Weak Interactions in the Crystal Structures of Tetraacetylenes Derived from Pentaerythrityl Tetraphenyl Ether Dominic
Laliberte´,†
Thierry Maris, Patrick E. Ryan, and James D. Wuest*
De´ partement de Chimie, UniVersite´ de Montre´ al, Montre´ al, Que´ bec H3C 3J7, Canada
CRYSTAL GROWTH & DESIGN 2006 VOL. 6, NO. 6 1335-1340
ReceiVed October 25, 2005; ReVised Manuscript ReceiVed March 9, 2006
ABSTRACT: Tetrakis(4-ethynylphenyl)methane (7) is known to crystallize as an interpenetrated diamondoid network held together in part by weak sCtCsH‚‚‚CtC interactions that define characteristic cyclic quartets of ethynyl groups. To test the ability of this motif to direct the crystallization of more flexible molecules, we synthesized a series of tetraacetylenes derived from pentaerythrityl tetraphenyl ether, and we solved their structures by X-ray diffraction. Pentaerythrityl tetrakis(4-ethynylphenyl) ether (4) and the more rigid analogue 7 crystallize isostructurally, even though their cores are significantly different in size and flexibility. This observation shows that sCtCsH‚‚‚CtC interactions may have value in engineering molecular crystals. However, widely different structures are obtained by crystallizing pentaerythrityl tetrakis(3-ethynylphenyl) ether (5) and pentaerythrityl tetrakis(4′-ethynyl1,1′-biphenyl-4-yl) ether (6), despite their close similarity to tetraacetylene 4. The unpredictably varied behavior of tetraacetylenes 4-7 highlights the difficulty of engineering crystals built from molecules that are flexible and unable to form dominant directional interactions. Introduction The central challenge in crystal engineering is to develop a clear understanding of the relationship between individual molecules and the structures and properties of their crystals.1 When intermolecular interactions in crystals are dominated by forces that are strong, directional, and reliable, such as hydrogen bonding, and when the molecules themselves have well-defined structures, it is frequently possible to foresee how they will be positioned in the crystalline state.2 In general, however, it remains impossible to predict the structure of molecular crystals with consistent accuracy.3 The challenge is particularly acute when molecules are conformationally mobile and when dominant intermolecular interactions are absent. Valuable insight in crystal engineering can come from structural studies in which molecular cores and peripheral functional groups that control association are varied systematically. For example, to assess how the flexibility of cores affects structure, identical groups known to participate in reliable hydrogen-bonding motifs can be attached to different cores of decreasing rigidity, such as four-armed cores derived from spirobifluorene (1), tetraphenylmethane (2), and pentaerythrityl tetraphenyl ether (3).4-6 Analogously, functional groups that direct intermolecular association in different ways can be attached to the same core.4-6 To extend these comparisons, we have now studied a family of compounds containing multiple sCtCsH groups, which have a modest ability to control association by forming sCtCsH‚‚‚CtC interactions.7-9 To put the directing effect of these groups to a severe test, we have attached them to a flexible core derived from pentaerythrityl tetraphenyl ether (3). In this paper, we report the structures of tetraacetylenes 4-6,5 and we compare them with those of rigid analogue 7 and related compounds.7,8 Results and Discussion Structure of Pentaerythrityl Tetrakis(4-ethynylphenyl) Ether (4). Tetraacetylene 4 was synthesized by the reported * To whom correspondence may be addressed. E-mail: james.d.wuest@ umontreal.ca. † Boehringer-Ingelheim Fellow, 2001-2002.
method5 and was found to crystallize from both CH3COOC2H5/ hexane and THF/hexane. The crystals proved to have the same structure and to belong to the tetragonal space group I4h. They are close-packed and are isostructural with those of the more rigid tetraphenylmethyl analogue 7.7 Views of the structure of compound 4 appear in Figures 1 and 2. In crystals of both flexible tetraacetylene 4 and its more rigid analogue 7, molecular cohesion is ensured in part by sCtCsH‚‚‚CtC interactions of the ethynyl groups, which create characteristic cyclic quartets (Figure 1). In this way, each molecule interacts with a total of eight neighbors, and the centers of the cyclic quartets define nodes to which four molecules are connected in an approximately tetrahedral orientation, thereby giving a diamondoid network (Figure 2).10 The -CH2O- arms that connect an aryl carbon atom (CAr) of each phenyl group to the nominally tetrahedral core (Ccore) are nearly fully extended, with a Ccore-CH2-O-CAr dihedral angle of 176.60(12)°. This extension separates neighboring nodes in each diamondoid network by 9.35(1) Å, and the resulting degree of openness is sufficient
10.1021/cg050568p CCC: $33.50 © 2006 American Chemical Society Published on Web 05/19/2006
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Figure 2. Representation of the triply interpenetrated diamondoid networks present in crystals of pentaerythrityl tetrakis(4-ethynylphenyl) ether (4) grown from CH3COOC2H5/hexane. Nodes in the networks correspond to the centers of the molecules (Ccore) and to the centers of the cyclic quartets shown in Figure 1. The centers of the cyclic quartets are represented by small spheres. The view is approximately along the a axis.
