6th International Conference on Gas Hydrates

AB INITIO STRUCTURE DETERMINATION OF GAS HYDRATES AND REFINEMENT OF GUEST MOLECULE POSITIONS BY POWDER.. Takeya, Satoshi 2008

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  AB INITIO STRUCTURE DETERMINATION OF GAS HYDRATES AND REFINEMENT OF GUEST MOLECULE POSITIONS BY POWDER X-RAY DIFFRACTION   Satoshi Takeya  , Konstantin A. Udachin, and John A. Ripmeester Steacie Institute for Molecular Sciences National Research Council Canada 100 Sussex Drive Ottawa, Ontario, K1A OR6 CANADA   ABSTRACT Structure determination of powdered crystals is still not a trivial task.  For gas hydrates, the difficulty lies in how to determine the rotational disorder and cage occupancies of the guest molecules without other supporting information or constraints because the complexity of the problem for the powder diffraction technique generally depends on the number of atoms to be located in the asymmetric unit.  Here, the crystal structures of gas hydrates of CO2, C2H6, C3H8, and Methylcyclohexane/CH4, as determined by the direct-space and Rietveld techniques are reported.  The resultant structures and cage occupancies were consistent with results found from conventional experimental methods using single crystal x-ray diffraction or solid-state 13 C-NMR. It was shown that the procedures reported in this study make it possible to determine guest disorder and absolute cage occupancy of gas hydrates even from powder crystal.  Keywords: ab initio, clathrate, direct-space method, hydrate, powder x-ray diffraction    Corresponding author (Permanent address): National Institute of Advanced Industrial Science and Technology (AIST) Central 5, Higashi 1-1-1, Tsukuba 305-8565, JAPAN Phone: +81 29 861 4506 Fax +81 29 861 4845  E-mail: s.takeya@aist.go.jp INTRODUCTION Single crystal x-ray diffraction is the most powerful technique for determining crystal structures.  However, this method does not work for solids that cannot be prepared in the form of single crystals of sufficient size and quality.  To determine the structure of such solids, we must instead use powder diffraction.  For structural solutions by traditional powder diffraction techniques, the complexity of the problem generally depends on the number of atoms to be located in the asymmetric unit.  Recently, significant advances have been made in the application of powder diffraction methods.  Direct- space techniques using powder diffraction overcome intrinsic problems encountered in the structure-solution stage of the structure determination process. [1]   For structural solutions by direct-space techniques, the complexity of a direct-space search procedure depends more directly on the number of degrees of freedom in the optimization rather than on the number of atoms in the asymmetric unit.  For gas hydrates, the main advantage of the direct-space techniques is the possibility of refining the guest molecule positions in the cage structures.  Here, crystal structures of gas hydrates structure I (space group Pm-3n), structure II (space group Fd-3m), and structure H (space group P6/mmm) as determined by the direct-space technique using powder x-ray diffraction (PXRD) are reported.  The procedure reported here is useful for the estimation of gas storage capacity of gas hydrate crystals from their Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, British Columbia, CANADA, July 6-10, 2008. cage occupancies, which encage large guest molecules such as THF with H2 or CH4. [2]   EXPERIMENTAL Gas hydrate samples were synthesized from fine ice powder using a method reported previously. [3]  Crystallite size of each synthesized powder sample was examined by measuring their Debye-Scherrer ring because it is important to eliminate preferred orientation effects of the crystallites when recording PXRD data.  