Line fast exchange

Figure B2.4.5. Simulated lineshapes for an intennolecular exchange reaction in which the bond joining two strongly coupled nuclei breaks and re-fomis at a series of rates, given beside tlie lineshape. In slow exchange, the typical spectrum of an AB spin system is shown. In the limit of fast exchange, the spectrum consists of two lines at tlie two chemical shifts and all the coupling has disappeared.

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 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. 

Mechanistic details are very similar for DMSO and water exchange. The reaction proceeds through a distorted trigonal bipyramidal reactive intermediate [Li(DMSO)5]+ that is reached via a late transition state. The enthalpy profile (see Fig. 13) is in line with the experimentally observed very fast exchange process. The five-coordinate intermediate is computed to be 7.9kcalmol 1 less stable than [Li(DMS0)4]+ and free DMSO, while an overall activation barrier of only 8.4kcalmol 1 is computed. Obviously,... 

The HCN exchange itself proceeds through a trigonal bipyr-amidal intermediate [Li(NCH)5]+ reached via a late transition state. The entering HCN molecule approaches the lithium cation directly, and pushes three coordinated solvent molecules away toward the equatorial positions. In line with the experimental observation of a very fast exchange process, the computed... 

Fig. 13. Observed and calculated pH dependence of 54.227 MHz 170 signal for the W(IV) complex (a) linewidth (oxo fast exchange ). Dashed lines 1 and 2 illustrate how the limiting value of kih was determined (6). (b) Chemical shift (oxo aqua/...

It is important to note that Eqs. (9)-(12) are valid only for very fast exchange. If the exchange is somewhat slower ( moderately fast exchange), there will be an exchange contribution to the line width, and Eq. (10) for the ligand resonance2 will be replaced by... 

In fast exchange, we must measure Tz for the coalesced line, and then calculate the exchange rates from that. Standard CPMG and Tip methods may be difficult to implement, but the offset-saturation experiment can be done on essentially any spectrometer. These Tz measurements can often extend the high-temperature side of the Eyring plot by substantial amounts, particularly in the case of unequally populated systems. Taken together with the other methods, they provide excellent data. 

In the case of fast exchange, the NMR rate constants were determined using a computer program that calculated rates, populations, and chemical shifts by nonlinear least-squares fitting of NMR line-shape data to the GMS equation (15). 

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. 

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