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

We demonstrate that supercycles of previously introduced two-fold symmetry dipolar recoupling schemes may be utilized successfully in homonuclear correlation nuclear magnetic resonance (NMR) spectroscopy for probing proximities among half-integer spin quadrupolar nuclei in network materials undergoing magic-angle-spinning (MAS). These (SR221)M, (SR241)M, and (SR281)M recoupling sequences with M=3 and M=4 offer comparably efficient magnetization transfers in single-quantum–single-quantum (1Q–1Q) correlation NMR experiments under moderately fast MAS conditions, as demonstrated at 14.1 T and 24 kHz MAS in the contexts of 11B NMR on a Na2O–CaO–B2O3–SiO2 glass and 27Al NMR on the open framework aluminophosphate AlPO-CJ19 [(NH4)2Al4(PO4)4HPO4·H2O]. Numerically simulated magnetization transfers in spin–3/2 pairs revealed a progressively enhanced tolerance to resonance offsets and rf-amplitude errors of the recoupling pulses along the series (SR221)M< (SR241)M< (SR281)M for increasing differences in chemical shifts between the two nuclei. Nonetheless, for scenarios of a relatively minor chemical-shift dispersions (≲3 kHz), the (SR221)M supercycles perform best both experimentally and in simulations.

In this article, we demonstrate the successful application of supercycled dipolar recoupling sequences-denoted (SR2 1 2 p )M and reviewed in Section 2-during the mixing period of the 1Q-1Q correlation NMR protocol. We provide 2D NMR experiments on a borosilicate glass of molar composition 0.124Na 2 O-0.124CaO-0.501B 2 O 3 -0.251SiO 2 (referred to as "NCBS"), as well as on the open framework aluminophosphate AlPO-CJ19 [(NH 4 ) 2 Al 4 (PO 4 ) 4 HPO 4 ·H 2 O] [72]. Furthermore, for altogether six (SR2 1 2 p )3 and (SR2 1 2 p )4 supercycles, we evaluate the robustness of the dipolar recoupling to resonance offsets and rf-amplitude mis-settings ("rf inhomogeneity") by numerical simulations of magnetization transfers in 23 Na- 23 Na pairs. Figure 1 illustrates the prototype rf-pulse protocol for homonuclear 1Q-1Q NMR correlations among half-integer spin quadrupolar nuclei by employing a dipolar recoupling scheme for driving longitudinal magnetization-exchange processes during the mixing period [30]. Note that all rf pulses are CT selective. Herein we consider recoupling sequences that provide a "ZQ effective Hamiltonian", meaning that it involves S + j S − k and S − j S + k "flip-flop" operators for two recoupled spins j and k [3][4][5][6][7]. Such a pulse sequence provides a magnetization transfer from spin j, resonating at ν j , to another nearby spin-site k that resonates at ν k . This j → k magnetization transfer is reflected by a cross peak centered at the 2D-frequency coordinate {ν 1 , ν 2 } = {ν j , ν k } in the 1Q-1Q NMR spectrum. Likewise, the k → j magnetization-transfer process yields a cross peak at {ν 1 , ν 2 } = {ν k , ν j }. Then in the absence of resonance-broadenings from second-order quadrupolar interactions and (potential) chemical-shift dispersions from structural disorder, the 1Q-1Q correlation NMR spectrum manifests two narrow cross peaks from the j-k spin-pair. In practice, however, distributions of resonances around each ν j and ν k frequency value produce broad "ridge-like" cross peaks in the 2D NMR spectrum [8,9].

Samples
A 6.0 g batch of the NCBS glass of molar composition 0.124Na 2 O-0.124CaO-0.501B 2 O 3 -0.251SiO 2 was prepared by a traditional melt-quench technique. Precursors of SiO 2 (99.99%), Na 2 CO 3 (99.5%), and CaCO 3 (99%) from ChemPur, and H 3 BO 3 (99.9%) from Sigma, were mixed in a mortar. The mixture was transferred to a Pt crucible and decarbonated by heating in an electric furnace at 950 • C for 2 h. The temperature was then raised to 1150 • C and the melt was held for 20 min, after which it was quenched by immersing the bottom of the crucible in water. The B 2 O 3 content was determined to be 54.0 wt% by 11 B MAS NMR, which is in excellent agreement with the nominal value 53.9 wt% (i.e., 0.2% relative discrepancy) [56]. Hence, given that B is the most volatile element in the melt, we may safely assume that the nominal elemental batch composition is representative for the glass.

