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2006, 110, 11620-11623 Published on Web 05/28/2006
Understanding the Structural Properties of a Dendrimeric Material Directly from Powder X-ray Diffraction Data Zhigang Pan,† Mingcan Xu,† Eugene Y. Cheung,† Kenneth D. M. Harris,*,† Edwin C. Constable,‡ and Catherine E. Housecroft‡ School of Chemistry, Cardiff UniVersity, Park Place, Cardiff CF10 3AT, Wales, U.K., and Department of Chemistry, UniVersity of Basel, Spitalstrasse 51, 4056 Basel, Switzerland ReceiVed: April 20, 2006
Complete structure determination of an early-generation dendrimeric material has been carried out directly from powder X-ray diffraction data, using the direct-space genetic algorithm technique for structure solution followed by Rietveld refinement. This work represents the first application of modern direct-space techniques for structure determination from powder X-ray diffraction data in the case of a dendrimeric material and paves the way for the future application of this approach to enable complete structure determination of other dendrimeric materials that cannot be prepared as single crystal samples suitable for single crystal X-ray diffraction studies.
Dendrimeric materials have received considerable attention in recent years,1 not only with regard to their novel structural and physicochemical properties but also because of the realization that such materials may be exploited in a broad range of applications. Dendrimers are large, highly branched molecules composed of a core moiety and radiating functionality with welldefined size, shape, and surface properties. The highly branched architecture can lead to spatially well-defined voids within the dendrimer, with the core and the surface exhibiting distinct microenvironments, and these unique characteristics underlie many of the applications that are being established for these materials. At all stages of the growth process, dendrimers are monodisperse, and their structural homogeneity and regularity are conducive to detailed structural characterization. In general, single crystal X-ray diffraction is the preferred technique for determination of time-averaged structural properties, although, for many materials, it can be difficult to grow single crystals of sufficient size and/or quality for investigation using conventional single crystal X-ray diffraction techniques. In such cases, structure determination using powder X-ray diffraction data may be the only viable opportunity for structural characterization. Within the past decade or so, new opportunities have been created for carrying out complete structure determination of organic molecular solids directly from powder X-ray diffraction data,2 particularly through the development of the direct-space strategy for structure solution,2a and it is clear that such techniques have the potential to play an important role in structural characterization of dendrimeric materials. Nowadays, the crystal structures of organic materials of moderate complexity can be determined by this approach, although challenges can arise when there is considerable molecular flexibility (i.e., * To whom correspondence should be addressed. E-mail: HarrisKDM@ cardiff.ac.uk. † Cardiff University. ‡ University of Basel.
10.1021/jp0624348 CCC: $33.50
Figure 1. Molecular structure of TDMM.
for a molecule defined by a large number of variable torsion angles) and/or when there are several independent molecules in the asymmetric unit. Given the highly branched nature of dendrimers, the molecular conformation is generally defined by a significant number of torsion angles, and these materials present specific challenges for direct-space structure determination from powder diffraction data. In this paper, we report the structure determination of the early-generation dendrimeric material tetrakis[(3,5-dimethoxybenzyloxy)methyl]methane (TDMM; Figure 1), which has exploited the opportunity to carry out complete structure determination directly from powder X-ray diffraction data using the direct-space genetic algorithm technique3 for structure solution followed by Rietveld refinement.4 This work represents the first application of direct-space structure determination techniques from powder X-ray diffraction data in the case of a dendrimeric material. Among recent developments in techniques for structure determination from powder X-ray diffraction data, the directspace strategy for structure solution has been shown to be © 2006 American Chemical Society
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Figure 2. High-resolution solid state 13C NMR spectrum of TDMM.