The Debye-Scherrer rings were collected with MoK radiation (= 0.7107 Å) on a BRUKER axs model SMART CCD diffractometer. PXRD measurements were done using in lab x-ray diffractmeter (40 kV, 40 mA; BRUKER axs model D8 Advance equipped with a solid state detector model LynxEye) in / step scan mode using CuK radiation ( = 1.5406 Å) with a step width of 0.01966 o in the 2 range of 5.0–90.0o. Powdered hydrate samples were mounted on a PXRD sample holder made from Cu 2.5 mm in thickness under a N2 gas atmosphere kept below 100 K.  The temperature was kept at 163 K using a low-temperature chamber (Anton Paar model TTK 450) during each PXRD measurement.  STRUCTURE ANALYSIS Structure solution calculations of gas hydrates encaging guest molecules were initiated by a global optimization of experimental diffraction profiles using a parallel tempering approach implemented in the direct-space method program FOX. [4]   A large number of trial structures were calculated by rotation and translation of guest molecules and cage occupancy changes.  Using the best fit model by the direct-space technique, refinements of the crystal structure of the hydrates were performed by a Rietveld method using the RIETAN-2000 program. [5]   To model the disorder of guest molecules, rigid-body constraints were used.  Virtual chemical species, Wa and M, whose atomic scattering factors are equal to the sum of those for H2O and CH4, -CH3 or -CH2 were used instead of refining hydrogen positions.  RESULTS AND DISCUSSION Figure 1-1 shows a comparison of the measured PXRD pattern of CO2 hydrate with the calculated pattern using the Rietveld method.  There are some extra diffraction peaks indicating the coexistence of hexagonal ice (10.6 wt %).  Figure 1-2 shows 10 20 30 40 50 60 70 80 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 2 [degrees] In te n si ty  [ a .u .] In te n si ty  [ a .u .] Figure 1-2 CO2 molecules (Carbon atom: white, Oxygen atom: black) in structure I large (5 12 6 2 ) and small (5 12 ) cage with full symmetry shown. Figure 1-1 PXRD pattern of the CO2 hydrate at 163 K.  The plus marks (+) denote the observed intensities; the solid line is that calculated from the best-fit model of the Rietveld refinement.  The bottom curve represents the deviation of observed and calculated intensities.  Rwp = 10.1 %, 2 = 28.5.  The upper tick marks represent the calculated peak positions for the structure I hydrate and the lower tick marks represent those for the hexagonal ice. Figure 1-3 CO2 molecules in CO2 hydrate found in this study (black) and by the single crystal x-ray diffraction (grey) reported by Udachin et al. [6]  for comparison.  The Structure I large cage is on the left, the small cage on the right.  cage. the CO2 molecules with full symmetry in small and large cages in cubic structure I (a = 11.882(6) Å).  Figure 1-3 shows the comparison of CO2 positions refined by PXRD with single crystal analysis. The refined model showed that CO2 occupied 99 % of the large cages and 67 % of the small cages in this study, whereas it was found that 100 % of the large cage and 71 % of the small cage by the single crystal analysis in the earlier study. [6] Refined atomic coordinates and isotropic displacement parameters for the structure are given in Table 1. Figure 2-1 shows the comparison of the measured PXRD pattern of C2H6 hydrate with the calculated pattern using the Rietveld method.  There are some extra diffraction peaks indicating the coexistence of hexagonal ice (14.4 wt %).  Figure 2-2 shows the C2H6 molecules with full symmetry in small and large cages in cubic structure I (a = 12.009(3) Å).  Figure 2-3 shows the comparison of C2H6 position refined by the PXRD with single crystal analysis.  The refined model showed that C2H6 occupied 98 % of the large cages and 12 % of the small cages in this study, whereas it was found to be 100 % of the large cages and 5.8 % of the small cages by single crystal analysis in the earlier study. [7]   Refined atomic coordinates and isotropic displacement parameters for the structure are given in Table 2. Figure 3-1 shows the comparison of the measured PXRD pattern of C3H8 hydrate with the calculated pattern using the Rietveld method.  There are some extra diffraction peaks indicating the coexistence of hexagonal ice (4.1 wt %).  