Article pubs.acs.org/crystal
Determination of 31P Chemical Shift Tensor from Microcrystalline Powder by Using a Magnetically Oriented Microcrystal Array Ryosuke Kusumi, Fumiko Kimura, and Tsunehisa Kimura* Division of Forest and Biomaterials Science, Kyoto University, Kyoto 606-8502, Japan S Supporting Information *
ABSTRACT: The 31P chemical shift tensor for phenylphosphonic acid (PPA) was determined by using a magnetically oriented microcrystal array (MOMA)a single-crystallike composite in which microcrystals are aligned threedimensionally in a polymer matrixprepared from a microcrystalline powder of PPA. High-resolution 31P NMR spectra were obtained for a PPA-MOMA without magic angle spinning (MAS), from which the chemical shift anisotropy (CSA) was determined. The single-crystal rotation method was applied to the MOMA to determine the principal axes of the 31P chemical shift tensor with respect to the crystallographic axes. The present results demonstrate that the MOMA method can provide a powerful means of determining all of the information on 31P CSA from a microcrystalline powder without MAS.
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INTRODUCTION Elucidation of crystal structures of materials is essential for pharmaceutical and materials sciences. Although diffraction techniques are most powerful for this purpose, attention has been paid recently to the use of solid-state NMR.1,2 Information derived from solid-state NMR includes dipolar coupling,3 quadrupolar coupling,4 shielding anisotropy,5 etc. The chemical shift anisotropy (CSA) is of particular importance because it directly relates to the electron distribution around the nucleus under consideration.6−8 CSA is fully described by a chemical shift tensor that includes the principal values and principal directions. The single-crystal rotation method, in which changes in the observed chemical shifts are measured as a function of the rotating angle of a single crystal, is a powerful and direct means for the complete determination of the chemical shift tensor.9,10 A two-dimensional (2D) crystal correlation method was also proposed as a technique to determine the complete CSA of all the observed nuclei in a complex single crystal.11,12 However, these two methods require a relatively large single crystal (several millimeters in each dimension), which is difficult to obtain in many cases. Although the principal values of the chemical shift tensor can be determined from a powder sample by using advanced techniques such as CSA recoupling,13−15 directly determining its principal axes with respect to a reference frame, e.g., crystallographic axes, remains difficult. Recently, we demonstrated that a magnetically oriented microcrystal array (MOMA) has a great potential to overcome such a problem relating to the size of the single crystal.16 A MOMA is a composite in which microcrystals are aligned threedimensionally.17−22 The three-dimensional (3D) alignment of magnetic axes (0 > χ1 > χ2 > χ3) embedded in the crystal lattice © XXXX American Chemical Society
is achieved by the application of a frequency-modulated rotating magnetic field, for which the rotation speed is switched between a slower rotation speed ωs and a quicker rotation speed ωq (>ωs) every 90° within one revolution.18 The MOMA method is applicable to biaxial crystal systems (orthorhombic, monoclinic, and triclinic systems) for which the three magnetic susceptibilities are different. In a previous study,16 we applied the single-crystal rotation method to a MOMA of L-alanine and successfully determined its 13C chemical shift tensors. In the present study, we demonstrate that the combination of MOMA with the single-crystal rotation method has high potential for characterizing CSA of phosphorus-31. 31P NMR spectroscopy has been widely used as an analytical tool in chemistry, biology, and medicine because 31P is a nucleus of 1/ 2 spin and 100% natural abundance. The 31P chemical shift tensor is of great use for structure elucidation of phosphorus compounds, e.g., phospholipid bilayers and biological membranes. However, like 13C, determining the 31P chemical shift tensor completely for phosphorus compounds that do not crystallize to sizes suitable for the conventional single-crystal rotational method is difficult. A combination of the MOMA method and the standard procedure of the single-crystal rotation method is expected to be a powerful tool for complete characterization of the 31P chemical shift tensor from a microcrystalline powder. Received: October 6, 2014 Revised: January 9, 2015
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DOI: 10.1021/cg501483s Cryst. Growth Des. XXXX, XXX, XXX−XXX
Article
Crystal Growth & Design
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(i.e., χ1, χ2, and χ3). The half widths of the spots obtained by using an azimuthal plot were 3.0−6.2° for most of the spots in all three patterns. This result indicates that the PPA microcrystals were aligned three-dimensionally in the MOMA. On the basis of the diffraction data in Figure 2 and the crystallographic data23 of PPA (orthorhombic, space group Pbca, Z = 8, a = 11.1603, b = 7.9791, and c = 15.6195 Å), we determined that the χ1, χ2, and χ3 axes are parallel to the a, c, and b axes, respectively, as illustrated in Figure 3.
