Inorganica Chimica Acta 358 (2005) 3398–3406 www.elsevier.com/locate/ica
Syntheses and structures of Ag(I) compounds containing btp ligands Ji Young Ryu a, Jun Yong Lee a, Seung Hoon Choi a, Sung Jin Hong a, Cheal Kim a,*, Youngmee Kim b,*, Sung-Jin Kim b a
Department of Fine Chemistry, Seoul National University of Technology, 172 Kongnung 2-Dong Nowon-Gu, Seoul 139-743, Korea b Division of Nano Sciences, Ewha Womans University, Seoul 120-750, Korea Received 24 February 2005; accepted 1 April 2005 Available online 23 May 2005
Abstract Four new Ag(I) complexes with three different modes of structures were obtained by varying the counteranions ðClO4 for 1; PF6 for 2; CF3 SO3 ðOTf Þ for 3; and CF3 CO2 for 4Þ, and their structures characterized by single-crystal Xray diffraction analysis. Compounds 1, 2, and 3 crystalize in the C-centered monoclinic space group C2/m. Compound 4 crystalizes in the monoclinic space group P21/c. The crystal structures of these complexes show that the complexes 1, 2, and 3 form ligand-supported dinuclear rings, and the dinuclear units of 1 and 3 are further linked by anions to form one-dimensional polymer, while the complex 4 forms an one-dimensional zigzag chain. The structural differences between 1, 2, 3, and 4 show the influences of the counteranions on the structures of the complexes. 2005 Published by Elsevier B.V. Keywords: Ag(I) complexes; Crystal structures; Polymeric compounds; btp ligand; Anion effect; Silver ring
1. Introduction Self-assembly of organic ligands and inorganic metal ions is one of the most efficient and widely used approaches for the construction of supramolecular architectures [1]. Owing to their potential as new functional solid materials such as gas or chemical absorption [2], ion-exchange [3], magnetism [4], host–guest chemistry [5], and catalysis [6], interest in self-assembled coordination polymers with interesting physical properties has grown rapidly. In this field, the coordination chemistry of bidentate organodiamine ligands has been the main interest. So far, several types of bidentate rigid organodiamine ligands such as 4,4 0 -bipyridine [7], 1,2-bis(4-pyridyl)ethene [8], and 1,2-bis(4-pyridyl)ethyne [9], and flexible organodiamine ligands such as 1,2-bis(4-pyr* Corresponding authors. Tel.: +82 2 970 6693; fax: +82 2 973 9149 (C. Kim), Tel.: +82 2 3277 3589; fax: +82 2 3277 2384 (Y. Kim). E-mail addresses:
[email protected] (C. Kim), ymeekim@ ewha.ac.k (Y. Kim).
0020-1693/$ - see front matter 2005 Published by Elsevier B.V. doi:10.1016/j.ica.2005.04.004
idyl)ethane [10] and 1,3-bis(4-pyridyl)propane [11], have been utilized. Consequently, a number of organic–inorganic coordination polymers based on those ligands have been successfully synthesized, including one-, two-, and three-dimensional motifs exhibiting honeycomb [12], grid [13], ladder [14], brick [15], bilayer [16], and diamondoid [17], but the possible network topologies for analogous metal complexes with angular bifunctional ligands are far less studied [18]. The selection of proper ligands as building blocks is absolutely a key point in manipulating the network structures [19]. Moreover, other factors such as metal ions with different coordination geometry or radius [20], counteranions [21], solvent [22], and metal-toligand ratio [23] have also been found to highly influence the structural topologies of such coordination frameworks. Therefore, in our attempt to investigate the design and control of the self-assembly of coordination polymers with the angular bridging ligands, we initiated a synthetic program for the construction of various supramolecular complexes with interesting extended
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frameworks based on the angular btp (2,6-bis(N 0 -1,2,4triazolyl)pyridine) ligand [24]. We have previously reported that Cu(II) salts with btp ligand produced coordination polymers as well as a monomeric molecule [6d,6e]. In addition, the polymeric Cu(II) compound showed, surprisingly, an unexpected heterogeneous catalytic reactivity and recyclability for alcoholysis of epoxides at ambient temperature. We have also employed various zinc salts to develop new polymeric complexes with the angular btp ligand that showed both non-covalent C–H X(Cl or Br) interactions and p–p interactions as well as covalent coordination bonds [25]. The reaction of Cd(NO3)2 with btp ligand revealed two kinds of coordination polymers which are the btp bridged Cd(NO3)2 chain and the btp bridged Cd(H2O)2 chain, and they are connected through hydrogen bonds [24b]. As a continuation of our efforts to investigate the influence of counteranions on the framework formations of the metal complexes with the angular btp ligand, we selected Ag(I) salts as the metal coordination sphere, because the coordination sphere of Ag(I) is very flexible and can adopt coordination numbers between two and six and various geometries from linear through trigonal to tetrahedral, trigonal pyramidal and octahedral [26], and because silver complexes containing the angular ligands are comparatively rare [18]. In this study, therefore, we have employed various silver salts with different counteranions to develop new polymeric complexes with the angular btp ligand, and four new Ag(I) complexes with three different modes were obtained by varying the counteranions ðClO4 ; PF6 ; CF3 SO3 ðOTf Þ; and CF3 CO2 Þ. Our results demonstrate that the anions can tune the structures of the Ag(I)–btp complexes through their coordination to Ag(I) atoms in different modes.