Figure 3-2 shows the C3H8 molecules with full symmetry in large cage of cubic structure II (a = 17.172(5) Å). Figure 3-3 shows a comparison of C3H8 position refined by PXRD with single crystal analysis. The refined model showed that C3H8 occupied 93 % of the large cages and 0 % of the small cages in this study, whereas it was found 100 % of the large cages and 0 % of the small cages were occupied in the single crystal analysis in the earlier study. [8]  Refined atomic coordinates and isotropic displacement parameters for the structure are given in Table 3. Figure 2-1  PXRD pattern of the C2H6 hydrate at 163 K.  The plus marks (+) denote the observed intensities; the solid line is that calculated from the best-fit model of the Rietveld refinement.  The bottom curve represents the deviation between the observed and calculated intensities.  Rwp = 10.5 %, 2 = 28.6.  The upper tick marks represent the calculated peak positions for the structure I hydrate and the lower tick marks represent those for the hexagonal ice. Figure 2-3 C2H6 molecules in C2H6 hydrate found in this study (black) and by single crystal x-ray diffraction (grey) reported by Udachin et al. [7]  for comparison. _ 10 20 30 40 50 60 70 80 90 0 10000 20000 30000 40000 50000 60000 70000 2 [degrees] I n te n s it y  [ a .u .] I n te n s it y  [ a .u .] Figure 2-2 C2H6 molecules in structure I large (5 12 6 2 ) and small (5 12 ) cage are shown with full symmetry.  Solid spheres express the virtual chemical species -CH3. Figure 3-1  PXRD pattern of the C3H8 hydrate at 163 K.  The plus marks (+) denote the observed intensities; the solid line is that calculated from the best-fit model of the Rietveld refinement.  The bottom curve represents the deviation between the observed and calculated intensities.  Rwp = 11.2 %, 2 = 33.1.  The upper tick marks represent the calculated peak positions for the structure II hydrate and the lower tick marks represent those for the hexagonal ice. Figure 3-2  C3H8 molecules in structure II large (5 12 6 4 ) shown with full symmetry. Solid spheres express the virtual chemical species -CH2 and -CH3. 10 20 30 40 50 60 70 80 90 0 10000 20000 30000 40000 50000 2 [degrees] I n te n s it y  [ a .u .] I n te n s it y  [ a .u .] Figure 3-3  C3H8 molecules in C3H8 hydrate found in this study (black) and by the single crystal x-ray diffraction (grey) reported by Udachin et al. [8]  for comparison.  Only the large cage of structure II is shown. Figure 4-2 MCH molecule in structure H large (5 12 6 4 ) cage and CH4 molecules in medium (4 3 5 6 6 3 ) and small (5 12 ) cage with full symmetry shown.  Solid spheres express the virtual chemical species -CH2, -CH3, and CH4. 10 20 30 40 50 60 70 80 90 0 10000 20000 30000 40000 50000 2 [degrees] In te n si ty  [ a .u .] In te n si ty  [ a .u .] Figure 4-1 PXRD pattern of the MCH/CH4 hydrate at 163 K.  The plus marks (+) denote the observed intensities; the solid line is that calculated from the best-fit model of the Rietveld refinement.  The bottom curve represents the deviation between the observed and calculated intensities.  Rwp = 11.3 %, 2 = 30.0.  The upper tick marks represent the calculated peak positions for the structure H hydrate and the lower tick marks represent those for the hexagonal ice. Figure 4-3 MCH and CH4 molecules in MCH/CH4 hydrate found in this study (black) and by the single crystal x-ray diffraction (grey) reported by Udachin et al. [7]  for comparison. Figure 4-1 shows a comparison of the measured PXRD pattern of Methylcyclohexane(MCH)/CH4 hydrate with the calculated pattern using the Rietveld method.  There are some extra diffraction peaks indicating the coexistence of hexagonal ice (1.7 wt %).  Figure 4-2 shows the MCH molecule in the large cage and the CH4 molecules in small and medium cages in hexagonal structure H (a = 12.2362(6) Å, c = 10.0525(5) Å).  