Combining dipolar–quadrupolar correlation spectroscopy with isotropic shift resolution in magic-angle-spinning 17O NMR

Journal of Magnetic Resonance 219 (2012) 4–12

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Combining dipolar–quadrupolar correlation spectroscopy with isotropic shift resolution in magic-angle-spinning 17O NMR M. Goswami 1, P.K. Madhu ⇑ Department of Chemical Sciences, Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India

a r t i c l e

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Article history: Received 9 July 2011 Revised 5 March 2012 Available online 10 April 2012 Keywords: Solid-state NMR Brucite Symmetry-based recoupling STMAS MQMAS

a b s t r a c t We explore the effect of heteronuclear dipolar recoupling on the satellite and multiple-quantum transitions of a half-integer-spin quadrupolar nucleus coupled to a single spin-12. A three-dimensional experiment is introduced that resolves different quadrupolar sites whilst allowing simultaneous extraction of the quadrupolar coupling constants, asymmetry parameters of the electric field gradient, and the isotropic shifts of the quadrupolar nucleus. The experiment also enables estimation of the heteronuclear dipolar coupling constant between the spin-12 and half-integer spin quadrupolar nucleus. The relative orientation of the dipolar tensor with respect to the quadrupolar tensor can be estimated by comparing experiments and simulations. Experimental results are shown on a sample of brucite, Mg(17OH)2, where the 1H–17O bond distance is estimated. Ó 2012 Elsevier Inc. All rights reserved.

1. Introduction Interest in 17O (nuclear spin quantum number I = 5/2) NMR has increased markedly in the last few years, particularly for characterising oxide gels and amorphous inorganic oxides [1,2] and in the study of hydroxyl groups and water molecules in peptides and biological samples [3–5]. 17O NMR has also been applied to the studies of zeolites [6–9], ionic conductors [10,11], glasses [12,13], phosphine oxides [14], and membrane-bound proteins [15]. The NMR study of 1H–17O pairs is of particular interest for the investigation of hydrogen-bonded systems [16,17] since the 17O quadrupolar interaction is sensitive to perturbations in the local environment [18]. Correlation of the electric quadrupole and dipolar interactions, first demonstrated by Linder et al. [19], provides additional insights into the local electronic environment. Experiments of this type have been performed on 1H–17O pairs by the groups of van Eck and Smith [20], Kentgens [21,22], and Levitt [23]. The estimation of 1H–17O dipolar couplings in OH groups is often complicated by the presence of 1H–1H homonuclear dipolar couplings. Van Eck and Smith [20] resolved the 1H–17O dipolar coupling on static samples using Hartman–Hahn 1H–17O cross-polarisation [24] together with Lee–Goldburg homonuclear decoupling [25] to reduce the effect of proton–proton couplings. They also performed two-dimensional (2D) separated local-field experiments to estimate ⇑ Corresponding author. Fax: +91 22 2280 4610. E-mail address: [email protected] (P.K. Madhu). Present address: Radboud University Nijmegen, Institute for Molecules and Materials, Heyendaalsweg 135, 6525 AJ Nijmegen, The Netherlands. 1