Solid-State NMR Experiments
The 11 B (S = 3/2) and 27 Al (S = 5/2) NMR experimentation was performed with a Bruker Avance-III spectrometer (Bruker BioSpin, Rheinstetten, Germany) at the magnetic field B 0 = 14.1 T, which gives 11 B and 27 Al Larmor frequencies of −192.5 MHz and −156.37 MHz, respectively. Powders of NCBS and AlPO-CJ19 were filled in 3.2 mm zirconia rotors and spun at ν r = 24.00 kHz. Neat BF 3 ·OEt 2 and a 1 M Al(NO 3 ) 3 aqueous solution were used for 11 B and 27 Al shift referencing, respectively, as well as for determining the nutation frequencies for 11 B (ν B ) and 27 Al (ν Al ) of all strong rf pulses. Note that nearly all parts of the experiments involved CT-selective pulses, where the CT nutation frequency is given by ν CT E ≈ (S + 1/2)ν E , with E ={Al, B} [10].
Resonance offsets were minimized by positioning the rf carrier (δ rf ) at the mid-point shift of the 11 B/ 27 Al NMR signal region, except during the dipolar recoupling rf-pulses (see below). To accomplish absorptive 2D NMR peaks with frequency-sign discrimination along the indirect spectral dimension, all 2D NMR acquisitions implemented the States-TPPI procedure [77]. Note that the number of t 1 increments stated below refers to that collected for each real and imaginary data-set of the hypercomplex protocol.
The 1Q-1Q correlation 11 B NMR spectra from the NCBS glass were recorded with the rf-pulse protocol of Figure  2 )4, (SR2 1 4 )4, and (SR2 1 8 )4 rf pulses, respectively, where the numbers in parentheses specify the frequency offset relative to the center-of-gravity frequency (which defines Ω = 0) of a CT-selective 11 B MAS NMR spectrum recorded under otherwise identical conditions. At the start of each transient of the 1Q-1Q correlation NMR experiment, a WURST pulse [80,81] of duration τ WURST = 1.00 ms (ν CT B = 25 kHz) was applied to enhance the CT-signal intensity [40]. The frequency of the pulse was swept by ±12 kHz around Ω =120 kHz. This provided 2.4 and 1.9 stronger NMR-signal intensities from the 11 B [3] and 11 B [4] sites, respectively, and resulting in "apparent" fractional populations of {x [3] time-points were recorded with dwell times {∆t 1 = 4τ r , ∆t 2 = 5.0 µs}, 32 accumulated signal transients per t 1 -value and 1.0 s relaxation delays. Although the 2D NMR experimentation required short relaxation delays for reducing the experimental time, the relative 11 B [3] and 11 B [4] NMR signal intensities adequately reproduced the corresponding site population in the glass. The data set was zero-filled to 256 × 16,384 points before Fourier transformation.
A 2Q-1Q correlation 11 B NMR spectrum was recorded by the rf-pulse scheme depicted in Figure 2d of Edén [8], using a short 2QC excitation period to ensure 2D NMR signal intensities proportional to the respective 11 B [p] -11 B [q] pair populations, as discussed in detail in ref. [56]. One completed [SR2 1 2 ] dipolar recoupling sequence [38] was employed for excitation of two-spin CT 2QC, using equal 2QC excitation and reconversion intervals of τ exc = 4τ r = 167 µs. Here the brackets [· · · ] imply sandwiching the SR2 1 2 pulse sequence by two CT-selective 90 • pulses [38,58]. The rf carrier was set at δ rf = 8.4 ppm for the recoupling pulses. A Hahn-echo of duration 2τ r was applied before the t 1 -evolution period to accomplish rotor-synchronized 2QC excitation and reconversion stages [38], as well as suppression of all undesirable single-spin 2QC associated with the satellite transitions [28]; this was ensured by an 8-step phase cycle of the CT-selective 180 • pulse [41], which was of duration 34.2 µs. The details of the phase-cycle implementation is given in the Supporting Information of ref. [41]. 23(t 1 )×600(t 2 ) time-points were recorded with dwell times {∆t 1 = 2τ r , ∆t 2 = 8.4 µs}, 768 accumulated signal transients/t 1 -value and relaxation delays of 1.5 s. The data set was zero-filled to 128 × 8192 points prior to Fourier transformation. Other conditions were as described for the 1Q-1Q correlation NMR experiments, except that no signal enhancement (i.e., WURST) was applied to avoid perturbing the relative 2D NMR signal intensities.

