Theoretical study of R(1rho) rotating-frame and R2 free-precession relaxation in the presence of n-site chemical exchange.

The n-site Bloch-McConnell equations describe the evolution of nuclear spin magnetization in the laboratory or rotating frames of reference for molecules subject to chemical or conformational interconversions between n species with distinct NMR chemical shifts. Perturbation theory is used to approximate the largest eigenvalue of the Bloch-McConnell equations and obtain analytical expressions for the rotating-frame relaxation rate constant and for the laboratory frame resonance frequency and transverse relaxation rate constant. The perturbation treatment is valid whenever the population of one site is dominant. The new results are generally applicable to investigations of kinetic processes by NMR spectroscopy.