Simulations of inorganic crystal structures

Current Opinion in Solid State and Materials Science 7 (2003) 13–19

Simulations of inorganic crystal structures Recent advances in structure elucidation ´ ´ Caroline Mellot-Draznieks*, Gerard Ferey Institut Lavoisier, UMR CNRS 8637, Universite´ de Versailles Saint-Quentin, 45 Avenue des Etats-Unis, 78035 Versailles Cedex, France Received 3 February 2003; accepted 14 March 2003

Abstract The aim of this paper is to show some recent developments of simulation approaches in the structure elucidation of inorganic crystalline compounds, highlighting at each step their role either as a complementary technique or as a tool to anticipate structure / properties relationships or even to imagine new inorganic architectures. Specific examples are taken in the area of zeolites to illustrate the use of energy minimizations and (N, V, T ) Monte Carlo techniques as a complement to experimental diffraction approaches, typically for the disordered placement of extra-framework species (cations, water molecules). In the still extending area of the synthesis of templated open-framework inorganic structures, we show that lattice energy minimizations may possibly be used to estimate or even anticipate the structures and energetics of the related template-free structures. A third section tackles the development of more sophisticated methods for the computational design of not-yet-synthesized structures using building block concepts.  2003 Elsevier Science Ltd. All rights reserved.

1. Introduction Predictive calculations of the crystal structures and properties of solids are topical and are recognized in materials sciences as a challenging and promising task [**1]. One of the driving force for developing systematic approaches through predictive simulation tools derives from the evergrowing demand for the design of new materials in specific areas (catalysts, nanoporous materials, ceramics, magnets, etc.) and the need for understanding, or even anticipating, structure / property relationships at an atomic level. Increasingly innovative and successful computational tools have emerged in various areas in the last 10 years. In that respect, the field of zeolites and nanoporous solids is particularly illustrative. Initially driven by the petroleum industry, this field has benefited from the unprecedented development of a collection of sophisticated simulation tools, ranging from minimization techniques, molecular dynamics, simulated annealing to first principles methods. Simulation tools have now an established role in the elucidation of inorganic structures.

*Corresponding author. Tel.: 133-1-39-25-4377; fax: 133-1-39-254358. E-mail address: [email protected] (C. Mellot-Draznieks).

The aim of this paper is to give insights into computational strategies recently developed in the simulation of microporous materials. In the expanding field of the hydrothermal synthesis of open-framework inorganic structures, research efforts lead to an evergrowing chemical and architectural diversity of structures [**2]. Such developments, while being driven by the ultimate goal to produce new materials with targeted properties, strongly rely on the more conventional approach based on structure elucidation and the study of structure / property relationships. In the field of inorganic open-framework materials, this starts with an accurate knowledge of the framework architecture, of the positions of extra-framework species, i.e., cations or water, and of the role of the organic templating agent. In the case of templated inorganic structures, the potential use of any as-synthesized compound for further adsorption / catalysis purposes requires the investigation of the stability of the structure upon calcination, i.e., template extraction, possibly leading to a microporous material. Along this line, we give in this paper specific illustrative examples of new simulations approaches, intended to show how they may be helpful in the field of structure elucidation as a complement to experimental diffraction techniques, or may be used to anticipate structural modifications of as-synthesized structures upon calcination or even be used for the numerical design of new and interesting architectures.

1359-0286 / 03 / $ – see front matter  2003 Elsevier Science Ltd. All rights reserved. doi:10.1016 / S1359-0286(03)00020-2

14

´ / Current Opinion in Solid State and Materials Science 7 (2003) 13–19 C. Mellot-Draznieks, G. Ferey

