Accepted Manuscript Single-crystal NMR approach for determining chemical shift tensors from powder samples via magnetically oriented microcrystal arrays Guangjie Song, Ryosuke Kusumi, Fumiko Kimura, Tsunehisa Kimura, Kenzo Deguchi, Shinobu Ohki, Teruaki Fujito, Tadashi Simizu PII: DOI: Reference:

S1090-7807(15)00071-3 http://dx.doi.org/10.1016/j.jmr.2015.03.009 YJMRE 5625

To appear in:

Journal of Magnetic Resonance

Received Date: Revised Date:

25 December 2014 10 March 2015

Please cite this article as: G. Song, R. Kusumi, F. Kimura, T. Kimura, K. Deguchi, S. Ohki, T. Fujito, T. Simizu, Single-crystal NMR approach for determining chemical shift tensors from powder samples via magnetically oriented microcrystal arrays, Journal of Magnetic Resonance (2015), doi: http://dx.doi.org/10.1016/j.jmr.2015.03.009

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Single-crystal NMR approach for determining chemical shift tensors from powder samples via magnetically oriented microcrystal arrays

Guangjie Song1, Ryosuke Kusumi1, Fumiko Kimura1, Tsunehisa Kimura1*, Kenzo Deguchi2, Shinobu Ohki2, Teruaki Fujito2, and Tadashi Simizu2 1

Division of Forest and Biomaterials Science, Kyoto University, Kyoto 606-8502, Japan. 2

National Institute of Materials Science, Tsukuba, Ibaraki 305-0003, Japan

*Corresponding author (E-mail: [email protected]; Phone: +81-75-753-6246; Fax: +81-75-753-6300)

ABSTRACT The single-crystal rotation technique was applied to magnetically oriented microcrystal arrays (MOMAs) of cellobiose (monoclinic) to determine the principal values and principal axes of the chemical shift tensors of C1 and C1′ carbons.

Rotations were performed about the magnetic  1 ,

 2 , and  3 axes of MOMA, and the measurements were taken at six different orientations with respect to the applied magnetic field.

Under these rotations, crowded peaks were reduced and the

peaks for the C1 and C1′ carbons were identified by comparing with simulation results.

Six

components of the chemical shift tensor expressed with respect to the magnetic 1  2  3 -frame were determined.

The tensors thus obtained were transformed into those relative to the molecular frame.

1

1. Introduction Structural analyses of materials are an important first step in understanding the functions of materials. X-ray diffraction is the most powerful and widely used technique for elucidating crystal structures by observing global electron distribution over a unit cell.

On the other hand, solid-state

NMR spectroscopy can provide information on the electron distributions around a local space in the vicinity of the resonant atom by utilizing phenomena such as chemical shift anisotropy and quadrupole interactions.

Although NMR spectroscopy may not be the best choice for investigating

global properties such as symmetry of crystals, the technique has potential in crystallography [1-4], and is being explored as NMR crystallography. Recently, the use of single crystals in solid-state NMR has received increasing attention. Numerous studies focusing on S/N improvement by DNP method [5] and reduction of bulk magnetism effect [6-8], and studies on quadrupole nuclei [9, 10], molecular conformations [11] and chemical shift tensors have been reported.

Generally, a large single crystal is required to obtain

sufficient S/N from the samples; this requirement limits the use of single crystals in NMR because it is difficult to grow large crystals under many circumstances.

Previously, we have shown that

microcrystals suspended in a liquid medium can undergo biaxial alignment when subjected to frequency-modulated rotating magnetic fields [12-16]. By solidifying the liquid medium after the alignment, we obtain a magnetically oriented microcrystal array (MOMA), which is a polymer composite with embedded microcrystals that are three-dimensionally aligned.

This technique is

applied to biaxial crystals including triclinic, monoclinic, and orthorhombic crystals. It has been shown that a MOMA can diffract X-ray in a manner similar to single crystals [17]. Furthermore, aligned microcrystals can facilitate the application of the single-crystal NMR technique to microcrystalline powder samples.

Previously, MOMAs were used to determine the chemical

shift tensors for the carboxyl and methyl

13

C of L-alanine [18] and

2

31

P of phenylphosphonic acid

[19]. In our previous works, a magic-angle spinning (MAS) probe was used for rotating a MOMA sample, and hence, the symmetry of MOMA was not fully utilized for reducing the number of peaks. However, the analyses were easy because the molecules studied were simple and no severe peak overlaps were present.

In the present study, we use a probe conventionally used for single-crystal

NMR measurements, which enables the rotation of a specimen about the magnetic  1 ,  2 , and  3 axes of a MOMA.

This allows the full utilization of the advantages of high symmetry about these

axes to reduce peak overlaps.