1090-7807/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.jmr.2012.03.018

the relative orientation of the 17O electric field gradient and OH dipole tensors. Brinkmann et al. [21] used symmetry-based recoupling sequences on magic-angle-spinning samples [26] to selectively recouple the heteronuclear interactions whilst implementing homonuclear proton decoupling. A radio frequency (RF) pulse sequence with symmetry SR421 was applied to the 1H nuclei, with fast magic-angle spinning (50 kHz) and a high static magnetic field (18.8 T), to achieve the required proton spectral resolution. Supercycled symmetry-based pulse sequences were used to determine 1 H–17O distances in several organic compounds [22]. Van Beek et al. [23] showed that the 1H–17O dipolar coupling can be resolved under moderately fast MAS (16 kHz) by using a spin-echo sequence on 17O and a symmetry-based recoupling sequence [26] of the type R1852 on the protons. They estimated the relative orientation of dipolar and quadrupolar tensors using two-dimensional techniques. An alternative technique for internuclear distance measurements between spin-12 and half-integer spin quadrupolar nuclei, called S-RESPDOR (symmetry-based resonance-echo saturation pulse double-resonance), has recently been proposed [27,28]. Although this method provides a robust response with very little dependence on homonuclear dipolar coupling, RF-field inhomogeneity, CSA, and resonance offset, this does not provide the quadrupolar interaction parameters. A related method based on REAPDOR [29], namely LA-REDOR, was introduced recently [30]. All of the methods described above concentrate on the 17O central transition. Here we consider the effect of symmetry-based hetreonuclear dipolar recoupling on the satellite and multiplequantum transitions of a 17O nucleus, in a dipolar-coupled 1H–17O

M. Goswami, P.K. Madhu / Journal of Magnetic Resonance 219 (2012) 4–12

system. Dipolar recoupling sequences are combined with spin-echo, multiple-quantum MAS (MQMAS) [31], and satellite-transition MAS (STMAS) [32] techniques. This gives high-resolution spectroscopy of the quadrupolar nucleus whilst simultaneously correlating the heteronuclear dipolar coupling and the 17O electric field gradient tensors. A similar experiment was reported by Grinshtein et al. [33] who combined the separated local field NMR technique with the MQMAS technique in a 3D fashion. This made use of an initial split-t1 delay encoding an isotropic evolution, a t2 labelling of the 1 H dipolar evolution, and a final t3 acquisition under conventional MAS. Using this scheme Grinshtein et al. reported correlation between different inequivalent quadrupolar resonances with the dipolar MAS sideband pattern to nearby heteronuclei. In this report we demonstrate a combination of heteronuclear dipolar recoupling with high-resolution quadrupolar NMR methods in a 3D way. The method resolves the resonances from inequivalent sites of the quadrupolar nucleus at the same time as elucidating their electric field gradient and dipolar coupling parameters. One of the 2D planes of the 3D spectrum provides the high-resolution spectrum for the quadrupolar nucleus whilst the other 2D plane provides the corresponding quadrupolar–dipolar (QD) correlation spectrum exhibiting heteronuclear dipolar splittings. From the 3D experimental data we extracted the quadrupolar interaction parameters of 17O and used these parameters to simulate the dipolar evolution of the 1H–17O pair. The 1H-17O dipolar coupling constant, and hence the OH bond length, were estimated. We compare experimental data with numerical simulations in order to estimate the relative orientations of the dipolar and electric field-gradient tensors. Hence, all the important interaction parameters of the two-spin system may be obtained from a single set of experimental data. 2. Experimental

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double-tuned MAS 2.5 mm probe at room temperature and a MAS frequency of 16 kHz. A symmetry-based recoupling sequence [26] of the type R1852 was applied on the 1H channel with a nutation frequency of 72 kHz, i.e. 4.5 times the MAS frequency. The R1852 sequence is made up of repeated sequences of the form 1805018050 where the pulse flip angles and subscript phases are given in degrees. The symmetry of this sequence ensures heteronuclear recoupling combined with homonuclear decoupling [35–37]. In all experiments, the swept-frequency two-pulse phase-modulation (SWf-TPPM) heteronuclear dipolar decoupling scheme [38] was applied using an RF amplitude of 103 kHz to remove the effect of the 1H–17O dipolar couplings during signal acquisition. 17Olabelled water (H217O) was used as the chemical-shift reference for 17O (0 ppm). We carried out the 2D quadrupolar–dipolar (QD) correlation experiments by combining R1852 symmetry-based recoupling sequence on the 1H channel with spin-echo (Fig. 2a), STMAS, or MQMAS schemes (Fig. 3a) on the 17O channel. Fig. 2a shows the pulse sequence involving a spin-echo experiment on 17O combined with R1852 symmetry-based recoupling on the 1H channel. The 90° pulse (denoted p1) and 180° 17O pulse (denoted p2) had durations of 5.0 and 10.0 ls respectively corresponding to a 17O nutation frequency of 50 kHz. 600 transients were