2. Extra-framework species in zeolite structures: towards more realistic models Simulations are valuable for helping to solve zeolite structures, especially when they are difficult to fully characterize with conventional diffraction techniques. In most cases, zeolites are simulated using simplified models in terms of structure and forcefield, using average T(Si,Al) atoms, for instance, or fully dehydrated zeolite models, therefore circumventing the partial disorder of framework / extra-framework species and partial occupancies or even specific forcefield developments. The present section wants to illustrate recent simulation strategies that have been developed in order to approach either the location of extra-framework cations in zeolites or deal with adsorbed water molecules in a more realistic fashion, where models tend to be closer to experimental systems. A substantial number of diffraction studies have examined the location of extra-framework cations in both hydrated and dehydrated aluminosilicate zeolites. A comprehensive determination of the crystal structure and especially of extra-framework cation positions in such materials is an important prerequisite for understanding their properties. Typically, the dehydrated forms of sodium- and lithium-exchanged X faujasite-type zeolites have attracted much attention [3–6], largely owing to the industrial use of zeolite X for gas adsorption and separation [7]. While the framework is made of well-ordered corner-sharing tetrahedra, the extra-framework cations are located in crystallographic sites, for which the number of crystallographically equivalent positions usually exceeds the number of cations required. The precise determination of cations positions using diffraction techniques is rendered difficult when they are located in low-symmetry sites with low occupancies, especially when cations with small scattering factors are considered. In addition, while zeolites are most of the time used in their dehydrated state, residual water molecules may always be adsorbed even after a dehydration treatment; these are often undetected—then neglected—when determining the crystal structure. Cationic zeolites are highly hydrophilic and even small amounts of adsorbed water are known to have an important impact on their adsorption / separation performance. Recent computational studies have tackled the statistical treatment of framework or extra-framework species, and have investigated the impact of adsorbed water molecules. For example, methodologies for simulating the distribution of aluminum atoms in the frameworks of low and medium Si /Al ratio zeolites using periodic lattice simulation techniques have been reported for various natural zeolites, such as heulandite [8] and clinoptilolite [9]. The structural and energetics effects of Al distribution in the frameworks and its interplay with cation placement and lattice relaxation were investigated. In Na-clinoptilotite for example, the simulations show that Al atoms are stabilized in specific crystallographic T sites in line with experimen-

tal findings, further showing for low Si /Al ratio how Al locations may be driven by interactions between neighbouring Al . . . Al and Al . . . Na interactions. Recent computational studies have included the interactions of water molecules when simulating the zeolite crystal structures [10–12]. For example, Lewis et al. [10] have simulated the hydrated and dehydrated structures of Goosecreekite using lattice energy minimizations. Different combination of Al sites, cations and water placement were compared using appropriate potential parameters for the zeolite / extra-framework cations [13] and for the water related interactions [14]. Their study highlights the interplay between adsorbed water molecules and the stabilization of specific Al distributions in the framework together with the stabilization of extra-framework cation positions that would be considered as unstable in the fully dehydrated zeolite. Energy minimizations have been used to study the effect of hydration on the preferential cation location of cation-exchanged zeolite A (Na 1 , Cs 1 , Ca 21 , Ba 21 , Cd 21 , Sr 21 ) [12]. Concerning the placement of cations in fully dehydrated zeolites, energy minimizations have been successfully applied to the siting of cations in Li-ABW [15] and NaCa-A [16], ETS-10 [17], faujasite-type zeolites [4,18]. In these studies, energy minimizations of individual cation distributions were performed that are equivalent to zero K calculations and produced minimized structures that can only be compared with low-temperature diffraction refinements. Indeed, it is typical to find in the system NaX (see Fig. 1), where the numbers of cations in high-symmetry sites (SI, SI9 and SII) are well-established, that the precise location of the remaining cations of the supercages (SIII / SIII9) is uncertain from diffraction analysis, essentially due to low occupancy factors for the general crystallographic positions. Moreover, the cation positions reported in the literature for the same system may vary from one study to another, depending on differences in Al / Si distribution in the samples, or the presence of residual water molecules left after dehydration. In such cases, Monte Carlo simulations in the canonical (N, V, T ) ensemble are particularly adequate for generating at finite temperature the statistically averaged information that is required for such systems [19,20]. The main steps of the (N, V, T ) simulations are as follows: (i) the random generation of a starting configuration of N cations, (ii) the generation of a new configuration by the translation of a randomly chosen cation, (iii) the acceptance / rejection of the new configuration according to an energetic criterion for acceptance. Each Monte Carlo ‘move’ leads to a different configuration of cations that is accepted or rejected according to Boltzman statistics. Long enough Monte Carlo simulations (10 6 steps) allow the averaging of the different instantaneous cation configurations and yield the equilibrium distribution of cations in the system, where the simulated averaged quantities may be directly compared to the experimental crystal structure.