We choose cellobiose crystals (monoclinic), which have many

carbon atoms, as the sample in this study.

The chemical shift tensors of C1 and C1′ carbons are

determined with respect to the magnetic 1  2  3 -frame ( χ -frame) using data obtained at six different orientations of the sample.

The tensors thus determined are then transformed to those

relative to the molecular frame and the deviation from the local symmetry rule is discussed.

To the

best of our knowledge, this is the first report on the analysis of the chemical shift tensor of cellobiose.

2. Experimental Cellobiose MOMA samples were prepared by following a method reported previously [17]. As-received cellobiose crystals (Wako Pure Chemical Industries, Ltd.) were pulverized with a mortar and passed through a 125/90-m mesh and 75/50-m mesh consecutively; then, a fraction of the powder on the 75/50m mesh was collected.

The obtained microcrystalline powder was

dispersed in a UV-curable monomer (POLY201 of Arakawa Chemical Industries, Ltd.; viscosity of 5.0 Pas).

This monomer was silicon-based and did not produce any 13C peaks in the chemical shift

range greater than 60 ppm.

The weight fraction of the microcrystals was ~0.2.

The obtained suspension was poured into a plastic tube with a diameter and height of 4 mm and

3

~15 mm, respectively. The tube was then mounted on a sample-rotating unit placed at the bore center of a cryogen-free superconducting magnet (Sumitomo Heavy Industry), which generates an 8-T static horizontal magnetic field.

The sample rotation axis was vertical (the z-axis) and the tube

axis was set either horizontal or vertical.

Three rod-shaped MOMA samples, M1, M2, and M3,

were prepared, where the rod axis (tube axis) was parallel to  3 axis (M1),  1 axis (M2), or  2 axis (M3). Here, we define 1 >  2 >  3 .

The sample was rotated at two different frequencies

within one revolution: the rotation frequency was switched between = 10 rpm and = 80 rpm every 90. After 70 min of this frequency-modulated rotation of the tube, the suspension was irradiated with UV light for 45 min to photopolymerize the UV-curable monomer.

Subsequently,

the consolidated specimen was removed from the tube to obtain a rod-shaped cellobiose MOMA (~3 mm in diameter and 10 mm in height) for NMR measurements. The three-dimensional alignment of the cellobiose microcrystals in the MOMA sample was confirmed using X-ray diffraction. X-ray diffraction data were collected on a Rigaku RAXIS RAPID

II system,

Cu-Kradiation.

equipped with an imaging plate,

using graphite-monochromatized

The collimator size and crystal-to-detector distance were 0.5 mm and 127 mm,

respectively. Data were collected via ω scans from −15 to 15 at ambient temperature. 13

C CP solid-state NMR measurements under proton decoupling were performed using a probe

with a goniometer [sample rotation axis (rod axis) is perpendicular to the applied magnetic field B0] at ambient temperature (20 C) with a JEOL ECA-500 system operated at the resonance frequency of a 13C (125 MHz). Recycle delay and contact time were 60 s and 2 ms, respectively. 600~2160 scans were performed.

A total of

The separation of undistorted powder patterns by effortless

recoupling (SUPER) experiment [20] was performed on a Varian 400 spectrometer operating at 100 MHz for 13C using a 4-mm zirconia rotor spinning at 3 kHz.

The principal values determined by

SUPER were used in simulations performed for peak assignments.

4

Recycle delay, total scans,

contact time, and complex points for 2D increments were 9 s, 4096, 2 ms, and 16, respectively. MAS measurement for 13C was performed on a Varian 400 spectrometer operating at 100 MHz and using a 4-mm zirconia rotor spinning at 15 kHz. Recycle delay, total scans, and contact time were 120 s, 256, and 2 ms. Chemical shifts for all measurements were referenced to adamantane (ADM).

3. Results and discussion 3.1 X-ray diffraction pattern Figure 1 shows the X-ray diffraction patterns of the obtained cellobiose MOMA sample (sample M2).

Well-separated diffraction spots are very apparent in the diffraction images taken from the

directions of 1 ,  2 , and  3 axes. The half widths in the azimuthal plot were ~5 for most spots in all of the images in the figure.

This result confirms that the microcrystals in the polymer

matrix are aligned three-dimensionally.

The same order of orientations was confirmed for the other

two MOMA samples (M1 and M3). NMR peaks will become sharper.

With higher magnetic fields, the X-ray peaks and the resultant Although the half widths of ~5 are larger than those for single

crystals, it is sufficient to separate the NMR peaks for samples with these half widths if there are no significant peak overlaps with different carbons.

>

3.2 Theoretical background 3.2.1 Crystal symmetry Cellobiose crystals belong to monoclinic system (space group P21, Z = 2, a = 5.0633 Å, b = 13.017 Å, c = 10.9499 Å, β = 90.811º) [21].