EXPERIMENTAL SECTION
The phenylphosphonic acid (PPA)-MOMA was prepared in a manner similar to the method reported previously.16−20 The detailed procedure for preparing the PPA-MOMA is shown in Supporting Information. The 3D alignment of the PPA microcrystals in the MOMA was confirmed by X-ray diffraction patterns. X-ray diffraction measurements were performed at ambient temperature (20 °C) using a Rigaku RAXIS RAPID II system equipped with an imaging plate (IP) and a graphite-monochromatized Cu Kα beam. The camera length between a sample and the IP was 127 mm, and ω scans were performed from −15° to 15°. The relationship between the magnetization axes and crystallographic axes was determined through a comparison of the diffraction data of the PPA-MOMA with those of a PPA single crystal.23 31 P Solid-state CP NMR measurements were performed under 1H decoupling, using a 4.0 mm ϕ double resonance MAS probe at ambient temperature (20 °C) with a Varian NMR system operated at a 31 P resonance frequency of 161.9 MHz. The parameters were as follows: 1H π/2 pulse width, 2.9 μs; contact time, 2 ms; recycle delay, 200 s. The 31P solid-state CP NMR spectra of the MOMA were collected every 10° of rotation angle ψ about the tube axis from 0° to 360° (Figure 1).16 The three principal values of the 31P chemical shift
Figure 3. Schematic diagram of magnetic and crystallographic axes in the PPA-MOMA.
Figure 4 shows 31P solid-state CP NMR spectra of the PPAMOMA, together with those of microcrystals under MAS at 15 kHz and without MAS. As seen in spectrum (a), the PPA powder exhibits one sharp resonance peak at 21.3 ppm under MAS, whereas it exhibits a broad resonance peak characteristic of a powder pattern when measured without MAS (spectrum (b)). From this powder pattern, the principal values of the 31P chemical shift tensor, δ11, δ22, and δ33, were estimated as 69.6, 24.2, and −30.0 ppm, respectively. On the other hand, the PPA-MOMA exhibits sharp and narrow resonance peaks as seen in the spectra of Figure 4c. In addition, the peak positions vary systematically depending on the sample-rotation angle ψ. We find up to four peaks that exhibit ψ-dependence. The number of resonance peaks observed in a MOMA depends on the point group of the crystal under consideration20 and the number of resonant nuclei in a unit cell located in magnetically distinguishable environments when subjected to a static magnetic field. The PPA crystal belongs to the point group mmm. Therefore, unlike other MOMAs prepared from crystals belonging to the triclinic and monoclinic crystal systems, a PPA-MOMA does not exhibit a twin structure. As a result, we need not to consider the multiplicity of the number of resonant peaks arising from the twin structure. The eight 31P nuclei in a unit cell are crystallographically equivalent because of mmm symmetry. However, each of the four pairs of atoms related by inversion symmetry are under magnetically different environments when an external magnetic field is applied, causing four resonance peaks in the spectra (Figure 4c).
Figure 1. Experimental setup for the 31P solid-state CP NMR measurement of the MOMA by using an MAS probe. The three magnetic axes (χ1, χ2, and χ3) are embedded in the MOMA. ψ is the rotation angle of the MOMA about the χ3 axis. tensor were determined from a powder spectrum obtained for PPA microcrystalline powder without MAS. The 31P chemical shifts in the collected spectra were calibrated indirectly through the NH4H2PO4 peak observed 1.0 ppm upfield of 85% aqueous H3PO4.
