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1 Wiley-VCH Weinheim, Germany

2 On the polymorphism of aspirin Andrew D. Bond, Roland Boese and Gautam R. Desiraju S1. Comparison of the form I and PZ structures S2. Transforming the unit cells in real space S3. The transformation in reciprocal space S4. Producing the PZ structure from simulated form I diffraction data S5. Producing the PZ structure from experimental form I diffraction data Electronic files available: formi.cif, formi.res, formi.hkl formii.res formi_simu.hkl transform_simu.hkl transform_simu.cif transform_exp.hkl, transform_exp.cif Form I structure as reported in this paper (CIF & SHELX files) Form II structure as reported by PZ (SHELX file, generated from the published CIF) hkl data simulated from form I structure Simulated data to 1.04 Å, transformed into the PZ cell CIF produced by refinement against F 2 (SHELXTL) Experimental data to 0.85 Å resolution, indexed and integrated according to the PZ cell. CIF produced by refinement against F 2 with 2σ cut-off (CRYSTALS) All CCD frames (Bruker APEX2 format) are available from the authors on request. References: APEX2 Bruker Nonius (2006). Version Delft, The Netherlands (in Essen). APEX2 Bruker Nonius (2004). Version Delft, The Netherlands (in Odense). PLATON A. L. Spek (1998). Utrecht University, Utrecht, The Netherlands. WinGX L. J. Farrugia (1999). J. Appl. Cryst., 32, SHELXTL G. M. Sheldrick (2000). Version Bruker AXS Inc., Madison, WI, USA. CRYSTALS P. W. Betteridge, J. R. Carruthers, R. I. Cooper, C. K. Prout & D. J. Watkin, (2003). J. Appl. Cryst. 36, MERCURY I. J. Bruno, J. C. Cole, P. R. Edgington, M. K. Kessler, C. F. Macrae, P. McCabe, J. Pearson & R. Taylor (2002). Acta Cryst. B58,

3 S1. Comparison of the form I and PZ structures Form I structure as reported in this paper Form II structure as reported by Vishweshwar, McMahon, Oliveira, Peterson and Zaworotko, JACS (2005), 127, (hereafter referred to as the PZ structure) (1) The unit-cell contents of the two structures are identical and can be overlaid with the b axes pointing in opposite directions: Red = form I (b pointing into the page) Blue = PZ structure (b pointing out of the page) (2) The overlay is complete in two dimensions parallel to the (100) planes, i.e. the diagram above can be tiled infinitely in the left and right directions, and along the directions in and out of the page, to give identical 2-D layers of O H O hydrogen-bonded dimers. (3) The two structures differ in the vertical direction of the diagram above. Physically, this corresponds to different stacking arrangements of the 2-D layers of O H O hydrogenbonded dimers. (4) In the region where the layers of O H O hydrogen-bonded dimers meet, the form I structure exhibits centrosymmetric C H O dimeric motifs. In the same region, the PZ structure exhibits C H O catemers running along b: Form I PZ structure S1

4 In crystallographic terms, the distinction between the two structures lies in the positions of the inversion centres and 2 1 screw axes relative to the molecules. In space group P2 1 /c, inversion centres and screw axes alternate along the c axis of the unit cell: Inversion centres 2 1 screw axes The inversion centres within the O H O hydrogen-bonded dimers (in the (200) plane of the unit cell) are coincident in both structures, and the c-glide is not affected since the b and c dimensions of the two structures are unchanged, i.e. the height of the glide planes with respect to b remains unchanged and the magnitude of the translational component of the glide along c remains unchanged. This is consistent with the complete overlay of the unit cells in two dimensions (i.e. along b and c), noted in point (2) above. The difference between the two structures therefore arises due to interchange of the 2 1 screw axes and inversion centres in the (100) planes of the unit cell. In form I (red), the C H O contacts between adjacent molecules are formed across inversion centres, making dimers. In the PZ structure (blue), C H O contacts between adjacent molecules are formed around 2 1 screw axes, making catemers. In each structure, all intermolecular contacts are entirely reasonable. S2. Transforming the unit cells in real space From the comparison above, it is clear that the appropriate transformation between the two unit cells should reverse the b direction, reverse the c direction (but keep its magnitude the same) and make the new a direction a combination of the previous a and c directions. Thus: Using the cell parameters [Å, º] reported by us (123 K): a = b = c = ½ a = b = c = α = 90 β = γ = α = 90 β = γ = Form I PZ Using the cell parameters [Å, º] reported by PZ (100 K): a = b = c = ½ a = b = c = α = 90 β = γ = α = 90 β = γ = PZ Form I S2

5 S3. The transformation in reciprocal space Consider the cell parameters reported by us for the form I structure: Real lattice parameters (Å, º) Reciprocal lattice parameters (Å 1, º) a = b = c = a* = b* = c* = α = 90 β = γ = 90 α = 90 β = γ = 90 The transformed version of this cell is: Real lattice parameters (Å, º) Reciprocal lattice parameters (Å 1, º) a = b = c = a* = b* = c* = α = 90 β = γ = 90 α = 90 β = γ = 90 Since b* is identical in both cases and α* = γ* = 90º, the relationship between the reciprocal lattices need be considered only in two dimensions, i.e. in the a*c* planes. The appropriate overlay of a general a*c* section (ignoring systematic absences) for the reciprocal lattices of form I and the PZ structure is: EXACT OVERLAY EXACT OVERLAY Red = reciprocal lattice for the form I unit cell (b* pointing into page) Blue = reciprocal lattice for the PZ structure (b* pointing out of page) With the b* axes pointing in opposite directions, the two reciprocal lattices can be overlaid exactly for every second row along c* (i.e. hkl with l even). For odd l, the reciprocal lattice points of the form II structure lie exactly half-way between those of the form I structure. From the diagram: 1 0 ½ hkl II = hkl I as was shown in real space for the unit cells. (Alternatively, for the monoclinic system, either lattice could be rotated with respect to the other by 180º about b* to give the relationship [ 1 0 ½, 0 1 0, 0 0 1]). S3