particularly suitable in the case of organic molecular materials. In this strategy, trial crystal structures are generated in direct space, and the quality of each trial structure is assessed by direct comparison between the powder X-ray diffraction pattern calculated for the trial structure and the experimental powder X-ray diffraction pattern (in our work, this comparison is carried out using the weighted powder profile R-factor Rwp, which takes peak overlap implicitly into consideration). In the present paper, direct-space structure solution was carried out using a genetic algorithm (GA) technique3 to search for the structure representing the global minimum in Rwp. In the GA technique, a population of trial structures is allowed to evolve subject to the types of rules and operations (mating, mutation, and natural selection) that govern evolution in biological systems. Each structure in the population is specified by its “genetic code”, which represents, for each molecule in the asymmetric unit, the position {x, y, z} and orientation {θ, φ, ψ} of the molecule, and the molecular conformation, defined by n variable torsion angles {τ1, τ2, ... , τn}. New structures are generated by the mating and mutation operations, and the quality (“fitness”) of each structure is assessed from its value of Rwp. In the natural selection procedure, only the structures of highest fitness (i.e., lowest Rwp) are allowed to pass from one generation to the next generation. After the population has evolved for a sufficient number of generations, the best structure in the population (i.e., the structure with the lowest Rwp value) should be close to the correct structure and is used as the starting structural model for Rietveld refinement. TDMM was prepared using standard synthetic procedures5 (we note that the pentaerythritol core in this molecule provides an attractive and versatile opportunity for the preparation of dendrimeric materials, although structural data for such systems are currently sparse6). The powder X-ray diffraction pattern of TDMM was recorded7 on a standard laboratory powder X-ray diffractometer operating in transmission mode. The powder X-ray diffraction pattern was indexed using the program ITO,8 leading to the following unit cell with orthorhombic metric symmetry: a ) 30.95 Å, b ) 39.04 Å, c ) 6.39 Å (V ) 7725 Å3). From systematic absences, the space group was assigned as Fdd2. For this unit cell and space group, a good quality Le
Bail fit9 to the experimental powder X-ray diffraction pattern was obtained (Rwp ) 2.35%, Rp ) 1.80%). Density considerations suggest that there are eight molecules in the unit cell (calculated density 1.26 g cm-3). As the multiplicity of space group Fdd2 is 16, the asymmetric unit must comprise half of the molecule. To obtain an independent assessment of this issue, the high-resolution solid state 13C NMR spectrum of TDMM was recorded10,11 (Figure 2); as this spectrum11 contains no more than one isotropic peak for each 13C site in half of the molecule, it is completely consistent with our proposal that the asymmetric unit comprises half of the molecule. We now consider the implementation of the direct-space GA structure solution calculation for TDMM. As the asymmetric unit comprises half of the molecule, the central carbon atom must lie on a special position (2-fold rotation axis) of the type (0, 0, z) in space group Fdd2 (Figure 3a). Taking the positional variables {x, y, z} (see above) as the coordinates of the central carbon atom, the values of x and y are fixed by the special position, while the value of z can be fixed arbitrarily for space group Fdd2 (variation of z does not change the structure but simply translates the entire structure along the z-axis). Next, we consider the orientational variables {θ, φ, ψ}, which define the orientation of the molecule about the central carbon atom. To maintain tetrahedral geometry of the CC4 core of the molecule, the two C-C bonds formed by the central carbon atom within the half-molecule in the asymmetric unit must be oriented such that the angles between these C-C bonds and the 2-fold axis of the special position are 54.7 and 125.3°, respectively (Figure 3a). This requirement effectively constrains the values of the orientational variables θ and φ, which define the orientation of the half-molecule about orthogonal axes perpendicular to the 2-fold axis. Thus, the only orientational variable that must be optimized in the structure solution calculation is ψ, which describes reorientation around the 2-fold axis. The number of variable torsion angles in half of the molecule is 12 (see Figure 3a). Thus, in the direct-space structure solution calculations for TDMM, each trial structure was defined by a total of 13 structural variables: {ψ, τ1, τ2, ... , τ12}. Structure solution was carried out using a single population version of the GA structure solution program EAGER.12,13 A
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Figure 3. (a) Molecular fragment (thick lines), comprising half the TDMM molecule, used in the direct-space structure solution calculation from powder X-ray diffraction data. The arrows indicate the variable torsion angles in the direct-space structure solution calculation. The central carbon atom is located on a 2-fold rotation axis (as indicated), and the other half of the molecule (faint lines) is generated by this symmetry operation. (b) Final Rietveld refinement for TDMM, showing the experimental powder X-ray diffraction pattern (+ marks), calculated powder X-ray diffraction pattern (solid line), and difference between the experimental and calculated powder X-ray diffraction patterns (lower line). Tick marks indicate reflection positions.
reasonable structure solution was obtained after ca. 80 generations of the GA calculation and was used as the initial structural model for Rietveld refinement,14 which was carried out using the GSAS program.15 The Rietveld refinement yielded a good quality fit (Figure 3b; Rwp ) 3.17%, Rp ) 2.36%), with the following final refined unit cell parameters: a ) 30.9583(5) Å, b ) 39.0295(7) Å, c ) 6.3938(1) Å. Details of the final refined structure, including fractional atomic coordinates, are given in the Supporting Information. The molecular conformation adopted by TDMM in the crystal structure is shown in Figure 4a. The conformation clearly has 2-fold symmetry, and in the half-molecule that represents the asymmetric unit, there are two independent branches (denoted A and B) radiating from the core. The conformational properties of these two branches differ significantly, in terms of both the conformation of the C-CH2-O-CH2-Ph chain and the conformation of the two methoxy substituents on the benzyloxy ring. Thus, in branch A, the two torsion angles that define the conformation of the C-CH2-O-CH2-Ph chain are close to trans/gauche (torsion angles around the CCH2-OCH2 and CH2O-CH2Ph bonds, respectively), whereas, in branch B, the corresponding conformation is close to trans/trans. For the benzyloxy ring of branch A, the two methoxy groups at the 3and 5-positions adopt a syn/anti conformation (where syn and anti refer to the orientations of the O-CH3 bonds relative to the C(ring)-H bond that lies between the two OCH3 substituents). For the benzyloxy ring of branch B, on the other hand, the two methoxy groups adopt an anti/anti conformation. In the crystal structure, the molecules are stacked along the c-axis, with adjacent molecules along the stack related by the
Figure 4. (a) Molecular conformation in the crystal structure of TDMM (with branch A and branch B indicated, as discussed in the text) and (b) the crystal structure of TDMM viewed along the c-axis (the stacking axis). Hydrogen atoms are omitted for clarity.