Figure 1. (a) Representation of the structure of crystals of pentaerythrityl tetrakis(4-ethynylphenyl) ether (4) grown from CH3COOC2H5/ hexane. Weak sCtCsH‚‚‚CtC interactions are shown as broken lines. Atoms of hydrogen appear in white, carbon in gray, and oxygen in red. (b) Detailed view of part of the characteristic cyclic quartet held together by sCtCsH‚‚‚CtC interactions.
to permit 3-fold interpenetration.11,12 Adjacent networks interact by forming characteristic 2-fold phenyl embraces.13 The corresponding nodes in the structure of the more rigid tetraphenylmethyl analogue 7 are separated by 8.44(1) Å, and the degree of interpenetration is again three. It is noteworthy that pentaerythrityl tetraphenyl ether 4, despite its potential flexibility and lack of strong directional intermolecular interactions, serves predictably for the purposes of crystal engineering by behaving like an expanded version of the more rigid analogue 7. The oxygen atoms of ether 4 do not interfere by engaging in sCtCsH‚‚‚O interactions, possibly because they lie in the core of compound 4 and are relatively inaccessible or because aryl ethers have inherently low basicity. Although flexible tetraacetylene 4 and its more rigid analogue 7 crystallize isostructurally, close scrutiny reveals subtle differences in molecular geometry. One difference can be best assessed by comparing the CPh‚‚‚Ccore‚‚‚CPh angles defined by the central carbon atom of the core (Ccore) and the para positions of the attached phenyl groups (CPh). In tetraphenylmethane 7, these angles are close to the tetrahedral ideal (4 × 111.6(4)° and 2 × 105.3(4)°), whereas in pentaerythrityl tetraphenyl ether
4 they are 4 × 115.7(4)° and 2 × 97.6(4)°, showing that the molecule deviates slightly from overall tetrahedral geometry. Much more significant deviations have been noted in other derivatives of pentaerythrityl tetraphenyl ether.14 The isostructural crystals of pentaerythrityl tetraphenyl ether 4 and the analogous tetraphenylmethane 7 also show subtle differences in the nature of the sCtCsH‚‚‚CtC interactions. In compound 7, the interacting atom of hydrogen is closest to the terminal carbon atom of the ethynyl group (2.76(1) Å), whereas in compound 4 the closest contact is with the internal carbon atom (2.72(1) Å). This change presumably arises to permit closer molecular packing and to prevent significant weakening of phenyl embraces that would otherwise occur when the tetraphenylmethyl core of compound 7 is expanded by inserting -CH2O- units to create the pentaerythrityl tetraphenyl ether core of compound 4. Structure of Pentaerythrityl Tetrakis(3-ethynylphenyl) Ether (5). Meta-substituted tetraacetylene 5 was synthesized by the reported method5 and was found to crystallize from both CH3COOC2H5/hexane and THF/hexane in the monoclinic space group C2/c. A view of the structure appears in Figure 3. Like para-substituted isomer 4 and the more rigid tetraphenylmethyl analogue 7, compound 5 forms close-packed crystals, but the structures are otherwise very different. This underscores the difficulty of engineering crystals from flexible molecules lacking clearly preferred modes of association. Unlike para-substituted isomer 4, which crystallizes in a nearly tetrahedral conformation, meta-substituted isomer 5 favors a more distorted geometry, with CPh‚‚‚Ccore‚‚‚CPh angles far from the tetrahedral ideal (1 × 82.8(4)°, 1 × 93.3(4)°, 2 × 119.0(4)°, and 2 × 123.0(4)°). The -CH2O- arms that connect each phenyl group to the core are nearly fully extended, with Ccore-CH2-O-CAr dihedral angles of 178.6(2)° (2) and -173.5(1)° (2). Molecular cohesion in the crystals is no longer ensured by sCtCsH‚‚‚CtC interactions of the ethynyl groups, as in the cases of compounds 4 and 7, but rather by face-to-face aromatic interactions (Figure 3).13 In two of the four arms, these interactions are reinforced by C-H‚‚‚CtC interactions involving a terminal acetylenic carbon atom and a hydrogen atom of an aryl group (H‚‚‚C distance ) 2.86(1) Å; C-H‚‚‚C angle ) 164.1(3)°). These C-H‚‚‚C interactions lie along the b axis and define rows that then form 2-fold phenyl embraces along the c axis. As in the
Weak Interactions in Crystals of Tetraacetylenes
Figure 3. Partial view of the structure of crystals of pentaerythrityl tetrakis(3-ethynylphenyl) ether (5) grown from CH3COOC2H5/hexane, showing stacked aryl groups and CsH‚‚‚CtC interactions, which appear as broken lines. Atoms of hydrogen appear in white, carbon in gray, and oxygen in red.
