On the Use of the Stochastic Liouville Equation in Nuclear Magnetic Resonance: Application to R1 Relaxation in the Presence of Exchange

The nuclear magnetic resonance (NMR) spin relaxation rate constant in the rotating frame of reference R1 provides information on microsecond to millisecond ( s-ms) timescale kinetic processes that stochastically modulate the resonance frequencies of nuclear spins in molecules. Expressions for R1 are presented for two-site chemical exchange using both the conventional perturbation approach for evolution of the density operator in the interaction frame of reference and the stochastic Liouville equation (SLE) for evolution of the average density operator in the rotating frame of reference. The former approach is limited to the fast-exchange regime, in which the chemical exchange kinetics are faster than the frequency difference between spins in the two sites. The latter approach provides approximate expressions for R1 that are accurate when chemical exchange is not fast. Expressions for R1 that are accurate over the widest range of experimental conditions facilitate the interpretation of chemical exchange phenomena. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part A 19A: 134–148, 2003