In the monoclinic crystals, the two-fold rotation or

5

inversion axis coincides with one of the three magnetic axes [22].

We reported previously [17, 23]

that the b axis (two-fold rotation axis) corresponds to the hard magnetization axis  3 in cellobiose crystals.

The other two magnetic axes,  1 (easy magnetization axis) and  2 (intermediate axis),

are located on the ac plane. The relationship between the magnetic  1 and  2 axes and the crystallographic a and c axes has been reported in our previous work [17, 24] and is shown in Figure 2.

There are two identical molecules in the unit cell, which are related by a two-fold screw axis.

These two molecules are denoted by A1(lmn) and A2(-l-mn), where (lmn) indicates the direction cosines with respect to the χ -frame.

>

3.2.2 Twin structure The magnetic axes,  1 ,  2 , and  3 , of each microcrystal are aligned three-dimensionally in a MOMA. However, this does not necessarily mean that the crystallographic axes, a, b, and c, are also aligned three-dimensionally because the a and c axes do not coincide with the  1 and  2 axes.

Owing to the axial nature of the magnetic axes, a  rotation of a microcrystal about the

magnetic axes induces an additional crystal orientation that has an equal magnetic energy. cell containing molecules A1(lmn) and A2(-l-mn) is rotated by  molecules A3(l-m-n) and A4(-lm-n) are created (Figure 2).

If a unit

about the  1 axis, two

These four molecules having mutually

different orientations are described by the point group (222) [25]. This symmetry is a characteristic of MOMA prepared from monoclinic crystals with point group 2.

Owing to this (222) symmetry, a

cellobiose MOMA can be considered equivalent to the orthorhombic crystal with point group (222), whereby the χ -frame corresponds to the crystallographic abc-frame of the orthorhombic system. 3.2.3 Determination of the principal values and principal axes

6

The chemical shift tensors σ χ s relative to the χ -frame are symmetric and are defined as

  11   12   13     23  ,    12  22   33   13  23

 12   13    11  12  13    11      22   23  , σ    12  22  23  ,   12      13  23  33     13   23  33  

  11   12  13       12  22   23     13   23  33  (1)

for the molecules A1(lmn), A2(-l-mn), A3(l-m-n), and A4(-lm-n), respectively.

The tensors σ χ is

transformed relative to the principal  1 2 3 -frame ( σ -frame) as

σ  R σ σ χ R σ1 ,

(2)

where R σ is the transformation matrix, whose ij component is defined as (R σ ) ij  s i  k j , with s i and k j being the normalized orthogonal base vectors for the - and χ -frames, respectively (Figure 3a).

The tensor σ is diagonal and its components are  1 ,  2 , and  3 .

The principal

values and principal axes of the tensor σ are determined as the eigenvalues and eigenvectors of the tensor σ χ , respectively. The tensor σ χ is transformed into

σ L  R Lσ χ R L1 ,

(3)

expressed with respect to the laboratory xyz-frame (L-frame), where R L is the transformation matrix, whose ij component is defined by (R L ) ij  e i  k j , with e i being the normalized orthogonal base vectors for the L-frame (Figure 3b).

7

>

We use three experimental settings, as shown in Figure 4. In these settings, MOMA samples, M1, M2, and M3, are set such that (i)  3  B 0 , (ii) 1  B 0 , and (iii)  2  B 0 , where B 0 is the NMR magnetic field. In each setting, the sample is rotated by an angle  about the respective axes. When   0 , the three settings are denoted by (i-0), (ii-0), and (iii-0), indicating that (i-0)

 1 || B 0 ,  3  B 0 , (ii-0)  2 || B 0 , 1  B 0 , and (iii-0)  3 || B 0 ,  2  B 0 , respectively. The rotation matrices R L for the settings (i), (ii), and (iii) are expressed as follows:

R (i) L

0 1 0 0  1 0   0 1  0       (ii) (iii)   sin   cos  0  , R L   0 sin   cos   , R L    cos  0 sin   .  cos  sin  0   0 cos  sin    sin  0 cos         (2)

The experimentally observed chemical shift is related to the components of σ  through the L  (R L σ  R L1 ) 33 . relationship σ zz

L For setting (i-0), the observed values of σ zz for four different

χ χ L L  σ 11  σ 22 molecules, A1, A2, A3, and A4, are the same: (i-0) σ zz . Similarly, (ii-0) σ zz , and (iii-0)

χ σ zzL  σ 33 . For settings (i), (ii), and (iii) at = 45, referred to as (i-45), (ii-45), and (iii-45),

χ χ χ L  σ 22  2σ12 )/ 2,  (σ11 respectively, we observe two peaks for each of these settings: (i-45) σ zz

χ

χ

χ

χ χ χ L  σ 33  2σ13 ) / 2 , giving rise to six  (σ 22  σ 33  2σ 23 ) / 2 , and (iii-45) σ zzL  (σ11 (ii-45) σ zz

equations.

