Determination of molecular geometry in solid-state NMR: Rotational-echo double resonance of three-spin systems

The precise measurement of internuclear distances in solids by NMR has been widely explored using experiments that measure the dipolar coupling between labeled spin pairs. The rotational-echo double-resonance (REDOR) experiment is one of the most successful techniques for quantifying distances between heteronuclei. In the present work, REDOR is applied to the precise determination of the angle between internuclear vectors in triply labeled spin systems. The time domain REDOR signal for two heteronuclear coupled spin pairs sharing a common partner (an I₂S spin system) is derived and analyzed with the aid of dipolar transforms. A two-step experimental approach for the structural analysis of I₂S spin systems is then developed. Independent θ-REDOR and traditional REDOR measurements are used to obtain the heteronuclear dipolar coupling constants and the angle between them. Demonstrations are carried out on labeled polycrystalline samples of glycine and uracil. The REDOR experiment is also examined using alternate nuclei in the three?spin system as the detection point, as a supplement to the θ-REDOR technique. The precision of the experimental angular determinations for glycine and uracil was calculated by the method of Crameré-Rao lower bounds and was found to be greater than in previous REDOR-based analyses. The approach demonstrated here is not limited to crystalline materials and may be employed for structural measurements in systems in which X-ray crystallographic studies are not feasible.