Nuclear spin–lattice relaxation and complex motion of macromolecules in solution

Abstract

The NMR spectral densities of a complex motion consisting of a combination of anisotropic overall motion and internal motion have been derived. Two approximations of the equations derived for the cases of slow, Jslow (ω), and fast, Jfast (ω), internal motions are presented. These equations imply that reduction in spectral density of overall motion can be observed if the maxima of internal and overall motions spectral densities versus temperature are well separated, as for fast internal motion. Slow intramolecular motion influences the values of spectral densities of the overall motion if one of the two spins performs a motion, for example a proton in double minimum of the 15N-H ··· N hydrogen bond. The analysis presented reveals small differences between the temperature dependencies of spectral densities of the isotropic and anisotropic overall motions. The theory is illustrated by the 13C protonated carbon spin-lattice relaxation of α-cyclodextrin macromolecule, using the expected motional parameters: D ∥/D ⊥ ≈ 5 at room temperature and for a fast or slow internal motion.