Modelling one- and two-dimensional solid-state NMR spectra

Transcription

1 MAGNETIC RESONANCE IN CHEMISTRY Magn. Reson. Chem. 02; 40: ling one- and two-dimensional solid-state NMR spectra Dominique Massiot, 1 *FranckFayon, 1 Mickael Capron, 1 Ian King, 1,2 Stéphanie Le Calvé, 1 Bruno Alonso, 1 Jean-Olivier Durand, 3 Bruno Bujoli, 4 Zhehong Gan 5 and Gina Hoatson 6 1 Centre de Recherche sur les Matériaux à Haute Température, CRMHT-CNRS, 1D avenue de la Recherche Scientifique, Orléans cedex 2, France 2 Department of Chemistry, University of Durham, Durham, UK 3 Laboratoire de Chimie Moléculaire et Organisation du Solide, UMR 5637, Case 007, Université Montpellier 2, Place Eugène Bataillon, Montpellier cedex 05, France 4 Laboratoire de Synthèse Organique, UMR CNRS 6513, 2 Rue de la Houssinière, BP 928, Nantes cedex 03, France 5 Center of Interdisciplinary Magnetic Resonance, NHMFL, Tallahassee, Florida 32310, USA 6 College of William & Mary, Department of Physics, Box 8795, Williamsburg, Virginia , USA Received 22 October 01; Accepted 26 October 01 With the description of more and more complex one- and two-dimensional NMR experiments comes the need to develop methods to make a comprehensive interpretation of the various different experiments that can be carried out on the same sample or series of related samples. We present some examples of modelling one- and two-dimensional solid-state NMR spectra of I = 1 spin and quadrupolar nuclei, using 2 laboratory-developed software that is made available to the NMR community. Copyright 01 John Wiley & Sons, Ltd. KEYWORDS: NMR; 1D, 2D solid-state NMR; fit or model; MQMAS; STMAS; HETCOR; Lee Goldburg INTRODUCTION It is one of the unique features of solid-state NMR to be able to provide different spectral insights into the observed sample: not only different possibly observed nuclei but also different excitation schemes aiming, for example, at enhancing resolution or reintroducing interactions. 1,2 Different philosophies exist in developing, simulation, fitting or modelling programs that could permit a comprehensive interpretation of the observed spectra. Among these we can mention GAMMA 3 and SIMPSON, 4 which are flexible programs, available to the community, allowing the complete simulation of (solid-state) NMR experiments, accounting for theefficiencyofthewholepulsesequencethroughacomplete programming of the spin system and its manipulation. Manufacturers or research groups also provide dedicated packages, some of them issued from research groups that allow the simulation of different classes of spectra, especially in the case of quadrupolar nuclei: STARS, 5 QUASAR 6 and Winfit. 7 Dedicated to Professor Robin K. Harris on the occasion of his 65th birthday. Ł Correspondence to: D. Massiot, Centre de Recherche sur les Matériaux àhautetempérature, CRMHT-CNRS, 1D avenue de la Recherche Scientifique, Orléans cedex 2, France. massiot@cnrs-orleans.fr Contract/grant sponsor: CNRS UPR4212, Région Centre and European Community; Contract/grant number: HPRI-CT ; HPMT-CT Contract/grant sponsor: NSF; Contract/grant number: DMR In this paper, we describe the general principles of a program that permits the fitting or modelling of experimental 1D and 2D spectra to a sum of lines or contributions characterized by their NMR parameters. 8 This program is an evolution of the Winfit program developed with Bruker. 7 It aims at accounting for some of the various 1D and 2D spectra that can be acquired on solids, but does not try to take into account the efficiency of the whole pulse sequences, always considering ideal excitation and lineshapes. In that sense this program is more oriented towards users of solidstate NMR experiments as a tool for the characterization of materials, ranging from fully ordered model crystalline phases to disordered crystalline phases and amorphous or glassy materials. GENERAL STATEMENTS In very general terms, we can consider that modelling or fitting experimental spectra to a set of relevant NMR parameters requires the following different steps: ž computation of a model powder spectrum, typically the sum of all the different sites present in the powdered sample, characterized by their NMR parameters (each interaction and their possible angular relations); ž definition of a mismatch criterion characterizing the quality of the model as compared with the experimental dataset; ž implementation of a minimization algorithm that allows one to vary the different parameters so as to minimize the mismatch criterion; and DOI: /mrc.984 Copyright 01 John Wiley & Sons, Ltd.

