Dephasing of spin echoes by multiple heteronuclear dipolar interactions in rotational echo double resonance NMR experiments

Abstract

The application of rotational echo double resonance (REDOR) nuclear magnetic resonance (NMR) for accurate distance measurements has thus far been largely restricted to isolated heteronuclear two-spin systems. In the present paper, the informational content of REDOR curves is explored for systems characterized by multi-spin interactions. To this end, numerical REDOR simulations are presented for cases in which single observe spins S are dipolarly coupled to groups of spins I in distinct geometries. To develop the utility of REDOR for characterizing dipolar couplings in unknown and/or ill-defined geometries, the validity ranges and systematic errors of certain analytical approximations are studied. In the limit of short dipolar evolution times where 0≤ ΔS S 0 ≤0.2 to 0.3 , the REDOR difference signal intensity increases approximately proportional to the square of the dipolar evolution time. Here, the curvature depends simply on the second moment M 2 characterizing the overall strength of the heterodipolar coupling, irrespective of specific molecular geometries. Fitting experimental REDOR data in this manner produces slight systematic underestimates of M 2. However, these errors tend to be counterbalanced by additional systematic errors made by neglecting weak couplings to more remote spins and distribution effects caused by disorder. Based on these findings, the results suggest a convenient method of obtaining site-resolved second moment information in disordered materials.