All the nine equations are then derived from the above experiments and are used to

χ χ χ χ χ χ determine the six unknown values: σ 11 , σ 22 , σ 33 , σ 12 , σ 23 , and σ 13 .

χ and σ 13 is rather arbitrary.

χ χ The sign of σ 12 , σ 23 ,

The six values are determined by the least square method. Now, the

principal values  1 ,  2 , and  3 , and the principal axes s1 , s 2 , and s 3 of the tensor σ are 8

derived as the eigenvalues and eigenvectors of the tensor σ χ , respectively.

>

3.3 Simulation for peak assignment The SUPER experiment was performed to determine the chemical shift values of C1 and C1΄ carbon; they are respectively σ1 = 119.4, σ 2 = 102.9, and σ 3 = 89.7 ppm and σ1 ' = 122.1,

σ 2 ' = 99.4, and σ 3 ' = 70.7 ppm (Figure 5). The isotropic values obtained from the CP/MAS experiment are 104.0 ppm for C1 and 97.4 ppm for C1΄.

Because of these large anisotropies in the

chemical shifts, C1 and C1′ carbons exhibit severe overlapping in the spectra obtained under experimental settings (i), (ii), and (iii). difficult.

This makes assigning the peaks under consideration

Furthermore, the peaks from other carbons may interfere with the assignment.

>

In order to assign C1 and C1′ carbons, we first perform simulations to identify the approximate locations of the peaks.

The simulation is based on the local symmetry assumption.

The

13

C

chemical shift tensor depends strongly on the anisotropy in electron density near the resonance nucleus.

The shielding is stronger in the direction where the electron density is high.

The

hybridization of the carbon and the atoms bonding to it dominates the electron environment. Therefore, the anisotropy of the chemical shift tensor of a

13

C nucleus depends on the bonding

symmetry of the nuclei [26, 27]. The C1 and C1′ carbons bond with two oxygen atoms (Figure 6). The direction of the C-O bond is the dominant direction of chemical shielding because the electron density is high in this

9

direction.

The bond length of C1-O1 is shorter than that of C1-O5 by 0.031Ǻ, and hence, the most

shielded direction is close to the direction of C1-O1 and the least shielded direction is close to the direction perpendicular to the O1-C1-O5 plane.

The C1′-O1′ bond is shorter than the C1′-O5′ bond

by 0.057 Ǻ, and hence, the most shielded direction is close to the direction of the C1′-O1′ bond and the least shielded direction is close to the direction perpendicular to the O1΄-C1΄-O5΄ plane. assumptions are confirmed experimentally for several saccharides [26, 27].

These

Therefore, in the

simulation, we assume that the σ 3 axis is parallel to the C1-O1 bond and the σ1 axis is perpendicular to the O1-C1-O5 plane; similarly, σ 3 ' axis is parallel to the C1′-O1′ bond and the

σ 1 ' axis is perpendicular to the O1′-C1′-O5′ plane. Experimental values of σ 1 , σ 2 , and σ 3 for C1 and σ1 ' , σ 2 ' , and σ 3 ' for C1′ determined by the SUPER experiment were used in the simulation.

Table 1 summarizes the results of the simulation.

> >

3.4 Peak assignment The spectra obtained under settings (i), (ii), and (iii) for Figures 7a and 7b respectively.

0

and   45 are shown in

We assign the C1 and C1′ carbons to the peaks in the figure by the

following steps. (Step 1) We begin by assigning the peaks in Figure 7a. First, the peak positions predicted by the simulation are applied.

The peak positions predicted for the C1 and C1′ carbons are indicated

by solid blue and dotted red arrows, respectively, in the figure.

Because the simulation is based on

the local symmetry assumption, the predicted peak positions in the spectra may not be precise; nevertheless, we assume to the first approximation that the peaks that are close to the predicted

10

position correspond to the respective peaks. (Step 2) The temporal assignments made are validated by the relations imposed to the chemical shift values of the respective peaks.

χ χ χ The values of σ11 , σ 22 , and σ 33 are determined from the

temporal assignments for the peaks in settings (i-0), (ii-0), and (iii-0), respectively, from the locations of these peaks.

χ χ χ  σ 22  σ 33 ) / 3 = σ iso , where σ iso If these values satisfy the relation (σ11

is the isotropic chemical shift determined by MAS measurements, then the assignments are valid. Otherwise, we go back to Step 1 and take nearby peak(s) as next candidate(s) until the criteria in Step (2) is satisfied.