2 ling 1D and 2D solid-state NMR spectra 71 ž implementation of a user interface that allows the user to present the experimental and modelled spectra, to judge the quality of the obtained parameter set and to select the parameters that he or she wants to refine manually or automatically. Individual line parameters and modelled spectrum Dealing with solid-state NMR experiments on typically dielectric solids we can consider a limited set of dominant interactions that will characterize each individual line present in the different spectra which can be obtained for a given sample and nucleus. The spectrum will differ as a function of the principal magnetic field and the sample manipulation [static or magic angle spinning (MAS) spinning rate]. Each line is characterized by the following parameters: isotropic chemical shift υ iso, amplitude (related to the integrated intensity), set of Gaussian/Lorentzian parameters (half-width at half-maximum and Gaussian/Lorentzian ratio), a chemical shift anisotropy tensor (axiality 1 CSA and asymmetry CSA ), quadrupolar tensor (coupling tensor C Q or Q and asymmetry Q ) for quadrupolar nuclei and possibly their relative orientation. There exist, in fact, two main different types of lineshapes, depending on whether they do or do not have a simple analytical expression: Gaussian/Lorentzian lineshapes or powder patterns, respectively. In the case of the latter we have to consider a supplementary parameter for the apodization (Gaussian or Lorentzian broadening) of the ideal lineshape. From these parameters, it is then possible to compute the model spectrum of an ideally perfect site under different conditions: static and MAS at different spinning rates and/or under different approximations (infinite or finite spinning rate). The change of representation is given through the different possible models that enable the user to choose the computing algorithm. It also allows the computation of spectra obtained at different principal fields or different spinning rates without modifying its NMR parameters. Given the NMR parameters of each line constituting the spectrum, it becomes possible to compute the modelled spectrum as the sum of the individual lines. Figure 1 shows an example for an I D 1 spin and a quadrupolar spin for 2 which the modelled spectra are computed in static, MAS at finite spinning rate and MAS at infinite spinning rate. To limit the complexity of the program and allow wide applicability, we never attempt to account for the efficiency of the pulse program and only consider ideal excitation of the spectra. Mismatch criterion and minimization algorithm The mismatch criterion that we use is a simple quadratic distance between the experimental and modelled spectrum. This could, of course, be improved in some cases but its advantage is to make no hypothesis about the type of data that we consider. The optimization algorithm aims at minimizing the mismatch criterion by varying the parameters of the different lines. As the computation of the model includes non-linear dependencies to the different parameters and, in some cases, no simple analytical form, CSA Static MAS finite MAS infinite Quadrupolar Figure 1. Example of computed powder lineshapes (left) for an I D 1 2 spin nucleus considering only chemical shift anisotropy and (right) for half-integer quadrupolar spin I D n 2 considering second-order quadrupolar interaction. The modelled lineshapes are computed in the static (top), MAS at finite spinning rate (centre) and MAS at infinite spinning rate approximation. we use an iterative algorithm. Starting with an approximate solution we compute and add an increment to try to converge to a local minimum. This does not ensure the unicity of the obtained solution that will only be the closest to the starting point. The algorithm used in our program is a constraint gradient protocol 9 which involves computation of the partial derivatives over each of the parameters for all variable parameters and each point of the experimental spectrum. The resolution of the n linear system of equations yields an increment that is finally added to the starting parameter set. This procedure is fairly robust when close to a final, well defined solution and the increment is forced to remain small enough not to jump too far from it. User interface The user interface, implemented in object CCC (Borland) to work in the Windows environment (Microsoft), provides visualization of the experimental and modelled spectra and allows the user to see the individual contributions shapes (lines) and modify individually their different parameters. In the case of simple models the user can graphically place the line in real time using the mouse to drag it on to the screen. Fit parameters can be saved in binary or text format to be