(a)

(b)

2.1. Sample The Mg(17OH)2 sample prepared according to Ref. [23] was kindly provided to us by Jacco van Beek. The sample was used without further purification. The 17O enrichment was of the order of 35–40%. The crystal structure of Mg(17OH)2 possesses very high symmetry and a small unit cell. The structure is made up of Mg2+ layers coordinated octahedrally by OH groups with the hydrogen atoms pointing in the direction of the next layer [34] as depicted in Fig. 1.

Fig. 2. (a) Pulse sequence for 2D QD correlation spectroscopy using R1852 dipolar recoupling sequence on 1H and a two-pulse spin-echo sequence on 17O. (b) The coherence pathway selected for spin-echo experiment. The duration T represents the constant rotor-synchronised delay. A 16-step phase cycling was used in (a): p1: +x, +y, x, y; p2: 4(+x), 4(+y), 4(x), 4(y); and receiver phase: +x, y, x, +y, x, +y, +x, y.

(a)

2.2. NMR experiments All 17O NMR experiments were performed on a Bruker Avance 500 MHz NMR spectrometer equipped with a standard Bruker

(b) (c)

Fig. 1. The unit crystal structure of Mg(17OH)2 following Ref. [34].

Fig. 3. (a) 2D pulse sequence for QD correlation spectroscopy using R1852 dipolar recoupling sequence on 1H and either STMAS or 3QMAS sequence on 17O. (b) The coherence pathway selected when STMAS sequence was applied on 17O. (c) The coherence pathway selected when 3QMAS sequence was applied on 17O. The duration T represents the constant rotor-synchronised delay. A four-step phase cycling was used for two-pulse STMAS in (b): p1: +x; p2: +x, +y, x, y, and receiver phase: +x, x; and for two-pulse 3QMAS sequence a six step phase cycling was used in (c): p1: 0°, 60°, 120°, 180°, 240°, 300°; p2: 0°; and receiver phase: 3(0°), 3(180°).

