A 3D experiment that provides isotropic homonuclear correlations of half-integer quadrupolar nuclei

Journal of Magnetic Resonance 246 (2014) 122–129

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A 3D experiment that provides isotropic homonuclear correlations of half-integer quadrupolar nuclei Dinu Iuga ⇑, Diane Holland, Ray Dupree Physics Department, University of Warwick, CV4 7AL Coventry, UK

a r t i c l e

i n f o

Article history: Received 16 May 2014 Revised 30 June 2014 Available online 21 July 2014 Keywords: NMR MAS MQMAS Quadrupolar nuclei Isotropic homonuclear correlations

a b s t r a c t Two 3D experiments, capable of producing enhanced resolution two-spin double-quantum (DQ) homonuclear correlations for half-integer quadrupolar nuclei, are described. The first uses a split-t1 MQMAS sequence followed by a sandwiched oR3 symmetry-based dipolar recoupling sequence to directly excite DQ coherences. In this case an isotropic single-quantum (SQ) coherence starts the homonuclear DQ excitation. In the second experiment a single strong pulse is used to create triple quantum (TQ) coherence followed by a further single pulse conversion to zero-order before a non-sandwiched oR3 DQ sequence. The first experiment is demonstrated using 87Rb in RbNO3, with three Rb sites in a 5 ppm range, and the second to 11B in caesium triborate, CsB3O5, with two three-coordinated sites separated by 2 ppm and one four-coordinated boron site. In both cases, all sites are clearly resolved and their connections observed. The second experiment has higher sensitivity and a good signal to noise is obtained in a reasonable time despite the long T1 relaxation time of 11B in this material. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Solid State Nuclear Magnetic Resonance (SSNMR) of half-integer quadrupolar nuclei (such as 27Al, 17O, 87Rb and 23Na) is used extensively for structural characterisation of a large variety of materials such as zeolites, ceramics and biomaterials. The sample is, in most of the cases, subject to magic-angle spinning (MAS) in order to remove the dipolar interaction, chemical shift anisotropy and part of the quadrupolar interaction. However the one-dimensional spectrum is often broadened by the uncancelled part of the second-order quadrupolar interaction. A possible next step is to remove this second-order quadrupolar broadening in order to obtain a spectrum with isotropic resolution. Two-dimensional experiments such as multiple quantum (MQ)MAS [1] and satellite transition (ST)MAS [2] are now routinely used in order to obtain the isotropic chemical shift and quadrupolar parameters of a halfinteger nucleus. Other techniques, where the sample is spun at two different angles, such as double rotation (DOR) [3,4] or dynamic angle spinning (DAS) [5,6] are also capable of removing quadrupolar broadening, however they require dedicated probeheads and will not be further considered in this paper. The MAS high-resolution spectrum is obtained at the cost of losing the structural information provided by the through-space ⇑ Corresponding author. Fax: +44 (0) 24 76150897. E-mail address: [email protected] (D. Iuga). http://dx.doi.org/10.1016/j.jmr.2014.07.003 1090-7807/Ó 2014 Elsevier Inc. All rights reserved.

dipolar interaction. In order to retrieve this information, the dipolar interaction can be reintroduced in a controlled fashion [7,8] to create two-spin coherences which are then measured in the indirect dimension of a two-dimensional experiment. A Fourier transform of such two-dimensional data shows peaks associated with homo- (or hetero-) nuclear couplings. These peaks can be further utilised to generate a proximity chart of the nuclei that can be used to assign the peaks and to further elucidate the structure. Alternatively, the through-space (or through-bond) dipolar interaction can be used as a filter [9] in one-dimensional experiments in order to simplify the spectra and retain only the peaks coming from homo- (or hetero-) coupled nuclei. For half-integer quadrupolar nuclei with a significant electric field gradient, high-resolution under MAS can only be obtained with a two-dimensional experiment and therefore measuring a two-spin coherence with isotropic resolution necessitates a three-dimensional experiment. Such three-dimensional experiments have been demonstrated for heteronuclear correlations between a half-integer quadrupolar nucleus and a spin I = 1/2 nucleus (27Al–31P) [10]. The through-bond dipolar coupling of quadrupolar nuclei (and the contribution from the residual through-space dipolar coupling) has been extensively studied and employed in hetero-nuclear correlation studies involving quadrupolar nuclei [11–17]. In the case of the half-integer quadrupolar nuclei, the dipolar and quadrupolar Hamiltonians do not commute, therefore in the presence of quadrupolar interaction the quantisation axis of the dipolar