´ / Current Opinion in Solid State and Materials Science 7 (2003) 13–19 C. Mellot-Draznieks, G. Ferey

15

Fig. 2. Predicted cation distribution of supercage cations in LiX. The pair distribution functions between cations of the supercages (sites II and III9) are shown.

when using diffraction techniques, and clearly show that the placement of extra-framework cations in zeolites is to be regarded as a cooperative process rather than the occupancy of sites with specific energies. Such effects are illustrated in Fig. 2 in the case of the LiX (Si:Al51.25) zeolite where the simulated pair distribution functions between the cations of the supercages show that cation– ˚ as cation distances are kept at a minimal distance of 4.6 A a result of electrostatic repulsions.

3. Anticipation of the calcined crystal structures of as-synthesized compounds upon template extraction Fig. 1. Schematic representation of the faujasite-type X zeolite with extra-framework cation positions. Sites III and III9 differ in their placement relative to the four-ring windows of the supercages.

The location of cations in faujasite X was simulated as follows. Part of the zeolite structure was considered as a rigid and negatively charged ‘host’, [Si /Al 192 O 384 ] 862 , while the missing cations were treated as ‘guest’ particles and moved during the simulation run. The frameworkcation interaction energy was estimated with an interatomic potential, written as the sum of a dispersion– repulsion term acting between cations and framework atoms (O, T5Si /Al), and a coulombic term using partial charges on all atoms. Random translational displacements ˚ were adjusted so as to of cations (maximum of 0.3 A) obtain an acceptance rate of 50%. Interestingly, the simulations in faujasite X show that a correct description of cation distribution cannot be obtained as long as Al and Si are not distinguished in terms of partial charges and dispersive–repulsive interactions with the cations. The best agreement with the most recent experimental crystal data is then obtained, especially regarding the positions of the cations in the supercages (sites III and III9) and their relative placement facing AlO 4 or SiO 4 tetrahedra. Such features are difficult to pinpoint

The numerous syntheses of templated inorganic open frameworks in hydrothermal conditions were the starting point for the development of porous solids obtained by calcination, for adsorption or catalytic purposes [**2]. For a number of silicates and aluminophosphates, the extracoordinated species in the as-synthesized structures (template, water, hydroxy groups, fluorinated species, etc.) may be partially or totally removed upon calcination, leaving behind stable open-framework materials. By contrast, in other families of compounds such as gallophosphates, the removal of the template is often a critical step that may lead to the collapse of the structure. The production of the related stable open-framework compound cannot be easily anticipated. Furthermore, whereas the crystal structures of as-synthesized solids are well characterized, those of calcined solids, which are of crucial interest, are scarcely described, because of their powder form and of the difficulties of ab initio resolution from powder data. We have recently undertaken an important effort to develop a computational strategy for anticipating the energetics and structures of open-framework structures upon calcination. The main feature of the method consists in starting from the as-synthesized structure exclusively and modifying it prior to lattice energy minimizations