The assignments thus determined are marked by thick black arrows in Figure

7a. (Step 3) Next, we assign the peaks in Figure 7b.

First, the peak positions predicted by the

simulation are applied. We assume to the first approximation that the peaks close to the predicted position correspond to the respective peaks. for example.

Let us consider the assignment of C1 carbon in (i-45)

Two peak positions are predicted and they are indicated by blue arrows. We select

two peaks that are close to the predicted positions as tentative assignments. (Step 4) These tentative assignments are examined by a corresponding relation.

For example,

in the case of (i-45), the chemical shift values for the two peaks are expressed by χ χ χ χ χ χ (σ11  σ 22  2σ12 ) / 2 and (σ11  σ 22  2σ12 ) / 2 . Therefore, the middle point of these two peaks,

χ χ χ χ (σ11  σ 22 ) / 2 , should be consistent with the σ11 and σ 22 values determined in Step 2. If this is

not satisfied, we go back to Step 3 and repeat the procedure until the condition is met. procedure is applied to (ii-45) and (iii-45).

A similar

The assignments thus determined are marked by thick

black arrows in Figure 7b. The peak positions for C1 and C1΄ carbons are assigned by following the procedure described above.

The chemical shift values of each peak are summarized in Table 2. 11

> >

3.5 Determination of the tensor σ χ The chemical shift values tabulated in Table 2 indicate the following relations in the case of C1 carbon:

χ σ11  108.7

,

χ σ 22  96.3

,

χ σ 33  107.6

,

χ χ χ (σ11  σ 22  2σ12 )/2

=

113.2,

χ χ χ χ χ χ χ χ χ (σ11  σ 22  2σ12 ) / 2 = 97.8, (σ 22  σ 33  2σ 23 ) / 2 = 105.4, (σ 22  σ 33  2σ 23 ) / 2 = 99.3,

χ χ χ χ χ χ (σ11  σ 33  2σ13 ) / 2 = 115.0, and (σ11  σ 33  2σ13 ) / 2 = 99.0. Here, we have a total of nine

χ χ χ χ χ χ equations for six parameters: σ11 , σ 22 , σ 33 , σ11 , σ12 , and σ13 .

Hence, we apply the least

square method to obtain the most plausible values for these six parameters.

We then obtain

χ χ χ χ χ χ σ11  109.4 , σ 22  98.1 , σ 33  106.6 , σ12  7.7 , σ13  8.0 , and σ 23  3.1 . Therefore, we

have eight possible matrices, which are classified into two, represented by the following matrices:

109.4  7.7 8.0    σ (C1) =   7.7 98.1  3.1  ,  8.0  3.1 106.6    χ

109.4 7.7  8.0     7.7 98.1 3.1    8.0 3.1 106.6   

(5a)

(5b)

The matrices belonging to the same type give rise to the same principal values and principal axes. The tensors for the other three molecules can be generated according to eq. (1). (5) is correct [27].

Either one of eq.

The principal values derived are  1  119.1 ,  2  100.9 ,  3  94.1 ppm

12

from eq. (5a) and  1  117.1 ,  2  105.7 ,  3  91.3 ppm from eq. (5b).

These are compared to

 1  119.4 ,  2  102.9 ,  3  89.7 ppm, determined by SUPER. It is difficult to determine which values are close to those obtained by SUPER.

In Figure 8a, the principal axes,  1 ,  2 , and

 3 , of C1 carbon are shown. The blue and red arrows are those determined using eqs. (5a) and (5b), respectively. According to the criteria [27, 28], we conclude that eq (5b) provides a better result because the  3 axis (red) derived from eq. (5b) is closer to the C1-O1 bond.

In Table 3, the

principal values and direction cosines in molecular XYZ-frame (Figure 6) are summarized.

>

χ On the other hand, because the σ 13 component happens to vanish, we obtain the tensors σ χ

(C1′) for C1′ carbons uniquely as follows:

108.0  7.7 0.0    σ (C1′)    7.7 109.0 14.2  . (6)  0.0 14.2 73.6   χ

The principal values are calculated as  1  118.9 ,  2  103.2 ,  3  68.5 ppm, which are compared to σ1 ' =122.1, σ 2 ' =99.4, and σ 3 ' =70.7 ppm obtained by SUPER.

σ1 ' , σ 2 ' , and σ 3 ' , are shown in Figure 8b.

The principal values and direction cosines in

molecular X′Y′Z ′-frame (Figure 6) are summarized in Table 3.

>

13

The principal axes,

4. Conclusions The chemical shift tensors of C1 and C1΄ carbons of cellobiose crystals were determined for the first time from its microcrystalline powder sample by using MOMA samples. In this study, MOMA samples were rotated about its magnetic axes, while a single crystal is rotated about its crystallographic axes in conventional single-crystal NMR methods.