2. Results and discussion 2.1. Construction Direct diffusion technique with silver salts (AgClO4, AgPF6, AgOTf, and Ag(O2CCF3)) and btp ligands produced two kinds of structures, dinuclear 20-membered rings and one-dimensional zigzag chain depending on different anions. For ClO4 and OTf anions, weak interactions between Ag(I) and anions make dinuclear 20-membered rings construct polymeric compounds. For PF6 anion, there are also weak interactions between AgðIÞ and FðPF6 Þ, but they do not construct a polymeric compound. For O2 CCF3 anion, btp ligands bridge Ag(I) atoms to make one-dimensional zigzag chain, and there are also interactions between Ag(I) and anions. The structures of all four Ag(I) compounds containing btp ligands are shown in the Scheme 1.
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Scheme 1.
2.2. Structure description 2.2.1. Dinuclear silver ring [Ag2(btp)2](ClO4)2 (1) The structure of dinuclear silver ring 1 is shown in Fig. 1(a). The asymmetric unit contains an Ag, a half of btp ligand, and a half of ClO4 anion in monoclinic cell with Z = 2. The complete structure is generated by the symmetry operations (x, y + 1, z), (x + 1, y + 1, z + 1), and (x + 1, y, z). Two btp ligands bridge two Ag(I) atoms to make a 20-membered ring with ˚ . There are weak interaAg Ag distance of 8.37(7) A tions between Ag(I) and anions with AgðIÞ–OðClO4 Þ ˚ (shown in Fig. 1(b)). distance of 2.79(5) and 2.80(2) A These interactions make another 8-membered rings consisting of two Ag(I) atoms, four oxygen atoms, and two chlorine atoms. The Ag Ag distance in a 8-membered ˚ . As one can see in Fig. 1(b), 20-memring is 5.34(5) A bered rings and 8-membered rings are connected alternatively to construct an one-dimensional chain. In addition, there are interchain interactions as shown in Fig. 1(c) with interchain Ag Ag bond distance of ˚ to form two-dimensional sheets. These two3.19(5) A dimensional sheets are packed through p–p interactions between btp ligands from each sheet with the shortest ˚ . The N–Ag(I)–N angle is distance of 3.37(5) A 148.23(1) (Table 2). 2.2.2. Dinuclear silver ring [Ag2(btp)2](PF6)2 (2) The structure of dinuclear silver ring 2 is shown in Fig. 2(a). The asymmetric unit contains an Ag, a half of btp ligand, and a half of PF6 anion in monoclinic cell with Z = 2. The complete structure is generated by the symmetry operations (x, y + 1, z) and (x + 1, y, z + 1). Similar to 1, two btp ligands bridge two Ag(I) atoms to make a 20-membered ring with Ag Ag dis˚ . There are weak interactions betance of 8.221(6) A tween Ag(I) and anions with AgðIÞ–FðPF6 Þ distance ˚ . As shown in Fig. 2(b), interactions beof 2.834(2) A tween Ag(I) and anions do not make a polymeric compound in contrast to 1. There are interactions between
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Fig. 1. (a) ORTEP drawing of [Ag2(btp)2](ClO4)2 (1). (b) Polymeric structure containing Ag–O(perchlorate) interactions. (c) Drawing of polymeric Ag compound 1 along b axis with interchain interactions.