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interaction is not aligned with the direction of the external magnetic field and MAS fails to completely average the dipolar interaction. These residual dipolar couplings have been reported since 1991 [18] and are actively used in hetero-nuclear correlation experiments involving quadrupolar nuclei [19]. In inorganic materials, the internuclear distances between quadrupolar nuclei are often relatively large and the through-bond couplings correspondingly small. In addition, the T 2 coherence life times of quadrupolar nuclei are short and therefore sequences that reintroduce the through-space dipolar coupling in the presence of the quadrupolar interaction are required. Rotary resonance recoupling (R3), [8,20,21] symmetry based recoupling sequences, [22–24], or spinning away from the magic angle [25,26] have been used to create homonuclear correlation spectra of half-integer quadrupolar nuclei. However, none of these experiments provide isotropic resolution of spectra from the quadrupolar nuclei. For half-integer quadrupolar nuclei further complications arise from the multitude of possibilities of two-spin couplings. Each spin I = 3/2 nucleus has three transitions (a central transition and two satellite transitions) and any of them can couple with any of the three transitions of the pair nucleus. For example in a spin system formed by two coupled spin I = 3/2 nuclei there are 16 energy levels with 9 double-quantum and 9 zero-quantum transitions [21]. In addition, during MAS the quadrupolar interaction felt by a spin oscillates with several zero-crossings per rotor period [27]. This induces adiabatic (or partly-adiabatic) transfers between energy level populations and coherences. The difficulty in designing a pulse sequence that creates two-spin coherences is obvious since any radio-frequency (RF) irradiation of the sample activates these zero-crossing transfers which cause coherence leakages. A partial solution to this problem is to use very weak recoupling pulses but they are inefficient in building up two-spin coherences. The recently introduced optimised R3 (oR3) [21] sequence, reduces the amplitude of the R sequence for four short (1–3 ls) periods of time during a rotor period in order to avoid adiabatic passages between the single spin quadrupolar energy levels. This allows slightly higher RF field strength for the recoupling pulses making them more efficient in creating two-spin coherences. Such optimisation can be used in combination with any recoupling sequence but is more effective for sites that experience a relatively large quadrupolar interaction. This paper demonstrates that the enhanced resolution provided by the MQ sequence can be used to create two-spin double-quantum (DQ) coherence. Two versions of the 3D experiment are demonstrated, the first on 87Rb in RbNO3 and the second is applied to 11 B in a CsB3O5 sample. An obvious problem one expects when combining two experiments with low sensitivity is of course sensitivity. Already in 1999–2000 several groups demonstrated that the sensitivity of the MQMAS experiment can be enhanced by using Rotation Induced Adiabatic Coherence Transfer [28], Double Frequency Sweep (DFS) [29,30] or Fast Amplitude Modulation [31,32] for the TQ ? SQ conversion pulse. One can also use Soft Pulse Added Mixing phase cycling [33] to enhance the sensitivity of the MQMAS experiment. In addition several recoupling sequences have been introduced to enhance the sensitivity of the DQ homonuclear correlation experiment. We believe that a major sensitivity enhancement was demonstrated by Wang et al. [34] who did not use sandwiched excitation and conversion pulses. Also it should be noted that now, with the increasing implementation of Dynamic Nuclear Polarization (DNP), one should not give up hope on low sensitivity experiments but rather actively look for new developments that, in combination with DNP, will reveal new interesting phenomena such as that previously described [21] which showed that the SQ coherences coming from different spins, initially broadened by equal quadrupolar interactions but with opposite orientation, can form a DQ coherence free of quadrupolar broadening.

2. Pulse sequences The two versions of the 3D MQ-DQ-MAS experiment are shown in Fig. 1. The first, a split-t1 MQ-DQ-MAS shown in Fig. 1a, combines a DFS enhanced MQMAS sequence, where the triple quantum (TQ) coherence is converted to a SQ coherence using a convergent DFS, with a sandwiched oR3 DQ excitation and conversion separated by a DQ filter. The second version of the MQ-DQ-MAS experiment is shown in Fig. 1b. In this case a single strong pulse is used to create the TQ coherence followed by a single strong pulse conversion to a zero order. A non-sandwiched oR3 sequence is then used to excite the two-spin DQ coherence which, after evolution and a two-spin DQ filter, is converted to zero-order using again a non-sandwiched oR3 sequence.