Numerical Simulations
The numerical simulations were performed with the SIMPSON package (version 4.2.1) [82,83], employing a small-step (<1 µs) integration of the Schrödinger equation [84] during each periodically repeated (SR2 1 2 p )M sequence throughout the mixing interval. The magnetization-transfer efficiency was calculated as the fraction of longitudinal CT magnetization of spin j that was transferred to spin k (S CT jz → S CT kz ) within a pair of S = 3/2, and was sampled at each completed SR2 1 2 p pulse-element of the (SR2 1 2 p )M supercycle out to τ mix 10 ms. The simulations accounted for all relevant spin-system parameters, i.e., the isotropic chemical shifts, dipolar, and first-as well as second-order quadrupolar interactions, which were typical for 23 Na; see the caption to Figure 2. Powder averaging [85] was performed using 3722 three-angle ZCW orientations [86,87]. The corresponding MAS NMR spectra of the two coupled S = 3/2 were calculated using the COMPUTE protocol [88,89] and employing the FWTASG spectral interpolation [90] with the ROSE LEBh6535 set of orientations [91] for efficient powder averaging. Only the CT signals were detected.

Numerically Simulated Magnetization-Transfer Efficiencies
The very low rf-power requirement of the (SR2 1 2 p )M dipolar recoupling schemes (see Section 2) ensures minimal CT-signal leakages to the STs, but compromises the robustness of the recoupling to variations in resonance offsets (Ω j = ν j iso − ν rf ) among the various nuclei in the sample. For quadrupolar nuclei, resonance offsets may originate from two sources: (i) Distinct isotropic chemical shifts, is the isotropic chemical shift of the spin-site j (k), and ν rf is the rf-carrier frequency. (ii) The second-order isotropic quadrupolar shift and the accompanying anisotropic resonance-broadening [10], where the latter presents the major obstacle; see the MAS NMR spectra in Figure 2a-c.
The dipolar recoupling must also be robust to spreads of spin nutation frequencies across the sample ("rf inhomogeneity"). The impact of rf inhomogeneity may be gauged from experiments and simulations where the applied rf-amplitude is deliberately mis-set, such that the actual CT nutation frequency during the recoupling pulses (ν CT nut ) deviates from the nominal value ν CT nut (nom), which for all (SR2 1 2 )M schemes obeys ν CT nut (nom) = ν r /2.  23 Na sites in Na 2 SO 4 , which were taken from ref. [92]: In the following, we evaluate the alterations observed in numerically simulated magnetization-transfer efficiencies for variations in either the resonance offset or the relative nutation frequency, ν CT nut /ν CT nut (nom). The transfer efficiency corresponds to the fraction of longitudinal CT-magnetization of spin j transferred to spin k during a given mixing period (τ mix ).  Figure 3, respectively. Here and in the following evaluations, a "zero resonance offset" (Ω = 0) implies that the rf carrier frequency coincides with the center-of-gravity frequency of the NMR spectrum [see Figure 2a-c]; the NMR frequency separation between the center-of-gravities of the two powder lineshapes of spins j and k is then given by ∆ iso in Figures 2 and 3.
All magnetization-transfer curves of Figure 3 reveal an oscillatory response when the resonance offset varies. Disregarding those undesirable oscillations that are discussed below, the bandwidth across which decent magnetization transfers are observed is markedly increased along the series (SR2 1 2 )M<(SR2 1 4 )M<(SR2 1 8 )M for each fixed value of M. This observation accords with previous inferences from simulations and experiments of double-quantum filtration (2QF) responses for both spins-1/2 [57,58] and half-integer spins [49,76], as well as from simulated magnetization transfers in spin-1/2 pairs [58]. Notably, while the construction of the most robust pulse scheme SR2 1 8 was outlined in ref. [76], it has hitherto not been evaluated in the context of half-integer spins.
