Investigation of the viability of solid-state NMR distance determinations in multiple spin systems of unknown structure

This paper presents theoretical rotational-echo double-resonance (REDOR) and transferred-echo double-resonance (TEDOR) curves calculated for several three-spin systems and explores the potential for determining reliable distances in multiple-spin systems of unknown geometry. These NMR techniques can provide distances which compare very well with those obtained by X-ray diffraction if the samples contain isolated heteronuclear (IS) spin pairs and are currently being used in structural investigations of solids including peptides, polymers, and inorganic materials. The situation is less clear when small clusters of spins (e.g., INS systems) are present, and although the multispin dephasing can be calculated, very few examples have been reported in the literature. In most cases the spin system geometry was known before analysis of the NMR data, thus it is unclear whether reliable distances can be determined when the geometry of the spin system is completely unknown. To investigate the uniqueness of distance determinations from fitting of multispin REDOR and TEDOR data, the theoretical dephasing was calculated for a selection of I2S systems. The effects of varying the two I-S dipolar couplings and the I-A-S-I-B angle, zeta, were studied. The full range of zeta (0 degrees less than or equal to zeta less than or equal to 180 degrees) was considered, and the magnitudes of the dipolar couplings selected are typical of couplings expected for commonly studied nuclei. A variation of 10 degrees or more is required to effect a noticeable change and the dephasing is identical for zeta and 180 degrees - zeta. The most distinctive behavior is observed when zeta is small (or close to 180 degrees), otherwise there are quite minor differences. Spin systems with quite different geometries may exhibit very similar dephasing, and in some cases the curves are identical to those for an isolated IS spin pair. These calculations indicate that it is highly unlikely that reliable distances can be obtained directly from REDOR and TEDOR experiments on multiple spin systems when the number of spins and their geometrical arrangement is completely unknown. Furthermore, it is possible to obtain incorrect distances if isolated spin pairs are assumed and multiple spins are present.