3. Experimental details The experiments were performed on a Bruker 850 MHz spectrometer using a 3.2 mm HXY probe configured for 2 channel HX experiments. The 87Rb 3D split-t1 MQ-DQ-MAS experiment performed on RbNO3 had 32 increments in the F1 (MQ) dimension, a sweep width of 3.375 kHz and 32 increments in the F2 (DQ) dimension with a sweep width of 12 kHz. The sample was spun at 12 kHz using an oR3 [21] sequence with y -y phase alternation [35] on successive rotor period spin lock pulses lasting 4 rotor periods (mixing time 0.67 ms) was used to excite and convert the DQ coherence. A 7 ls, strong (RF field strength 100 kHz) pulse was used to excite the triple quantum TQ coherence and a quarter of the rotor period DFS (RF field strength 40 kHz) from 400 kHz to 100 kHz was used to convert the TQ coherence into a single quantum (SQ) coherence. 192 scans with 0.25 s relaxation delay have been applied for each increment (experiment time 13.65 h).

(a)

t1

7 t1 9

t2 o 180

t3 90o

3 2 1 0 -1 -2 -3

(b) o 180

t1

90o

t2

t3

3 2 1 0 -1 -2 -3 Fig. 1. Pulse sequences for the 3D MQ-DQ MAS experiments: (a) a split-t1 MQMAS sequence results in a SQ coherence which is further used in a conventional DQ experiment; (b) a simple 2 pulse MQMAS sequence ends in a zero-order along the B0 field which is further used in a DQ sequence.

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The 11B 3D MQ-DQ-MAS experiment performed on CsB3O5 had 64 increments in the F1 (MQ) dimension with a sweep width of 12 kHz and 32 increments in the F2 (DQ) dimension with a sweep width of 24 kHz. The sample was spun at 24 kHz and an oR3 sequence lasting 6 rotor periods (mixing time 0.50 ms) was used to excite and convert the DQ coherence. A 5 ls, strong (RF field strength 100 kHz) pulse was used to excite the TQ coherence and a short 1.5 ls (RF field strength 100 kHz) pulse was used to convert the TQ coherence into an SQ coherence. 192 scans with 0.24 s relaxation delay have been accumulated for each increment (experiment time 26.2 h). RbNO3 was purchased from Sigma–Aldrich. The CsB3O5 sample (characterised and used in Ref. [39]) was prepared starting from 11 B2O3 (99.27% isotope) and Cs2CO3 (Alfa Aesar 99.9%) by Sinclair et al. [36].

Table 1 NMR parameters for

87

Rb in RbNO3.

Site

diso (ppm)

dQIS (ppm)

dcg (ppm)

CQ (MHz)

g

Rb1 Rb2 Rb3

32.0 ± 0.5 28.9 ± 0.5 27.6 ± 0.5

1.0 1.6 0.9

33.1 30.6 28.6

1.7 ± 0.2 2.0 ± 0.2 1.7 ± 0.2

0.5 ± 0.1 0.9 ± 0.1 0.2 ± 0.1

experiment is presented in Fig. 2b (with the simulated MQMAS spectrum in Fig. 2d) and clearly shows the three distinct Rb sites, the projection in the F1 dimension being free of second-order quadrupolar broadening. Simulation of the 87Rb lines in both MAS and MQMAS spectra can then straightforwardly reveal the parameters given in Table 1[37,38]. The centre of gravity of a half-integer quadrupolar spectrum, obtained with Larmor frequency m0, is determined not only by the isotropic shift, diso, but also by dQIS the quadrupolar induced shift [4]:

4. Results and discussions 4.1. RbNO3

dcg ¼ diso  dQIS ¼ diso 

The 87Rb MAS spectrum of RbNO3 is well known in the NMR community since RbNO3 is often used to optimise MQMAS and STMAS experiments[37]. The resonances from the three crystallographically distinct Rb sites are broadened by the second-order quadrupolar interaction and, even in a 20 T magnetic field, there is considerable overlap of the lines from the different sites (Fig. 2a). The short longitudinal relaxation time, T1, allows pulse delays of 0.25 s and isotropic MQMAS spectra can be obtained within 20 min. The MQMAS spectrum obtained with a split-t1