Because a MOMA is formed in

a rod-like shape and its magnetic axis coincides with the rod axis, the rotation axis is easily identified when taking measurements during sample rotation. rotation of single crystals.

This is a marked contrast to the

We conducted six measurements at designated sample orientations with

respect to the applied field to determine the six components of the chemical shift tensor expressed relative to the χ -frame.

We obtained two chemical shift tensors for C1 carbon, between which the

correct one was chosen based on the criteria that the  3 direction is close to the C1-O1 bond vector. We have demonstrated that the use of MOMAs is of great advantage when large single crystals are unavailable, whereby the rotations about the magnetic axes are appropriate choices.

Acknowledgements This study was supported by the Japanese Ministry of Education, Culture, Sports, Science and Technology (24350119).

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References [1] F. Taulelle, Fundamental Principles of NMR Crystallography, in, eMagRes, 2009. [2] B. Bouchevreau, C. Martineau, C. Mellot-Draznieks, A. Tuel, M.R. Suchomel, J. Trebosc, O. Lafon, J.-P. Amoureux, F. Taulelle, An NMR-Driven Crystallography Strategy to Overcome the Computability Limit of Powder Structure Determination: A Layered Aluminophosphate Case, Chem. Eur. J., 19 (2013) 5009-5013. [3] R.K. Harris, NMR crystallography: the use of chemical shifts, Solid State Sciences, 6 (2004) 1025-1037. [4] R.K. Harris, R.E. Wasylishen, M.J. Duer, NMR Crystallography, Wiley, 2009. [5] K. Tateishi, M. Negoro, S. Nishida, A. Kagawa, Y. Morita, M. Kitagawa, Room temperature hyperpolarization of nuclear spins in bulk, PNAS, 111 (2014) 7527-7530. [6] S. Dugar, R. Fu, N.S. Dalal, Increasing C-13 CP-MAS NMR Resolution Using Single Crystals: Application to Model Octaethyl Porphyrins, J. Phys. Chem. B, 116 (2012) 9215-9222. [7] N.S. Dalal, K.L. Pierce, J. Palomar, R. Fu, Single-crystal magic-angle spinning O-17 NMR and theoretical studies of the antiferroelectric phase transition in squaric acid, J. Phys. Chem. A, 107 (2003) 3471-3475. [8] A. Klymachyov, N. Dalal, Spinning crystals leads to significant enhancement in C-13 spectral resolution in MAS experiments on organic compounds: a new aid in studying phase transitions, Solid State Nucl. Magn. Reson., 9 (1997) 85-89. [9] M. Fu, D.A. Torchetti, T. Imai, F.L. Ning, J.Q. Yan, A.S. Sefat, NMR Search for the Spin Nematic State in a LaFeAsO Single Crystal, Phys. Rev. Lett., 109 (2012) 247001. [10] S. Indris, P. Heitjans, R. Uecker, B. Roling, Li Ion Dynamics in a LiAlO2 Single Crystal Studied by Li-7 NMR Spectroscopy and Conductivity Measurements, J. Phys. Chem. C, 116 (2012) 14243-14247.

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[11] M.J. Potrzebowski, J. Helinski, W. Ciesielski, Two-dimensional and variable temperature P-31 solid-state NMR studies of single crystals containing symmetrical/unsymmetrical bis 6-O,6-O΄-(1,2 : 3,4-diisopropylidene-alpha-D-galactopyranosyl) thiophosphoryl dichalcogenides, Chem. Commun., (2002) 1582-1583. [12] T. Kimura, M. Yoshino, Three-dimensional crystal alignment using a time-dependent elliptic magnetic field, Langmuir, 21 (2005) 4805-4808. [13] T. Kimura, F. Kimura, M. Yoshino, Magnetic alteration of crystallite alignment converting powder to a pseudo single crystal, Langmuir, 22 (2006) 3464-3466. [14] T. Kimura, C. Chang, F. Kimura, M. Maeyama, The pseudo-single-crystal method: a third approach to crystal structure determination, J. Appl. Crystallogr, 42 (2009) 535-537. [15] F. Kimura, T. Kimura, K. Matsumoto, N. Metoki, Single-Crystal Neutron Diffraction Study of Pseudo Single Crystal Prepared from Microcrystal line Powder, Cryst. Growth Des., 10 (2010) 48-51. [16] F. Kimura, T. Kimura, W. Oshima, M. Maeyama, K. Aburaya, X-ray diffraction study of a pseudo single crystal prepared from a crystal belonging to point group 2, J. Appl. Crystallogr., 43 (2010) 151-153. [17] F. Kimura, W. Oshima, H. Matsumoto, H. Uekusa, K. Aburaya, M. Maeyama, T. Kimura, Single crystal structure analysis via magnetically oriented microcrystal arrays, CrystEngComm, 16 (2014) 6630-6634. [18] R. Kusumi, F. Kimura, G. Song, T. Kimura, Chemical shift tensor determination using magnetically oriented microcrystal array (MOMA): C-13 solid-state CP NMR without MAS, J. Magn. Reson., 223 (2012) 68-72. [19] R. Kusumi, F. Kimura, T. Kimura, Determination of

