NMR line shapes for exchanging systems at high rf field

A method is described by which NMR line shapes at high rf may be calculated for chemically exchanging systems. First order exchange results in a set of manifestly linear density matrix equations that are solved with standard methods. Second order exchanging systems, a model example of which is considered here, give rise to second order density matrix equations. Inspection of sample values of density matrix elements reveals that products of off-diagonal elements are small enough to drop from the equations, while products of off-diagonal and diagonal elements, respectively, may be linearized as ρi jAρk,kB=ρi jA/n B. This selective neglect of bilinear terms (SNOB) leads to a set of first order density matrix equations. Inspection of the calculated line shapes reveals that NMR at high rf in exchanging systems allows more precise determination of rate constants for exchange (compared to low power) in the slow, and, in a limited sense, in the fast exchange limits.