P2 3 f ðIÞ Q2 40 m0 1=2

where PQ ¼ C Q ð1 þ g2Q =3Þ and f ðIÞ ¼ ½IðIþ1Þ3=4 I2 ð2I1Þ2 A 2D DQ correlation experiment can also be obtained in few hours (Fig. 2c) but in this case the interpretation of the spectrum is very difficult since both dimensions have different anisotropic broadening coming from the second-order quadrupolar broadening. The DQ correlation spectrum has in its F1 dimension two-spin DQ signals coming from 87Rb–87Rb pairs. From the crystal structure[39] we can see that each Rb site has six rubidium neighbours

(a)

- 20

- 25

- 30

- 35

(b)

- 40

[ppm]

- 28

- 30

- 32

- 54

DQ [ppm]

- 62 - 58

Iso [ppm]

- 27

- 29

- 31

- 66

(c)

- 28

- 34

- 30

- 32

SQ [ppm]

SQ [ppm]

(e)

Rb3 -28

-30

-32

SQ [ppm]

-34

DQ [ppm]

-62 -58 -54

-27

Rb2

Iso [ppm]

-29

-31

Rb1

-66

(d)

-28

-30

-32

SQ [ppm]

Fig. 2. Experimental 87Rb NMR spectra of RbNO3: (a) MAS; (b) MQMAS experiment 96 scans, relaxation delay 0.5 s and 128 increments, experimental time 1.7 h; (c) DQ experiment 128 scans, relaxation delay 0.5 s and 128 increments, experimental time 2.3 h. Simulated 87Rb NMR spectra of RbNO3: (d) MQMAS and (e) DQ.

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D. Iuga et al. / Journal of Magnetic Resonance 246 (2014) 122–129 Table 2 Expected position in F1 and F2 of the 9

87

Rb DQ peaks of RbNO3.

Pair

F2 (ppm)

F1 (ppm)

Pair

F2 (ppm)

F1 (ppm)

Pair

F2 (ppm)

F1 (ppm)

Rb1–Rb1 Rb1–Rb2 Rb1–Rb3

33.1 33.1 33.1

66.2 63.7 61.7

Rb2–Rb1 Rb2–Rb2 Rb2–Rb3

30.6 30.6 30.6

63.7 61.2 59.2

Rb3–Rb1 Rb3–Rb2 Rb3–Rb3

28.6 28.6 28.6

61.7 59.2 57.2

F2

(p

pm

)

F3 (p

pm)

(a)

)

F1 (ppm

(b)

-28

-30

-32

-28

-34

- 65 - 60

Rb1- Rb3

Rb3- Rb1

DQ [ppm]

Rb1- Rb2

- 55

Rb1- Rb3

Rb3- Rb1

- 60

Rb1- Rb2

DQ [ppm]

Rb2- Rb1

Rb1- Rb1

Rb2- Rb1

- 55

Rb1- Rb1

- 65

(e)

-30

-32

-34

Iso [ppm]

Iso [ppm]

-30

-32

Rb3- Rb2

-34

-28

Rb2- Rb3

-30

- 65 - 60

Rb2- Rb2

- 55

Rb2- Rb3 Rb3- Rb2

Rb1- Rb2

Rb2- Rb1

- 55

Rb2- Rb2

-28

- 65 - 60

Rb1- Rb2

DQ [ppm]

Rb2- Rb1

DQ [ppm]

(f)

(c)

-32

-34

Iso [ppm]

Iso [ppm]

- 65 - 60

Rb2- Rb3

- 55

- 65

Rb1- Rb3

Rb3- Rb3

Rb3- Rb3 -28

Rb3- Rb1 Rb3- Rb2

- 55

Rb2- Rb3

- 60

Rb1- Rb3

DQ [ppm]

Rb3- Rb1 Rb3- Rb2

DQ [ppm]

(g)

(d)

-30

-32

Iso [ppm]

-34

-28

-30

-32

-34

Iso [ppm]

Fig. 3. 87Rb split-t1 MQ-DQ-MAS experiment of RbNO3: (a) 3D cube; (b) F1–F2 plane extracted at F3 = 33 ppm; (c) F1–F2 plane extracted at F3 = 31 ppm; (d) F1–F2 plane extracted at F3 = 29 ppm. Simulated 87Rb DQ spectrum of RbNO3 involving the (e) Rb1 site, (f) Rb2 site and (g) Rb3 site.

