Restricted Internal Segmental Rotational Diffusion Model with Segment-Segment Interactions. Application to “C NMR

The restricted rotational-diffusion model developed by Wittebort and S&o (J. Chem. Phys. 69, 1722 (1978)) and London and Avitabile (J. Am. Chem. Sot. 100,7159 (1978)) is extended to include in a mean field sense, dynamic interactions between the diffusing motional unit, and an environment that may have Fourier components on the same time scale as the reorienting unit. Furthermore in contrast to previous work, an exact closed form, analytical expression for the spectral density is derived. Illustrative calculations are presented for the spin-lattice relaxation time, T,, spin-spin relaxation time, T2, and nuclear Overhauser enhancement factor for a 13C nucleus relaxing by a dipolar mechanism with the directly bonded proton; a comparison of r,, rr, and NOE of the weak and strong coupling limits of the segment-segment dynamic interaction model is also made. It is proposed that NMR relaxation experiments be performed over a range of external field strengths H,, to differentiate between a restricted rotational model with and without dynamic interactions.