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RESULTS AND DISCUSSION The 3D alignment of PPA microcrystals in MOMA was confirmed by using X-ray diffraction. Figure 2 shows the X-ray diffraction patterns of the obtained PPA-MOMA. In the case of microcrystalline powder, the diffraction patterns exhibit Laue rings arising from the random orientation of the microcrystals. In contrast, the PPA-MOMA exhibits well-separated diffraction spots when measured from each of three different directions
Figure 2. X-ray diffraction patterns of the PPA-MOMA measured from three different directions, indicating that the microcrystals are threedimensionally aligned. The direction of the impinging X-ray is approximately along the χ3, χ1, and χ2 axes from left to right. B
DOI: 10.1021/cg501483s Cryst. Growth Des. XXXX, XXX, XXX−XXX
Article
Crystal Growth & Design
δ22, and δ33 were fixed to 69.6, 24.2, and −30.0 ppm, respectively, which were determined from the powder spectrum of PPA. The angles ϕ2, θ2, and ψ2, which show slight deviations arising from the sample setting, should be common among PPA molecules in the MOMA. Thus, global curve fitting with nonlinear least-squares was performed under the condition that these angles were shared among four data sets of the peak positions. The initial values of ϕ1, θ1, and ψ1 for each phosphorus atom were determined by comparing four sets of angular dependence data with the theoretical curves calculated at different orientations of the chemical shift tensors on the basis of the PPA crystallographic data.23 Figure 5 shows the angular dependence of the 31P chemical shifts for the PPA-MOMA. The fitted results are also shown in
Figure 4. P solid-state CP NMR spectra of PPA obtained for (a) powder sample with MAS at 15 kHz, (b) powder sample without MAS, and (c) MOMA without MAS, where ψ is the sample-rotation angle about the axis inclined by the magic angle.
Figure 5. 31P Chemical shifts plotted against the sample-rotation angle ψ. The four data sets correspond to the four sets of magnetically nonequivalent phosphorus atoms (I, II, III, and IV) in the unit cell. The curve-fitting results are shown by the solid lines, from which the principal axes of the chemical shift tensors are determined, as shown in Table 1.
The directions of the principal axes of the 31P chemical shift tensor were determined from the angular dependence of the peak positions of the 31P NMR signals following the procedure reported previously.16 In the traditional single-crystal rotation method, a single crystal is placed in a probe with a goniometer. Then, a series of spectra is recorded by rotating the crystal in steps of 5−10° from 0° to 180° about three mutually perpendicular axes. In the present case, however, the PPAMOMA is inserted into a MAS probe at the magic angle. Thus, we used δLzzthe zz component of chemical shift tensor δL in the laboratory coordinate systemexpressed in the form to be fitted to the experimental results obtained at a general angle.16 δL is obtained by transforming δP expressed in terms of the principal axes by using the three transformation matrices expressed by Eulerian angles: (i) R1, which transforms δP to the crystallographic abc coordinate system, δC = R1δPR−1 1 ; (ii) R2, which transforms δC to the sample-tube coordinate system, δT = R2δCR−1 2 , which in turn is introduced to account for a slight experimental deviation of the b axis from the axis of the sample tube; and (iii) R3, which transforms δT to the laboratory xyz coordinate system where the tube rotation axis is set to 54.7° (the magic angle), δL = R3δTR−1 3 . In this study, we employed the expression in ref 24. for the transformation matrix Ri(ϕi,θi,ψi) (i = 1, 2, 3). δLzz is a function of ψ (= ψ3), where δ11, δ22, δ33, ϕ1, θ1, ψ1, ϕ2, θ2, and ψ2 are adjustable parameters when fitting the experimental results. The principal values δ11,
Figure 5 by the solid lines. From the fitting analyses described above, we obtained the directions of the principal axes of the 31 P chemical shift tensor components. Table 1 summarizes the directions, which are expressed in terms of the direction cosines with respect to the crystallographic a, b, and c axes. The deviation angles ϕ2, θ2, and ψ2 were 0.5°, −2.5°, and −0.4°, respectively. The absolute values of the direction cosines should be averaged over the four data sets because the direction cosines have the following relation: I {(l, m, n), (−l, −m, −n)}, II {(−l, −m, n), (l, m, −n)}, III {(−l, m, −n), (l, −m, n)}, and IV {(l, −m, −n), (−l, m, n)}. The averaged direction cosines are also shown in Table 1. The directions of the principal axes, of which components were converted to the shielding values by using the absolute 31P shielding of 85% H3PO4 aq. (328.35 ppm),25 are illustrated in Figure 6. The direction of σ33, which is the most shielded direction around the phosphorus nucleus, is close to that of the PO bond. On the other hand, the least shielded component σ11 is almost perpendicular to the C−P O plane. The remaining component σ22 component tends to be parallel to the C−P bond. These orientations of the tensor are in good agreement with those of other phosphonic acids26 and phosphonate systems.27,28 The results show that the full information on the 31P chemical shift tensor can be determined even from a microcrystalline powder by using the MOMA technique.