16

´ / Current Opinion in Solid State and Materials Science 7 (2003) 13–19 C. Mellot-Draznieks, G. Ferey

atoms that are presumed to be evacuated upon calcination are eliminated, leaving behind a neutral open-framework model. It may have the chemical composition AlPO 4 for an as-synthesized aluminophosphate for example, or GaPO 4 for an as-synthesized gallophosphate. The model is then submitted to a constant pressure minimization (allowing both cell parameters and atomic coordinates to relax). The method was first tested and validated on aluminophosphates that are known both in their as-synthesized and calcined forms, such as AlPO-14 [21] and AlPO-53 [22]. As an illustrative example, we show here the simulation steps that allow the prediction of the calcined form of as-synthesized AlPO-53, Al 12 (PO 4 ) 12 (OH) 4 (CH 3 NH 2 ) 4 (H 2 O) 7 . This compound was shown experimentally to transform, upon calcinations, into a stable zeotype structure, AFN [23], that was solved in the Pbca space group, while the as-synthesized structure was solved in P2 1 2 1 2 1 . The as-synthesized AlPO-53 comprises alternating Al and P atoms, linked by bridging oxygen atoms, with P atoms in a tetrahedral environment and Al atoms in various coordinations (IV, V, VI). A polyhedral representation of as-synthesized AlPO-53 is

shown in Fig. 3a. The experimental as-synthesized crystal structure was taken as a starting point in our simulations. Atoms that are presumed to be evacuated upon calcination, i.e., bridging hydroxy groups, methylamine templates and water molecules, were removed, leaving behind a neutral structure, namely, Al 12 (PO 4 ) 12 . This results in a structure where all inequivalent Al atoms are in tetrahedral coordination, retaining four Al atoms in a highly distorted environment that emanates from the 6- and 5-fold coordinated Al atoms of the as-synthesized structure. This intermediate model is shown in Fig. 3b. Finally, this model was submitted to a constant pressure minimization in space group P2 1 2 1 2 1 and the symmetry of the minimized structure was analyzed with the Find]Symmetry algorithm. Fig. 3c shows the calcined AlPO-53 as predicted by the simulations, with an excellent agreement with the experimental calcined crystal structure. Indeed, the simulations successfully predicted the change in space group of the crystal structure upon calcination, from P2 1 2 1 2 1 to Pbca symmetry. The initial model of calcined AlPO 4 -53, 21 with an initial lattice energy of 212 383.76 kJ mol per 3 ˚ ), converged rapidly towards tetrahedral unit (per 1000 A

Fig. 3. (a) Polyhedral representation of the as-synthesized AlPO-53; (b) modified AlPO-53 prior minimizations after elimination of the organic template and hydroxy groups; (c) simulated calcined AlPO-53 after lattice energy minimizations.

´ / Current Opinion in Solid State and Materials Science 7 (2003) 13–19 C. Mellot-Draznieks, G. Ferey

the structure in which all Al atoms are in regular tetrahedral environments, with a final lattice energy of 212 932.1 kJ mol 21 . The AlPO 4 -53 structure is thus 4.30 ˚ 3, kJ mol 21 less stable than a-berlinite per T-site / 1000 A making it relatively stable when compared to other existing polymorphs [24]. We have also investigated the dehydroxylation process and organic-template elimination of two as-synthesized aluminophosphates, namely AlPO-14 (Al 8 P8 O 32 (OH) 2 (C 3 H 10 N) 2 (H 2 O) 2 ) [21] and MIL-34 (Al 4 P4 O 16 (OH)(C 4 H 10 N)) [25]. Interestingly, the calcined form of MIL-34 was successfully anticipated before it was actually experimentally calcined. The simulated structure of MIL-34 was used later to start the Rietveld refinement of the powder sample. Also, this type of approach was extended to gallophosphates and to their defluorination / dehydroxylation during the calcination process [26,*27] using an appropriate forcefield for gallium in inorganic frameworks [28]. Indeed, fluorine anions are deemed to stabilize the assynthetized structures, due to their position in the framework and their high electronegativity, so that they are often involved in strong hydrogen bonding and tight amine / framework interactions. The dehydrofluorination and template extraction of two isotypic as-synthesized oxyfluorinated structures, an aluminophosphate (UT-6: (Al 6 P6 O 24 F) 2 -(C 5 H 5 NH) 2 (H 2 O) 0.3 )) and a gallophosphate (GaPO-tricl.CHA: Ga 6 P6 O 24 F2(C 4 N 2 H6) 2 (H 2 O)) were successfully anticipated using this computational method [*27], leading to the isostructural AlPO 4 and GaPO 4 chabazite structures in excellent agreement with the expected experimental template-free structures. One essential feature of such simulations is the capture in one single step of a complex sequence of chemical reactions involved during calcination of templated compounds, such as defluorination, dehydration, dehydroxylation and template decomposition, that would be difficult to simulate in a step-by-step approach. The method yields a possible candidate structure with its relative stability to existing compounds. While not adapted to predict phase transformations involving complex atomic rearrangements such as topotactic transformations, for example, the method is simple and may be used to anticipate when is possible the formation of a template-free stable openframework upon calcination, with valuable insight into its energetics and structures.