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(a)

(b)

15

20

10

5

0

-5

[ppm]

(c)

60 10

δ2 [ppm]

5

0

25

20

15

10

5

0

5

0

SQ [ppm]

(e)

(f)

B2 15

10

δ2 [ppm]

5

0

10 20 30 40

60

B1

δ1 [ppm]

40

20

0

B3

DQ [ppm]

15

DQ [ppm]

40

δ1 [ppm]

40 30 20 10

20

0

(d)

25

20

15

10

SQ [ppm]

Fig. 4. a) triborate ring structure; experimental 11B NMR spectra of CsB3O5: (b) MAS; (c) MQMAS experiment 24 scans, relaxation delay 1 s and 128 increments, experimental time 0.9 h; (d) DQ experiment 32 scans, relaxation delay 1.2 s and 96 increments, experimental time 1 h. Simulated 11B NMR spectra of CsB3O5: (e) MQMAS and (f) DQ.

Table 3 NMR parameters for

11

B in CsB3O5.

Site

diso (ppm)

dQIS (ppm)

dcg (ppm)

CQ (MHz)

g

B2 (3-coordinated) B1 (3-coordinated) B3 (4-coordinated)

19.9 ± 0.5 17.8 ± 0.5 1.2 ± 0.5

2.6 2.1 0.0

17.3 15.7 1.2

2.8 ± 0.2 2.5 ± 0.2 0.1 ± 0.1

0.2 ± 0.1 0.2 ± 0.1 0.2 ± 0.1

situated between 4 Å and 4.6 Å. The natural abundance of the 87Rb is 27.8% and therefore a statistical distribution of 87Rb neighbours is expected with nearly 87% of 87Rb having at least one 87Rb neighbour. Therefore one would expect to see all 9 DQ peaks with their approximate positions indicated in Table 2 The position in the F1 dimension can vary slightly since the quadrupole induced shift of a DQ coherence can add fully or only partially, depending on the relative orientation of the quadrupolar tensors of the two spins involved. Therefore, unambiguous identification of the 9 DQ peaks in the spectrum shown in Fig. 2c is not feasible. Fig. 2e shows the simulated spectra obtained by convoluting the quadrupolar line shapes of the three sites in a two dimensional spectrum. Each line is convoluted with all the three sites as is expected from the crystal structure. For simplification the lineshape in the indirect dimension (F1) is considered to be the normal MAS lineshape of the half-integer quadrupolar nuclei. A combination of the MQMAS pulse sequence with a DQ correlation experiment can deliver 3D experiments in which one

dimension has the isotropic information, the second dimension reveals the DQ correlations and the third dimension (the acquisition dimension) has the second-order quadrupolar broadening. The 3D cube (Fig. 3a) obtained with the MQ-DQ-MAS experiment looks initially somewhat disappointing as the 9 distinct DQ peaks cannot be readily identified. This of course is due to the quadrupolar interaction that broadens the two SQ coherences involved in the DQ signal. However the split-t1 MQMAS sequence at the beginning of the DQ correlation experiments creates a SQ coherence with the second-order quadrupolar broadening compensated by the initial evolution of the TQ coherence. Therefore, an isotropic SQ coherence starts the two-spin homonuclear DQ sequence which is then combined with a regular SQ coherence broadened by a part of the second-order quadrupolar interaction so that the 9 DQ peaks are identifiable in different 2D planes extracted from the centre of gravity for each of the peaks in the F3 dimension. For example the F1–F2 plane for F3 = 33 ppm (Fig. 3b) shows the two-spin DQ peaks involving the Rb1 site (diso = 32.0 ppm); a

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( F2

pp

m)

(a)

)

pm

p 1(

F

)

ppm

F3 (

(d)

25

B 3 - B2

20

15

10

-10 B3 - B1 B3 - B 2

B2 - B3

5

25

δ2 [ppm]