case of para-substituted isomer 4, competing sCtCsH‚‚‚O interactions are not observed. Structures of Pentaerythrityl Tetrakis(4′-ethynyl-1,1′biphenyl-4-yl) Ether (6). Because inserting -CH2O- spacers into the tetraphenylmethyl core of tetraacetylene 7 yielded an expanded molecule that crystallized isostructurally, we were encouraged to probe the effect of incorporating even longer spacers. Expanded tetraacetylene 6 was prepared in 96% yield by desilylating the corresponding tetrakis[(trimethylsilyl)acetylene] 8 (Bu4N+F-/THF), which was synthesized in 91% yield by coupling the known tetraiodide 95 with (trimethylsilyl)acetylene. Expanded tetraacetylene 6 crystallized from CH3COOC2H5/ hexane in the orthorhombic space group Pbca. Views of the structures appear in Figures 4 and 5. Like the more compact analogues 4, 5, and 7, compound 6 forms close-packed crystals under these conditions, but the structures are otherwise very different. Not surprisingly, our straightforward attempt to engineer more highly expanded isostructural crystals failed with compound 6, presumably in part because the core is inherently flexible and no dominant intermolecular interactions are present. The CPh‚‚‚Ccore‚‚‚CPh angles range from 23.1(4)° to 169.7(4)° and are therefore far from the tetrahedral ideal. In addition, the -CH2O- spacers that connect each biphenyl group to the core adopt varied conformations, with Ccore-CH2-O-CAr dihedral angles of 105.7(2)°, 110.8(2)°, 138.3(2)°, and 147.1(2)°. In this way, compound 6 assumes an elongated conformation that permits pairs of biphenyl groups to engage in characteristic intramolecular aromatic interactions. Within the four biphenyl groups, the aryl rings form dihedral angles of 10.0(4)°, -17.8(3)°, -33.0(3)°, and 36.4(3)°. The pair of biphenyl groups that are the most nearly coplanar participate in an intramolecular face-to-face interaction, in which the shortest distances are (1) between C(36) and the centroid of the C(11)-C(16) ring (3.33(1) Å) and (2) between C(18) and C(42) in the other rings (3.54(1) Å). In the other two arms, the biphenyl groups pair to form both face-to-face and edge-toface intramolecular interactions. The shortest contact between the stacked aryl groups is 3.27(1) Å (C(51)‚‚‚C(76)), whereas
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the closest C‚‚‚H contact between the other rings is 2.92(1) Å (H(58)‚‚‚C(82)), with a C-H‚‚‚C angle of 150.0(4)°. Intermolecular cohesion in crystals of expanded tetraacetylene 6 is ensured by multiple sCtCsH‚‚‚CtC interactions of the ethynyl groups, as well as by aromatic interactions. The sCtCsH‚‚‚CtC interactions involve H(64)‚‚‚C(23) (H‚‚‚C distance ) 2.84(1) Å; C-H‚‚‚C angle ) 165.6(4)°) and H(44)‚‚‚C(83) (H‚‚‚C distance ) 2.70(1) Å; C-H‚‚‚C angle ) 152.4(3)°). These acetylenic interactions link compound 6 into sheets, which then stack along the a axis by forming multiple aromatic interactions. As in the case of analogous tetraacetylenes 4 and 5, no sCtCsH‚‚‚O interactions are observed. Tetraacetylenes 4 and 5 crystallize from both CH3COOC2H5/ hexane and THF/hexane to give the same structure, whereas crystals of expanded tetraacetylene 6 obtained under these two conditions have different structures. Crystals of compound 6 grown from THF/hexane proved to belong to the triclinic space group P1h and to correspond to an inclusion compound with the approximate composition 6‚0.5THF‚0.5hexane.15 The resulting structure is complex, and compound 6 is present in two distinct conformations, 