Pulse-assisted homonuclear dipolar recoupling of half-integer quadrupolar spins in magic-angle spinning NMR

Chemical Physics Letters 410 (2005) 24–30 www.elsevier.com/locate/cplett

Pulse-assisted homonuclear dipolar recoupling of half-integer quadrupolar spins in magic-angle spinning NMR Mattias Ede´n a

˚ sa Zazzi , Hans Annersten b, A

a,*

c

Physical Chemistry Division, Arrhenius Laboratory, Stockholm University, SE-106 91 Stockholm, Sweden b Department of Earth Sciences, Uppsala University, SE-752 36 Uppsala, Sweden c Department of Chemistry, Royal Institute of Technology, SE-100 44 Stockholm, Sweden Received 2 March 2005 Available online 9 June 2005

Abstract We demonstrate numerically and experimentally that zero-quantum homonuclear dipolar recoupling techniques employing rotor-synchronized 180
pulses, previously introduced for spin-1/2 applications, are useful also for magnetization transfers between half-integer quadrupolar nuclei in rotating solids. The recoupling sequences are incorporated as mixing periods in two-dimensional experimental protocols, that correlate either single-quantum coherences of coupled spins, or triple-quantum with single-quantum coherences for improving spectral resolution. We present 23Na and 27Al NMR experiments on powders of sodium sulphite [Na2SO3], YAG [Y3Al5O12] and a synthetic chlorite mineral [Mg4.5Al3Si2.5O10(OH)8].  2005 Elsevier B.V. All rights reserved.

1. Introduction Pulse sequences to recover averaged through-space dipolar couplings between spins-1/2 have become central ingredients in magic-angle spinning (MAS) solid state NMR methodology for probing molecular structure and dynamics. While homonuclear dipolar recoupling involving spins-1/2 is well developed both from theoretical and application standpoints [1–3], this field is significantly less explored in the case of half-integer quadrupolar nuclei, despite their presence in a large number of important natural and synthetic materials such as minerals, ceramics and glasses. This is partly due to the fact that radio-frequency (rf) fields no longer dominate the internal spin-system parameters; intense first- and second-order quadrupolar interactions lead often to intractable spin dynamics and magnetization losses during the rf irradiation.

*

Corresponding author Fax: +46 8 152187. E-mail address: [email protected] (M. Ede´n).

0009-2614/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.cplett.2005.04.030

It has been demonstrated that homonuclear dipolar recovery occurs spontaneously in quadrupolar spin systems undergoing MAS, either due to the presence of heteronuclear couplings to nearby protons [4–6], or by interference effects between quadrupolar and homonuclear dipolar interactions [6–11]. Such recoupling processes result in minimal signal losses and are advantageous in their simplicity for implementation. However, they are often quenched in cases of large frequency separations between the spins, either due to chemical or quadrupolar shifts [6,7,10]. Some of the existing methodology to actively recover homonuclear dipolar interactions among quadrupolar spins is very efficient, but rely on off-magic-angle spinning and compromise spectral resolution unless specialized probeheads are used [12–14]. Nevertheless, variants of the rf-based rotary resonance recoupling (R3) technique introduced for spins-1/2 [15,16], have been demonstrated also for recoupling of quadrupolar nuclei [11,17–19], as has rotational resonance (R2) recoupling [20]. In this Letter, we investigate alternative approaches for recovering homonuclear dipolar interactions between

M. Ede´n et al. / Chemical Physics Letters 410 (2005) 24–30

our samples involve spins with longitudinal relaxation times in the order of 5–15 s, the experiment starts with a saturation-recovery block to ensure reproducible results. Next follows a set of FAM (RAPT) pulses, typically providing a CT signal enhancement factor of S + 1/2 for a nucleus with spin S [25,26]. This technique is useful for all applications starting with CT magnetization, and has also been applied for enhancing crosspolarization transfers between quadrupolar nuclei and spins-1/2 [27], and for homonuclear 2QC–1QC correlations of quadrupolar nuclei [28]. The scheme in Fig. 1a continues by a weak (ÔselectiveÕ) [29] p/2-pulse to excite CT 1QC, which evolve during the interval Ôt1Õ prior to being stored as longitudinal magnetization by another selective p/2-pulse. Magnetization transfers between coupled spins occur during the subsequent mixing period (discussed below), and are revealed in the resulting 2D spectrum as off-diagonal Ôcross-peaksÕ [4–6,17]. To improve spectral resolution by removing second-order quadrupolar broadening, the mixing period may be incorporated in a z-filter MQMAS experiment [5,30,31] (Fig. 1b): here triple-quantum coherences (3QC) are first created by a strong pulse of duration sexc, and subsequently converted into longitudinal magneti-