For a small isotropic chemical-shift dispersion (∆ iso 3 kHz), Figure 3a  scheme. Experimentally observed magnetization-transfer efficiencies are also similar for the (SR2 1 2 p )3 and (SR2 1 2 p )4 schemes (to be discussed elsewhere), in accordance with the simulated results of Figure 3. Moreover, the (SR2 1 2 p )M supercycles employed herein generally offer better spectral signal-to-noise (S/N) ratios relative to their windowed (SR4 1 4 )M counterparts utilized in ref. [30]; see Section 4.2.3. The primary weakness with the (SR2 1 2 p )M dipolar recoupling schemes is the strong oscillations observed even for small variations in the precise rf-carrier position (Figure 3). This feature is a clear disadvantage in 1Q-1Q NMR correlation applications for multi-site structures because the cross-peak intensities may not in general be translated into reliable (relative) internuclear distances among the various spin-pairs in the structure, as is possible for spin-1/2 implementation of the (SR2 1 2 p )M sequences and other homonuclear recoupling options [3,5,62]. As will be demonstrated and discussed further in an upcoming paper, however, the undesirable property of offset-dependent magnetization transfers appears to be a quite general feature and is by no means specific for the (SR2 1 2 p )M recoupling sequences. This observation underscores the difficulties in devising robust homonuclear dipolar recoupling sequences for half-integer spins.
The underlying reasons for the strong resonance-offset dependent oscillations are not known, but similar trends as those observed herein for magnetization transfers when using (SR2 1 2 p )M schemes for ZQ mixing (Figure 3) are also present in previous evaluations of 2QF responses when varying the resonance offset of the [SR2 1 2 ] and [SR2 1 4 ] recoupling pulses in 2Q-1Q NMR correlation experiments [49]. Yet, considering the absence of oscillations in both magnetization-transfer and 2QF processes for spins-1/2 under otherwise comparable conditions and recoupling sequences [57,58,63], it is evident that the resonance-offset dependent oscillations must stem from interferences between the (very substantial) first-order quadrupolar interactions and the rf pulses. Indeed, the results of Figure 3 suggest that the oscillatory responses versus the resonance offset correlate with the pulse-sequence order p of the (SR2 1 2 p )M (see Section 2), meaning that the more complex the pulse train, the faster/more pronounced the oscillations. Hence, they increase in the order (SR2  Figure 4 presents the evaluations of the robustness of each (SR2 1 2 )M, (SR2 1 4 )M, and (SR2 1 8 )M recoupling scheme to rf-amplitude mis-settings from the nominal value ν CT nut = ν r /2. Using the conditions and parameters as in Figure 3, each magnetization-transfer efficiency curve was evaluated at the optimal resonance-offset value but with the (relative) nutation frequency of the CT varied. As for the resonance offset compensation, the results of Figure 4 reveal a progressively enhanced robustness to rf-amplitude errors along the series (SR2 1 2 )M<(SR2 1 4 )M<(SR2 1 8 )M, whereas no significant differences are observed among each (SR2 1 2 p )3 and (SR2 1 2 p )4 scheme. When operating near the nominal nutation frequency, all (SR2 1 2 p )M sequences provide efficient magnetization transfers among spins with equal chemical shifts (∆ iso = 0); see Figure 4a,b. For such cases, the (SR2 1 2 )3 and (SR2 1 2 )4 schemes perform better than than their more complex analogs. Nonetheless, the magnetization transfers obtained from the (SR2 1 2 )M sequences become quenched even for moderately large ∆ iso -values and minor deviations from the nominal nutation frequency ν CT nut = 12 kHz. While the largest magnetization-transfer efficiency deteriorates for increasing ∆ iso for all recoupling schemes, the compensation to rf-amplitude mis-settings (and thereby to rf inhomogeneity) of the (SR2 1 4 )M and (SR2 1 8 )M members are markedly better than for the (SR2 1 2 )M counterparts. Also, for a growing chemical-shift dispersion, the relative advantage of the (SR2 1 8 )M schemes become more pronounced relative to their (SR2 1 4 )M analogs. Indeed, as discussed in refs. [57,58,76], the robustness to the combined effects of resonance offsets and rf-amplitude errors improves at each recursive pulse-sequence expansion step (increasing p of SR2 1 2 p ). The improved performance of the SR2 1 4 scheme relative to SR2 1 2 was reported earlier in the context of 2QF applications to half-integer spins [49,76]. Here, we show that these relative merits also apply to the (SR2 1 2 )M and (SR2 1 4 )M schemes when used for magnetization transfers in 1Q-1Q correlation NMR experiments.