4. Computational design of not-yet-synthesized structures Besides the desire to complement the experimental characterization of the structures and properties of solids, the design of new and interesting crystal structures using computational tools is an ongoing challenge. An evergrowing effort to develop powerful computational techniques is being undertaken not only to aid the often difficult task of crystal structure determination (Section 2 gives some

17

illustration in this area), but also to rationalize the relationships between different but related existing structures, and, in a more explorative perspective, to help limit the domain of structures or topologies that are possible in a given system. The latter is the subject of the present section. Starting from the observation that (meta)stable compounds are kinetically stable local minima of the free energy, the most general approach to address this task is to identify candidate structures through an analysis of the ‘energy’ landscape of the system of interest. This approach is directly or indirectly behind almost all structure prediction computational methods. Most of them use global minimization techniques, such as simulated annealing or genetic algorithm methods, for example. Assuming a minimum prior knowledge of the system of interest, such as symmetry, cell parameters, chemical composition or building units, such methods allow one to identify the local minima of the ‘energy ’ landscape and yield the corresponding candidate crystal structures. Indeed, due to their ability to cross energy barriers and to search regions with low-energy structures, global optimizations techniques have opened the way to the prediction of atomic-scale arrangement of inorganic structures. More details about this still emerging area and the recent development of such methods in inorganic materials sciences may be found in Ref. [**29]. The prediction of zeolites structures was an early application of simulated annealing methods: candidate structures could be generated according to imposed criteria of symmetry, cell-size, number of tetrahedral sites, together with a cost function based on the geometrical characteristics of zeotype structures [*30]. The further development of new simulation tools for structure prediction has gradually evolved towards the use of a minimal amount of input data. From the important number of imposed criteria (symmetry, cell parameters and chemical composition) there has been a gradual reduction of the a priori knowledge needed to predict crystal structures. The elimination of symmetry constraints during the simulation has opened the door to solving a structure, given its chemical composition and its cell-parameters, by optimizing the arrangement of atoms, ions or molecules according to prescribed rules contained in a cost-function (bond valence model, Born lattice energy, etc.). In this way, various chemical systems have been explored, such as NbF 4 [*31], Li 3 RuO 4 [32], SiO 2 [33] and TiO 2 [34] polymorphs, and various families of ionic / metallic compounds [35] and binary / ternary oxides [36]. As a further step, simulation studies were performed where symmetry, cell parameters and even chemical composition are kept unconstrained during the global search. Such approaches typically allowed the exploration of the phase diagram of hypothetical oxides, [37], and the comparison in terms of stability of structure candidates to that of known ones. The computational design of hypothetical structures using building block concepts has recently emerged as an