unit cell translation (note that the c-axis is significantly shorter than the other two unit cell axes). Along the stack, the orientations and conformations of the branches in the molecule are such that adjacent molecules nestle almost perfectly into each other with their van der Waals surfaces in contact. The planes of the phenyl rings of one molecule in the stack are parallel to the planes of the corresponding phenyl rings of the adjacent molecule, but the relatively large tilt angle of the planes of the phenyl rings with respect to the stacking axis is such that there are no significant π‚‚‚π interactions between adjacent molecules. As shown in Figure 4b (in which the structure is projected onto the plane perpendicular to the c-axis), adjacent stacks are arranged in the ab-plane such that the periphery of each molecule is close to van der Waals contact with its neighbors. In adjacent stacks, individual molecules are offset with respect to each other by displacements of c/2 along the c-axis. In conclusion, the successful structure determination of the dendrimeric material TDMM reported here, which has been carried out directly from conventional laboratory powder X-ray
Letters diffraction data using the direct-space GA technique for structure solution followed by Rietveld refinement, augurs well for the future application of similar structure determination strategies for structural characterization of other dendrimeric materials, including those of greater complexity than the specific example considered here. Acknowledgment. We are grateful to EPSRC for general support (to K.D.M.H.) and to Bruker AXS and the University of Birmingham for the award of a Ph.D. studentship (to Z.P.). Supporting Information Available: Structural data. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) (a) Newkome, G. R.; Moorefield, C. N.; Vo¨gtle, F. Dendrimers and Dendrons: Concepts, Syntheses, Applications; Wiley: 2001. (b) Zeng, F. W.; Zimmerman, S. C. Chem. ReV. 1997, 97, 1681. (c) Constable, E. C. Chem. Commun. 1997, 1073. (d) Balzani, V.; Campagna, S.; Denti, G.; Juris, A.; Serroni, S.; Venturi, M. Acc. Chem. Res. 1998, 31, 26. (e) Bosman, A. W.; Janssen, H. M.; Meijer, E. W. Chem. ReV. 1999, 99, 1665. (f) Astruc, D.; Chardac, F. Chem. ReV. 2001, 101, 2991. (g) Grayson, S. K.; Frechet, J. M. J. Chem. ReV. 2001, 101, 3819. (h) Boas, U.; Heegaard, P. M. H. Chem. Soc. ReV. 2004, 33, 43. (i) McCarthy, T. D.; Karellas, P.; Henderson, S. A.; Giannis, M.; O’Keefe, D. F.; Heery, G.; Paull, J. R. A.; Matthews, B. R.; Holan, G. Mol. Pharm. 2005, 2, 312. (2) (a) Harris, K. D. M.; Tremayne, M.; Lightfoot, P.; Bruce, P. G. J. Am. Chem. Soc. 1994, 116, 3543. (b) Harris, K. D. M.; Tremayne, M.; Kariuki, B. M. Angew. Chem., Int. Ed. 2001, 40, 1626. (c) Chernyshev, V. V. Russ. Chem. Bull. 2001, 50, 2273. (d) David, W. I. F., Shankland, K., McCusker, L. B., Baerlocher, C., Eds. Structure Determination from Powder Diffraction Data, OUP/IUCr, 2002. (e) Harris, K. D. M.; Cheung, E. Y. Chem. Soc. ReV. 2004, 33, 526. (f) Baerlocher, C., McCusker, L. B., Eds. Z. Kristallogr. 2004, 219, (12), 782-901. (3) (a) Kariuki, B. M.; Serrano-Gonza´lez, H.; Johnston, R. L.; Harris, K. D. M. Chem. Phys. Lett. 1997, 280, 189. (b) Harris, K. D. M.; Johnston, R. L.; Kariuki, B. M. Acta Crystallogr., Sect. A 1998, 54, 632. (c) Harris, K. D. M.; Habershon, S.; Cheung, E. Y.; Johnston, R. L. Z. Kristallogr. 2004, 219, 838. (4) (a) Rietveld, H. M. J. Appl. Crystallogr. 1969, 2, 65. (b) Young, R. A., Ed. The RietVeld Method; International Union of Crystallography: Oxford, U.K., 1993. (c) McCusker, L. B.; Von Dreele, R. B.; Cox, D. E.; Loue¨r, D.; Scardi, P. J. Appl. Crystallogr. 1999, 32, 36. (5) A mixture of pentaerythritol (204 mg, 1.5 mmol) and sodium hydride (190 mg, 7.5 mmol) in dry THF (20 mL) was heated to 70 °C and kept at this temperature for 30 min until the mixture changed to a pale yellow suspension. Then, 3,5-dimethoxybenzyl bromide (1.72 g, 7.5 mmol)
