Progress, Opportunities, and Challenges for Applying Atomically

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Ind. Eng. Chem. Res. 2009, 48, 2355–2371

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Progress, Opportunities, and Challenges for Applying Atomically Detailed Modeling to Molecular Adsorption and Transport in Metal-Organic Framework Materials Seda Keskin,† Jinchen Liu,‡,§ Rees B. Rankin,‡,§ J. Karl Johnson,‡,§ and David S. Sholl*,† School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, National Energy Technology Laboratory, Pittsburgh, PennsylVania 15236, and Department of Chemical and Petroleum Engineering, UniVersity of Pittsburgh, Pittsburgh, PennsylVania 15261

Metal-organic framework (MOF) materials are a class of nanoporous materials that have many potential advantages over traditional nanoporous materials for adsorption and other chemical separation technologies. Because of the large number of different MOFs that exist, efforts to predict the performance of MOFs using molecular modeling can potentially play an important role in selecting materials for specific applications. We review the current state-of-the-art in the molecular modeling and quantum mechanical modeling of MOFs. Quantum mechanical calculations have been used to date to examine structural and electronic properties of MOFs and the calculation of MOF-guest interactions. Molecular modeling calculations using empirical classical potential calculations have been used to study pure and mixed fluid adsorption in MOFs. Similar calculations have recently provided initial information about the diffusive transport of adsorbed fluids in MOFs. 1. Introduction Microporous materials such as zeolites and activated carbons have long played a prominent role in many large-scale applications of chemical separations and catalysis. A crucial feature of these materials is that they contain large numbers of pores with widths on the order of 1 nm, that is, of a size similar to individual molecules. The strong confinement experienced by molecules inside these pores leads to physical and chemical properties that are extremely different from bulk properties. These properties often depend sensitively on the structure of the pore. Examples are known in zeolite adsorption and catalysis, for example, where small changes in pore structure lead to enormous changes in reaction selectivity or molecular diffusion rates.1,2 Over approximately the past decade, metal-organic framework (MOF) materials have attracted a great deal of attention as a new addition to the classes of microporous materials mentioned above. MOFs are composed of metal ligand complexes forming vertices of a framework that is connected with organic linkers that form porous structures with pores of molecular dimensions. Much of the excitement associated with MOFs stems from the fact that their synthesis can be readily adapted to control pore connectivity, structure, and dimension by varying the linkers, ligands, and metal in the material. This type of “rational design” of pore structures has been elusive in the development of more traditional microporous materials. A number of comprehensive reviews are available describing experimental synthesis and characterization of MOFs.3-9 The pores in these MOFs have characteristic diameters or widths on the order of 1 nm. There has been a rapid growth in the number of publications relating to MOFs over the past decade or so. The interest in MOFs stems from potential applications of these materials in gas storage,9-15 separation,16-23 and * To whom correspondence should be addressed. E-mail: david.sholl@ chbe.gatech.edu. † Georgia Institute of Technology. ‡ National Energy Technology Laboratory. § University of Pittsburgh.

catalysis.8,24 MOFs typically have extraordinarily low densities (0.2-1 g/cm3) and high surface areas (500-4500 m2/g), which make them interesting for gas storage and separation applications.14 Most of the publications relating to MOFs are experimental in nature. Thousands of different MOFs have been synthesized to date.24-35 However, the enormous number of different possible MOFs means that purely experimental means for designing optimal MOFs for targeted applications is inefficient at best. Atomic-level simulations provide a means to complement experimental methods for screening MOFs.21 There have been numerous papers reporting various modeling efforts relating to MOFs. The aim of this paper is to review atomically detailed modeling of MOFs. Section 2 deals with ab initio quantum mechanical modeling of MOF and MOF-guest interactions, while the remaining sections describe calculations based on classical force fields. Modeling of pure fluid adsorption in MOFs is covered in section 3. Section 4 reviews work on modeling of the adsorption of mixed fluids. Section 5 presents modeling of diffusion and transport of gases in MOFs. Finally, we present the conclusions and outlook for the future in section 6. 2. Quantum Mechanics Calculations for MOFs Quantum mechanical (QM) calculations employ approximations to the multibody Schro¨dinger equation for a system in order to compute properties of interest. An enormous variety of QM approaches exist that vary in both their accuracy and computational complexity. As we will discuss below, methods that give reliable information for one property of a system (for example, the lattice constant of a periodic material) do not necessarily give reliable results for other properties (for example, the binding energy of weakly physisorbed molecules). This means that understanding the limitations of any QM approach is crucial in using information from these calculations in describing complex materials. Below, we review QM calculations for several distinct properties of MOFs, ordered roughly in terms of decreasing accuracy of the calculations: (1) lattice

10.1021/ie800666s CCC: $40.75  2009 American Chemical Society Published on Web 08/20/2008

2356 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 Table 1. Lattice Constants of IRMOF-1 As Calculated in Various Periodic DFT Calculations authors Bahret al.

