SPATIAL-ASPECTS OF HOMONUCLEAR, PROTON NMR CROSS-RELAXATION .1. THE EFFECTS OF MOLECULAR SHAPE AND INTERNAL MOTION

A detailed theoretical analysis of longitudinal NMR cross-relaxation for a proton pair attached to molecules with a variety of sizes and shapes is presented. The universally applied rigid isotropic model for calculating cross-relaxation behavior has been extended to treat a rotating proton pair on a spherical molecule and on prolate and oblate ellipsoids and a rigid proton pair on prolate and oblate ellipsoids. The nuclear Overhauser effect enhancement and the time dependence of two-dimensional NMR cross-peak intensity are calculated and compared to the simpler rigid isotropic case. When internal rotation is considered, it is shown that the nuclear Overhauser enhancement depends on the spatial aspects of the proton pair's motion. Likewise, the initial slope of the cross-peak evolution is a function of not only the intemuclear distance but also the geometrical orientation of the proton pair and of rates of global and internal rotation as well. These results differ significantly with use of the rigid isotropic model. When the spatial aspects of motional averaging and internal rotation are ignored, calculated proton intemuclear distances can be overestimated by up to 300%. The classification of cross-relaxation being either in spin-diffusion or extreme-narrowing conditions does not necessarily characterize the rotational motion of the molecule as a whole if more than one rotational correlation time is included in the spectral density terms. Rigid protons in macromolecules such as proteins and small DNA/RNA segments are least sensitive to geometric factors. When internal motion or highly anisotropic global molecular motion is present, accurate interpretation and simulation of cross-relaxation behavior requires the full form of the spectral density functions described here. © 1990, American Chemical Society. All rights reserved.