Ag atoms from each ring with the inter-ring distance of ˚ , and dinuclear silver rings are stacked 3.593(4) A through p–p interactions between btp ligands from each ˚ as shown rings with the shortest distance of 3.549(4) A in Fig. 2(c). The N–Ag(I)–N angle is 153.03(11) (Table 2).
2.2.3. Dinuclear silver ring [Ag2(btp)2](OTf)2 (3) The asymmetric unit contains an Ag, a half of btp ligand, and a half of O3 SCF3 ðOTf Þ anion in monoclinic cell with Z = 2. The complete structure is generated by the symmetry operations (x, y, z), (x, y, z + 1), and (x, y, z + 2). The structure of
the disordered dinuclear silver ring 3 is shown in Fig. 3(a). The btp ligands and OTf anions are highly disordered even though compound 3 has the same space group (C2/m) as those of compounds 1 and 2. That is why compound 3 has a little higher R value than those in compounds 1 and 2. Similar to 1, two btp ligands bridge two Ag(I) atoms to make a 20-membered ring, and weak interactions between Ag(I) and anions (Ag(I)–F and Ag(I)–O distances of 2.656(1) and ˚ , respectively) make another 10-membered 2.469(1) A rings consisting of two Ag(I) atoms, two fluorine atoms, two oxygen atoms, two sulfur atoms, and two carbon atoms. As shown in Fig. 3(b), 20-membered rings and 10-membered rings are connected alternatively to
Table 1 Crystallogrphic data for compounds 1, 2, 3, and 4
a
Ag(PF6)–btp (2)
Ag(OTf)–btp (3)
Ag(O2CCF3)–btp (4)
C18H14Ag2Cl2N14O8 841.07 150(1) 0.71073 C2/m 7.6348(15) 18.806(4) 9.1269(18) 90 101.14(3) 90 1285.7(5) 2 2.172 1.808 824 0.36 · 0.26 · 0.16 6105 1510 (0.0543) 1510/0/108 1.025 R1 = 0.0342, wR2 = 0.0808 wR2 = 0.0461, wR2 = 0.0888 1.144 and 1.068
C18H14Ag2F12N14P2 932.11 150(1) 0.71073 C2/m 8.0230(4) 19.6090(6) 8.7750(4) 90 101.474(2) 90 1352.9(1) 2 2.288 1.692 904 0.10 · 0.10 · 0.04 6252 1603 (0.0381) 1603/0/121 1.114 R1 = 0.0281, wR2 = 0.0666 wR2 = 0.0334, wR2 = 0.0694 0.760 and 0.678
C20H14Ag2F6N14O6S2 940.31 293(2) 0.71073 C2/m 8.8252(7) 19.5911(14) 8.8075(6) 90 99.260(1) 90 1502.93(19) 2 2.078 1.544 920 0.15 · 0.10 · 0.10 8374 1783 (0.0485) 1783/10/163 1.211 R1 = 0.1192,a wR2 = 0.3568a wR2 = 0.1225,a 0.3588a 2.27 and 1.756
C22H14Ag2F6N14O4 868.21 150(1) 0.71073 P21/c 7.9520(3) 23.0200(7) 15.1000(6) 90 92.9520(18) 90 2760.46(17) 4 2.089 1.521 1696 0.12 · 0.10 · 0.08 16 115 16 141 (0.0890) 16 141/0/435 1.058 R1 = 0.0615, wR2 = 0.1321 wR2 = 0.0945, wR2 = 0.1485 1.485 and 1.477
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Empirical formula Formula weight Temperature (K) ˚) Wavelength (A Space group ˚) a (A ˚) b (A ˚) c (A a () b () c () ˚ 3) Volume (A Z Dc (Mg/m3) Absorption coefficient (mm1) F(0 0 0) Crystal size (mm3) Reflections collected Independent reflections (Rint) Data/restraints/parameters Goodness-of-fit on F2 Final R indices [I > 2r(I)] R indices (all data) ˚ 3) Largest difference peak and hole (e/A
Ag(ClO4)–btp (1)
The R value is a little high since whole molecule is highly disordred, and atoms of OTf anion except a sulfur atom were refined isotropically. It was the best crystal for data collection.