further retrieved or used in other programs. Several instances of the program can run independently at the same time. User can select different regions of the experimental spectrum and the general philosophy of the program is to compute and optimize only the displayed region of the spectrum: what youfitiswhatyousee. Two-dimensional spectrum There exist a variety of different two-dimensional experiments in today s solid-state NMR. Among others we can mention autocorrelation spectra, double quantum to single quantum correlation, heteronuclear correlation, DAS, MQ- MAS or STMAS high-resolution spectra for quadrupolar nuclei. The main problem in modelling multi-dimensional experiments (two-dimensional in our case) arises with the size of the experimental datasets and the large number of

3 72 D. Massiot et al. variable parameters that we have to consider. Both difficulties can be dealt with not only by limiting the computation to limited domains, but also by introducing constraints to the minimization algorithm, considering intrinsic properties of the experiment (symmetries of autocorrelation experiments, interdependences of F 1 and F 2 in MQMAS and related experiments), and introducing knowledge from the one-dimensional experiments. Final statement or warning Before proceeding further and showing examples, it is important to mention that any fitting program such as the one which we describe here only proposes a mathematically optimized solution and does not guarantee its physical or chemical interpretation, which remains for the user. The more the user knows about the system, the more constraints one can put to the algorithm to limit the number of optimized parameters so as to improve the quality of the interpretation. HOMONUCLEAR CORRELATIONS Exchange on homogeneously broadened spectrum Not all the homonuclear correlation spectra can be treated easily under our implementation, but a simple case is that of an exchange experiment with a finite number of homogeneously broadened lines. This case can be encountered with 1 H NMR spectra of organic or hybrid materials under high speed spinning MAS. Plate 1 presents the spectra of a (p-vinylbenzyl)phosphonic acid obtained at 600 MHz while spinning at 35 khz. The one-dimensional spectrum shows eight resolved proton lines that can be ascribed to the different proton sites of the structure. During the mixing time of a simple exchange experiment, magnetization can be exchanged between dipolar-coupled sites through a spin diffusion process. The experimental spectra can be modelled with two equivalent dimensions (eight lines in that case), adapting the intensities of the 64 cross-peak intensities. To limit this large number of adaptable parameters, the positions and linewidths have been taken from the fit of the 1D CH 2 OH φ Figure 2. f 1 H-LGg/ 1 H correlation spectrum of a zinc phosphonate, Zn(O 3 PC 2 H 4 COOH)0.5C 6 H 5 NH The aliphatic (two lines at 0.7 and 2.0 ppm), phenyl (7.0 ppm) and hydroxyl (12.5 ppm) protons are resolved in the indirect dimension and considering only on diagonal cross peaks can fit the whole spectrum. dataset and kept constant while adapting selected intensities of cross peak. A more automatic possibility would be to constrain the cross-peak intensities always to remain positive and/or to take benefit from the symmetric nature of the experiment. This fairly simple fitting procedure can be applied in that case because most of the linewidth of the different lines remains homogeneous. In a heterogeneously broadened spectrum, dominated by distribution of chemical shift, for example, it would be necessary to build a more complex computing algorithm that would account for the sharp diagonal ridge. Two-dimensional f 1 Hg 1 H Lee-Goldburg MAS correlation spectra It has become more and more popular to obtain enhanced resolution in solid-state proton NMR by acquiring it as an indirect dimension in a two-dimensional experiment that correlates the better resolved Lee Goldburg decoupled spectrum with the MAS spectrum. 10 The advantage of this procedure is to keep with windowless sequence and to provide a direct way to measure the scaling factor of the homonuclear decoupling sequence that can be further used in heteronuclear correlation using the same proton encoding method. 11 Figure 2 gives an example of the f 1 H-LGg/ 1 H correlation spectrum of a zinc phosphonate, Zn(O 3 PC 2 H 4 COOH)0.5C 6 H 5 NH The aliphatic (two lines at 0.7 and 2.0 ppm), phenyl (7.0 ppm) and hydroxyl (12.5 ppm) protons are resolved in the indirect dimension and considering only on-diagonal cross peaks can fit the whole spectrum. Further experiments including supplemental spin diffusion mixing times, could then be fitted on the same basis by introducing off-diagonal cross peaks. 