Carbon‐13 spin–lattice relaxation of tropane alkaloids. II—models for isotropic, axially symmetric and fully anisotropic overall rotational diffusion with diffusional or three‐state jump internal motion, and their application to the N‐methyl groups of tropine and pseudotropine

Abstract

Models for isotropic, axially symmetric and fully anisotropic overall rotational diffusion with single difhional or three-state internal motion are reviewed or derived and applied to uC spin-lattice relaxation data for the N-methyl groups of tropine and psendotropine. The results are compared. Complete equations containing the dependence on the equilibrium positions are given for the three-state jump models. Despite the considerable approximations which these models imply, they are able to predict the expected features of the internal N-methyl group motion in tropine and pseudotropine: hindered three-state jumping, which is of the same rate for tropine and pseudotropine and which is moderately independent of concentration and the model for overall motion. Although the nitrogen inversion in these compounds is slow compared with methyl rotation, and does not affect the relaxation, the equations are also derived for double internal motion where the internal rotation axis jumps between two non-equivalent sites having an arbitrary but fixed orientation within the molecule, and where the innermost internal motion is diftusional or jumpwise as in single internal motion. Some considerations regarding the units of the rotational diffusion constants, errors in measurements, and the reduction of the equations for fully anisotropic overall motion to equations for axially symmetric and, further, for isotropic overall motion are presented.KEY WORDS 13C NMR Spin-lattice relaxation data Tropine Pseudotropine Rotational diffusion.