Slow-exchange limit

Moderately slow exchange. The state lifetime is 2t we ask how the absorption band is affected as this becomes smaller. The uncertainty principle argument given earlier is applicable here lifetime broadening will occur as the state lifetime decreases. Thus, we expect resonance absorption at (or near) frequencies Va nnd Vb but the bands will be broader than in the very slow exchange limit. Equation (4-68) is applicable in this regime. 

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.

In the slow exchange limit, where 22 > A2, two Lorentzians, centered at cb + A and bb — A, respectively, are observed with width 2/Tf + 20. The exchange imposed by the molecular motion thus causes an extra broadening of the lines observed in absence of motion. 

Certain other metal ions also exhibit catalysis in aqueous solution. Two important criteria are rate of ligand exchange and the acidity of the metal hydrate. Metal hydrates that are too acidic lead to hydrolysis of the silyl enol ether, whereas slow exchange limits the ability of catalysis to compete with other processes. Indium(III) chloride is a borderline catalysts by these criteria, but nevertheless is effective. The optimum solvent is 95 5 isopropanol-water. Under these conditions, the reaction is syn selective, suggesting a cyclic TS.63... 

The absorption signal, of course, is the imaginary part of eqn (5.18) the equation is too horrible to contemplate, but computer-simulations, such as those shown in Figures 5.3 and 5.4, are relatively easy to produce. There are two limiting cases where the equations are easier to understand. In the slow exchange limit, where xA-1 and xB 1 are both small compared with ooA - ooBl, the... 

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. 

Since acetone is a reasonable model for benzaldehyde, the presence of Complex I provides support for Step 3a. (A resolved A2B2X pattern cannot be reached using benzaldehyde since the solvent freezes before the slow exchange limit is achieved however, exchange broadening is evident.) Although additional experiments are needed to establish the presence of Complex I at higher temperatures, the fact that Complex I is the only species observed at low temperature... 

Cases III and IV represent the slow exchange limits for longitudinal (III) and transverse (IV) relaxation enhancements. The observed enhancements are proportional to the exchange rate, independently of the values of R m and R2m-... 

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... 

Carbon-13 NMR spectra for the cyclic phosphate (8) over a temperature range of 25 °C to — 113°C show that a slow exchange limit is reached at which the low-field signals due to equatorial methoxy carbons are twice as intense as the resonances at higher field due to the apical methoxy group. This means the 1,3,2-dioxaphosphorinane ring is attached apical/equatorial and not diequa-torial. 

Fig. 11. Schematic representation of the six possible diastereoisomeric geometries the symmetry point group and expected number of TV-methyl NMR signals at the slow exchange limit for complexes with X = Y and for X Y are given under each structure.45 Reproduced with permission from the American Chemical Society.

Let us investigate what happens to the NMR spectrum of DMF as we increase the exchange ratio from the slow-exchange limit to the fast-exchange limit. 

When R is less than 0.1, the system is essentially frozen at the slow-exchange limit, and Eq. (10.1) predicts two sharp signals, one at vA, the other at vB (Figure 10.1, R = 0.10). The halfwidth of these signals (v /2 is the inverse of the effective spin-spin relaxation time. 

Figure 10.1. The NMR lineshape for exchange between two equally populated sites [Eq. (10.1)] as a function of exchange ratio R. The following conditions are shown the slow-exchange limit (R = 0.10), moderately slow exchange (R = 2.66), coalescence (R = 4.44), moderately fast exchange (R = 8.90), and approaching the fast-exchange limit (R = 50).

Alas, there is a fly in the ointment. Equations (10.14)-(10.16) all require that both H and 5C be known. Although the former is easily determined by direct measurement in the absence of a guest, the latter cannot usually be determined directly for two reasons. First, the rate constants for com-plexation and decomplexation [k] and k y Eq. (10.9)] are often very large, making it impossible to reach the slow-exchange limit. Second, unless the value of K is substantially greater than 10, it may be difficult to approach the 5C limit of 8 at any readily attainable ratio of [G]0 to [H]0 (see Figure 10.3, lines A, B, and C). So, we are left with one equation [Eq. (10.15) or (10.16)] with two unknown parameters, 5C and K. 

It is important to be aware of certain assumptions that are implicit in the derivation of the above equations. Most importantly, it is assumed that 5C and 8H are themselves independent of concentration and temperature effects. While this can often be experimentally verified for 8H, it is generally impossible to verify for 5C unless the slow-exchange limit can be attained. Another potential error is the failure to include activity coefficients in the equilibrium expressions, even though concentrations often exceed 1 M. Since iterative nonlinear curve fitting often involves locating a relatively shallow minimum, effects such as these can lead to significant error in derived K. 

---