RF-Amplitude Errors
For the (SR2 1 4 )M and (SR2 1 8 )M recoupling schemes, Figure 4 manifests transfer-efficiency profiles that are somewhat skewed in that the highest efficiencies are normally not observed at the nominal nutation frequency ν CT nut = 12 kHz (i.e., for a relative nutation frequency of 1.0). This is particularly evident for the (SR2 1 4 )M schemes that reveal the best performance in the range of relative nutation frequencies of 0.85-0.90 (see Figure 4), while their performance for ν CT nut > 12 kHz deteriorates rapidly for increasing ν CT nut /ν CT nut (nom) [except for (SR2 1 4 )3 in (c)]. This feature accentuates for ∆ iso -values, and may be understood from the dependence of the effective CT-nutation frequency according to [26]. Hence, for increasing ∆ iso , lower values of ν CT nut satisfy the condition ν CT nut (eff) = ν CT nut (nom). These effects are much less pronounced for the (SR2 1 8 )M sequences, owing to their improved compensation to variations in ∆ iso (and Ω). The simulations employed the spin-system parameters of Figure 2 with isotropic chemical shift differences of (a,b) ∆ iso = 0, (c,d) ∆ iso = 3.0 kHz, and (e,f) ∆ iso = 6.0 kHz. 2 ] sequence for 2QC excitation and reconversion (τ exc = τ rec = 167 µs). The 2D NMR spectrum reveals 2Q-1Q correlations from B [3] -O-B [3] , B [3] -O-B [4] , as well as B [4] -O-B [4] linkages in the borosilicate glass network. Projections along the 2Q and 1Q dimensions are shown to the right and at the top of the 2D NMR spectrum, respectively, together with the MAS NMR spectrum acquired directly by single pulses (red trace).

Introduction to the NCBS Glass Structure
The NCBS glass structure consists of SiO 4 and BO 4 tetrahedra (B [4] coordinations) along with planar BO 3 (B [3] coordination) groups, which are interlinked to form a borosilicate network [56,93]. This glass is nominally free from non-bridging oxygen (NBO; O − ) species, where NMR indicated 3% of NBO out of the O population [56]. Hence, essentially all of the Na + and Ca 2+ cations balance the negative charges of the [BO 4 ] − groups. In analogy with the [AlO 4 ] − tetrahedra in crystalline and amorphous aluminosilicate phases [10,94,95], the negatively charged [BO 4 ] − moieties have generally been assumed not to form direct linkages (B [4] -O-B [4] ) in borate/borosilicate glasses [96,97], disregarding B-rich borosilicate glass compositions for which B [4] -O-B [4] bridges cannot be avoided, owing to a high fractional population of the BO 4 groups and/or a high NBO content of the glass; see Equation (1) of ref. [56]. Yet, recently Yu et al. [56] provided unambiguous experimental evidence that B [4] -O-B [4] are abundant motifs in Na and mixed-Na/Ca based borosilicate glasses over large compositional spaces (we also note that aluminosilicate glasses comprising trivalent rare-earth ions revel an essentially random Al/Si intermixing that implies substantial amounts of Al [4] -O-Al [4] bridges [10,54]). The presence of B [4] -O-B [4] bonding was established by 2Q-1Q correlation 11 B MAS NMR experiments using one completed [SR2 1 2 ] sequence for 2QC excitation [56], such as that obtained from the NCBS glass and shown in Figure 5.