36

DFT functional/methods

lattice constant (Å)

Mueller and Ceder40 Mulder et al.41 Samanta et al.43 Fuentes-Cabrera et al.38 Civalleri et al.37

PAW-GGA PAW-LDA PBE-GGA USPP-GGA PAW-LDA USPP-LDA B3LYP-GGA

26.04 25.59 26.14 25.84 25.64 25.61 26.09

Mattesini et al.39 Sagara et al.47 Zhou et al.44 Li et al.32

PZ-LDA 6-31G* PBE P-Z USPP-LDA experiment

25.89 25.77 25.58 25.88

constants and geometries, (2) elastic properties and dynamics, (3) atomic point charges, and (4) molecular physisorption interactions. 2.1. MOF Lattice Constants and Atomic Geometries. Multiple groups have used density functional theory (DFT) calculations to calculate the lattice constant of IRMOF-1.36-44 Results from calculations that used the full periodicity of the material are summarized in Table 1. The DFT calculations range within (1% of the experimental value, with results from GGA (LDA) functionals tending to slightly overestimate (underestimate) experimentally measured values. Similar results were seen by Nagaoka et al.45 in their LDA calculations of CPL-1 and CPL-2. Ramsahye et al. employed DMOL GGA calculations to calculate the extended structure of MIL-53.46 Fuentes-Cabrera et al. used periodic DFT calculations to examine how metal atom substitutions into IRMOF-1 changed the material’s lattice constant and electronic structure.38 The largest observed lattice constant was for Ca substituents (26.94 Å). The calculated band gap was found to be insensitive to the substituted metal atom, at ∼3.5 eV. It should be noted that DFT calculations of this kind typically substantially underestimate band gaps. An alternative to fully periodic DFT calculations is to apply DFT (or other QM methods) to clusters representing MOF structures. Although cluster calculations do not reproduce the full extended geometry of the material, they have advantages in terms of applying all-electron basis sets. Civalleri et al. compared cluster-based calculations to periodic calculations for IRMOF-1.37 Agreement between the bond lengths and bond angles from their calculations tend to be within 1.5% of those observed from experiment. Gao48 and Braga et al.49 have examined clusters representing portions of IRMOF-1, establishing that geometric aspects of these clusters agree well with experimental data for the full material when appropriate basis sets are chosen. Other examples of cluster calculations for MOFs include linker groups of IRMOF-3, -6, -8, -12, -14, -18, and -993,42 linkers in IRMOF-2 and -3,49 fragments of CuBTC,23,50 and fragments of IRMOF-105.51 2.2. MOF Elastic Properties and Dynamics. For dense materials such as metals and metal oxides, calculating elastic properties with periodic DFT calculations is straightforward. The calculations reported to date for MOFs, however, indicate that extracting accurate elastic properties for these materials may be more challenging. Bahr et al.36 using periodic DFT calculations initially found disagreement in Young’s modulus for IRMOF-1 as compared to experiment: values of 20 (calculated) versus 2 GPa (experimentally measured). By applying corrections for anisotropy in the elastic response of the bulk crystal, the experimentally measured Young’s modulus increased from 2 to 8 GPa. It should be noted that the IRMOF-1 samples measured experimentally were observed to undergo plastic deformation in testing, an observation that complicates the

additional comments

deviation from Fm3j space group reported also substituted metal cations in the framework band gap 5.0 eV; comparison of full periodic to cluster based calculations space group Fm3jm experimental value

