Calculation of dipolar nuclear magnetic relaxation times in molecules with multiple internal rotations

Author： Levine Y.K. Partington P. Roberts G.C.K.

ISSN： 1362-3028

Source： Molecular Physics, Vol.25, Iss.3, 1973-03, pp. : 497-514

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

A general method is described for calculating angular autocorrelation functions and thence longitudinal and transverse dipolar nuclear magnetic relaxation times ( T 1 and T 2 ) for nuclei in a methylene group of a hydrocarbon chain attached to a spherical molecule. The method is applicable for any value of the rotational diffusion coefficient of the molecule ( D 0 ), and for any length of chain. Numerical results for autocorrelation functions and for 13 C, 1 H and 19 F dipolar relaxation times are presented. These show that for atoms more than four carbon-carbon bonds removed from the isotropically tumbling molecule the autocorrelation function is a single exponential and the relaxation times are independent of the motion of the molecule, provided that D i > D 0 (where D i is the diffusion coefficient for rotation about the i th carbon-carbon bond). For the first few methylene groups in the chain, the auto-correlation function is not a single exponential, and the relaxation times show more complex behaviour. In particular, under the condition. where &ohgr; is the relevant Larmor frequency for the dipolar interaction under consideration, the following phenomena are predicted for nuclei on the first three or four methylene groups: (i) As the rate of internal motion increases, the spin-lattice relaxation time first decreases, then passes through a minimum and increases to a value determined by the rotational diffusion of the molecule as a whole. This behaviour has been indicated previously by Doddrell et al. [11] for the particular case of a single internal motion. (ii) Even if the spin-lattice relaxation time, T 1 , increases with increasing temperature, indicating that &ohgr; 2 τ app 2 < 1 (where τ app is the apparent correlation time calculated from the T 1 value) T 1 will be longer than T 2 . (iii) Even if, again &ohgr; 2 τ app < 1 under some circumstances increasing motion can lead to a decrease in T 1 . Thus the proton T 1 of the first methylene may be longer than that of the second methylene group in the chain. Finally, methods for calculating the diffusion coefficients, D i , from measured relaxation times, and extensions of the theory to fluorescence polarization and E.S.R. spin-label experiments are briefly discussed.