6r and 6β (Figure 6). In both, the -CH2Oarms are almost fully extended (dihedral angles of 153.9(2)°174.2(2)° in conformer 6r and 172.5(2)°-178.9(2)° in conformer 6β). In addition, the CPh‚‚‚Ccore‚‚‚CPh angles range from 93.3(2)° to 122.8(2)°, giving both conformers a roughly tetrahedral topology similar to those observed in crystals of contracted tetraacetylenes 4 and 5 but unlike the one seen in close-packed crystals of expanded tetraacetylene 6 grown from CH3COOC2H5/hexane. As shown in Figure 6, the structure of the inclusion compound incorporates a complex array of sCtCsH‚‚‚O interactions and C-H‚‚‚C interactions involving both acetylenic and aryl hydrogens as donors and both -CtC- bonds and aryl groups as acceptors. Interactions of conformer 6β with itself define corrugated sheets, which are linked by additional interactions with conformer 6r to create a porous three-dimensional network. The structure incorporates channels aligned with the a axis (Figure 7), which accommodate partly disordered guests. Approximately 17% of the volume of the crystals is available for inclusion.16,17 Conclusions Tetraphenylmethane 7 is known to crystallize as an interpenetrated diamondoid network held together in part by sCtCsH‚‚‚CtC interactions that define characteristic cyclic quartets of ethynyl groups.7 Our work suggests that this motif is persistent enough to permit analogous tetraacetylene 4 to crystallize isostructurally, even though its core is expanded and more flexible. This observation shows that weak sCtCsH‚‚‚CtC interactions may have value in crystal engineering. However, widely different structures are obtained by crystallizing tetraacetylenes 5 and 6, although they are both derived similarly from pentaerythrityl tetraphenyl ether cores. The unpredictably varied behavior of tetraacetylenes 4-7 highlights the difficulty of engineering crystals built from molecules that are flexible and unable to form dominant directional interactions. Experimental Section Pentaerythrityl tetrakis(4-ethynylphenyl) ether (4), pentaerythrityl tetrakis(3-ethynylphenyl) ether (5), and pentaerythrityl tetrakis(4′-iodo1,1′-biphenyl-4-yl) ether (9) were all synthesized by known methods.5 Tetrakis[[4′-(trimethylsilyl)ethynyl-(1,1′-biphenyl-4-yl)oxy]methyl]methane (8). Ethynyltrimethylsilane (0.64 mL, 0.44 g, 4.5 mmol)
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Figure 4. View of the structure of pentaerythrityl tetrakis(4′-ethynyl-1,1′-biphenyl-4-yl) ether (6) when crystallized from CH3COOC2H5/hexane, with the atom-numbering scheme. Displacement ellipsoids are drawn at the 30% probability level, and hydrogen atoms are represented by spheres of arbitrary radius.
Figure 6. Partial view of the structure of crystals of pentaerythrityl tetrakis(4′-ethynyl-1,1′-biphenyl-4-yl) ether (6) grown from THF/ hexane. The figure shows one central molecule of 6β in blue with its six neighbors. These neighbors consist of three molecules of 6β (green, light blue, and purple) and three molecules of 6r (red, orange, and pink), linked to the central molecule by a total of 13 weak C-H‚‚‚C and C-H‚‚‚O interactions (shown as broken lines). All hydrogen atoms not involved in significant intermolecular interactions are omitted for clarity. Figure 5. Representation of the structure of crystals of pentaerythrityl tetrakis(4′-ethynyl-1,1′-biphenyl-4-yl) ether (6) grown from CH3COOC2H5/hexane, with sCtCsH‚‚‚CtC interactions shown as broken lines. Atoms of hydrogen appear in white, carbon in gray, and oxygen in red. was