31

P chemical shift tensor from

microcrystalline powder by using magnetically oriented microcrystal array (MOMA), Cryst. Growth

16

Des., 15 (2015) 718-722. [20] S.F. Liu, J.D. Mao, K. Schmidt-Rohr, A robust technique for two-dimensional separation of undistorted chemical-shift anisotropy powder patterns in magic-angle-spinning NMR, J. Magn. Reson., 155 (2002) 15-28. [21] E. Kalenius, T. Kekaelaeinen, R. Neitola, K. Beyeh, K. Rissanen, P. Vainiotalo, Size- and structure-selective noncovalent recognition of saccharides by tetraethyl and tetraphenyl resorcinarenes in the gas phase, Chem. Eur. J., 14 (2008) 5220-5228. [22] J.F. Nye, Physical properties of crystals : their representation by tensors and matrices, Clarendon Press, Oxford, 1985. [23] G. Song, F. Kimura, T. Kimura, G. Piao, Orientational Distribution of Cellulose Nanocrystals in a Cellulose Whisker As Studied by Diamagnetic Anisotropy, Macromolecules, 46 (2013) 8957-8963. [24] S. Guangjie, K. Matsumoto, K. Fujita, F. Kimura, T. Kimura, Determination of Ratio of Diamagnetic Anisotropy of a Biaxial Crystal by X-ray Diffraction Measurement, Jpn. J. Appl. Phys., 51 (2012) 060203. [25] F. Kimura, K. Mizutani, B. Mikami, T. Kimurat, Single-Crystal X-ray Diffraction Study of a Magnetically Oriented Microcrystal Array of Lysozyme, Cryst. Growth Des., 11 (2011) 12-15. [26] M.H. Sherwood, D.W. Alderman, D.M. Grant, ASSIGNMENT OF C-13 CHEMICAL-SHIFT TENSORS IN SINGLE-CRYSTAL SUCROSE, J. Magn. Reson., Ser A, 104 (1993) 132-145. [27] D.L. Sastry, K. Takegoshi, C.A. McDowell, DETERMINATION OF THE C-13 CHEMICAL-SHIFT

TENSORS

IN

A

SINGLE-CRYSTAL

OF

METHYL

ALPHA-D-GLUCOPYRANOSIDE, Carbohydr. Res., 165 (1987) 161-171. [28] S.C. Shekar, A. Ramamoorthy, R.J. Wittebort, Determination of the chemical shielding tensor orientation from two or one of the three conventional rotations of a single crystal, J. Magn. Reson., 155 (2002) 257-262.

17

Figures, tables, and captions

Figure 1 X-ray diffraction images of a MOMA (sample M2) taken from three different directions. Sharp spots indicate three-dimensional orientation of the microcrystals in MOMA.

 1 ,  2 , and

 3 indicate the directions of the magnetic axes.

1 A3(l-m-n)



c A1(lmn)

b

2

3 A4(-lm-n) Figure 2



a

A2(-l-mn)

Unit cell of cellobiose crystals and twin structure that occurs in a MOMA sample.

There

are two identical molecules with different orientations in a unit cell, denoted by A1(lmn) and A2(-l-mn), where (lmn) indicates the direction cosines with respect to the -frame. In a MOMA, another orientation (twin) is generated due to a  rotation of the unit cell about the  1 (or  2 ) axis. The orientations of the twin molecules are denoted by A3(l-m-n) and A4(-lm-n). The direction of the  1 axis with respect to the c and a axes are  = 67.2 and  = 21.8, respectively.

18

(a) s3

(b)

k3

k3 e3

s2

k2

k1 Figure 3

k2

e1

e2

k1

s1

Relationship of the magnetic frame (-frame) with (a) the principal frame (-frame) and

(b) the laboratory frame (L-frame).

Orthogonal unit base vectors in each frame are represented by

si (-frame), ki (-frame), and ei (L-frame), respectively, where i = 1,2, and 3.

