Effect of the frequency of intramolecular motions on the NMR relaxation in liquid state temperature regime

Abstract

Equations for the spectral densities of complex motion of a spin pair undergoing internal motion and isotropic/anisotropic overall rotation have been considered. The fluctuations of the interproton distances, caused by internal motion, have been taken into account in the theoretical equations. A method allowing a distinction between the isotropic and the anisotropic overall rotation of molecules has been proposed. The effect of the activation parameters of internal motions (known from the solid state study) on the measured T ₁ relaxation of the ¹³C and ¹H–¹H cross-relaxation rates has been analysed for methyl-β-D-galactopyranoside in DMSO-d6 solution. The conformational trans-gauche jumps of the methylene group are not fast enough to affect the T ₁ value of carbon C6 in the liquid state temperatures regime. Only the methyl group rotation is a very fast internal motion. This motion influences the carbon C7 relaxation and methyl protons–anomeric proton cross-relaxation. The values of interatomic distances between anomeric H(C1) and H(C5) as well as the three methyl protons H(C7) have been calculated from the cross-relaxation rates. The distance H(C1)–H(C7) fluctuates due to the rotation of methyl group. The application of the ‘model-free approach’ to study molecular dynamics in solutions is discussed.

Keywords:

• spectral densities of complex molecular motion
• activation parameters of internal motions
• interatomic distances
• model-free approach
• ¹³C T₁ NMR relaxation
• NOE cross-relaxation rate
• dynamics of mono-saccharide in solution

Acknowledgements

This paper is dedicated to the memory of the NMR relaxation specialist Donald Eduard Woessner (1930–2008).

Notes

Note

1. The spectral density due to the complex motion which is a combination of the fully anisotropic overall molecular tumbling with the internal motion has been recently published in 36,37. The formulas obtained in these papers (Equation (15) in 36) seem to be incorrect, because the authors have neglected the space averaging of the products of the random functions. They wrote , while it should be .