quadrupolar nuclei under MAS, by borrowing a set of zero-quantum recoupling techniques initially introduced for spin-1/2 applications. These schemes originated from the RFDR (Ôradio-frequency driven recouplingÕ) method, involving application of a strong p-pulse every consequtive rotational period [21]. More recently, symmetry-based arguments in MAS NMR [2] were employed to engineer more efficient recoupling using either lowamplitude (ÔfiniteÕ) p-pulses, or composite pulses involving continuous rf-irradiation [22,23]. By the numerical simulations and experiments presented below, we show that such sequences are also applicable for establishing connectivities between half-integer quadrupolar spins, provided that low rf amplitudes are employed. The symmetry-based pulse sequence C7 [2] has also been demonstrated in the context of double-quantum coherence excitation between quadrupolar spins [24].

2. Pulse sequences and numerical simulations Fig. 1a depicts a two-dimensional experiment for correlating central transition (CT) single-quantum coherences (1QC) of coupled quadrupolar spins [4–6,17]. As

π/2 (a)

Saturate

τ relax

X

25

π/2

t1

X

π/2

t2

mixing

nRAPT +1 -1

π/2 (b)

Saturate

τ relax

τ exc

t1

τ rec

mixing

t2

+3 0 -3 1

(c)

(R44)0

(π)π/4 (π)−π/4 (π)π/4 (π)−π/4

4τ r

Fig. 1. 2D protocols for probing connectivities between half-integer quadrupolar nuclei under MAS conditions, based on (a) CT 1Q–1Q correlations and (b) 3Q–1Q correlations within the z-filter MQMAS scheme [30,32]. The coherence transfer pathways are indicated beneath each pulse scheme. All pulses employed are CT-selective, except the FAM (RAPT) [25,26] block in (a) and the pulses for exciting and reconverting 3QC in (b). (c) Supercycles of the symmetry-based R414 sequence [23] are implemented during mixing, as discussed in Section 2.

M. Ede´n et al. / Chemical Physics Letters 410 (2005) 24–30

26

zation by another pulse of duration srec. Hence, the evolution of 3QC during t1 is correlated with that of CT 1QC during t2 [32]. Fig. 1c illustrates the recoupling sequence R414 [23] employed in this work. It corresponds to four rotor-synchronized pulse elements R [2], each comprising a weak (selective) p-pulse flanked by windows such that the total duration of R equals one rotational period sr = 2p/xr, with xr being the spinning frequency. The phases alternates between ±p/4 and each pulse is of duration CT sp ¼ p=xCT nut , with the CT nutation frequency xnut relating approximately to the rf amplitude x1 =
cB1 as xCT nut =2p  ðS þ 1=2Þx1 when the rf field is much weaker than the quadrupolar couplings [29]. f = sp/sr denotes the Ôpulse fractionÕ [33], with the limit f = 1 implying a continuous p-pulse of duration sr. In practice, we incorporated R414 in MQ phase-cycles [33], denoted ðR414 ÞM 1 1 and ðR414 R4
1 4 ÞM ,

       ðR414 ÞM 1  R414 0 R414 2p=M R414 4p=M . . . R414 2pðM
1Þ=M ð1Þ  1
1   1
1  1 ðR414 R4
1 4 ÞM  R44 R44 0 R44 R44 2p=M    1
1   R414 R4
1 4 4p=M . . . R44 R44 2pðM
1Þ=M ð2Þ 1 where R4
1 4 implies phase-reversal of all pulses in R44 and [  ]/ represents an overall phase-shift by / of the sequence within brackets. Refs. [23,33] provide definitions of all pulse parameters employed here, and review the distinctions between the supercycles from theoretical perspectives. When applied to a pair of spins-1/2 (denoted j and k), R414 -based pulse schemes engineer a zero-quantum
 jbjk ðS þ S
þ average dipolar Hamiltonian [22,23], H j k
þ S j S k Þ, effecting inter-spin longitudinal magnetization

transfer amplitude

0.4 0.6

(a)

(b)

0.4

0.2 0.3 0.5 0.7 1.0

0.2

S=1/2

0.2

S=3/2 0.0

0.0 0

5

τ mix [ms]

10

0

5

τ mix [ms]

transfer amplitude

ωr/2π= 10 kHz 0.2

10

ωr/2π= 20 kHz

(c)