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DOI: 10.1021/cg501483s Cryst. Growth Des. XXXX, XXX, XXX−XXX
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Crystal Growth & Design Table 1. Direction Cosines of the 31P Chemical Shift Tensor for PPA Determined by Using a MOMA
microcrystals is also required because the PPA-MOMA exhibits somewhat broad diffraction spots, i.e., insufficient alignment of the microcrystals (see Figure 2). The degree of alignment can be improved by optimizing the parameters of the applied magnetic field for preparing a MOMA, on the basis of the magnetic anisotropy ratio.29−31 The accuracy of the chemical shift tensors that can be determined from a MOMA can be improved to a level similar to that of a single crystal by considering the points described above.
direction cosines phosphorus
a
I (l, m, n) δ11 0.843 δ22 0.368 δ33 0.392 II (−l, −m, n) δ11 −0.852 δ22 −0.350 δ33 −0.390 III (−l, m, −n) δ11 −0.860 δ22 −0.340 δ33 −0.381 IV (l, −m, −n) δ11 0.846 δ22 0.376 δ33 0.379 averagea (l, m, n) δ11 0.850 δ22 0.359 δ33 0.385 a
b
c
0.493 −0.237 −0.837
−0.215 0.899 −0.381
−0.477 0.211 0.853
−0.216 0.913 −0.346
0.463 −0.205 −0.862
0.215 −0.918 0.334
−0.485 0.244 0.840
0.223 −0.894 0.388
0.479 −0.224 −0.848
−0.218 0.906 −0.362
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CONCLUSION We have demonstrated that a MOMA can provide highresolution 31P NMR spectra of microcrystalline powder; these spectra contain all the information on 31P CSA, including the orientation of the principal axes, even without MAS. The 31P chemical shift tensor was successfully determined from the accumulated spectra by a combination of a MOMA and a standard procedure of the single-crystal rotation method. The present results show that the MOMA technique has great potential to expand the application of single-crystal methods (both 1D and 2D methods), which although traditional are the most accurate means of determining the orientations of chemical shift tensors, to crystals that are difficult to obtain in sizes large enough for NMR measurements. In the present study, an MAS probe was used, and the information on the crystal symmetry of PPA was not fully utilized to reduce the number of peaks. Peaks might be numerous and crowded when materials have more than one 31P nuclei in a molecule. This problem will be partially solved by using a probe with a goniometer, by which the number of peaks is reduced by appropriate setting of the direction of the magnetic axes with respect to the NMR magnetic field. A twodimensional crystal correlation method has been proposed for a single crystal composed of complex molecules.11,12 The combination of this 2D method with a MOMA can be a powerful means for determination of the chemical shift anisotropy in a complex system.
The standard deviations of the direction cosines are ±(0.003−0.02).
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Figure 6. Orientation of the 31P chemical shift tensor for PPA determined by using a PPA-MOMA. The principal values (δ11 > δ22 > δ33), which were determined from the powder spectrum, are converted to the shielding values (σ11 < σ22 < σ33) by using the relation25 δii = 328.35 − σii. The lengths of the ellipsoid axes are proportional to the corresponding shielding values.
ASSOCIATED CONTENT
S Supporting Information *
Experimental procedure for preparing the PPA-MOMA. This material is available free of charge via the Internet at http:// pubs.acs.org.
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It should be noted that the magnetic χ1χ2χ3 frame of a MOMA is used as the orthogonal bases to describe the orientation of a MOMA sample with respect to the NMR magnetic field. Therefore, the chemical shift tensor is expressed with respect to this frame. In the case of PPA, the magnetic frame coincides with the crystallographic abc frame, and hence the chemical shift tensor relative to the crystallographic frame is directly related with respect to the magnetic frame. However, we need to express the chemical shift tensor with respect to the molecular frame, which is the concern of chemists. For this purpose, the crystallographic data on the crystal by diffraction method is inevitable. This situation is similar to the conventional single-crystal NMR method. Note that the quality of data reported here is insufficient to investigate the intermolecular interactions and structural distortions. In the present study, we used a general probe for MAS to accumulate spectra at different sample-rotation angles ψs, which resulted in an experimental error of a few degrees in ψ. Further improvement of the 3D alignment of the
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Phone: +81-75-753-6246. Fax: +81-75-753-6300. Notes
The authors declare no competing financial interest.
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DOI: 10.1021/cg501483s Cryst. Growth Des. XXXX, XXX, XXX−XXX