The 11 B MAS NMR spectrum shown in Figure 5 reveals two main resonances: one narrow from the symmetric 11 BO 4 tetrahedra and one broad from the planar 11 BO 3 groups. The respective 11 B [4] and 11 B [3] sites are associated with average quadrupolar products C [4] Qη = 0.44 MHz and C [3] Qη = 2.67 MHz, respectively. The second-order quadrupolar broadening of the 11 B [3] NMR signals produce 2Q-1Q correlation "ridges" that extend along both dimensions of the 2D NMR spectrum (Figure 5), where the 2QC shift is the sum of each δ [3] B and δ [4] B shift of the respective correlated 1Q 11 B [3] and 11 B [4] shifts. The 2Q-1Q correlation 11 B NMR spectrum in Figure 5 gives evidence that all three B [3] -O-B [3] , B [4] -O-B [4] , and B [3] -O-B [4] linkages are present, with the latter dominating in the NCBS glass networks. The 11 B-11 B dipolar coupling constants in borosilicate glasses range between 700-900 Hz, where those of 11 B [3] -11 B [3] and 11 B [4] -11 B [4] are at the higher and lower end, respectively [56]. Analysis of the 2D NMR spectrum revealed the set of fractional populations (x   [8,38,41], 1Q-1Q correlation NMR experimentation may only unambiguously establish proximities among distinct sites in an inorganic network structure, i.e., the B [3] -O-B [4] linkages for the present case of the NCBS glass. Nonetheless, they account for 58% of all B [p] -O-B [q] bridges (see Section 4.2.1). These signals appear as a pair of cross peaks connecting the two diagonal peaks associated with each 11 B [3] and 11 B [4] resonance [8,9,30]. The 11 B [3] -11 B [3] and 11 B [4] -11 B [4] "auto-correlation" peaks from the respective 11 B [3] → 11 B [3] and 11 B [4] → 11 B [4] magnetization transfers overlap with the strong 11 B [3] and 11 B [4] NMR signals from non-exchanged magnetization along the diagonal. Unfortunately, this makes the proof of spatial proximities among "like" 11 B [p] sites ambiguous. In Figure 6, the identification of direct B [3] -O-B [3] and B [4] -O-B [4] structural fragments are hinted by a diffuse broadening of the respective NMR peaks along the diagonal, as may be verified from the 2D NMR spectra that were recorded for increasing mixing periods. Such signal-broadening effects of the 11 B autocorrelation signals from borosilicate glasses were discussed further by Murakami et al. [69], and by Edén and Frydman [17] in the context of vitreous B 2 O 3 . Figure 7. Relative integrated 2D NMR cross-peak intensities of the 1Q-1Q NMR spectra in Figure 6 plotted against the mixing period for the (a) 11 B [4] → 11 B [3] (upper left cross peak) and (b) 11 B [3] → 11 B [4] (lower right cross peak) magnetization transfers observed using either the (SR2 1 2 )4, (SR2 1 4 )4, or (SR2 1 8 )4 schemes. The sum of integrated intensities are normalized to unity for each 2D NMR spectrum, such that each plotted data-point represents the fraction of the total 2D NMR intensity for the respective mixing period and recoupling sequence. We next focus on the unambiguously evidenced B [3] -O-B [4] linkages associated with the cross-peak ridges observed in Figure 6. Regardless of which (SR2 1 2 p )4 recoupling scheme is applied during the mixing period, the 11 B NMR cross-peak intensity grows. Yet, at a fixed value of τ mix , the (SR2 1 2 )4 scheme produces stronger correlation signals than its (SR2 1 4 )4 and (SR2 1 8 )4 counterparts. The overall trend of improved magnetization exchange along the series of recoupling schemes, (SR2 1 8 )4 < (SR2 1 4 )4 < (SR2 1 2 )4, is most apparent in Figure 7 that contrasts the integrated 2D NMR-signal intensities of the two cross peaks in each spectrum of Figure 6. Notably, we experimentally observed similar 2D NMR signal-intensity oscillations against the resonance offset as in the simulations of Figure 3. The 2D NMR spectra shown for the (SR2 1 4 )4 and (SR2 1 8 )4 schemes in Figure 6 were selected from the best results of 2D NMR acquisitions using two distinct rf-carrier frequencies (i.e., resonance-offset values), where the resulting NMR intensities varied by 20-30% among the two frequency values. Because the most/least favorable offset is not a priori known, it is not possible to arrange precise comparisons among the three (SR2 1 2 p )4 schemes at their respective optimum conditions.