It is a comparison of MCH and CH4 positions refined by PXRD with single crystal analysis. The refined model showed that MCH occupied 100 % of the large cages, and CH4 occupied 95 % of the small cages and 91 % of the medium cages in this study, whereas it was found MCH occupied 100 % of the large cages, and CH4 occupied 82 % of the small cages and 81 % of the medium cages by single crystal analysis in the earlier study. [7]   The cage occupancies of MCH/CH4 hydrate synthesized in the same batch as the sample for the PXRD suggest good consistency between PXRD result with C 13 -NMR result: MCH occupied 100 % of the large cage,  CH4 occupied 90 % of the small cage, and 99 % of the medium cage by C 13 -NMR. Refined atomic coordinates and isotropic displacement parameters for the structure are given in Table 4. Many crystal structures of gas hydrates have been solved using the Rietveld method by localizing the disordered guest molecule in the center of cages. [9- 16]   However, all of the guest molecules found in this study lie off the geometrical center of the cages, and the positions are quite similar to those found by the single crystal x-ray diffraction technique in the earlier studies.  The absolute cage occupancies determined in this study are also similar to those refined by the single crystal diffraction technique even though there are small differences because of different hydrate formation conditions. [17] We suggest that the guest disorder model for gas hydrates as solved by the direct- space technique is sufficient for structural refinement of nonstoichiometric guest molecules. For the estimation of absolute cage occupancies, the appropriate disorder model for guest molecules should be used due to a strong correlation between displacement parameters and cage occupancies. Here, we conclude that the procedure reported in this study is suitable to refine guest disorder and absolute cage occupancies using PXRD data.    atom x  y z B (Å2) Wa1 0.1839(2) 0.1839 0.1839 4.8(1) Wa2 0 0.3095(3) 0.1173(2) 4.8 Wa3 0 1/2 1/4 4.8 C1L 0.0362 0.2209 0.4862 0.5(4) O1L 0.1177 0.2330 0.5383 0.5 O2L -0.0453 0.2089 0.4340 0.5 C1S 0.4835 0.5026 0.5108 0.5 O1S 0.5590 0.4730 0.4564 0.5 O2S 0.4080 0.5322 0.5651 0.5  Table 1. Atomic coordinates and isotropic displacement parameters for CO2 hydrate   atom x  y z B (Å2) Wa1 0.1843(2) 0.1843 0.1843 3.6(1) Wa2 0 0.3066(3) 0.1157(2) 3.6 Wa3 0 1/2 1/4 3.6 M1L 0.0804 0.2499 0.5355 1.7(4) M2L -0.0362 0.1991 0.5270 1. 7 M1S 0.9518 0.0272 0.0385 1. 7 M2S 1.0540 -0.0318 -0.0098 1. 7  Table 2. Atomic coordinates and isotropic displacement parameters for C2H6 hydrate   atom x  y z B (Å2) Wa1 3/8 3/8 3/8 2.4(1) Wa2 0.2822(1) 0.2822 0.2822 2.4 Wa3 0.3176(1) 0.3176 0.1299(1) 2.4 M1L 0.9428 0.8933 0.9233 0.6(5) M2L 0.8927 0.9123 0.8523 0.6 M3L 0.8071 0.9051 0.8753 0.6  Table 3. Atomic coordinates and isotropic displacement parameters for C3H8 hydrate   atom x  y z B (Å2) Wa1 0.1310(3) 0.2620 0 3.1(1) Wa2 1/3 2/3 0.1392(8) 3.1 Wa3 0.2091(2) 0.4182 0.2236(4) 3.1 Wa4 0.3873(3) 0.3873 0.3630(4) 3.1 M1L 1.0033 0.9722 0.4290 6.1(7) M2L 1.0992 1.0896 0.5053 6.1 M3L 1.0670 1.0779 0.6560 6.1 M4L 1.0498 0.9525 0.7153 6.1 M5L 0.9561 0.8368 0.6324 6.1 M6L 0.9941 0.8530 0.4863 6.1 M7L 1.0298 0.9843 0.2786 6.1 M1S 0.5269 0.0470 0.0429 2.4(4) M1M 0.2892 0.6427 0.4766 2.4  Table 4. Atomic coordinates and isotropic displacement parameters for MCH/CH4 hydrate    CONCLUSIONS We have shown that powder x-ray diffraction analysis by means of the direct-space technique and the Rietveld method is a powerful tool for determining gas hydrate structures and compositions.  If high quality powder samples can be obtained, it is possible to obtain absolute cage occupancies without the need of a single crystal.  ACKNOWLEDGEMENTS We thank Dr. I. Moudrakovski of NRC for NMR measurements and Dr. D. D. Klug and R. Susilo of NRC for their assistance on sample preparations.   REFERENCES [1] Harris K. D. M., Tremayne M., Kariuki B. M. Contemporary advances in the use of powder x- ray diffraction for structure determination. Angew. Chem. Int. Ed. 2001; 40: 1626-1651. [2] Takeya S., Hori A., Uchida T., Ohmura R. Crystal Lattice Size and Stability of Type H Clathrate Hydrates with Various Large-Molecule Guest Substances. J. Phys. Chem. B 2006; 110: 12943-12947. [3] Handa Y. P. 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