added dropwise at 25 °C to a stirred mixture of tetrakis[[4′-iodo(1,1′-biphenyl-4-yl)oxy]methyl]methane (9; 1.25 g, 1.00 mmol), CuI (9.5 mg, 0.050 mmol), deoxygenated triethylamine (6 mL), and PdCl2(PPh3)2 (70 mg, 0.10 mmol) in deoxygenated THF (60 mL). The black mixture was kept at 25 °C for 14 h, and volatiles were then removed by evaporation under reduced pressure. The solid residue was purified by flash chromatography (silica, CH3COOC2H5 (5%)/hexane (95%), Rf 0.39) to give tetrakis[[4′-(trimethylsilyl)ethynyl-(1,1′-biphenyl-4-yl)oxy]methyl]methane (8; 1.03 g, 0.912 mmol, 91%) as a colorless solid: mp 167 °C; IR (KBr) 3032, 2956, 2897, 2155, 1605, 1579, 1521, 1492, 1467, 1399, 1310, 1281, 1248, 1174, 1111, 1028, 1007, 999, 866, 841, 820, 758, 697, 637, 523 cm-1; 1H NMR (300 MHz, CDCl3) δ 7.53-7.46 (m, 24H), 7.03 (d, 3J ) 8.8 Hz, 8H), 4.45 (s, 8H), 0.28 (s, 36H); 13C NMR (75 MHz, CDCl3) δ 158.84, 140.84, 133.48, 132.59, 128.28, 126.59, 121.59, 115.27, 105.27, 94.85, 66.85, 45.14, 0.23; MS (FAB, 3-nitrobenzyl alcohol) m/e 1129.8. Tetrakis[[4′-ethynyl-(1,1′-biphenyl-4-yl)oxy]methyl]methane (6). At 25 °C, tetrabutylammonium fluoride (1.0 M in THF, 2.5 mL, 2.5 mmol) was added to a stirred solution of tetrakis[[4′-(trimethylsilyl)ethynyl-(1,1′-biphenyl-4-yl)oxy]methyl]methane (8; 564 mg, 0.499
mmol) in THF (20 mL). After 3 h, water was added, and the product was extracted with CH3COOC2H5. The extracts were dried over MgSO4 and filtered through silica gel. Volatiles were then removed by evaporation under reduced pressure, and the residue was crystallized from CH3COOC2H5/hexane to provide tetrakis[[4′-ethynyl-(1,1′-biphenyl-4-yl)oxy]methyl]methane (6; 403 mg, 0.479 mmol, 96%) as a colorless solid: mp 199-200 °C; IR (KBr) 3279, 3033, 2938, 2883, 2103, 1734, 1604, 1579, 1522, 1492, 1466, 1384, 1311, 1284, 1241, 1178, 1111, 1040, 999, 852, 820, 651, 632, 514 cm-1; 1H NMR (300 MHz, CDCl3) δ 7.56-7.48 (m, 24H), 7.04 (d, 3J ) 8.8 Hz, 8H), 4.46 (s, 8H), 3.13 (s, 4H); 13C NMR (75 MHz, CDCl3) δ 158.88, 141.24, 133.42, 132.75, 128.33, 126.74, 120.57, 115.29, 83.82, 77.81, 66.83, 45.13; MS (FAB, 3-nitrobenzyl alcohol) m/e 840.2. X-ray Crystallographic Studies. Structures were solved by direct methods using SHELXS-97 and refined with SHELXL-97.18 All nonhydrogen atoms were refined anisotropically, except those of disordered molecules of solvent in crystals of tetraacetylene 6 grown from THF/ hexane. Hydrogen atoms attached to aromatic rings were placed in ideal positions and refined as riding atoms. Structure of Pentaerythrityl Tetrakis(4-ethynylphenyl) Ether (4). Crystals of tetraacetylene 4 were grown by allowing hexane to diffuse slowly into a solution in CH3COOC2H5. X-ray diffraction data were collected at 293 K with Cu KR radiation using an Enraf-Nonius CAD4 diffractometer. Crystals of compound 4 proved to belong to the tetragonal space group I4h with a ) 13.1200(19) Å, b ) 13.1200(19)
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and the Canada Research Chairs Program for financial support. In addition, we thank Prof. Jurgen Sygusch for providing access to a Bruker SMART 6000 CCD diffractometer equipped with a rotating anode generator, which was used to collect data for tetraacetylene 5. Supporting Information Available: ORTEP drawings and tables of crystallographic data, atomic coordinates, anisotropic thermal parameters, bond lengths, bond angles, and packing diagrams for compounds 4-6. This material is available free of charge via the Internet at http://pubs.acs.org.
