Dipolar relaxation and nuclear Overhauser effects in nonrigid molecules: The effect of fluctuating internuclear distances

Abstract

A simple treatment of the dipolar contribution to nuclear magnetic relaxation is developed for molecules in which conformational fluctuations modulate the relevant internuclear distances. Expressions are given for AX system spectral densities using a general model in which conformational fluctuations occur as random jumps among discrete conformations, while the molecule as a whole undergoes rotational diffusion as either a spherical or a symmetric top. Approximations valid for proton spin systems are given for cases in which the jumping rates are either fast or slow compared to rotational diffusion; the results are independent of the jumping rates. Similar results are obtained for cross‐correlation spectral densities. For complex spin systems, e.g., A_n1M_n2X_n3..., the cross‐relaxation constants σ_ij which couple pairs of magnetizations, depend only upon autocorrelation, spectral densities and are thus easily obtained from the AX system results. Measurement of σ_ij by time resolved Overhauser effect experiments is discussed with special attention to the problems raised by dipolar cross‐correlation and spin diffusion. Numerical calculations of σ_ij are given for several geometries describing dipolar relaxation of a rotating methyl proton, and a fixed nonmethyl proton in a slowly tumbling macromolecule.