Relative Merits of the (SR2 1 2 p )M Recoupling Schemes
We conclude that while any (SR2 1 2 p )4 dipolar recoupling sequence give unambiguous evidence for 11 B [3] -O-11 B [4] linkages in the NCBS glass network for mixing intervals τ mix 1.3 ms (Figure 6), the M = 4 MQ-phase cycle based on the simplest SR2 1 2 scheme performed best. In the case of the NCBS glass, no advantages are offered by the more complex (SR2 1 4 )4 and (SR2 1 8 )4 supercycles, where the (SR2 1 8 )4 option gives a significantly worse NMR-signal sensitivity and magnetization transfers as compared with (SR2 1 2 )4 (see Figures 6 and 7). 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. In the following, we consider the relative NMR-signal sensitivities (rather than the magnetization transfer efficiencies) offered by the various (SR2 1 2 p )M and (SR4 1 4 )M dipolar recoupling schemes. Notably, the 11 B NMR-signal intensities observed from the NCBS glass when employing the present (SR2 1 2 )M and (SR2 1 4 )M sequences are markedly better then those of the windowed (SR4 1 4 )M recoupling options utilized by Edén et al. [30] (see Section 2): relative to the integrated 2D NMR-signal intensity obtained from the (SR2 1 2 )4 scheme in Figure 6g, only 41% and 6% was observed when applying the (SR4 1 4 )3 or (SR4 1 4 )4 sequences with f 180 = 0.30 (see Section 2) for a mixing period of τ mix = 10.7 ms, respectively (as obtained by recording a 1D NMR spectrum according to the protocol of Figure 1 with t 1 = 0; data not shown). Next considering the NMR-signal intensity obtained among the various (SR2 1 2 p )M sequences and again monitoring the fractional intensity relative to the 2D NMR spectrum of Figure 6g, 1 2 p )M, recoupling schemes offer markedly better S/N than the windowed (SR4 1 4 )M counterparts of ref. [30].
The low-power (SR2 1 2 p )M rf-pulse trains are particularly advantageous for recoupling spin sites with low quadrupolar coupling constants/products, such as the 11 B [4] nuclei in the NCBS glass (and the 27 Al [6] sites of AlPO-CJ19; see Section 4.3). All (SR2 1 2 p )M schemes retain similar NMR-signal fractions of 0.32-0.38 from the 11 B [4] sites in the 2D NMR spectrum for the mixing period of 10.7 ms, in excellent agreement with the "apparent" fractional population x [4] B = 0.36 of the NCBS structure (see Section 3.2.1). In contrast, the corresponding integrated 11 B [4] NMR signal fraction obtained from the (SR4 1 4 )3 and (SR4 1 4 )4 schemes with f 180 = 0.30 only amounted to 0.20 and 0.13, respectively. Hence, only a few percent of the initial 11 B [4] magnetization remains after application of the (SR4 1 4 )M schemes that involve stronger rf pulses. These losses accentuate for prolonged mixing periods and/or for stronger 180 • recoupling pulses.
Concerning the merits of the M = 3 supercycles relative to their M = 4 counterparts, often (but not always), we observe experimentally that for a given dipolar recoupling sequence S of the (S)M supercycle, the NMR-signal strength is slightly higher for the M = 3 scheme as compared with its M = 4 counterpart. However, these effects appear to be spin-system-dependent (i.e., sample dependent), where for instance the 11 B NMR experiments on the NCBS glass manifest even slightly higher NMR-signal intensities from the (SR2 1 2 p )4 schemes than those of (SR2 1 2 p )3 (see above). In contrast, the windowed (SR4 1 4 )4 supercycle yields much higher NMR-signal losses than its (SR4 1 4 )3 analog. The reasons for these observations are unknown, but a more comprehensive evaluation of the various (SR2 1 2 p )M and (SR4 1 4 )M recoupling options is in progress and will be published elsewhere. All shortest Alj-Alj distances between equivalent sites (j = 1, 2, 3, 4) are around 5.1 Å. The Al1, Al2, Al3, and Al4 sites are identified with their respective Al [4] , Al [5] , and Al [6] coordinations in the legend. (b) 1Q-1Q correlation 27 Al MAS NMR spectrum recorded from AlPO-CJ19 (B 0 = 14.1 T, ν r = 24.0 kHz), using the (SR2 1 4 )3 sequence for magnetization transfers during a mixing period of τ mix = 30.0 ms. Slices extracted at the as-indicated shifts along the vertical spectral dimensions are shown in the right panel.