12,13 Double quantum single quantum correlation Double quantum to single quantum correlation spectra provide a way of obtaining a more detailed structural characterization of organic and inorganic solids by reintroducing spatial information through short distance dipolar coupling. We recently studied the case of Zirconium phosphate, ZrP 2 O 7, in which this experiment allowed the description of up to 27 different individual P sites pertaining to 14 different dimers (13 asymmetric dimers and a single symmetric dimer). 14 The DQ/SQ spectrum of this sample, obtained using the post-c7 sequence, 15 together with its modelled spectrum are shown in Plate 2. The model spectrum was computed as correlating two independent dimensions (DQ and SQ) and adjusting only intensities of the cross peaks pertaining to dimers. From this modelling we could extract the exact chemical shifts of the 27 different lines overlapping in the 1D spectrum. Improvement of this procedure would be obtained by directly introducing the existing relation between positions of the double quantum lines at the sum of the positions in the single quantum dimension; this would improve the reliability of the computations and speed up the optimization process. HETERONUCLEAR CORRELATIONS The case of heteronuclear correlation is simpler than that of homonuclear correlations. We define two independent

4 ling 1D and 2D solid-state NMR spectra of solids 2.8 ppm ms ( ) C 6 H 4 PO 3 H 2 CH 2 CH CH 2 P ms Plate 1. 1 H NMR spectra of a (p-vinylbenzyl)phosphonic acid obtained at 600 MHz while spinning at 35 khz. The one-dimensional spectrum shows eight resolved proton lines that can be ascribed to the different proton sites of the structure. The 2D exchange experimental data, obtained with two different mixing times, were modelled considering only a selected subset of the 64 possible cross peaks. Copyright 01 John Wiley & Sons, Ltd. Magn. Reson. Chem. 02; 40

5 D. Massiot et al Double Quantum Single Quantum 72 Plate P DQ/SQ spectra of ZrP 2 O 7 modelled considering 14 P O P dimers (13 of them being pairs of inequivalent sites). The 1D spectrum is modelled considering the 27 different lines of nearly equal intensities, the positions of which were measured from the 2D experiment. 14 Copyright 01 John Wiley & Sons, Ltd. Magn. Reson. Chem. 02; 40

6 ling 1D and 2D solid-state NMR spectra 73 CH 2 φ OH Figure 3. f 1 HLGg 31 P HETCOR (CP transfer) spectrum of a zinc phosphonate, Zn(O 3 PC 2 H 4 COOH)0.5C 6 H 5 NH 2, 12 under 10 khz spinning at 400 MHz. The spectrum was modelled considering four (two CH 2, one phenyl and one OH) different lines in the f 1 HLGg dimension and two lines in the 31 P dimension. dimensions (frequency and nucleus) and the cross peaks between lines in the two dimensions can be individually defined and optimized. The spectrum shown as an example in Fig. 3 is a HETCOR 11 correlation spectrum between an f 1 H-LGg dimension obtained indirectly and correlated with a 31 P dimension with a cross-polarization step (1 ms) under a 10 khz MAS spinning rate at 400 MHz. 12 The sample is the same as that considered in Fig. 2. In the proton dimension, for this short contact time, we obtain an enhanced resolution with a partial resolution of the intense correlation to the aliphatic protons, the phenyl protons are not perfectly accounted for by a single resonance and there is a weak correlation to the hydroxyl protons which are the most remote from the P sites of the structure. A detailed study of the build-up curves of the cross peaks with varying contact time and/or introducing a spin diffusion mixing time during the proton evolution would allow a more detailed understanding of the P H distances. As the two dimensions are completely independent, the program as it stands could also fit HETCOR correlations between I D 1 nuclei and 2 quadrupolar nuclei. isotropic chemical shift and isotropic second-order shift) 21,22 (Z. Gan, Rocky Mountain Conference, August 01, Denver, CO, USA). Well defined quadrupolar interaction parameters When considering perfectly crystalline samples exhibiting well-defined quadrupolar parameters, the only parameter that has to be added to compute the two-dimensional spectrum and its isotropic projection is a linewidth in the indirect dimension. In MQMAS experiments, this linewidth may vary depending upon the multiple quantum transition considered 22 and in STMAS it may be conditioned by the preciseness of the angle setting and higher order or crossterms which affect the non-symmetric satellite transitions (Z. Gan, Rocky Mountain Conference, August 01, Denver, CO, USA; L. Frydman, ISMAR Conference, August 01, Rhodos, Greece, Jerusalem, Israel). Examples of fitting MQ- MAS and STMAS spectra are given in Fig. 4 with the classical case MQ-MAS spectra of 87 Rb in RbNO 21 3 and 27 Al in sillimanite. 