References
Figure 7. Representation of the structure of crystals of pentaerythrityl tetrakis(4′-ethynyl-1,1′-biphenyl-4-yl) ether (6) grown from THF/ hexane. The structure is viewed along the a axis and shows a 3 × 3 × 3 array of unit cells. Guests are omitted, and atoms are shown as spheres of van der Waals radii to reveal the cross sections of the channels. Atoms of hydrogen appear in white, carbon in gray, and oxygen in red. Å, c ) 8.8810(18) Å, V ) 1528.7(4) Å3, Dcalcd ) 1.166 g/cm3, and Z ) 2. Full-matrix least-squares refinements on F 2 of 98 parameters led to final residuals R1 ) 0.0397 and wR2 ) 0.0892 for 1242 observed reflections with I > 2σ(I). Structure of Pentaerythrityl Tetrakis(3-ethynylphenyl) Ether (5). Crystals of tetraacetylene 5 were grown by allowing hexane to diffuse slowly into a solution in CH3COOC2H5. X-ray diffraction data were collected at 293 K with Cu KR radiation using a Bruker SMART 6000 CCD diffractometer with an FR591 rotating anode generator. Crystals of compound 5 were found to belong to the monoclinic space group C2/c with a ) 19.338(10) Å, b ) 8.849(4) Å, c ) 18.388(11) Å, β ) 90.329(18)°, V ) 3146(3) Å3, Dcalcd ) 1.133 g/cm3, and Z ) 4. Fullmatrix least-squares refinements on F2 of 186 parameters led to final residuals R1 ) 0.0570 and wR2 ) 0.1465 for 2226 reflections with I > 2σ(I). Structure of the Close-Packed Form of Pentaerythrityl Tetrakis(4′-ethynyl-1,1′-biphenyl-4-yl) Ether (6). Crystals of tetraacetylene 6 were grown by allowing hexane to diffuse slowly into a solution in CH3COOC2H5. X-ray diffraction data were collected at 220 K with Cu KR radiation using a Bruker SMART 2000 CCD diffractometer. Crystals of compound 6 proved to belong to the orthorhombic space group Pbca with a ) 10.0538(5) Å, b ) 25.6951(12) Å, c ) 34.3888(17) Å, V ) 8883.8(7) Å3, Dcalcd ) 1.258 g/cm3, and Z ) 8. Fullmatrix least-squares refinements on F2 of 586 parameters led to final residuals R1 ) 0.0511 and wR2 ) 0.1181 for 5346 reflections with I > 2σ(I). Structure of the Inclusion Compound Derived from Pentaerythrityl Tetrakis(4′-ethynyl-1,1′-biphenyl-4-yl) Ether (6). Crystals of tetraacetylene 6 were grown by allowing hexane to diffuse slowly into a solution in THF. X-ray diffraction data were collected at 220 K with Cu KR radiation using a Bruker SMART 2000 CCD diffractometer. Crystals of compound 6 proved to belong to the triclinic space group P1h with a ) 13.3774(10) Å, b ) 18.5479(14) Å, c ) 21.6543(15) Å, R ) 91.400(4)°, β ) 98.717(4)°, γ ) 98.773(4)°, V ) 5242.5(7) Å3, Dcalcd ) 1.166 g/cm3, and Z ) 2. Full-matrix least-squares refinements on F2 of 1259 parameters led to final residuals R1 ) 0.0589 and wR2 ) 0.1472 for 8135 reflections with I > 2σ(I).
Acknowledgment. We are grateful to the Natural Sciences and Engineering Research Council of Canada, the Ministe`re de l’EÄ ducation du Que´bec, the Canada Foundation for Innovation,
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Laliberte´ et al. (16) The percentage of volume accessible to guests was estimated by the PLATON program.17 PLATON calculates the accessible volume by allowing a spherical probe of variable radius to roll over the van der Waals surface of the network. PLATON uses a default value of 1.20 Å for the radius of the probe, which is an appropriate model for small guests such as water. The van der Waals radii used to define surfaces for these calculations are as follows: C 1.70 Å, H 1.20 Å, and O 1.52 Å. If V is the volume of the unit cell and Vg is the guestaccessible volume as calculated by PLATON, then the porosity P in % is given by 100Vg/V. (17) Spek, A. L. PLATON, A Multipurpose Crystallographic Tool; Utrecht University: Utrecht, The Netherlands, 2001. van der Sluis, P.; Spek, A. L. Acta Crystallogr. 1990, A46, 194-201. (18) Sheldrick, G. M. SHELXS-97, Program for the Solution of Crystal Structures and SHELXL-97, Program for the Refinement of Crystal Structures; Universita¨t Go¨ttingen: Germany, 1997.
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