Exchange of excess metal ligands

When the paramagnetic site is the least populated, and the difference in population is very large, Eqs. (4.2)-(4.4) can be simplified [3-6]. For example, the chemical shift for the signal in the diamagnetic site evolves as follows as a 

In analogy with the chemical shift, the relaxation rates of the bulk nuclei will be termed / id and Ri. In the presence of chemical exchange with nuclei in the paramagnetic site, such rates will be enhanced by an amount V ip or Rip, and the measured values will be 

1 Note that the equations in Section 2.2 report the paramagnetic shifts ( con, S1, etc.) in ppm. To obtain AcoM (in units of rad s l) one should multiply the shift in ppm by the nuclear Larmor frequency (in MHz), and further multiply by In. For example, a proton experiencing 5con = 3.75 ppm yields Aa u = 3.75 x 500 x 2n = 11,775 rad s-1 when measured in a 500 MHz spectrometer, whereas a deuteron in the same chemical environment yields = 3.75 x 76.75 x 2jt = 1807.5 rads-1, where 76.75 MHz is the deuterium Larmor frequency in a magnetic field corresponding to a 500 MHz proton Larmor frequency. 

The longitudinal relaxation rate enhancement R p goes asymptotically from zero to fMRiM with increasing r 1 (Fig. 4.3A), according to the following equation  

The transverse relaxation rate enhancement / 2P could be treated in the same way if it were not for the difference in chemical shift A com between the paramagnetic and the diamagnetic species. As has already been shown, the difference in chemical shift causes a line broadening — an increasing in R2M — even when the 

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