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Table 2 Selected bond lengths and angles for compounds 1, 2, 3, and 4
Ag–N(btp) Ag–L(anion) Ag Ag (in a 20-membered ring) Ag Ag (interchain interaction) N–Ag–N
1
2
3
4
˚ 2.160(2) A Ag–O(ClO4) 2.794(46), ˚ 2.801(17) A ˚ 8.37(7) A
˚ 2.161(2) A ˚ Ag–F(PF6) 2.834(2) A
˚ 2.190(4), 2.210(4), 2.165(4), 2.172(4) A ˚ Ag–O(O2CCF3) 2.518(4), 2.460(3) A
˚ 8.221(6) A
˚ 2.160(14) A ˚, Ag–O(OTf) 2.469(1) A ˚ Ag–F(OTf) 2.656(1) A ˚ 8.253(3) A
˚ 8.751(6), 8.853(6) A
˚ 3.19(5) A
˚ 3.593(4) A
˚ 3.359(2) A
˚ 3.163(1), 3.434(1) A
148.23(1)
153.03(11)
148.23(15)
150.11(15), 154.91(15)
Fig. 2. (a) ORTEP drawing of [Ag2(btp)2](PF6)2 (2). (b) Drawing of 2 with Ag–F(PF6) interactions. (c) Packing diagram of compound 2 with p–p interactions between btp ligands from each rings.
construct an one-dimensional chain. There are interactions between Ag atoms from each chain with the inter˚ , and there are also p–p chain distance of 3.359(2) A ˚ ) beinteractions (the shortest distance of 3.549(4) A tween btp ligands from each rings for construction of a crystal structure as shown in Fig. 3(c). The N– Ag(I)–N angle is 152.2(8) (Table 2).
2.2.4. Zigzag chain (Ag(btp)(O2CCF3))n (4) The structure of a zigzag chain 4 is shown in Fig. 4(a). A symmetric unit contains two Ag(I) atoms, two btp ligands, and two O2 CCF3 anions. The btp ligands bridge Ag(I) atoms to make an one-dimensional zigzag chain. The anions are bonded to Ag(I) atoms with Ag(I)–O dis˚ . All anions are tances of 2.518(4) and 2.460(3) A
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Fig. 3. (a) ORTEP drawing of [Ag2(btp)2]2+ (3). All hydrogen atoms are omitted, and disordered OTf anions are shown for clarity. (b) Polymeric structre containing Ag–F(OTf) and Ag–O(OTf) interactions. (c) Packing diagram of compound 3 with p–p interactions between btp ligands from each ring.
oriented to the one side of the one-dimensional chain, and two chains are fit each other like a toothed wheel as shown in Fig. 4(b). There are interactions between Ag atoms from each chain with Ag Ag interchain dis˚ , and there are also p–p tances of 3.163(1) and 3.434(1) A interactions between btp ligands from each chain with ˚ in a the shortest interchain distance of 3.341(3) A toothed wheel. The N–Ag(I)–N angles are 150.11(15) and 154.91(15) (Table 2). In our efforts to systematically investigate the influences of terminal groups and counteranions on the coordination polymer formations of the Ag(I) complexes with the angular ligand btp (2,6-bis(N 0 -1,2,4-triazolyl)pyridine), the coordination chemistry of the angular ligand btp with inorganic Ag(I) salts has been studied. The btp ligands with silver salts produce three different modes of structures, dinuclear silver rings (2), dinuclear units linked by anions to form an one-dimensional polymers (1 and 3), and one-dimensional zigzag chains (4). The ClO4 and PF6 are known as non-coordinating anions, and the coordinating ability of the OTf anion
is between the coordinating and non-coordinating anions. Those ClO4 ; PF6 and OTf anions produce dinuclear silver rings with the same space group (C2/ m). The dinuclear units of 1 and 3 are further linked by anions to form one-dimensional polymers, while the dinuclear silver rings of 2 are weakly interacted with F atoms of PF6 anions. All three compounds 1, 2, and 3 show Ag Ag interchain interactions, and are packed through p–p interactions between btp ligands from each chain or ring to form a higher dimensional polymeric compound. The coordinating O2 CCF3 anions are bonded to Ag(I), and btp ligands bridge Ag(I) atoms to construct an one-dimensional zigzag chain. Chelating bonds between AgðIÞ and O2 CCF3 anions and their orientations may prevent making dinuclear silver rings. These results demostrate that the structural differences between 1, 2, 3, and 4 show the influences of the counteranions on the structures of the complexes, and that p–p interactions between btp ligands from each chain or ring are also important roles for construction of crystal structures.