(i) 2

Figure 4

(ii)

zB0 

1 y

3

(iii)

zB0 

2 y

1

3

1

2

x

x

x

zB0 

3 y

Experimental settings of MOMA samples in a probe. The NMR magnetic field B0 is in

the z direction and the sample rotation axis is about the laboratory x axis. Setting (i): sample M1 is set with  3  x axis; settings are referred to as (i-0) and (i-45) when = 0° and 45, respectively. Setting (ii): sample M2 is set with  1  x axis; settings are referred to as (ii-0) and (ii-45) when = 0° and 45, respectively.

Setting (iii): sample M3 is set with  2  x axis; settings are referred to as

(iii-0) and (iii-45) when = 0° and 45, respectively. It is noted that  1 k1,  2 k2, and  3 k3, where vector ks are defined in Figure 3.

19

C1

CP/MAS

C1’

2 C1

C1’ 125

Figure 5

3

1

′2

′3

′1

115

105

95

85

75

65

55

CP/MAS spectrum and powder patters of C1 and C1′ carbons obtained by performing

SUPER of cellobiose.

Dotted red curves in powder spectra are simulation results and the principal

values obtained by the simulation are indicated by arrows.

O5

Y

Z

C1′ O1′

X C1

Figure 6

O1 O5′ Y′

Molecular axes (XYZ) at C1 and (X′Y′Z′) at C1′ carbons.

Z′

X′

The X axis is parallel to the

C1-O1 bond, the Y axis is on the O1-C1-O5 plane, and the Z axis is defined according the right-handed rule.

The X′ axis is parallel to the C1′-O1′ bond, the Y′ axis is on the O1′-C1′-O5′

plane, and the Z′ axis is defined according to the right-handed rule. that X σ 3 , Y σ 2 , Z σ 1 , X′ σ 3 ' , Y′ σ 2 ' , and Z′ σ1 ' . 20

In simulations, it is assumed

(a)

(b)

C1 C1’

(i-0)

120

C1 C1’

(i-45)

90

60

C1 C1’

120

90

60 C1’

(ii-0)

(ii-45) C1

C1 C1 C1’

C1’

120

90

60

120

C1’

(iii-0)

(iii-45)

90

60

C1’ C1’

C1

C1 C1

120

90

60

120

90

60

Figure 7 Spectra observed under (a) settings (i-0), (ii-0), and (iii-0) and (b) settings (i-45), (ii-45), and (iii-45). Peak positions (ppm) for C1 and C1′ predicted by the simulation (Table 1) are indicated by thin arrows (blue for C1 and dotted red for C1′) and those assigned are indicated by thick arrows.

21

O5’

O5

σ2′

σ2

σ1

C1

σ1′

σ3

C1’

O1’

σ3′

O1

(b)

(a)

Figure 8 (a) Principal axes of C1 carbon determined from eqs. (5a) and (5b). Blue and red arrows correspond to eqs. (5a) and (5b), respectively. (b) Principal axes of C1′ determined from eq (6).

22

C1

C1

(i-0)

105.6

(i-45)

(ii-0)

96.6

(ii-45)

(iii-0)

109.8

(iii-45)

(i-0)

104.9

(i-45)

(ii-0)

108.1

(ii-45)

(iii-0)

79.2

(iii-45)

108.3 93.8 105.0 101.5 118.7 96.7 117.2 95.7 110.8 76.5 91.5 92.7

Table 1 Simulation results for peak positions (ppm) expected to appear under different experimental settings: (i-0), (ii-0), (iii-0), (i-45), (ii-45), and (iii-45) for C1 and C1′ carbons.

C1

C1

(i-0)

108.7

(i-45)

(ii-0)

96.3

(ii-45)

(iii-0)

107.6

(iii-45)

(i-0)

108.7

(i-45)

(ii-0)

112.0

(ii-45)

(iii-0)

71.5

(iii-45)

113.2 97.8 105.4 99.3 115.0 99.0 113.2 97.8 105.4 77.0 93.0 93.0

Table 2 Peak positions (ppm) determined from the spectra shown in Figure 7, with the help of simulation peak positions (Table 1) indicated in Figure 7.

23

Carbons nucleus C1

C1

Table 3

Direction cosines with respect to

Principal value of tensor

X (X)

Y (Y)

Z (Z)

3

91.3

0.9949

0.0509

0.0870

2

105.8

0.0292

0.9718

0.2340

1

117.1

0.0964

0.2303

0.9683

3

68.4

0.9917

0.1090

0.0685

2

103.3

0.1132

0.9917

0.0604

1

118.9

0.0613

0.0677

0.9958

Principal values and direction cosines of the C1 and C1′ chemical shift tensors relative to

the molecular frame defined in Figure 6.

24

Graphical abstract

25

Highlights 

Magnetically oriented microcrystal array (MOMA) of cellobiose was prepared.



MOMA was analyzed using single crystal C NMR technique.



Principal axes and values of chemical shift tensors of C1 and C1’ were determined.

13

26