J. Phys. Chem. B, Vol. 110, No. 24, 2006 11623 was added to the mixture portion by portion. After complete addition of 3,5-dimethoxybenzyl bromide, the suspension became clear and the mixture was kept at 70 °C for 50 h. THF was removed under reduced pressure, and the residue was treated with dichloromethane (20 mL) and distilled water (20 mL). The organic layer was separated and the aqueous layer was extracted with dichloromethane (2 × 20 mL). The combined organic layers were washed with distilled water and then brine. The solution was dried with sodium sulfate and evaporated under reduced pressure. The residue was purified by chromatography on silica gel (1:2 acetone/hexane) to give TDMM (680 mg, 61%) as a colorless oil, which became solid when stored in the refrigerator at 0 °C for 48 h. The product was characterized by mass spectrometry, IR spectroscopy, and solution state 1H and 13C NMR. (6) (a) Armspach, D.; Cattalini, M.; Constable, E. C.; Housecroft, C. E.; Phillips, D. Chem. Commun. 1996, 1823. (b) Constable, E. C.; Housecroft, C. E.; Cattalini, M.; Phillips, D. New J. Chem. 1998, 22, 193. (7) For powder X-ray diffraction data collection, a finely ground sample of TDMM was loaded into a borosilicate glass capillary (0.7 mm diameter), and data were recorded at ambient temperature in transmission mode on a Bruker D8 diffractometer (CuKR1 radiation; Ge-monochromated; VANTEC detector covering 12° in 2θ; 2θ range, 4-70°; step size, 0.017°; total data collection time, 12 h). (8) Visser, J. W. J. Appl. Crystallogr. 1969, 2, 89. (9) Le Bail, A.; Duroy, H.; Fourquet, J. L. Mater. Res. Bull. 1988, 23, 447. (10) The high-resolution solid state 13C NMR spectrum of TDMM was recorded on a Chemagnetics CMX-Infinity 300 spectrometer (75.48 MHz) under conditions of 13C r 1H cross-polarization (CP), magic angle sample spinning (MAS), high-power 1H decoupling using the TPPM decoupling technique, and total suppression of spinning sidebands (TOSS) (CP contact time, 5 ms; recycle delay, 5 s; MAS frequency, 3 kHz). (11) The high-resolution solid state 13C NMR spectrum of TDMM is assigned as follows: central quaternary carbon atom, single peak at 46 ppm; CH2 groups, two peaks at ca. 55 ppm; OCH3 groups, three peaks in the region 65-75 ppm; aromatic carbon atoms directly bonded to hydrogen, six peaks in the region 95-110 ppm; other aromatic carbon atoms, three peaks in the region 140-165 ppm. (12) Habershon, S.; Turner, G. W.; Zhou, Z.; Kariuki, B. M.; Cheung, E. Y.; Hanson, A. J.; Tedesco, E.; Albesa-Jove´, D.; Chao, M.-H.; Lanning, O. J.; Johnston, R. L.; Harris, K. D. M. EAGERsA Computer Program for Direct-Space Structure Solution from Powder X-ray Diffraction Data; Cardiff University and University of Birmingham. (13) In the structure solution calculations, the population comprised 100 trial structures, and in the evolution of the population from one generation to the next generation, 50 mating operations and 25 mutation operations were carried out. (14) In the Rietveld refinement, standard restraints were applied to bond lengths and bond angles, and planar restraints were applied to the phenyl rings. Isotropic displacement parameters were refined for the non-hydrogen atoms. Hydrogen atoms were placed at calculated positions with a fixed value (0.05 Å2) for the isotropic displacement parameter. (15) Larson, A. C.; Von Dreele, R. B. GSAS; Los Alamos Laboratory Report No. LA-UR-86-748, 1987.