18

´ / Current Opinion in Solid State and Materials Science 7 (2003) 13–19 C. Mellot-Draznieks, G. Ferey

interesting alternative [**29,38]. The prediction of periodic inorganic structures is a difficult task involving many degrees of freedom. Any means to reduce the number of degrees of freedom is potentially valuable. Assuming, where appropriate, the occurrence of ‘building units’ is one such means. Many inorganic structures can be regarded as building units assembled in 1-, 2- or 3-D space, leading to related structures that may be differentiated by the way the building units are connected to one another. When encapsulated in a computational method, the building unit, while replacing many individual atoms, allows a reduction in the size of parameter space to be explored. This concept is already routinely explored in organic chemistry or polymer science, where candidate structures are predicted by assembling molecular entities through simple hydrogen-bond type intermolecular interactions. However, such developments were rendered difficult in the case of inorganic structures due to the infinite extent of the crystal structures. For example, ‘primary’ building units, that represent either individual atoms or a rigid collection of atoms, were used to predict the experimentally observed structure Mg(CN) 2 together with another candidate hypothetical structure [**29]. In this study, the simulations handled Mg 21 cations and (CN) 222 rigid anions as input, along with point charge distributions and a potential

function which includes a Coulomb interaction and a Lennard–Jones potential for describing the repulsion–dispersion between neighboring atoms. Another interesting method is to use the building units as a topological entity and scan their possible arrangement in three-dimensional space to generate infinite crystal structures. This is the basis for the AASBU method (Automated Assembly of Secondary Building Units) [38]. The key features of the method are the use of predefined building units and a simple cost function (attractive Lennard–Jones potential) designed to ‘glue’ the SBUs together at predefined linkage points. The SBUs are assembled in space through a sequence of simulated annealing plus minimization steps, with optional symmetry constraints, leading to a list of candidate structures. One advantage of the method is that the simulation can be run free of any chemical composition constraint. The search is then topologically oriented and allows one to rationalize the relationships between known structures, or to search for new structures made of the same building units. We have used the AASBU method for the aggregation of large structural motifs, like the hexameric unit found in the ULMs and MILs families of compounds, or cages, such as sodalite cages found in zeolites, or the double four rings [39]. Fig. 4 shows a selection of hypothetical

Fig. 4. Selection of hypothetical frameworks generated by the assembly of building blocks in 3D space, using the hexameric unit found in the UML-n family of compounds (left), a sodalite cage (middle) and a double-four ring (right).

´ / Current Opinion in Solid State and Materials Science 7 (2003) 13–19 C. Mellot-Draznieks, G. Ferey

frameworks generated by the AASBU method employing large structural motifs such as an hexameric unit, a sodalite cage and a double-four ring. Using such large motifs may be regarded as a basis for designing new and interesting materials containing targeted local structures of interest. The above approach shows that the generation and design of new open-frameworks, while now being accessible with available simulation tools, raises the challenging question of their possible chemical composition. The estimation of lattice energies of hypothetical frameworks may be performed for various possible candidate chemical compositions of interest, typically silicates or aluminophosphates, yielding useful insight into their potential viability when compared to those of related, existing compounds. The combination of the computational design of new frameworks together with the estimation of their relative stability may be a powerful incentive for developing synthesis strategies towards targeted structures that possess desirable properties.

References Papers of particular interest, published within the annual period of review, have been highlighted as: * of special interest; ** of outstanding interest. [**1] Catlow CRA, editor, Computer modelling in inorganic crystallography, London: Academic Press; 1997. ´ [**2] Cheetham AK, Ferey G, Loiseau T. Angew Chem Int Ed 1999;38:3268. ´ [3] Plevert J, DiRenzo F, Fajula F, Chiari G. J Phys Chem 1997;101:10340. [4] Vitale G, Mellot CF, Bull LM, Cheetham AK. J Phys Chem 1997;101:4559. [5] Feuerstein M, Lobo RF. Chem Mater 1998;10:2197. [6] Zhu L, Seff K. J Phys Chem 1999;103:9512. [7] Gaffney TR. Curr Opin Solid State Mater Sci 1996;1:69–75. [8] Ruiz-Salvador AR, Gomez A, Lewis DW, Rodriguez-Fuentes G, Montero L. Phys Chem Chem Phys 1999;1:1679. [9] Ruiz-Salvador AR, Lewis DW, Rubayo-Soneira J, RodriguezFuentes G, Sierra LR, Catlow CRA. J Phys Chem B 1998;102:8417. [10] Almora-Barrios N, Gomez A, Ruiz-Salvador AR, Mistry M, Lewis DW. Chem Commun 2001;6:531–2.

