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J. Phys. Chem. C 2010, 114, 19116–19126
Accurate Prediction of Hydrogen Adsorption in Metal-Organic Frameworks with Unsaturated Metal Sites via a Combined Density-Functional Theory and Molecular Mechanics Approach Michael Fischer,† Bogdan Kuchta,‡ Lucyna Firlej,§ Frank Hoffmann,† and Michael Fro¨ba*,† Institute of Inorganic and Applied Chemistry, Department of Chemistry, UniVersity of Hamburg, Martin-Luther-King-Platz 6, D-20146 Hamburg, Germany, Laboratoire Chimie ProVence, Centre de Saint-Je´roˆme, UniVersite´ de ProVence, F-13397 Marseille Cedex 20, France, and LVCN, UniVersite´ Montpellier 2, Place Euge`ne Bataillon, F-34095 Montpellier Cedex 5, France ReceiVed: June 26, 2010; ReVised Manuscript ReceiVed: August 29, 2010
The incorporation of coordinatively unsaturated metal sites in microporous metal-organic frameworks (MOFs) has emerged as an important synthetic strategy for the development of potential room-temperature hydrogen storage materials, because the relatively strong, localized interaction of hydrogen with the metal centers induces an increase of the isosteric heat of hydrogen adsorption. Previous modeling studies have shown that these interactions are not adequately modeled when literature force-field parameters are used. Typical results of grand-canonical Monte Carlo (GCMC) simulations exhibit a pronounced underestimation of the hydrogen uptake at low pressures and low temperatures. In this study, it is shown that this shortcoming can be resolved by deriving a new set of potential parameters to represent the metal-dihydrogen interaction from ab initio calculations for molecular model systems. The approach is computationally efficient and could be applied for any coordination environment of the metal center. The present work focuses on three MOFs with unsaturated copper centers. The newly derived Cu-H2 potential model is combined with literature force-field parameters to model the dispersive interactions with other framework atoms. At cryogenic temperatures and pressures up to 1 bar, GCMC simulations using these parameters provide for a massively improved prediction of the hydrogen storage characteristics when compared to parameters from a literature force field. On the other hand, the unmodified literature parameters perform best in predicting the saturation uptake. At room temperature, the effect of the potential modification is much smaller, and the best agreement with experiment is obtained when the localized metal-dihydrogen interaction is not accounted for in the simulations. This indicates that the metal-dihydrogen interaction is too weak to permit a significant adsorption at the metal sites under these conditions. Calculations using an artificially enhanced potential model show that a drastic increase of the interaction strength could boost the hydrogen storage capacity at room temperature, although the attainable uptake remains limited by the number of available metal sites. The implications of these results for the synthesis of new MOFs are critically discussed. Introduction The safe and efficient storage of hydrogen remains a bottleneck in the replacement of gasoline-operated engines by fuel cells, particularly in mobile applications.1 Recently, much scientific effort has been directed toward the development of new materials with improved hydrogen storage characteristics in terms of gravimetric and volumetric storage density, delivery properties, and economic efficiency.2,3 Among the materials based on the physisorption of molecular hydrogen (as opposed to chemisoprtion, e.g., in hydrides), highly porous metal-organic frameworks (MOFs) have evolved as particularly promising materials, providing for a gravimetric (excess) hydrogen uptake which may exceed 7 wt % at moderate pressures (40-70 bar) and a temperature of 77 K.4-6 However, the performance of these compounds at room temperature is still far from satisfactory, because the solid-fluid interactions are too weak to allow * To whom correspondence should be addressed. E-mail: froeba@ chemie.uni-hamburg.de. Phone: (+49)-40-42838-3137. Fax: (+49)-40-428386348. † University of Hamburg. ‡ Universite´ de Provence. § Universite´ Montpellier 2.