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recorded for each of the 30 t1 increments. The interval T was kept constant at a value corresponding to 15 rotor periods (937.5 ls). Fig. 2b depicts the 17O coherence pathways. The pulse sequence in Fig. 3a shows STMAS/MQMAS scheme on 17 O combined with R1852 symmetry-based recoupling on the 1H channel. The durations of the pulses p1 and p2 were optimised according to whether the STMAS or MQMAS scheme was used. For the STMAS (Fig. 3a) experiment p1 was optimised for singlequantum satellite-transition coherence excitation and p2 was optimised for single-quantum satellite-transition to single-quantum central-transition coherence conversion. The duration of the pulses p1 and p2 was 2.1 and 1.4 ls respectively, at an RF amplitude corresponding to a 70 kHz of nutation frequency. The interval T was kept constant at a value of 15 rotor periods (937.5 ls). 512 transients were collected for 30 t1 increments. The coherence pathway corresponding to (0 ? +1 ? 1) was selected by proper phase cycling (given in the Fig. 3b caption) to form an echo signal (Fig. 3b). The pathway (0 ? 1 ? 1) which leads to an anti-echo signal for spin-52 systems [39] was neglected, as it is known that the lineshape resulting from the acquisition of an echo signal, although not purely absorptive, has much better phase properties than those arising from an anti-echo signal [39]. It is preferable to combine both the coherence pathways (0 ? ±1 ? 1) to obtain purely absorptive lineshape. This requires both the p = ±1 coherences for all the crystallites within the powder to be excited with equal amplitude which is not trivial owing to the weakness of the nutation frequency in relation to the quadrupolar frequency [39]. One way to ensure such an equal combination of the echo and antiecho signals is to use three pulse z-filtered or shifted-echo schemes. However, to avoid loosing any signal due to pulse imperfections or inefficient transfer of desired coherence we preferred to use two-pulse scheme with acquisition of only echo signal. In the case of the two-pulse 3QMAS experiment, the pulse p1 was optimised for triple-quantum coherence excitation and p2 was optimised for triple-quantum coherence to single-quantum central-transition coherence conversion. The duration of the pulses p1 and p2 was 5.0 and 2.8 ls respectively, using an RF amplitude corresponding to 63 kHz of nutation frequency. In the 3QMAS scheme a total of 4200 transients was collected for 16 t1 increments. The interval T was kept constant at a value of 250 ls corresponding to four rotor periods. A small value of T could be used in this case since the 3Q coherence experiences an effective dipolar field that is 3 times larger than what the single-quantum coherence experiences [40–42]. Since the multiple-quantum projection along the indirect dimension is a symmetric dipolar-split spectrum, Fourier transformation provides absorptive lineshapes directly. All other experimental details are provided in the figure captions. Fig. 3c shows the 17O coherence pathways involved in the 3QMAS experiment. The 3D experimental scheme shown in Fig. 4 was carried out to obtain the high-resolution spectrum for quadrupolar nucleus along with the QD correlation spectrum. In this case, a double-quantumfiltered (DQF)-STMAS [43] scheme was applied on the 17O channel, with a R1852 symmetry-based recoupling sequence on the 1H channel. STMAS was preferred to MQMAS on sensitivity grounds. The DQF-STMAS is superior to other STMAS schemes since it completely removes the diagonal and outer satellite peaks [43]. A total of 1024 transients was collected for each of 16 t1 and 16 t2 increments. The interval T between the excitation pulse and the first soft p pulse was kept constant at 250 ls. All other relevant experimental details are given in the figure caption. The nutation frequency of the excitation pulse, p1, and the conversion pulse, p3, was 70 kHz and that for the soft p pulses (p2 and p4) were 32 kHz. The DQFSTMAS scheme was incorporated with a shifted-echo mixing sequence [44–46] by applying a second soft p pulse at a fixed delay of s from the conversion pulse p3 (Fig. 4a). This was done to obtain

(a)

(b)

Fig. 4. (a) Pulse sequence for 3D scheme using high-resolution DQF-STMAS on 17O and R1852 symmetry sequence on 1H. The duration T represents the constant rotorsynchronised delay. (b) The coherence pathway selected for this experiment. A 64 step phase cycling was used to select the desired coherence pathway shown in (b) with p1: +x, x, +y, y; p2: 4(+x), 4(+y), 4(x), 4(y); p3: 16(+x), 16(+y), 16(x), 16(y); p4: +x; and receiver phase: p3  p2  p1.

pure absorption-mode lineshapes in the high-resolution plane of the 3D experiment. Only one coherence pathway (0 ? +1 ? +2 ? +1 ? 1) was selected by phase cycling (given in the Fig. 4b caption) to form an echo signal. As shown in Fig. 4a the t1 and t2 delays are dependent on each other. In this 3D experiment, as the t1 duration was incremented, the t2 duration was decremented, so that the total interval T remained constant. The 2D QD correlation spectrum appears in the F1–F3 plane after Fourier transformation with respect to the intervals t1 and t3. The high-resolution spectrum of 17 O, from which all the quadrupolar parameters may be extracted, appears in the F2–F3 plane after Fourier transformation with respect to the intervals t2 and t3. The R1852 symmetry-based recoupling sequence also recouples the 1H CSA. However, we have observed through simulations that at our moderate magnetic field, the proton CSA interaction has a negligible effect on the QD correlation spectrum. 2.3. Data processing All the data processing was done with TOPSPIN (version 2.1) software of Bruker. For all the 2D plots the lower threshold of the contour levels was selected such that the contours corresponding to the peak at 5 kHz (Fig. 5) of the quadrupolar powder pattern are just visible. Only positive contour levels are shown with a total of 28 levels for all the plots. For the experiment with twopulse spin-echo and STMAS schemes on 17O, contours are drawn with the maximum value of the contour levels confined to a value which is 11 times the value of the base contour level. Each contour level was incremented by a multiplying factor of 1.09 to create geometric sequence of levels. Exponential weighting function with a linewidth of 100 Hz was used along the direct dimension and no weighting function was used along the indirect dimension. For the experiment with two-pulse 3QMAS scheme on 17O, again the maximum value of the contour level was fixed to a value which is 5 times the lowest contour level where each contour level was incremented by a multiplying factor of 1.06. Exponential weighting function with a linewidth of 50 Hz was used along the direct dimension and no weighting function was used along the indirect dimension. To process the t1–t3 or the QD plane of the 3D experiment we have again used exponential weighting function with a linewidth of 55 Hz along the quadrupolar dimension and no weighting function along the dipolar dimension. Here, the maximum value used for the contour level was 330 times than that of the base contour level where each level was incremented by a