19

[11] Lewis DW, Ruiz-Salvador AR, Almora-Barrios N, Gomez A, Mistry M. Mol Simul 2002;28(6–7):649–61. [12] Higgins FM, de Leeuw NH, Parker SC. J Mater Chem 2002;1:124– 31. [13] Jackson RA, Catlow CRA. Mol Som 1988;1:207. [14] De Leeuw NH, Parker SC. J Am Ceram Soc 1999;82:3209. [15] Newsam J, Freeman CM, Gorman AM, Vessal B. Chem. Commun. 1996:1945–6. ` [16] Lignieres J, Newsam JM. Microporous Mesoporous Mater 1999;28(2):305–14. [17] Grillo ME, Carrazza J. J Phys Chem 1996;100:12261. [18] Jaramillo E, Auerbach SM. J Phys Chem B 1999;103:9589. [19] Mellot-Draznieks C, Butterfey S, Boutin A, Fuchs AH. Chem Commun 2001;21:2200–1. [20] Buttefey S, Boutin A, Mellot-Draznieks C, Fuchs AH. J Phys Chem B 2001;105(39):9569–75. ´ [21] Girard S, Mellot-Draznieks C, Gale JD, Ferey G. Chem Commun 2000;3:1161–2. [22] Kirchner RM, Grosse-Kunstleve RW, Pluth JJ, Wilson ST, Broach RW, Smith JV. Microporous Mesoporous Mater 2000;39:319–32. [23] Baerlocher C, Meier WM, Olson DH. In: Atlas of zeolite framework types, Amsterdam: Elsevier; 2001. [24] Henson NJ, Cheetham AK, Gale JD. J Chem Mater 1996;8:664. [25] Loiseau T, Mellot-Draznieks C, Sassoye C, Girard S, Guillou N, ´ Huguenard C, Taulelle F, Ferey G. J Am Chem Soc 2001;123:9642– 51. ´ [26] Girard S, Gale JD, Mellot-Draznieks C, Ferey G. J Am Chem Soc 2002;124(6):1040–51. ´ [*27] Girard S, Tuel A, Mellot-Draznieks C, Ferey G. Angew Chem 2002;41:972. ´ [28] Girard S, Gale JD, Mellot-Draznieks C, Ferey G. Chem Mater 2001;13:1732. ´ ¨ JC, Cancarevic Z, [**29] Mellot-Draznieks C, Girard S, Ferey G, Schon Jansen M. Chem Eur J 2002;8:4102–13. [*30] Deem MW, Newsam J. Nature 1989;342:260; Deem MW, Newsam J. J Am Chem Soc 1992;114:7189; Falcioni M, Deem MW. J Chem Phys 1999;110:1754. [*31] Pannetier J, Bassas-Alsina J, Rodriguez-Carvajal J, Caignaert V. Nature 1990;346:343. [32] Bush TS, Catlow CRA, Battle PD. J Mater Chem 1995;5:1269. [33] Boisen Jr. MB, Gibbs GV, O’Keeffe M, Bartelmehs KL. Microporous Mesoporous Mater 1999;29:219. [34] Freeman CM, Newsam JM, Levine SM, Catlow CRA. J Mater Chem 1993;3:531. ¨ JC, Jansen M. J Appl Crystallogr 1999;32:864. [35] Putz H, Schon [36] Woodley SM, Battle PD, Gale JD, Catlow CRA. Phys Chem, Chem Phys 1999;1:2535. ¨ JC, Jansen M. Comput Mater Sci 1998;11:309. [37] Putz H, Schon [38] Mellot-Draznieks C, Newsam JM, Gorman AM, Freeman CM, ´ Gerey G. Angew Chem Int Ed 2000;39(13):2270–5. ´ [39] Mellot-Draznieks C, Girard S, Ferey G. J Am Chem Soc 2002;124:15326–35.