for a significant uptake under noncryogenic conditions. The strength of these interactions is characterized by the isosteric heat of adsorption, qst, for which an optimal value of 15 kJ mol-1 has been estimated for H2 storage at ambient temperature,7 while the values of typical MOFs lie below 10 kJ mol-1. It has been recognized that the presence of coordinatively unsaturated metal sites can enhance the solid-fluid interactions,8 and isosteric heats of adsorption of up to 12.3 kJ/mol have been reported for these systems.9 These relatively large values of qst have been reached at cryogenic temperatures and very low coverages only, and it must be kept in mind that the isosteric heat depends on both coverage and temperature.10 As a complement to experimental studies, molecular simulations are a widely employed tool to predict the hydrogen adsorption characteristics of MOFs.11-13 In particular, forcefield-based grand-canonical Monte Carlo (GCMC) simulations permit the calculation of an adsorption isotherm for any desired temperature at a moderate computational expense. Furthermore, the isosteric heat of adsorption can be derived from the simulations, and simulation snapshots and density/energy distributions deliver insights into the structural features which determine the adsorption behavior. Most studies in the field rely
10.1021/jp1058963 2010 American Chemical Society Published on Web 10/19/2010
Hydrogen Adsorption in Metal-Organic Frameworks on “generic” parameters from literature force fields, although there have been some attempts to derive new parameter sets from quantum-mechanical calculations.14,15 However, a general advantage of this more elaborate approach yet has to be proven, as the generic parameters often perform surprisingly well. While a good agreement between simulation and experiment has been observed in numerous studies of different MOFs,16,17,18 deviations have frequently been reported for systems with coordinatively unsaturated metal sites (also termed “open” metal sites): A combined experimental and theoretical study of Cu3(btc)2, a well-studied MOF containing unsaturated copper centers, revealed a significant underestimation of the hydrogen uptake at pressures below 1 bar and cryogenic temperatures, whereas the agreement between simulation and experiment at high pressures was excellent.19 A subsequent investigation showed that the inclusion of charge-quadrupole interactions does not significantly improve the prediction of the low-pressure isotherm.20 Similarly, a necessity to adjust some of the force-field parameters to reproduce experimental data was observed in a molecular simulation study of hydrogen adsorption in MOF-505.21 A more recent investigation covering several MOFs with and without unsaturated metal sites showed that a systematic underestimation of the low-pressure isotherm at T ) 77 K occurred only for those systems which contain coordinatively unsaturated metal centers.22 Furthermore, no increased hydrogen density was visible at the metal sites in the calculated density distribution. These observations were rationalized in the way that the interactions of hydrogen with the metal sites is not dominantly of a dispersive type, and thus not included in simulations that account for van der Waals interactions only. This is in line with the short metal-deuterium distances of 2.3-2.6 Å observed in neutron diffraction experiments of D2loaded MOF samples, which are significantly lower than typical van der Waals contacts (>3 Å).8,23,24 While standard molecular modeling approaches have been shown to fail in the description of the interaction of hydrogen with unsaturated metal sites, density-functional theory (DFT) calculations can provide valuable insights on a atomistic level. This methodology has been used both for molecular model systems25-27 and periodic MOF structures.28-30 It should be noted that hydrogen is not the only sorbate species for which a specific attraction to the metal centers exists. For example, spectroscopic measurements indicate an increased interaction of CO2, CO, and NO with the open copper sites in Cu3(btc)2.31 Another MOF with unsaturated copper sites exhibits a high selectivity for carbon dioxide over methane due to the strong interaction of the CO2 molecules with the metal sites.32 Experimental measurements and subsequent theoretical investigations show that the high acetylene storage capacity of Cu3(btc)2 is also due to the preferential adsorption of C2H2 at the copper sites.33,34 Similarly, combined experimental and simulation studies of propylene adsorption in the same system give evidence for a strong Cu-π bonding.35,36 In this study, a combined approach is used to bridge the gap between the ab initio methods, which are able to capture the interaction of hydrogen with unsaturated metal sites, but computationally too demanding to predict macroscopic properties like adsorption isotherms, and force-field based methods, which fail to predict the metal-dihydrogen interaction in a standard setup. The first step involves the calculation of the potential energy curve of hydrogen adsorbed at an unsaturated metal center using DFT. Then, an appropriate potential function is fitted to this curve and integrated into the GCMC code. The interactions with all other framework atoms are treated with
J. Phys. Chem. C, Vol. 114, No. 44, 2010 19117 the conventional Lennard-Jones potential, permitting the usage of standard force-field parameters. An extensive set of GCMC calculations is run to explore the applicability of the improved potential, both at cryogenic temperatures and room temperature. Two Cu-MOFs with identical inorganic building units are used as reference systems, and additional calculations for a third MOF with copper in a different environment are employed to test the transferability of the potential model. The results are compared to available experimental data and simulation results obtained with standard force-field parameters. In order to assess the properties of a hypothetical system with a massively increased metal-dihydrogen interaction in terms of roomtemperature hydrogen storage, the potential parameters derived from the DFT calculations are complemented by artificially enhanced parameters. Models and Methods Choice of Model Systems. The presence of unsaturated metal sites has been evidenced for a number of structurally different MOFs.8 In many cases, however, the coordination environment of the metal centers is a unique feature of the MOF, implying that every new system would require a repetition of the procedure outlined above. An exception is the Cu2(OOCR)4 paddle wheel, which is a common building unit of many CuMOFs. In order to develop a model that can be applied for more than one system, two MOFs containing these building units were chosen, namely, Cu3(btc)2 (btc )1,3,5-benzene-tricarboxylate) and PCN-12. Cu3(btc)2, also known as HKUST-1, is one of the most thoroughly characterized MOFs.37 The structure of Cu3(btc)2 consists of Cu2 paddle wheels connected by trigonal btc linker molecules, leading to a cubic pto topology (pto ) Pt3O4) with a bimodal pore size distribution. PCN-12 is the tetragonal polymorph of Cu2(mdip) (mdip )5,5′-methylene-diisophthalate).38 In this system, the connectivity of the nonlinear linker molecules leads to the formation of cuboctahedral cages, with the unsaturated metal centers pointing toward the cage center. Moreover, the structure of PCN-12 contains many small pores and pockets with diameters