23 A second example is presented in Fig. 5 with the MQ-MAS (9.4 T) 24 spectrum and STMAS (19.5 T) of 27 Al in A 9 B 2 (9Al 2 O 3-2B 2 O 3 ) sample. These two spectra were fitted with the same quadrupolar and chemical shift parameters, and intensities (related to the efficiency of the pulse sequence) and linewidths were adapted to fit best the observed experimental spectra. Partly disordered systems When dealing with partly disordered systems, the problem becomes more complicated but remains a major challenge in the scope of the characterization of partly disordered, amorphous or glassy materials. These two-dimensional experiments (DAS, MQMAS and STMAS) provide a unique opportunity for sorting out the distributions of isotropic chemical shifts and the distributions of quadrupolar parameters. Some authors have proposed inversion methods that can partly address this problem. 25,26 These methods allow a change of representation of the spectrum to an isotropic chemical shift to a quadrupolar coupling representation QUADRUPOLAR NUCLEI: DAS, MQ-MAS, STMAS Owing to second-order quadrupolar interactions, MAS only proves to be able to provide ultimately resolved spectra for half-integer quadrupolar nuclei. This can nevertheless be obtained by going to double orientation rotation (DOR) 16 or to two-dimensional experiments: dynamic angle spinning (DAS), 17 multiple quantum MAS (MQ-MAS) 18 or satellite transition MAS (STMAS). 19, In all these 2D experiments the two dimensions are closely related. The F 2 dimension is the usual MAS (or 2 ) spectrum (filtered by the excitation sequence) and the F 1 dimension, obtained by a shearing transformation, is a mixture of evolutions during t 1 ( 1,mQor satellite evolution) and t 2, providing isotropic resolution. The F 1 dimension can thus be recalibrated on the ppm scale and position in that dimension is a function of isotropic terms: Exp Rb RbNO 3 27 Al Sillimanite Figure 4. MQMAS experimental (bottom) and modelled (top) spectra of well-defined model compounds: 87 Rb spectrum of RbNO 3 21 and 27 Al spectrum of sillimanite (SiAl 2 O 5 ) 23.

7 74 D. Massiot et al. and proved to be efficient in providing a better understanding of the spectra of real materials. Nevertheless, the inversion method requires a hypothesis about the asymmetry parameter of the quadrupolar tensor and suffers from MQ-MAS Al A 9 B STMAS 830 Figure Al MQMAS (9.4 T) and STMAS (19.5 T) spectra of A 9 B 2 (9Al 2 O 3 Ð2B 2 O 3 ) compound, showing one Al IV,twoAl V and one Al VI (ð2) sites. These two spectra were modelled with the same quadrupolar and chemical shift parameters, but different intensities accounting for the different excitation regimes. intrinsic instability, which requires non-trivial mathematical handling. In our program we introduce Gaussian distributions of both isotropic chemical shifts and quadrupolar coupling and directly compute and optimize the whole set of parameters. These distributions themselves can be questioned but prove to give interesting and self-consistent results when applied to series of spectra obtained in one- and two-dimensional experiments at different principal fields. Figure 6 shows the 27 Al MAS and MQ-MAS spectra of the Sr 3 Al 10 SiO compound. The MAS spectra were acquired at three different principal fields (7.0, 9.4 and 14 T) and the MQMAS spectrum was obtained at 9.4 T. In the MQMAS spectra there is clear evidence of at least three different lines that can be modelled considering the limited distributions of isotropic chemical shifts and quadrupolar interaction. A broader contribution of a less intense supplemental Al VI site hardly shows up in the MQMAS spectrum owing to loss in the efficiency of the triple quantum excitation with limited r.f. power. All the sites show up in the possibly quantitative MAS spectra but remain severely overlapped even at 14 T. Owing to distributions of isotropic chemical shifts and quadrupolar interactions, these line have broadened asymmetric shapes. The modelling of the whole set of spectra was carried out using a single set of NMR parameters (average values and distributions) and computing the lineshapes in the finite spinning rate approximation. A second example is given in Fig. 7, for with the case of ferroelectric relaxors of the PMN (Pb/Mn/Nb) family of compounds substituted with scandium. Figure 7 presents the MQMAS spectrum of 93 Nb at 9.4 T and MAS spectra at 7, 9.4 and 14 T for a PMSN (xsc D 0.2) sample. At low fields the MAS 7.0 T MAS 9.4 T MAS 14.1 T MQMAS 9.4 T Figure Al MAS and MQMAS spectrum of the Sr 3 Al 10 SiO compound. The model spectra were computed using the same set of NMR parameters (average and distribution) considering four different sites: two Al IV and two Al VI. Quantitative interpretation is derived from the MAS spectra.

