Central-transition double-quantum sideband NMR spectroscopy of half-integer quadrupolar nuclei: estimating internuclear distances and probing clusters within multi-spin networks

Abstract

We introduce a strategy to estimate the size of clusters of recoupled homonuclear half-integer quadrupolar nuclei under magic-angle spinning (MAS) conditions, by combining double-quantum (2Q) sideband NMR experiments with an approximate numerical analysis based on the summation of all spin-pairs present over a given radius of the structure. The experiment relies solely on the evolution of homonuclear 2Q coherences (2QC) among the central-transitions (CT) of half-integer spins and is suitable for probing clusters in network structures, such as those encountered in large groups of oxide-based materials. Experimental (11)B, (23)Na and (27)Al NMR results are presented on bis(catecholato)diboron, Na2SO4 and Al2O3, respectively; in each case, the growth of the spin-cluster size was monitored from a series of experiments that employed progressively lengthened 2QC excitation intervals. Our new approach is the first option for probing larger constellations of half-integer spins; it provides similar information as the "multiple-quantum spin counting" experiment, which is well-established for spin-1/2 applications but has hitherto not been demonstrated for half-integer spins undergoing MAS. We also discuss various options for determining the internuclear distance within a (nearly) isolated pair of half-integer spins by comparing the experimental 2Q sideband NMR spectra with results from numerical simulations involving various degrees of approximation.

Improved Magnetization Transfers among Quadrupolar Nuclei in Two-Dimensional Homonuclear Correlation NMR Experiments Applied to Inorganic Network Structures

“…Considering the simulation results of Figure 3, the experimentally observed relative merits of the three (SR2 1 2 p )4 recoupling schemes are rather surprising. Yet, the chemical-shift separation between the 11 B [3] and 11 B [4] sites is relatively small (≈ 17 ppm, i.e., 3.3 kHz), where a good performance of SR2 1 2 -based schemes are indeed reported in previous 2QF and 2Q-1Q correlation NMR evaluations for similar cases where resonance offsets are low or absent [38,[51][52][53]55,56]. Experiments reveal that the (SR2 1 4 )M and (SR2 1 8 )M schemes give significantly better magnetization only for scenarios of (moderately) large chemical-shift differences, for which the (SR2 1 2 )M counterparts perform poorly.…”

“…These pulse sequences were introduced for two-spin 2QC excitation among the CTs of half-integer spins [9,38,49]. The recoupling schemes have been exploited for probing proximities among homonuclear 11 B, 23 Na, and 27 Al sites in a multitude of structurally well-ordered, as well as disordered, network-based materials [8,9,38,41,[49][50][51][52][53][54][55][56]. Moreover, they have also been employed in several structural studies of both organic and inorganic systems where spin-1/2 nuclei were used as probes, e.g., 13 C [57-60], 1 H [61,62], and 31 P [63][64][65].…”

Refined Structures of O-Phospho-l-serine and Its Calcium Salt by New Multinuclear Solid-State NMR Crystallography Methods

“…Hence, all hitherto presented work based on rotor-encoded 2Q spinning sidebands from 3D crystal structures invoked approximations to avoid prohibitive calculations of large spin systems, such as the summation of numerically exact simulations of a large number of NMR spectra from as-assumed isolated pairs of half-integer spins. 121,122 Although such approximative analysis procedures have had some success in validating single structure models, The NMR crystallography protocol applied herein is unique. However, out of the currently existing options, it shares many of the favorable properties of the 1 H spin-diffusion-based approach by Emsley and co-workers, 100,106,107 which also offers structural validations of large 1 H− 1 H distance sets with comparatively low investments in experimental and computational time/efforts, stemming from a phenomenological (and thereby approximate) analysis of the cross-peak signal buildup in a series of 2D NMR spectra with increasing mixing periods.…”

“…Hence, all hitherto presented work based on rotor-encoded 2Q spinning sidebands from 3D crystal structures invoked approximations to avoid prohibitive calculations of large spin systems, such as the summation of numerically exact simulations of a large number of NMR spectra from as-assumed isolated pairs of half-integer spins. 121 , 122 Although such approximative analysis procedures have had some success in validating single structure models, they require assumptions that are difficult to justify rigorously; see refs ( 121 )– 123 for details.…”

“…Another internuclear-distance analysis strategy does not involve the direct monitoring of the dependence of the 2QC or polarization-transfer amplitudes for increasing dipolar recoupling periods but merely targets either the (slow) MAS 1 H NMR spectrum , or the rotor-encoded 2QC spinning sideband formation in a 2Q–1Q correlation NMR spectrum recorded with Δ t 1 = τ r / N . ,, While being fairly effortless experimentally, the subsequent numerical analyses are equally time-/computer-intensive as the NMR-signal buildup approaches discussed above. Hence, all hitherto presented work based on rotor-encoded 2Q spinning sidebands from 3D crystal structures invoked approximations to avoid prohibitive calculations of large spin systems, such as the summation of numerically exact simulations of a large number of NMR spectra from as-assumed isolated pairs of half-integer spins. , Although such approximative analysis procedures have had some success in validating single structure models, they require assumptions that are difficult to justify rigorously; see refs – for details.…”