A UNIFIED THEORY OF EXCHANGE EFFECTS ON NUCLEAR MAGNETIC RESONANCE LINE SHAPES

A general theory of line shapes in high-resolution nuclear magnetic resonance spectra of liquids is developed in the framework of the Liouville representation of quantum mechanics. It is shown that both short-memory as well as strong-correlation effects can simultaneously be accounted for in a compact and transparent manner if the full-state vector is projected into a composite Liouville subspace. The equation of motion is governed by a complex non-Hermitian operator that may be broken up into an ordinary Hermitian Liouville operator, a relaxation operator, and an exchange operator. It is demonstrated that the total information content of an unsaturated steady-state nmr spectrum can be contracted into two complex vectors, a radiofrequency-independent “shape vector” and a “spectral vector” which is a trivially simple function of the radiofrequency. A sample calculation for an exchanging three-spin system serves as an illustration of the usefulness of the theory for accurate determinations of rate constants and activation parameters in systems of chemical interest. © 1969, American Chemical Society. All rights reserved.