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multiplication factor of 1.23. For processing the t2–t3 or the highresolution plane of the 3D experiment we used exponential weighting function with a linewidth of 100 Hz along both the quadrupolar and the high-resolution dimensions. Contours were drawn with the maximum value of the contour level confined to a value which was 517 times the value of the base contour. Each contour level was incremented by a multiplication factor of 1.25. 2.4. Numerical simulations Both 1D and 2D numerical simulations were carried out using the SIMPSON simulation program (version 3.0.1) [47] that included all pulses, timings, and field strengths as executed in the experiments. For 2D simulation of the QD experiment the powder-averaged spectra were calculated using molecular orientations derived from 28656 {a, b} pairs selected using the method of Zaremba, Conroy, and Wolfsberg [48–50], combined with 10 equally-spaced c angles. For 1D dipolar evolution simulations, 656 {a, b} pairs and 10 c angles were used. Numerical integrations were performed using a minimum time-step of 0.5 ls. The SIMPSON simulation for calculating the dipolar evolution typically took 30 min. A full 2D QD simulation took about 90 h to complete on a HP XW 4400 workstation running on a Windows XP operating system. 3. Results and discussion 3.1. Quadrupolar–dipolar correlation experiments Quadrupolar–dipolar (QD) correlation spectra of 17O-brucite, obtained using the pulse schemes in Figs. 2 and 3a, are shown in Figs. 5–7. The particular shapes of the correlation spectra reflect the fact that the secular part of the dipole–dipole coupling varies across the quadrupolar powder pattern. Fig. 5 shows the QD spectrum of 17O-brucite, obtained using the pulse sequence of Fig. 2. The result is similar to that obtained by

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van Beek et al. [23]. Fig. 5b shows the projection onto the quadrupolar dimension, whilst Fig. 5c and d show the slices in the dipolar (indirect) dimension, at the positions of the right- and left-hand side singularities of the 17O quadrupolar powder pattern. The two-peak or the split structure of the slices is due to the recoupled heteronuclear dipolar interaction between the 17O and the directly-bonded 1H. Fig. 6 shows the QD spectrum of 17O-brucite, obtained using STMAS pulse sequence in Fig. 3a, and the coherence transfer pathway of Fig. 3b. The result is similar to that shown in Fig. 5, but with an enhanced signal-to-noise ratio. This is probably because the STMAS scheme superposes contributions from all the single-quantum transitions, whereas only the central transition contributes to the spin-echo experiment. As expected, the heteronuclear dipolar splitting of the 17O satellite transitions is the same as that of the central transition. Fig. 7 shows the QD spectrum of 17O-brucite, obtained using 3QMAS pulse sequence in Fig. 3a, and the coherence transfer pathway of Fig. 3c. The lineshape in the directly-detected dimension is strongly distorted in this case since the 3Q excitation is highly orientation-dependent. Nevertheless the heteronuclear splitting of the 17 O triple-quantum coherences is visible along the indirect dimension of the QD spectrum. As expected, this splitting is 3 times larger than for the single-quantum experiments, as discussed further below. The low signal strength of the 3QMAS experiment might be alleviated by incorporating a sensitivity enhancement scheme such as DFS (Double Frequency Shift) or FAM (Fast Amplitude Modulation) [51,52]. Fig. 8 shows the results of a 3D experiment in which the QD correlation is combined with a high-resolution DQF-STMAS technique, using the pulse sequence in Fig. 4. After Fourier transformation, the F1  F3 plane generates the 2D QD correlation spectrum (Fig. 8a), with the dipolar slices of the right-hand side singularity (Fig. 8b) and the left-hand side singularity (Fig. 8c). The high-resolution spectrum of the 17O nucleus was obtained from the F2  F3 plane