interpretation of the experiments. Mattesini et al.39 also used periodic DFT to calculate the elastic constants of IRMOF-1; their calculated Young’s modulus is 14.8 GPa. Although periodic DFT calculations accurately predict the Young’s modulus of dense silica polymorphs (specifically, quartz and cristobalite), large discrepancies have been seen between calculated and measured results for silicalite, a zeolitic silica.52 Astala et al. have discussed how this discrepancy may be related to the presence of twinning defects in silicalite crystals,52 and it is possible that similar effects are important for MOFs. The work of Astala et al. also provides a useful discussion of the subtleties associated with calculating the Young’s modulus from the stress tensor in an anisotropic material. Zhou et al.44 calculated shear moduli, elastic constants, and phonon density of states for IRMOF-1 using periodic DFT calculations. There is some disagreement between the work of Zhou and Mattesini on the elastic constants. The effects of substituting various metal atoms into IRMOF-1 on the material’s bulk modulus were calculated by Fuentes-Cabrera et al.38 DFT calculations can provide insight into spectroscopic characterization of MOFs. Zhou et al.44 calculated phonon dispersion curves for a fully periodic IRMOF-1 lattice. They also estimated that the barrier for linker twisting in IRMOF-1 is 48 kJ/mol, implying that room-temperature inversion is not likely to occur. Vibrational frequencies for the atoms in the IRMOF-1 lattice have also been computed by two other groups. Civalleri et al.37 have examined the full lattice framework and calculated the vibrational frequencies using periodic DFT methods in the CRYSTAL package with DFT B3LYP calculations. Tafipolsky et al.53 used a cluster approach to compute vibrational frequencies for IRMOF-1 with DFT B3LYP. Agreement between the two studies is not quantitatively strong for active modes with frequencies under 1000 cm-1. Typical differences for similar modes in this range of frequencies are on the order of 10% between the two calculations. Tafipolsky et al. compared their results to experimental IR spectra and concluded that the calculated results are qualitatively accurate for modes with frequencies up to ∼1400 cm-1. 2.3. Atomic Point Charges. As we will see below, force field-based classical calculations of MOFs typically treat electrostatic interactions between adsorbates and MOFs by assigning fixed point charges to each atom. An important role for QM calculations in this context is to assign the point charges that can later be used in force field calculations. Unfortunately, multiple methods exist for partitioning the net electron density determined in a QM calculation, and none of these methods give an unambiguous definition of the resulting point charges. Quantum mechanical calculations of MOFs have been used to develop atomic point charges for the atoms in the framework for use in force fields for classical simulations. Table 2 presents the results available for IRMOF-1. There is significant variation

Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 2357 Table 2. Partial Charges Assigned to Atoms in IRMOF-1 on the Basis of QM Calculationsa authors 53

Tafipolsky et al. Yang et al.50 Sagara et al.47 Civalleri et al.37 a

calculation method

charge calculation method

qOcent

qZn

B3LYP DFT for cluster B3LYP DFT for cluster 6-31+G* PBE DFT for cluster B3LYP DFT for cluster

Merz-Kollman ChelpG ChelpG Born effective charges

-1.44 -1.85 -1.79 -1.1to -2.0

1.26 1.50 1.31

The charges on oxygen and zinc in the metal ligand are represented by qOcent and qZn, respectively.

Table 3. Similar to Table 2 but for MOFs Other Than IRMOF-1a authors 23,50

Yang and Zhong Yang and Zhong51 Ramsahye et al.46,54,55 Belof et al.56

material

calculation method

charge calculation method

CuBTC MOF-505 MIL-47 (V) MIL-53 (Al) SOC-MOF

B3LYP DFT for cluster B3LYP DFT for cluster PW-91 DFT for cluster

ChelpG ChelpG Mulliken

HF calculation

GAMESS fitting

qO

metal and qM

-0.67, Ocarb -0.66, Ocarb -0.50, Ocarb, -0.60, OAl -0.56, Ocarb, -0.73, OAl -1.39 to -1.54, OIn

Cu 1.11 Cu 1.10 V 1.21 Al 1.42 In 2.07 to 2.23

a

Ocarb, OAl, and OIn denote O atoms in carboxylate groups, bridging between Al atoms, and in the 3-fold coordinated positions relative to In atoms, respectively.