Conclusions
We have explored MQ-phase cycles of the SR2 1 2 p family of homonuclear dipolar recoupling sequences for driving longitudinal magnetization transfers among half-integer spin quadrupolar nuclei undergoing fast MAS (20-30 kHz) at a moderately high magnetic field of 14.1 T. These (SR2 1 2 )M, (SR2 1 4 )M, and (SR2 1 8 )M recoupling schemes with M = 3 and M = 4 were utilized in 1Q-1Q correlation NMR experiments applied in the contexts of 11 B NMR on a borosilicate glass (NCBS) and 27 Al NMR on the open framework aluminophosphate AlPO-CJ19. Numerical simulations of pairs of dipolar-coupled spins-3/2 revealed a progressively improved stability of the magnetization transfers for variations in resonance offsets and rf-amplitude errors of the recoupling pulses along the series (SR2 1 2 )M<(SR2 1 4 )M<(SR2 1 8 )M, in agreement with previous findings from related 2Q-1Q correlation NMR applications of the [SR2 1 2 ] and [SR2 1 4 ] schemes to quadrupolar nuclei [49,76].
For dipolar recoupling applications where the chemical-shift dispersion is relatively low (∆ iso 3 kHz), we recommend using the simplest (SR2 1 2 )3 and (SR2 1 2 )4 schemes, which outperformed the more complex (SR2 1 4 )M and (SR2 1 8 )M recoupling options for magnetization exchange among the 11 B [3] and 11 B [4] sites in the NCBS glass (which feature ∆ iso ≈3 kHz). In such cases of low resonance spreads, no advantages are offered by the (SR2 1 4 )M and (SR2 1 8 )M supercycles with M = {3, 4}. In contrast, for dipolar recoupling scenarios manifesting a substantial chemical-shift dispersion, such as the 27 Al [4] , 27 Al [5] , and 27 Al [6] sites in AlPO-CJ19 at 14.1 T, we recommend using either of the (SR2 1 4 )M or (SR2 1 8 )M schemes. Yet, our experimental evaluations thus far do not reproduce the superiority of the new (SR2 1 8 )3 and (SR2 1 8 )4 schemes predicted by the numerical simulations. Concerning the relative merits of the M = 3 supercycles relative to their M = 4 counterparts, we often (but not always) observe experimentally that for a given dipolar recoupling sequence S of the (S)M supercycle, the NMR-signal strength is slightly higher for the M = 3 supercycle relative to its M = 4 counterpart. Yet, the precise responses of the M = {3, 4} supercycles appear to depend both on the sample and particular pulse sequence. Moreover, numerical simulations (e.g., see Figures 3 and  4) do not indicate any significant advantage of either option. We found that the M = 3 and M = 4 MQ-phase cycle options gave similar results when combined with any SR2 1 2 p scheme and employed during the mixing segment in 1Q-1Q correlation NMR experiments on the NCBS glass. For the windowed (SR4 1 4 )M schemes of ref. [30], on the other hand, much higher NMR-signal losses resulted when using the (SR4 1 4 )4 scheme relative to (SR4 1 4 )3. Furthermore, both (SR4 1 4 )M recoupling schemes yielded overall larger NMR-signal losses than their (SR2 1 2 )M and (SR2 1 4 )M counterparts. Here the small (average) quadrupolar product of the 11 B [4] sites (C [4] Qη = 0.44 MHz) severely compromises its NMR-signal sensitivity obtained when utilizing the (SR4 1 4 )M schemes, which involves stronger 180 • pulses and thereby higher CT-magnetization losses from the 11 B [4] sites than when using the (SR2 1 2 p )M supercycles. In contrast, the latter recoupling sequences preserved each relative 11 B [3] and 11 B [4] NMR-signal intensity according to that of the respective site population of the NCBS glass, which is a decisive advantage.
A comprehensive experimental and numerical evaluation of the (SR2 1 2 p )M supercycles relative to the (SR4 1 4 )M schemes of ref. [30], as well as to other zero-quantum recoupling options, is underway and will be presented elsewhere.