Nuclear Spin‐Lattice Relaxation in a Three‐Spin Molecule of the SI2‐Type

Abstract

AbstractThe longitudinal relaxation of the nuclear magnetization is calculated by use of the density matrix theory for a system of three nuclei each with spin 1/2, however, with one nucleus having a gyromagnetic ratio different from that of the other two (SI2‐type). The three spins are located at the corners of an isosceles triangle. Typical examples for such systems are partially fluorinated methyl groups (isosceles triangle) or internally non‐rotating methyl groups (equilateral triangle) in which one hydrogen nucleus shows a chemical shift different from that of the other two hydrogens. The calculations are based on a relaxation mechanism due to fluctuating magnetic dipolar interaction. It is shown that the size of the relaxation matrix can be considerably reduced using group theoretical methods. By numerical evaluation of the reduced relaxation matrix for different ratios of the gyromagnetic ratios γS/γI and internuclear distances rSI/rII, under the condition of extreme narrowing the influence of correlations between different pairwise interactions is studied. It is found that such correlation effects are completely negligible in all cases. Furthermore it is shown that for internally rotating methyl groups the theory for three like spins is applicable.