in the calculated results, with values for the charge on oxygen (zinc) varying by almost 0.9 (0.45) e. Variations of this magnitude may have a significant impact on the outcome of classical force field calculations in examples where electrostatic interactions are important. Because the methods for assigning local charges within QM cluster calculations are typically not currently implemented in periodic QM calculations, it remains unclear whether the use of a cluster-based approach for the results in Table 2 rather than the full periodic structure plays a significant role on the local atomic charges. Table 3 summarizes the atomic partial charges assigned using QM calculations on MOF materials other than IRMOF-1. None of these materials has been examined by more than one group to date. One striking observation from these results is that charges for O atoms in carboxylate groups, Ocarb, in several of these materials are considerably smaller than the charges seen for O atoms in the metal ligand in IRMOF-1. The variation between these Ocarb charges in these materials is nearly as large as was the case for IRMOF-1 Ocent charges. It is not currently clear how much of this variation in O charges is characteristic of differences in the real bonding in the materials as opposed to simply differences in the charge fitting methods that have been used. 2.4. Molecular Adsorption. Using QM calculations to examine molecular adsorption in MOFs is more problematic than applying the same methods to the structural properties discussed above. The central problem is that only high level ab initio methods can describe dispersive (i.e., van der Waals) interactions with any degree of precision, because these interactions are a direct result of electron correlation effects. DFT calculations are notorious for not correctly describing dispersive interactions.57-64 Two distinct approaches to this challenge are evident in the literature. One approach is to simply accept the limitations of DFT methods and use these methods within fully periodic calculations to examine molecular adsorption. In our view, results from calculations of this kind should be interpreted with a heavy dose of skepticism; they cannot be expected to give quantitatively accurate interaction energies. The second approach is to use more accurate QM methods (e.g., MøllerPlesset theory). Unfortunately, these higher level calculations are extremely computationally intensive and can only currently be performed for small clusters representing MOFs. This difficulty does not only exist for MOFs, of course; the same challenges exist for describing van der Waals interactions of molecules with other adsorbing materials such as zeolites. 2.4.1. H2 Adsorption. Most QM calculations for molecular adsorption have focused on H2 because of interest in hydrogen

storage in MOFs. Unfortunately, the very weak interactions of H2 with MOFs (and most other materials) make this molecule perhaps one of the most challenging from the point of view of performing accurate QM calculations. Mueller et al.,40 Mulder et al.,41 and Sagara et al.47 have each reported results for H2 interactions with IRMOF-1 based on periodic DFT calculations. Other groups have used cluster-based QM calculations to probe the same interactions. Gao et al.48 used DFT and MP2 methods to study the adsorption on benzene-like linker fragments. The MP2 results fortuitously fall between LDA and GGA DFT results; we note that LDA and GGA calculations cannot be considered to be bounds on the binding energy in any rigorous sense. Binding energies were observed to be sensitive to H2 rotations by up to 5 kJ/mol. Lee et al.65 employed cluster calculations for fragments of IRMOF-1 using a variety of GGA functionals previously tested on benzene. This work suggested that high loading of H2 on the fragments could cause coupling in the interaction energies to help further increase the net adsorption energy per H2 adsorbed. Negri et al.66 used Gaussian calculations with the PW DFT functionals and also MP2 calculations to characterize H2 interactions with a suite of MOFlike cluster fragments. In all cases, the observed adsorption energies were weak: ranging from 0.5 to 5.9 kJ/mol-site. Sagara et al.47 supplemented their periodic DFT calculations on the material IRMOF-1 with MP2 calculations for the adsorption energy of representative fragment clusters and found binding energies of 4-9 kJ/mol-site on the benzyl linker areas and 10 kJ/mol-site on the ZnO fragment “corner” area. Bordiga et al.67 used DFT and MP2 calculations on representative fragment clusters; for most sites they reported binding energies of ∼3 kJ/mol-site. Besides the cluster calculations for representative fragments of IRMOF-1, the interaction of H2 with several other MOF materials has received attention in the literature. Han and Goddard have performed X3LYP and MP2 calculations to quantify the effect on H2 binding energy on moieties of MOFC6, 10, 16, 22, and 30 when doped with Li atoms,68 and RIMP2 calculations for the same MOF-based moieties when substituted with the metal cations Be and Mg.69 The results of their calculations show that H2 interacts with similar strength to Zn and Mg nodes in the MOFs (6.2, 6.8 kJ/mol, respectively) but ∼30% weaker with the Be nodes in the substituted MOFs. Sagara et al.42 characterized the adsorption sites and energies of H2 with linker groups of IRMOF-1, IRMOF-1-4NH2, IRMOF-3, -6, -8, -12, -14, -18, and -993 with MP2 calculations. In their work, it is observed that the larger linker groups tend to promote stronger interactions and that the linker group of