6 S4. Producing the PZ structure from simulated form I diffraction data To remove any question of experimental issues (multiple crystals, double reflections, etc.), the relationship between the form I and PZ structures can be illustrated purely by simulation: (1) Take the form I structure as reported by us. (2) Simulate single-crystal X-ray diffraction data (using HKL Gener in PLATON) reflections generated to 2θ max = 27.5º (formi_simu.hkl). (3) Transform the simulated hkl data by the matrix [1 0 ½, 0 1 0, 0 0 1]. The transformation leads to 50% data (those with odd l) that do not conform to the primitive lattice. These must be thrown out so that the transformed data set is 50% complete (1033 reflections, 980 observed at 2σ level). (4) For the new data, the space group is readily identified as P2 1 /c (e.g. in XPREP). To simulate more closely the conditions of the PZ refinement, the data can be truncated to 1.04 Å resolution (2θ max = 40º; 437 reflections, 424 observed at 2σ level; transform_simu.hkl). (5) Take the reported PZ structure (with H atoms bound to C atoms treated as riding) and refine against this data set. Isotropic refinement against all F 2 data (unit weights) converges to give R1 = , wr2 = (6) The H atom on the carboxyl group shows up clearly in the difference Fourier map. The final refinement (optimal weights) converges to give R1 = , wr2 = (transform_simu.cif). Molecular unit (displacement ellipsoids at 50% probability) in the PZ structure refined against simulated form I data that has been appropriately transformed Attempts at anisotropic refinement fail with non-positive-definite displacement parameters, emulating the PZ refinement. Our improved R factors, and more acceptable range of U iso values compared to those reported by PZ originate from the fact that the data are simulated. The result shows that even a theoretical form I data set can be erroneously indexed to provide a data set (albeit artificially 50% complete) that will emulate the PZ refinement. S4

7 S5. Producing the PZ structure from experimental form I diffraction data To examine the consequences of the PZ indexing choice on our experimental data, we performed the following procedure: (1) Index a portion of our data frames with the form I cell: a = (2), b = (9), c = (2) Å, β = 95.78(1)º From 1588 reflections harvested, 1035 reflections are indexed at a relatively conservative tolerance. (2) Apply the matrix [1 0 ½, 0 1 0, 0 0 1] and refine the result: a = (3), b = 6.538(2), c = (3) Å, β = (2)º From 1588 reflections, 558 reflections are indexed (ca 50%) at the same tolerance. NOTE: the a and c axes must be treated in the very specific way described throughout this document. Since the cell lengths are so similar, there is a possibility that the initial indexing procedure could produce a cell setting in which the a and c axes are interchanged. Under these circumstances, the appropriate matrix to obtain the PZ cell is [½ 0 1, 0 1 0, 1 0 0], rather than [1 0 ½, 0 1 0, 0 0 1]. (3) Integration performed on the basis of this cell to upper resolution 0.85 Å (i.e. the PZ resolution plus a little extra). Resulting merged data statistics prior to multi-scan correction: Angstroms #Obs Theory %Compl Redund Rsym Pairs %Pairs Rshell #Sigma %<2s to to to to to to to to to to Note the large proportion of unobserved data. These correspond (principally) to the odd l reflections, for which the integration samples only background. (4) Multi-scan correction applied by SADABS, Laue group 2/m, accepting all defaults. (5) After multi-scan correction, data passed through XPREP, accepting all defaults. Space group identified clearly as P2 1 /c, without transformation of the unit cell. Resulting intensity statistics (22853 data input): S5

8 Resolution #Data #Theory %Complete Redundancy Mean I Mean I/s R(int) R(sigma) Inf Inf [Friedel pairs merged, lowest resolution = Angstroms, 1075 outliers downweighted] (6) SHELXS with default settings provides the molecule completely in the resulting E-map. R(E) = for 15 atoms (2 spurious), from 269 E-values. This is the PZ structure. (7) Refinement of this structure against all data is stable (i.e. the molecular geometry and U iso values remain acceptable), although the R-factors are very high (R1 ca 0.6). This can be attributed to the fact that 50% of the data included in this refinement will have negligible intensity. The issue can be resolved for the experimental data by applying a 2σ cut-off to omit these reflections from the refinement this emulates the 50% complete data set derived from the simulated data. This procedure is permitted (although not recommended!) in the CRYSTALS program. Refinement against F 2 (data to 0.85 Å) with a 2σ cut-off in place gives: Parameters refined R1 Notes Scale factor Quasi-unit weights Scale factor + positions Geometry OK Scale factor + positions + U iso U iso range Anisotropic O4, C3, C7, C8 physically unreasonable Isotropic, add H atoms Optimal weights (Chebyshev 3-term) wr2 = (transformed_exp.cif) Molecular unit (displacement ellipsoids at 50% probability) in the PZ structure refined against experimental form I data that has been indexed and integrated on the basis of the PZ unit cell. The H atom on O1 is omitted from the model. S6