(b)

(a) (c)

(d)

Fig. 5. (a) 2D QD spectrum using spin echo on 17O, (b) projection along the direct (quadrupolar) dimension, (c) slice along the indirect (dipolar) dimension of the right-hand side singularity, and (d) slice along the indirect (dipolar) dimension of the left-hand side singularity. The vertical (dipolar) and horizontal (quadrupolar) axes correspond to the Fourier transforms with respect to the intervals t1 and t2 respectively. The relaxation delay was 2 s and the total experimental time was 10 h. The length of each t1 increment was 27.77 ls corresponding to two pairs of R blocks.

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(b)

(a) (c)

(d)

Fig. 6. (a) 2D QD spectrum using two-pulse STMAS on 17O, (b) projection along the direct (quadrupolar) dimension, (c) slice along the indirect (dipolar) dimension of the right-hand side singularity, and (d) slice along the indirect (dipolar) dimension of the left-hand side singularity. The vertical (dipolar) and horizontal (quadrupolar) axes correspond to the Fourier transforms with respect to the intervals t1 and t2 respectively. The relaxation delay was 2 s with total acquisition time of 8.5 h. The length of each t1 increment was 27.77 ls corresponding to two pairs of R blocks.

(a)

(b)

(c)

Fig. 7. (a) 2D QD spectrum using two pulse 3QMAS on 17O, (b) projection along the direct (quadrupolar) dimension, (c) slice along the indirect (dipolar) dimension of the right-hand side singularity. The vertical (dipolar) and horizontal (quadrupolar) axes correspond to the Fourier transforms with respect to the intervals t1 and t2 respectively. The relaxation delay was 2 s with total acquisition time of 37 h. The length of each t1 increment was 13.88 ls corresponding to a single pair of R block.

(Fig. 8d). The isotropic axis of the 2D STMAS plane was scaled by a factor of 17/31 in accordance with Refs. [39,53–55]. A slice of the high-resolution spectrum (shown as an inset in Fig. 8d) was analysed using the program DMFIT [56] to estimate the 17O quadrupolar coupling parameters in brucite as follows: quadrupolar coupling constant CQ = 6.21 ± 0.03 MHz and asymmetry parameter of the electric field gradient tensor g = 0.02 ± 0.01. We also obtained the average isotropic value, d = 71.36 ± 0.68 ppm which is a combination of both the isotropic chemical shift dCS and the the isotropic quadrupolar shift miso Q . The value of the isotropic quadrupolar shift miso Q was determined to be 50.36 ± 0.48

ppm using the method given in Refs. [57,58]. The isotropic chemical shift dcs for the p-quantum coherence can be evaluated by [59]:

h i dðpÞ ¼  dcs p þ miso Q ðpÞ=m0 where miso Q is the isotropic qudrupolar shift, the expression of which is given in Ref. [57], m0 is the Larmor frequency of the nucleus, and p = 1 for the direct dimension of the 2D DQF-STMAS experiment. This was the method used to estimate the isotropic chemical shift as dCS = 21.00 ± 0.48 ppm, which is in good agreement with the previously reported value of 25 ppm [60]. The uncertainties in the val-