(d)

0.1

9.4 T

9.4 T

transfer amplitude

0.0

(e)

0.2

(f)

0.1

14.1 T 0.0 0

5

τ mix [ms]

1.5 MHz 2.5 MHz 3.5 MHz 4.5 MHz 10

14.1 T 0

5

τ mix [ms]

10

Fig. 2. Numerically exact simulations of a pair of spins (a) S = 1/2 and (b) S = 3/2, assuming xr/2p = 20.0 kHz and a dipolar coupling constant bjk/ 2p =
500 Hz, but no chemical shifts (nor quadrupolar interactions in b). The calculations represent the buildup of longitudinal magnetization of 1 spin k, assuming initial magnetization solely of j, after application of the pulse sequence ðR414 R4
1 4 Þ4 with different pulse fractions f = sp/sr (specified 1 in (a)), during a mixing interval smix. (c–f) Calculations for ðR414 R4
1 Þ4 (f = 0.5) at different spinning frequencies and magnetic fields, including a 4 constant isotropic chemical shift difference of 4.0 kHz as well as first- and second-order quadrupolar interactions for a pair of spins-3/2, with symmetric and coinciding quadrupolar tensors. The quadrupolar coupling constant C jQ ¼ e2 qQ=h ¼ 2.5 MHz was kept fixed, whereas C kQ was varied, as indicated in (e). We assumed Larmor frequencies x0/2p =
105.9 MHz in (c,d) and x0/2p =
158.9 MHz in (e,f). Only the central transition is excited and detected in the simulations (b–f).

M. Ede´n et al. / Chemical Physics Letters 410 (2005) 24–30

3. Experimental results NMR experiments were performed on polycrystalline powders using Varian/Chemagnetics Infinity spectrometers operating at B0 = 9.4 T for 27Al (S = 5/2, x0/2p =
104.3 MHz) experiments on YAG and chlorite, and 4.7 T for 23Na (S = 3/2, x0/2p =
53.0 MHz) acquisitions on Na2SO3. Filled 4 mm zirconia rotors were employed for chlorite and Na2SO3, and a 6 mm rotor for YAG. Detailed acquisition parameters are given in the figure captions. Fig. 3 shows 27Al 1Q–1Q correlation experiments on YAG (Y3Al5O12) at xr/2p = 8.0 kHz. Its structure contain Al in octahedral (Oh) and tetrahedral (Td) coordination, associated with 27Al quadrupolar coupling constants of CQ = e2qQ/h  0.6 MHz and 6 MHz, respectively, and an isotropic chemical shift difference of 73 ppm [20]. The closest Oh–Td distance gives a dipolar coupling constant around
0.2 kHz. The correlation spectrum of Fig. 3a was obtained using the scheme in Fig. 1a with a mixing delay of 150 ms in the absence of rf irradiation: magnetization exchange occurs between the Oh sites and the crystallites contributing to the outer parts of the Td powder pattern, likely because this spectral region is closest to a rotational resonance condition (7 kHz) [20]. However, no exchange is visi-

spontaneous recoupling 150 ms

ω1/2π [kHz]

5

*

* 0

-5

*

(a)

Oh 1

ω1/2π [kHz]

5

-1

Oh

*

Td

Td (b) 1

ω1/2π [kHz]

1

(R4 4 R4 4 )2 2 ms

0

-5

-1

1

-1

1

5

(R4 4 R4 4 )2 6 ms

0

* *

-5

(c) 1

(R4 4 R4 4 )2 10 ms

5

ω1/2π [kHz]

transfers, whose rates depend on the dipolar coupling l0 2 constant bjk ¼
4p cS
hr
3 jk and the scaling factor j. The value of j is related to the pulse fraction of the windowed element [22,23,33]. This is demonstrated by the simulated Sjz ! Skz transfers from sequences 1 ðR414 R4
1 4 Þ4 associated with different values of f (Fig. 1 2a). Similar recoupling dynamics occur if ðR414 R4
1 4 Þ4 is applied to a pair of spins-3/2 in the absence of chemical shifts and quadrupolar interactions (Fig. 2b). However, CT magnetization transfers occur also in realistic cases including quadrupolar interactions [Fig. 2c-f]. Despite a strong dependence on the quadrupolar couplings, the dipolar recovery is sufficient to establish inter-spin connectivities. To ensure that the recoupling is indeed rf-driven, all simulations employed coinciding quadrupolar and dipolar tensors to suppress quadrupolar-driven recoupling [6,10]. We explored different supercycles (M = 2, 3, 4) by numerical simulations and experiments. The recoupling performance of all schemes depended strongly on the particular quadrupolar couplings involved, but best re1 sults were usually obtained by ðR414 R4
1 4 Þ4 . Application of these sequences to half-integer quadrupolar nuclei require CT-selective pulses, necessitating usage of minimal rf amplitudes [17–19]. Unfortunately, this is incompatible with also achieving a large inversion bandwidth and in practice a compromise between reasonable inversion performance and CT selectively need to be made.