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Fig. 4. (a) ORTEP drawing of zigzag chain [Ag(O2CCF3)(btp)]n (4). (b) Drawing of zigzag chains which are fit like a toothed wheel. The black bonds represent one chain, and the green bonds represent the other chain.
3. Conclusion A series of Ag(I) complexes with the angular bridging ligand, btp, have been synthesized and structurally characterized. The molecular structures of these Ag(I) complexes are profoundly influenced by the anions: from a simple dinuclear ring and dinuclear units connected by anions to novel one-dimensional chains. In additon, each one-dimesional chain is stacked through p–p interactions between btp ligands to construct crystal structures. These results clearly indicate that counter anions play a very important role in the formation of different coordination polymers and p–p interactions are also important roles to build crystal structures.
4. Experimental 4.1. Materials The compounds Ag(ClO4), Ag(PF6), Ag(O3SCF3), and Ag(O2CCF3) were purchased from Aldrich and
used as received. The btp ligand was prepared as described previously [24]. 4.2. Instrumentation IR spectra were measured on a Bio-Rad FTS 135 spectrometer as KBr pellets. Elemental analysis for carbon, nitrogen, and hydrogen was carried by using an EA1108 (Carlo Erba Instrument, Italy). 4.3. Synthesis of dinuclear silver ring [Ag2(btp)2](ClO4)2 (1) 20.0 mg (0.10 mmol) of Ag(ClO4) was dissolved in 20 mL water and carefully layered by 20 mL CH3OH solution of btp ligand (42.0 mg, 0.2 mmol). Suitable white-crystals of compound 1 for X-ray analysis were obtained in a few days. Anal. Calc. for C18H14Ag2Cl2N14O8, 1: C, 25.70; H, 1.68; N, 23.32. Found: C, 25.59; H, 1.65; N, 23.22%. IR (KBr): m(cm1) = 3143(m), 1589(s), 1568(s), 1513(s), 1456(s), 1434(s), 1366(w), 1311(m), 1284(w), 1230(w), 1186(w),
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1097(s), 989(m), 905(w), 799(s), 762(s), 723(w), 662(m), 623(s). 4.4. Synthesis of dinuclear silver ring [Ag2(btp)2](PF6)2 (2) 25.0 mg (0.1 mmol) of Ag(PF6) was also dissolved in 20 mL methanol and carefully layered by 20 mL methylene chloride solution of btp ligand (42.0 mg, 0.2 mmol). Suitable white-crystals of compound 1 for X-ray analysis were obtained in a few days. Anal. Calc. for C18H14Ag2F12N14P2, 2: C, 23.19; H, 1.52; N, 21.04. Found: C, 23.37; H, 1.79; N, 21.24%. IR (KBr): m(cm1) = 3176(m), 1614(s), 1586(m), 1518(s), 1476(s), 1283(m), 1218(s), 1141(m), 1075(m), 985(m), 848(s), 777(w), 668(m), 557(s). 4.5. Synthesis of dinuclear silver ring [Ag2(btp)2](OTf)2 (3) 26.0 mg (0.1 mmol) of Ag(OTf)2 was also dissolved in 20 mL methanol and carefully layered by 20 mL methylene chloride solution of btp ligand (42.0 mg, 0.2 mmol). Suitable white-crystals of compound 1 for X-ray analysis were obtained in a few days. Anal. Calc. for C20H14Ag2F6N14O6S2, 3: C, 27.67; H, 1.63; N, 22.59. Found: C, 27.55; H, 1.57; N, 22.43%. IR (KBr): m(cm1) = 3104(m), 1613(s), 1588(m), 1514(s), 1479(s), 1438(w), 1364(m), 1276(brs), 1223(w), 1172(m), 1143(m), 1074(m), 1036(s), 985(m), 893(m), 800(s), 669(s), 642(s). 