(c)

20

15

δ2 [ppm]

10

δ1 [ppm]

B2- B3

B3- B3 B1 - B3

50 40 30 20 10 0

B3 - B1

δ1 [ppm]

B3- B3

B1 - B3

50 40 30 20 10 0 - 10

(b)

5

B1 - B2

B2 - B2

25

20

15

δ2 [ppm]

10

-10

5

B1 - B1

B2 - B3

B2 - B1

B3 - B2

B 1 - B2

B2- B2

25

B 3 - B1

20

15

δ2 [ppm]

10

δ1 [ppm]

B2 - B1

B1 - B3

50 40 30 20 10 0

B1 - B1

δ1 [ppm]

50 40 30 20 10 0 - 10

(e)

5

Fig. 5. 11B MQ-DQ-MAS experiment of CsB3O5: (a) 3D cube, (b) F1–F2 plane extracted at F3 = 1 ppm, (c) F1–F2 plane extracted at F3 = 18 ppm. The two extracted spectra were referenced as a SQ dimension on both d1 and d2 axis. This however is partially incorrect as the d2 axis is a combination of SQ and TQ signals. The peaks are tilted in a 3D cube and the positions of the peaks on the F1–F2 planes are only approximately correct. A formal convention to calibrate the axis will be presented in a future paper. Simulated 11B MQ-DQ-MAS spectrum of CsB3O5 involving the (d) B1 site and (e) B2,3 sites.

corresponding simulated spectrum shown in Fig. 3e can be obtained by convoluting the quadrupolar line shapes of the three Rb sites with an isotropic (without quadrupolar broadening) lineshape corresponding to the Rb1 site. Of course this simplified simulation considers only the theoretical second-order quadrupolar MAS lineshape of the central transition without calculating the density matrix evolution under the experimental pulse sequence and therefore the positions of the peaks are only approximate. Similarly Fig. 3c shows the F1–F2 plane for F3 = 31 ppm (the simulation shown in Fig. 3f) corresponding to the Rb2 site (diso = 28.9 ppm) whereas the F1–F2 plane for F3 = 29 ppm (Fig. 3d, and the simulation shown in Fig. 3g) shows the two-spins DQ peaks involving the Rb3 site (diso = 27.6 ppm). 4.2. CsB3O5 The CsB3O5 crystal phase [40] contains the triborate ring structure (Fig. 4a) consisting of two 3-coordinated (B1 and B2) and one 4-coordinated (B3), boron atoms linked by oxygen atoms to give a

six atom ring which is connected to other triborate rings by B1–O–B3 or B2–O–B3 links. The distances between different B sites in the same ring are very similar at 2.41–2.48 Å. The distances from B1 and B2 to B03 (adjacent rings) are not much longer (2.53 and 2.41 Å) but the B1,2–B2,1’ distance is 3.50 Å and the B1–B01 3.77 Å. The B2–B02 and B3–B03 distances are longer still at 4.39 and 4.47 Å respectively. The B1,2 boron atoms have two B3 and one B1,2 boron neighbours and B3 has four B1,2 neighbours. Given the 11B enrichment to 99.27%, interactions could occur with all neighbouring boron atoms. Examples of MAS, MQMAS and DQ correlation spectra are shown in Fig. 4. The 11B MAS spectrum (Fig. 4b) resolves the tetrahedral B3 site (1.2 ppm) and shows the B1,2 sites overlapped [41–43]. The MQMAS spectrum, this time using a single TQ excitation pulse and a single TQ ? SQ conversion pulse, is shown in Fig. 4c with the simulated MQMAS spectrum in Fig. 4e. This unambiguously separates the B1 (diso = 17.8 ppm) and B2 (diso = 19.9 ppm) sites [39] and provides an enhanced resolution for 11B in CsB3O5. The DQ correlation spectra shown in Fig. 4d provides further structural information in the sense that it demonstrates that two BO4