27

*

0

-5

(d) -5

0

ω2 /2π[kHz]

5

-5

0

5

ω2/2π [kHz]

Fig. 3. 1Q–1Q 27Al correlation spectra of YAG at B0 = 9.4 T and xr/2p = 8.0 kHz using (a) unassisted recoupling and (b–d) 1 ðR414 R4
1 4 Þ2 (f = 0.2) during mixing. Here, as well as in other figures, asterisks denote positions of spinning sidebands (in slices) and sideband ridges (in 2D spectra). Note that folded sidebands appear around the diagonal peak in (b–d). For easier visualization, we have employed the same vertical scale for slices from a given 2D spectrum, but allowed the scale to vary between different 2D spectra. CTtransition selective pulses ðxCT nut =2p ¼ 24 kHzÞ of duration 12 ls and 24.5 ls was used for p/2 pulses and p-pulses, respectively. Hard pulses ðxCT nut =2p ¼ 228 kHzÞ were employed for RAPT, with equal durations of pulses and delays (1 ls) and nRAPT = 45. (120(t1) · 220(t2)) time coordinates were recorded with srelax = 5 s and 16 (a,b) and 32 (c,d) transients/t1-value.

ble over the remaining of the Td powder spectrum, even after 500 ms mixing (data not shown). On the other 1 hand, upon ðR414 R4
1 4 Þ2 irradiation during a mixing interval of 2.0 ms, cross-peak ridges appear across the entire powder spectrum (Fig. 3b). No significant improvement is obtained after longer mixing periods

M. Ede´n et al. / Chemical Physics Letters 410 (2005) 24–30

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Td Oh (a)

(b)

* ω1/2π [kHz]

5

0

-5 -5

0

5

ω2/2π [kHz]

-5

0

5

ω2/2π [kHz]

Fig. 4. (a) Layered structure of chlorites. (b) 1Q–1Q 27Al correlation spectrum of a chlorite at B0 = 9.4 T and xr/2p = 11.0 kHz employing 5.8 ms 1 ðR414 R4
1 4 Þ4 (f = 0.27) recoupling during mixing. Other acquisition parameters were similar to those in Fig. 3.

(Fig. 3c,d), except that the Td ! Oh exchange peak gains intensity over the Td signal on the diagonal. It appears that at spinning frequencies exceeding the rotational resonance condition, only pulse-assisted techniques may drive magnetization transfers in this sample. Chlorites include a mineral group with the generic structure built from a 2:1 talc-like layer (with an octahedral sheet sandwiched between two tetrahedral sheets) alternated with a brucite-like octahedral interlayer (Fig. 4a). As natural chlorites usually contain significant amounts of paramagnetic iron species, we employed a synthetic sample of nominal composition Mg4.5Al3Si2.5O10(OH)8, prepared from MgO, c-Al2O3 and SiO2 in cold sealed autoclaves at 650
C and 1.2 kb pressure for 7 weeks. Powder X-ray diffraction indicated a phase-pure sample. From a 3QMAS acquisition we estimated the following 27Al chemical shifts and quadrupolar coupling constants: diso = 72 ppm, CQ  3 MHz for Td, and diso = 14 ppm, CQ  4 MHz for Oh. The 2D spectrum recorded at xr/2p = 11.0 kHz manifests Oh M Td exchange peaks upon application of 1 ðR414 R4
1 4 Þ2 for 5.8 ms. However, the exchange is significantly weaker than in the case of YAG. The magnetization transfer occurs in this case between Al within the 2:1 layer, in which the minimum Oh–Td distance is ˚ (similar to that in YAG), whereas the corre3.3 A sponding separation between the tetrahedral sheet of the 2:1 layer and the octahedral interlayer is substan˚ ). No cross-peaks resulted in the tially longer (4.8 A absence of pulses over mixing intervals up to 230 ms at xr/2p = 11.0 kHz as well as at 8.5 kHz (data not shown), indicating that spontaneous recoupling is inactive in this sample at moderately fast spinning. Finally, we consider Na2SO3 at B0 = 4.7 T and xr/2p = 10 kHz. Recoupling sequences are in fact unnec-

