The line-shape analysis of nuclear magnetic resonance peaks broadened by the presence of a 'hidden' exchange partner

Abstract

In nmr spectroscopy involving organic substrates, one often has a situation in which there is a dominant species in rapid equilibrium with one or more minor components. In general, one knows, a priori, neither the population of these minor components nor the rate constants involved in the equilibrium process. In fact, from the physical appearance of these spectra, one cannot normally even deduce that such an equilibrium exists. For example, in cases involving 13C nmr spectroscopy, this minor component may not be observable under slow exchange nmr conditions because of signal-to-noise ratio problems and hence is referred to as a 'hidden' exchange partner. In this paper, we have analyzed the extent of nmr line broadening to be expected from a two-component system of this type, varying the populations, chemical shift separations, and intrinsic line widths. Thus, the presence of a 'hidden' partner can sometimes be detected by a characteristic, but often very subtle, peak broadening–resharpening sequence involving first of all the 'averaged' peak and finally the peak of the dominant component, these peaks being virtually identical in area and very similar in chemical shift so that one is not easily alerted. Assuming there is some experimental line broadening, equations developed in this paper, together with chemical shift estimates for this 'hidden' partner, allow one to quickly estimate both the amount of the minor partner and the rate constant involved. Three 'real life' situations are subsequently analyzed.