fig. 9.2 Schematic representation of the three basic experiments useful for the determination of (A) transient NOE experiment, (B) 2D NOESY and (C) 2D ROESY. The gray-filled half-circle represents a frequency-selective inversion pulse which inverts the spin to which the cross-relaxation...

---