M. Goswami, P.K. Madhu / Journal of Magnetic Resonance 219 (2012) 4–12

(a)

(b)

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(d)

(c)

(e)

Fig. 8. (a) 2D QD spectral plane from the 3D experiment using the pulse sequence in Fig. 4. The vertical (dipolar) and horizontal (quadrupolar) axes correspond to the Fourier transforms with respect to the intervals t1 and t3 respectively. (b) Slice along the indirect (dipolar) dimension of the right-hand side singularity from the 2D QD spectrum and (c) slice along the indirect (dipolar) dimension of the left-hand side singularity from the 2D QD spectrum. (d) High-resolution 2D 17O spectral plane. The vertical (isotropic) and horizontal (anisotropic) axes correspond to the Fourier transforms with respect to the intervals t2 and t3 respectively. The anisotropic slice along the quadrupolar dimension (black) and the corresponding modelled spectrum (red) are shown in the box (the dotted line indicates the row which was extracted for the fitting). (e) The anisotropic projection taken parallel to the direct dimension of the 2D 17O spectrum and (f) the high-resolution projection along the isotropic dimension. The relaxation delay was 2 s and the total acquisition time was 145 h. The length of each t1 increment was 27.77 ls corresponding to two pairs of R blocks. The length of each t2 decrement was also equal to two pairs of R blocks. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

ues of miso Q , and dCS were estimated by the propagation of error method [61]. Fig. 9 compares the experimental dipolar evolution curves for the central transition, the single-quantum satellite transition, and the triple-quantum transition of 17O. The dipolar evolutions of the central and satellite transitions are similar, since both are single-quantum transitions. The dipolar oscillation frequency of the right-hand side singularity in the triple-quantum experiment is 2.93 ± 0.05 times faster than for the two single-quantum experiments, which agrees with the expected ratio of 3, within experimental error. The amplification of effective heteronuclear dipolar couplings according to the multiple-quantum order has been observed before [40–42]. Only the evolution of the right-hand side singularity could be observed for the triple-quantum experiment since the triple-quantum excitation was not efficient enough to properly excite the whole powder pattern.

(a)

3.2. Estimation of heteronuclear dipolar coupling Fig. 10a and b shows numerically simulated dipolar oscillation curves generated assuming isolated two-spin 1H–17O model compared with experimental dipolar evolutions of the left-hand side singularity and the right-hand side singularity of the 17O quadrupolar powder pattern. The numerical simulations were done using the quadrupolar parameters of 17O found from the 3D experiment. The best fit simulations use heteronuclear 1H–17O dipolar coupling constants of 12.5 ± 0.2 kHz and 15.6 ± 0.2 kHz respectively. However, it is evident from the experimental 2D QD plots generated using spin-echo and STMAS schemes on 17O that the experimental dipolar splitting for the left-hand side singularity is 3.35 ± 0.05 kHz and that for the right-hand side singularity is 4.18 ± 0.05 kHz. Hence, the effective scaling factor observed in each experiments is of the order of 0.268 ± 0.005. Similar observations were made

(b)

Fig. 9. The experimental dipolar oscillations of (a) left-hand side singularity and (b) right-hand side singularity of brucite using different pulse schemes.

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(a)

(b)

Fig. 10. The experimental and simulated dipolar oscillations of (a) left-hand side singularity and (b) right-hand side singularity of brucite.

by Hou et al. [62] where they claimed that the effective scaling factor of R1852 sequence can reach as high as 0.303 under fast MAS condition. It is evident that the simulated best-fit evolutions show remarkably good correspondence with the experimental evolutions for both the singularities. From the simulations we obtained the dipolar information in the form of secular part of direct dipole–dipole coupling notated as d(t). d(t) depends on hjk(t) [63], the instantaneous angle between the internuclear vector and the magnetic field. The secular dipole–dipole coupling is given by:

1 dðtÞ ¼ bjk ð3cos2 hjk ðtÞ  1Þ 2 where the dipole–dipole coupling constant is given by:

bjk ¼ 

l0 cj ck h 4p r3jk

where rjk is the internuclear distance. So it is evident from above that the maximum possible value the secular dipole–dipole coupling d(t) can have is equal to the dipole coupling constant bjk when hjk(t) is equal to zero i.e, when the internuclear vector and magnetic field is collinear. It is clearly observable from all the 2D QD correlation experiments that the dipolar projections corresponding to the right-hand side singularity displays maximum splitting whereas it is minimum for the left-hand side singularity. As was mentioned earlier the best fit between a simulated dipolar evolution curve and the experimental dipolar evolution curve of the right-hand side singularity of the quadrupolar powder pattern was obtained for dipole–dipole coupling of 15.6 ± 0.2 kHz. Since it is evident from the 2D QD experiments that the maximum value possible for the secular dipole–dipole coupling was achieved for powder orientations corresponding to the right-hand side singularity of the

(a)

quadrupolar powder pattern, it can be safely assumed that the value of the dipole–dipole coupling constant is 15.6 ± 0.2 kHz. Moreover, the dipole–dipole coupling constant value of 15.6 ± 0.2 kHz corresponds to 1H–17O bond length of 101 ± 1 pico metre which is in very good agreement with the distance of 99.5 ± 0.8 pico metre predicted by neutron diffraction study [34] and a distance of 98 ± 2 pico metre that was found by combining proton NMR and X-ray data [64]. We also investigated if the presence of 1H from the next layer of the Mg(OH)2 may have any effect on the dipolar spectrum. However, it turned out that the distance between the oxygen atom of the hydroxyl group of one layer and the hydrogen atom of the hydroxyl group of the next layer (1H–17O  1H–17O) at ambient condition is of the order of 250 pico meter [65], which means that the resulting heteronuclear dipolar coupling will be 15.5 times lesser than the directly bonded 1H–17O pair. As a result we do not see any significant change in the simulation taking into account the presence of an extra 1H in the vicinity of a 1H–17O pair. This fact is further corroborated by Mookherjee and Stixrude [65] where they reported very weak to complete absence of H-bonding between two layers. We performed a series of 2D numerical simulations by varying the relative orientation of dipolar coupling tensor with respect to the quadrupolar coupling tensor. From the comparison of these simulations with the experimental results (Fig. 11), we concluded that the dipolar tensor and quadrupolar tensors are coaxial in agreement with the previous observations [23]. 4. Conclusions We have shown that by performing 2D quadrupolar–dipolar correlation experiments using different echo sequences such as spin echo, STMAS, and MQMAS the effects of recoupled heteronu-

(b)

Fig. 11. (a) Experimental QD spectrum (same as in Fig. 6) and (b) simulated QD spectrum. The horizontal and vertical axes are the quadrupolar and dipolar axes respectively.

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clear dipolar coupling on single-quantum and multiple-quantum transitions can be probed. We have observed heteronuclear splitting for both single-quantum and multiple-quantum transitions. We have further shown that high-resolution NMR schemes for quadrupolar nuclei can be combined with symmetry-based heteronuclear recoupling sequence to simultaneously obtain dipolar and quadrupolar informations. This method will be of particular importance for materials with more than one quadrupolar site since one can get the dipolar information of all the individual sites separately. From the experimental dipolar oscillations we observed the value of dipolar coupling constant and the 1H–17O bond distance in brucite sample which showed close correspondence with the previously reported values. We have also done the simulation of 2D QD correlation experiment from which it is concluded that the dipolar tensor and quadrupolar tensor are coaxial in brucite in agreement with previous observations.

Acknowledgments We acknowledge the use of National Facility for High-Field NMR, TIFR, for the use of the Bruker AV500 spectrometer, Malcolm Levitt for discussions and a careful reading of the manuscript, and M.V. Naik for technical assistance. This research was supported by the Royal Society (UK), British Council (India), and EPSRC (UK).

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