4.6. Synthesis of zigzag chain (Ag(btp)(O2CCF3))n (4) 22.0 mg (0.1 mmol) of Ag(O2CCF3) was also dissolved in 20 mL methanol and carefully layered by 20 mL methylene chloride solution of btp ligand (42.0 mg, 0.2 mmol). Suitable white-crystals of compound 1 for X-ray analysis were obtained in a few days. Anal. Calc. for C22H14Ag2F6N14O4, 4: C, 28.10; H, 1.50; N, 20.86. Found: C, 28.06; H, 1.76; N, 20.42. IR (KBr): m(cm1) = 3103(m), 1681(s), 1612(s), 1588(w), 1477(s), 1279(m), 1217(s), 1141(s), 1075(m), 982(s), 801(s), 779(m), 720(w), 668(m). 4.7. Crystallography The diffraction data for compounds 1, 2, and 4 were collected on a Nonius Kappa-CCD diffractometer using ˚ ) [27]. The crystals were mounted Mo Ka (k = 0.71073 A on glass fibers under epoxy. The CCD data were integrated and scaled using the DENZO-SMN software package [28], and the structures were solved and refined by using SHEXTL V5.0 [29]. All non-hydrogen atoms were located in the calculated positions. The X-ray diffraction data for compound 3 were collected on a Bruker SMART APX diffractometer equipped with a mono-
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˚ ) incident beam. chromater in the Mo Ka (k = 0.71073 A The crystal was mounted on a glass fiber. The CCD data were integrated and scaled using the Bruker-SAINT software package, and the crystal structure was determined by the direct method and Fourier techniques. All the calculations were performed on an IBM Pentium computer using SHELXS-97 and SHELXL-97, and atomic scattering factors for all non-hydrogen atoms were supplied by SHELXS-97 [30]. Whole molecule is highly disorded, and atoms of the OTf anion except a sulfur atom were refined isotropically. All hydrogen atoms were located in the calculated positions. The molecular structure was drawn by the Ortep-3 for Windows program [31]. The crystallographic data for compounds 1, 2, 3, and 4 are listed in Table 1. 5. Supplementary material CCDC-259827 for 1, CCDC-259828 for 2, CCDC259829 for 3, and CCDC-259830 for 4 contain the supplementary crystallographic data for this paper. These data can be obtained free of charge at www.ccdc.cam. ac.uk/conts/retrieving.html [or from the Cambridge Crystallographic Data Centre, 12, Union Road, Cambridge CB2 1EZ, UK; fax: (internat.) +44 1223/336-033; e-mail:
[email protected]]. Acknowledgments This research was supported by the Korea Research Foundation (2002-070-C00053) and the Korean Science & Engineering Foundation (ABRL R14-2003-014-01001-0). We thank Dr. Alan J. Lough in University of Toronto, Canada for X-ray data collection. References [1] (a) S.R. Batten, R. Robson, Angew. Chem., Int. Ed. 37 (1998) 1460; (b) D.B. Moler, H. Li, B. Chen, T.M. Reineke, M. OÕKeeffe, O.M. Yaghi, Acc. Chem. Res. 34 (2001) 319; (c) B. Moulton, M.J. Zaworotko, Chem. Rev. 101 (2001) 1629; (d) A.N. Khlobystov, A.J. Blake, N.R. Champness, D.A. Lemenovskii, A.G. Majouga, N.V. Zyk, M. Schroder, Coord. Chem. Rev. 222 (2001) 155; (e) O.R. Evans, W. Lin, Acc. Chem. Res. 35 (2002) 511; (f) C. Janiak, Dalton Trans. (2003) 2781; (g) P.J. Hagrman, D. Hagrman, J. Zubieta, Angew. Chem., Int. Ed. 38 (1999) 2638; (h) S.-L. Zheng, M.-L. Tong, X.-M. Chen, Coord. Chem. Rev. 246 (2003) 185; (i) S.L. James, Chem. Soc. Rev. 32 (2003) 276. [2] (a) H. Li, M. Eddaoudi, T.L. Groy, O.M. Yaghi, J. Am. Chem. Soc. 120 (1998) 8571; (b) M. Kondo, T. Okubo, A. Asami, S. Noro, T. Yoshitomi, S. Kitagawa, T. Ishii, H. Matsuzaka, K. Seki, Angew. Chem., Int. Ed. 38 (1999) 140; (c) S. Noro, S. Kitagawa, M. Kondo, K. Seki, Angew. Chem., Int. Ed. 39 (2000) 2081.
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