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tetrahedra are in proximity; and at the same time the BO4 tetrahedra are in proximity with the trigonal planar BO3. Also, despite the lack of resolution for the three co-ordinated B1 and B2 sites in the DQ correlation spectrum one can conclude that at least one of these sites correlates either with itself or with the other three co-ordinated site. Again we simulated the spectra by convoluting the quadrupolar line shapes of the three sites in the two dimensional spectrum. Each isotropic line is convoluted with all the three sites as is expected from the crystal structure (Fig. 4f). The parameters used in the simulation are shown in Table 3[36,39]: The T1 relaxation time of 11B in CsB3O5 is very long so that the signal is significantly reduced at the short delays needed to complete a 3D experiment in a reasonable time thus, in order to improve the sensitivity and reduce the offset dependence (since the separation of the resonances is larger for CsB3O5), a different 3D MQ-DQ-MAS correlation experiment was employed. This experiment uses a non-sandwiched DQ sequence[34] which increases the efficiency of double quantum excitation and conversion and is less sensitive to offset. However it requires the TQ part of the experiment to end up with zero quantum coherence as shown in Fig. 2b. Thus a single TQ excitation pulse and a single TQ ? SQ conversion pulse was used to excite the coherence. The result of this MQ-DQ-MAS experiment is shown in Fig. 5. Again the 3D cube spectrum (Fig. 5a) is difficult to interpret but one can extract F1–F2 planes at precise F3 positions. Fig. 5b shows the F1–F2 planes at F3 = 1 ppm (B3) and one would expect to see the two-spin DQ coherences corresponding to the B3–B3; B1–B3 and B2–B3 as shown in the simulated spectrum in Fig. 5d. The simulated spectrum, as before, was obtained by convoluting the isotropic (without quadrupolar broadening) lineshape of the B3 site with the quadrupolar lineshapes of the B1, B2 and B3 sites. In the F1–F2 plane for F3 = 18 ppm (B2 and B1) one can identify the B1–B1; B1–B2 and B2–B2 as well as B2–B3 and B1–B3 peaks (Fig. 5c with the simulated spectrum shown in Fig. 5e). The simulated spectra are only meant as a guide since they only consider the analytical lineshape of the second-order quadrupolar MAS lineshapes of the central transition without taking into account the lineshapes of the DQ or TQ transitions. The consequence of not using a split-t1 experiment is that the F1 dimension no longer represents a fully isotropic line but rather a TQ coherence tilted in the F1–F2–F3 cube. However the difference between the TQ and the SQ coefficients provides enhanced resolution on the F1–F2 planes.

5. Conclusions This paper introduces two versions of an experiment capable of producing isotropic two-spin DQ correlations of half-integer quadrupolar nuclei in which MQMAS is combined with doublequantum homonuclear pulse sequences into a 3D experiment. The experiments were performed on 87Rb in RbNO3 and on 11B in CsB3O5 and in both cases homonuclear correlation spectra with high resolution were obtained. Whilst 2D homonuclear correlation spectra of the two samples show very limited resolution with the expected 9 DQ peaks overlapping, the newly introduced experiments clearly separate the nine DQ peaks. The first experiment, which was applied to RbNO3, uses a split-t1 MQMAS sequence followed by an optimised R3 symmetry-based dipolar recoupling sequence to directly excite DQ coherences. Since isotropic SQ coherence starts the two spin homonuclear DQ excitation the spectrum is easier to interpret than in the second experiment and is also able to clearly resolve the Rb2 and Rb3 sites which are separated by 1 ppm. However it is less sensitive since sandwiched DQ pulse sequences have been shown to be considerably less effective in generating DQ coherence than the non-sandwiched sequence used in the second experiment. In that experiment, which

was applied to CsB3O5, a single strong pulse is used to create triple quantum coherence followed by a further single pulse conversion to zero order before the DQ sequence. Thus the homonuclear DQ coherence is created from a mixture of TQ and SQ coherences and none of the 3D axes correspond to the isotropic chemical shift. A fast and simplified simulation obtained by convoluting isotropic lineshapes with the second-order quadrupolar lineshapes is shown in order to assist in the peak assignment. These experiments open new possibilities in NMR structural studies involving quadrupolar nuclei, as they can potentially provide information about inter-nuclear distances and relative orientation of quadrupolar tensors to aide refinement of structure.

Acknowledgments The UK 850 MHz solid-state NMR Facility used in this research was funded by EPSRC and BBSRC, as well as the University of Warwick including via part funding through Birmingham Science City Advanced Materials Projects 1 and 2 supported by Advantage West Midlands (AWM) and the European Regional Development Fund (ERDF).

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