8 ling 1D and 2D solid-state NMR spectra 75 #A #B (1) Isotropic dimension 7.0 T-MAS 12 khz 9.4 T-MAS 12 khz 14 T-MAS 33 khz MAS dimension Figure Nb spectra of PMSN (ðsc 0.2) sample. Two different types signals, A and B, are separated in the MQMAS spectrum at 9.4T. Signal A correspond to overlapping sites undergoing large spreading of isotropic chemical shift and moderate second-order quadrupolar shift and broadening; signal B correspond to sites undergoing much large second-order effects. This interpretation is consistent with high-field MAS spectra obtained at 14 T. MAS spectrum shows two types of sites that we have labelled A and B. A is a sharper contribution and B a wider one, strongly overlapping at moderate principal fields. These two contributions are clearly separated in the MQMAS spectrum. Line A is aligned with the isotropic shift correlation line and its signature is dominated by a distribution of chemical shift anisotropy with low second-order quadrupolar shift and broadening, whereas line B is much further from the chemical shift line and indicates an important distribution of quadrupolar interaction. A MAS spectrum acquired at higher field (14 T) shows improved resolution and confirms this first interpretation. From these preliminary results it seems likely that we can discriminate between ordered and disordered domains and even resolve the different possible 93 Nb environments in the ordered domains. Work in progress confirms these first results (G. Hoatson, Rocky Mountain Conference, August 01, Denver, CO, USA). CONCLUSION We have described the general principles of a program that allows the fitting or modelling of experimental 1D and 2D solid-state NMR spectra to a sum of lines or contributions characterized by their NMR parameters. 8 This program can be used to model a wide variety of experimental results ranging from autocorrelation to double quantum/single quantum, heteronuclear correlation, or MQMAS and STMAS for quadrupolar nuclei. As it is, we hope that it could be a very useful tool to help in interpreting results obtained through a variety of different experiments, not only for well ordered crystalline phases but also more widely for partly disordered, amorphous or glassy materials for which NMR is a unique technique that maintains resolution. Of course, there are a lot of aspects where we could improve the reliability, efficiency and versatility of the computing or optimizing algorithm, but we hope that it will be of some use to the community. Acknowledgements We acknowledge financial support from CNRS UPR4212, Région Centre and European Community contracts HPRI-CT and HPMT-CT Z.G. acknowledge financial support from NSF, grant DMR REFERENCES 1. Grant DM, Harris RK. Encyclopedia of Nuclear Magnetic Resonance. Wiley: Chichester, Schmidt-Rohr K, Spiess HW. Multi-dimensional Solid State NMR and Polymers. Academic Press: New York, Smith SA, Levante TO, Meier BH, Ernst RR. J. Magn. Reson. A 1994; 106: Bak M, Rasmussen JT, Nielsen NC. J. Magn. Reson. 00; 147, Jakobsen HJ, Aarhus University, Denmark. STARS Package. Varian: Palo Alto, CA. 6. (a) Amoureux JP, Fernandéz C, Granger P. NATO ASI Ser., Ser. C 1990; 322: 409; (b) Amoureux JP, Fernandéz C. QUASAR Solid- State NMR Simulation for Quadrupolar Nuclei, University of Lille, France. 7. Massiot D, Thiele H, Germanus A. Bruker Rep. 1994; 140: Massiot D. dmfit program; available at 9. Press WH, Teukolsky SA, Vettering WT, Flannery BP. Numerical Recipes in C, Cambridge University Press: Cambridge, Vinogradov E, Madhu PK, Vega S. Chem. Phys. Lett. 314: , and references cited there in. 11. van Rossum BJ,Forster H,de Groot JH.J. Magn. Reson. 1997; 124: Massiot D, Alonso B, Fayon F, Fredoueil F, Bujoli B. Solid State Solid State Sci. 01; 3: Ladizhansky V, Hodes G, Vega S. J. Phys. Chem. B 00; 104, King IJ, Fayon F, Massiot D, Harris RK, Evans JSO. Chem. Commun. 01; Hohwy M, Jakobsen HJ, Edén M, Levitt MH, Nielsen NC. J. Chem. Phys. 1998; 108: Wu Y, Sun BQ, Pines A, Samoson A, Lippmaa E. J. Magn. Reson. 1990; 89: 297.

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