essary under these conditions, as significant quadrupolar-driven recoupling between all three distinct Na sites (whose chemical shift and quadrupolar parameters are given in [34]), occur over mixing intervals J 50 ms [6]. The left panel of Fig. 5 displays 1Q–1Q exchange results using both unassisted recoupling and ðR414 Þ41 -based sequences during mixing. The various pulse sequences display minor differences in performance, but provide significantly faster magnetization transfers than in the case of unassisted recoupling. The overall best transfers were obtained using ðR414 Þ41 with a continuous p-pulse (Fig. 5f). Similar exchange results (Fig. 5, right panel), were obtained from the z-filter MQMAS protocol of Fig. 1b, except that in this case, the use of a continuous p-pulse lead to large signals losses, for unknown reasons (data not shown).

4. Conclusions We have shown that CT-selective rotor-synchronized p-pulses in the guise of symmetry-based recoupling [2,22,23] may be used to establish connectivities between half-integer quadrupolar nuclei in rotating solids. However, the magnetization transfers are lower than in typical spin-1/2 applications. While also being inferior to offMAS-based techniques [12–14], these sequences are easily implemented under conventional MAS conditions. The recoupling efficiency needs to be improved, but the current experimental results on spins-3/2 and -5/2 in model systems are encouraging for future developments, and also triggers intriguing questions regarding the details of the recoupling mechanisms: we have applied symmetry-based sequences, a well-developed and powerful machinery for spins-1/2, to scenarios well out-

M. Ede´n et al. / Chemical Physics Letters 410 (2005) 24–30

29

Fig. 5. 2D 23Na correlation spectra from Na2SO3 at B0 = 4.7 T and xr/2p = 10.0 kHz. This compound has three crystallographically inequivalent Na sites corresponding to the signals indicated in (b) and (g). The left and right panels of 2D spectra were obtained from the pulse schemes in Fig. 1a and b, respectively. (a,b,g,h) are results of spontaneous (unassisted) recoupling during mixing [6–11], whereas (c–f) and (i–k) utilized either 1 CT ðR414 Þ41 or ðR414 R4
1 4 Þ4 irradiation, combined with a windowed element having f = 0.6 ðxnut =2p ¼ 8.3 kHzÞ, except in (f), which used a continuous =2p ¼ 5.0 kHz. The dashed lines mark selected slices taken through the x p-pulse; f = 1, xCT 2-dimension of each 2D spectrum. The upper slices from nut each 1Q–1Q spectrum (bottom slices of the 3Q–1Q spectra) are taken through one of the peak maxima of site 3, and reveals its exchange with sites 1 and 2, whereas the lower slices (upper slices of 3Q–1Q spectra) were taken through the resonance of site 2. Typical acquisition parameters were as CT follows: CT-transition selective p/2 pulse-lengths were 10.5 ls ðxCT nut =2p ¼ 24 kHzÞ. Hard pulses ðxnut =2p ¼ 143 kHzÞ were used for 3QC excitation (sexc = 8.5 ls) and reconversion (srec = 2.8 ls), as well as for RAPT, with nRAPT = 25 and equal durations of pulses and delays (0.9 ls). Data-sets comprising (170 · 170) time-points were acquired with srelax = 2.5 s and number of signal transients/t1-value as follows: 16 (a,c); 32 (b,d–f); 144 (g,i); 288 (h) and 432 (j,k). All 2D acquisitions employed TPPI [35], which is incompatible with shearing and therefore (g)–(k) represent unsheared 3QMAS spectra. Processing of the 3Q–1Q spectra employed 80 Hz Gaussian broadening in both dimensions, whereas no broadening was applied to the 1Q–1Q spectra.

30

M. Ede´n et al. / Chemical Physics Letters 410 (2005) 24–30

side of their operational prerequisites. In the quadrupolar case, the pulses reinforce (and reintroduce) ÔspontaneousÕ recoupling processes [6–11], thereby giving a strong recoupling dependence on the sizes of the quadrupolar couplings relative to the spinning frequency. Theoretical investigations are underway to shed light on these effects.

Acknowledgements This work was supported by the Swedish Research Council (VR), the Carl Trygger Foundation and the Magn. Bergvall Foundation. We thank Zhijian Shen for providing the YAG sample, Jekabs Grins for discussions and XRD characterization of the chlorite mineral, and Zheng Weng for instrumental NMR support.

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