Fast-exchange limit

Figure 4-8. NMR absorption by a hypothetical two-identical site system with chemical exchange (/I) Slow exchange limit. (B) Moderately slow exchange. (D) Coalescence. (F) Fast exchange limit.

The usable time ranges can be estimated from the following considerations. The slow and fast exchange limits correspond to r-1 relaxation times are roughly 10-3 < r < 1 s for protons, or less for other nuclei with larger (8 v) values. 

In presence of molecular motion the NMR line shape will change. A particularly simple situation arises, if the motion is rapid on timescale defined by the inverse width of the spectrum in absence of motion 6 1. In this fast exchange limit, which in 2H NMR is reached for correlation times tc < 1CT7 s, the motion leads to a partially averaged quadrupole coupling and valuable information about the type of motion can directly be obtained from analysis of the resulting line shapes. The NMR frequency is then given by... 

In the fast exchange limit ft2 A2, a Lorentzian at the centre d>, is observed with full width at half height 2/T + A2/Q. In the ultrafast exchange limit discussed in the previous section, A2/fi 2/T, the line shape becomes independent of the exchange... 

In principle, in both slow and fast exchange limits, the analysis of the ligand-protein interaction could be performed by a direct integration of the two well-separated resonances of free and bound ligand and by the analysis of their chemical shift. However, these methods are limited by the broadness of the protein-ligand NMR spectra, and numerical values of association constants are barely obtainable. 

In the fast exchange limit, where xA 1 and xB 1 are both large compared with coA-coB, the absorption is ... 

In the so-called intermediate exchange region, eqn (5.18) is not easily tractable and recourse is usually made to computer simulations. Qualitatively, however, it is clear that as the rate increases, the separate resonances of the slow exchange limit broaden, shift together, coalesce and then begin to sharpen into the single line of the fast exchange limit. 

The ENDOR data demonstrate that intermolecular interactions dominate the potential function for the ring rotation. The fast exchange limit of V(bz)2 is reached at lower temperatures in Fe(cp)2 than in Cr(bz)2. This is in qualitative agreement with the NMR relaxation results of Campbell et al.280) on the pure host materials. Since a transition temperature of Tc = 79 K is predicted for Fe(cp)2 from the NMR data, one can conclude that the dynamic behavior of the guest molecules is not entirely determined by the host properties alone, but that the guest V(bz)2 introduces a significant local perturbation into the host lattice by its larger size. 

Expressions for determining rate constants from exchange contributions to observed linewidth for unequally populated systems in the fast exchange limit have been derived from the formal solutions to the Bloch equations modified for chemical exchange [3, 127-129]. These equations relate each rate constant to the site populations, chemical shift difference between sites, and spin relaxation times T and T2. For example, the forward rate A i 2 is given by [3, 127] ... 

Pisaniello and Lincoln have made detailed H NMR studies of the amide complexes [ScL6][C104]3 in CD3CN and CD3N02.M With NMF, DMF, N, (V-diethylformamide and 7V,7V-dibutylformamide, exchange between free and bound ligand occurred in the fast exchange limit at all accessible... 

In a study of rates of degenerate 1,2-shifts in tertiary carbocations, Saunders and Kates854 used higher-field (67.9 MHz) 13C NMR line broadening in the fast-exchange limit. The 2-butyl cation showed no broadening at — 140°C. Assuming the hypothetical frozen out chemical shift difference between C(2) and C(3) to be 227 ppm, an upper limit for AG was calculated to be 2.4 kcal mol 1. 

The first palladium alkenyls, pzTpPd C,N-C(Cl) CHCMe2NMe2 (484)144 and the 3-oxo-hexenyl complex 493,160 were obtained systematically by halide displacement and dimer cleavage (Scheme 36). In common with alkyl and aryl systems (462—479, Section III.C.3), the pzTp ligand was in each case concluded to adopt a -coordination mode in solution, on the basis of (i) spectroscopic data, (ii) literature precedent, and (iii) the assumption that the Pd(II) centers in these complexes were too electron rich to permit coordination of the third pyrazole no solid-state data were reported. Both materials are fluxional in solution, and for 484 the slow-exchange limit was attained at —30 °C, with equilibration of the pyrazolyl environments becoming rapid at 79 °C, though the fast exchange limit... 

The H NMR spectra of the related [La(THED)]3+ as a function of temperature reveal a dynamic process at room temperature similar to that observed for [Ln(DOTA)] complexes [143]. At ambient temperature, the 13C NMR spectra (methanol-d, ) consists of two sharp resonances assigned to the pendant arms and one broad resonance attributed to the ethylene ring carbons, which sharpens as the fast exchange limit is approached (ca. 50°C). Likewise, at -20°C the broad resonance resolves into two peaks. The increased flexibility observed for [La(THED)]3+ as compared to DOTA complexes suggests that the pendant groups contribute to the structural rigidity of the macrocyclic ring. 

The a-substituted tropolonates 2 which are tris chelate complexes with a M06 coordination core have received considerable study by DNMR.27, 4S 46) The complexes are of the M(A-B)3 and M(A-B )3 types and therefore the averaging sets of Eaton efa/.26, 27 in Table 1 are applicable. The metal ions and a-R-substituents used in these studies include M = Al(III), Ga(III), Co(III), V(III), Mn(III), Ru(III), Rh(III) and Ge(IV) R = isopropyl (C3H7) and isopropenyl (C3HS), however, only complexes of Al(III), Ga(III), and Co(III) have yielded definitive mechanistic information.27, 45 46> On the basis of line shape changes of the methyl resonances these complexes can be classed kinetically as follows stereochemically nonrigid complexes which attain the fast-exchange limit of inversion and/or isomerization... 

Fig. 3. Calculated NMR lineshapes for equally populated two-site exchange as a function of the dimensionless parameter a = nf rA. The abscissa is the dimensionless relative offset parameter, x = A/// (see Eq. (18)). (a) a = 4 (b) a = 2 (c)a=l (d) a = l/ /2 (e) a = 0.5 (f) a = 0.2. Spectra (a) and (f) are near the slow and fast exchange limits, respectively. Reproduced with permission from R. K. Harris, Nuclear Magnetic Resonance Spectroscopy A Physicochemical View, p. 124, Longman Scientific and Technical, Harlow, 1986.

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