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IRMOF-8 can support 2 H2 adsorbed per side. Using DFT calculations, the interaction of H2 with IRMOF-505 has been studied by Yang et al.,51 and possibly in corroboration of the above point of Sagara, slightly larger binding energies are seen than in IRMOF-1; values of 8-14 kJ/mol were reported. However, because the interaction of H2 with MOFs is generally weak, the choice of QM methods used to calculate the interaction energy plays a critical role in the observed value and, hence, the reliability of the calculations. In particular, DFT results should be interpreted cautiously for the reasons stated earlier. 2.4.2. Adsorption of Other Gases. The interaction of CO2 has been characterized in IRMOF-1 by Dubbledam et al.,70 in MIL-53 and MIL-47 by Ramsahye et al.,54,55 and in CuBTC by Yang et al.23,50 In the work of Dubbledam et al., PBE DFT calculations were used to determine the effect of bond length and bond angle on the adsorption energy. Ramsahye using PW91 GGA calculations determined that CO2 binds strongly in MIL53 (∼35 kJ/mol) but almost not at all in MIL-47. It should be noted that the materials MIL-53 and MIL-47 are structurally identical except for an OH group extending into the pores. Yang employed atomic point charge characterization of CO2 and of the CuBTC material based on fragment B3LYP DFT calculations to parametrize classical simulations for the adsorption of CO2 in the CuBTC framework sites. In addition to the calculations mentioned above for CO2, Dubbledam et al. also used PBE DFT calculations to probe the adsorption sites of N2 in the material IRMOF-1. The CpPY MOF materials CPL-1 and CPL-2 have been studied by Nagaoka et al.45 using fullperiodic PZ-LDA DFT calculations to characterize the bonding sites, bond lengths, and angles of O2. In this work, they reported an O2 binding energy of ∼40 kJ/mol at the lowest energy bonding site. Yang et al.23,50 have also performed B3LYP DFT calculations to characterize the point charges of CH4 for parametrization of classical simulations to study the adsorption of CH4 in the MOF material CuBTC. The calculated adsorption energies for the examples just listed are ∼1 order of magnitude larger than those seen for H2. 2.5. Challenges and Opportunities for QM Calculations with MOFs. The status of using QM calculations to describe MOFs differs widely for the various physical properties that can be treated with these methods. QM calculations, particularly using spatially periodic DFT methods, are well suited to accurately describing structural properties of MOFs. Most work to date has focused on demonstrating the feasibility of this task via comparison with well-known experimental data. The main opportunity that exists with these methods lies in extending these calculations to sets of materials that have not yet been synthesized to seek materials with desirable structural properties. One application of QM calculations for MOFs is to assign partial charges to atoms in the frameworks that can later be used in a classical force field calculation. The accuracy of these kinds of calculations is much less than for structural properties because of the well-known complications associated with partitioning electron densities into unambiguous point charges. This challenge also exists in assigning charges in simulations of cationic zeolites.71,72 It is quite reasonable to use charges from these calculations in classical calculations, but it is worth keeping in mind that the precise value of these charges is dependent on the charge partitioning strategy applied to the QM results. It is clearly important in work of this type that consistency is maintained in the methods that are used if a variety of different materials are to be examined.

Although a number of calculations have applied QM methods to describe molecular adsorption in MOFs, the methods that are widely used today are not really suitable for this task. DFT calculations do not treat dispersion interactions accurately, so calculation of adsorbate binding energies that are computed with DFT cannot be expected to give quantitatively accurate results. This situation is completely analogous to work on properties of molecules inside zeolites, where DFT calculations are a useful tool for studying catalytic processes involving bond-breaking and bond-forming, but where physisorbed molecules are best described using empirical interatomic potentials that are parametrized using experimental data. 3. Molecular Simulation of Single-Component Adsorption in MOFs We now turn to molecular simulations of MOFs based on classical force fields. In calculations of this kind, force fields defining interactions between each pair of atoms in a system of interest are used. Once these force fields are specified, a broad range of molecular dynamics (MD) and Monte Carlo (MC) methods are available to probe dynamical and equilibrium properties of the simulated material. 3.1. Simulation Techniques. Adsorption isotherms are routinely calculated in atomistic simulations using the grand canonical Monte Carlo (GCMC) method.73,74 This method is analogous to the experimental procedure of specifying the temperature and external (bulk) pressure of a gas and measuring the uptake as a function of these variables. It is the chemical potential of the adsorbate that is specified in GCMC simulations, rather than the bulk pressure. The chemical potential can easily be related to the bulk pressure through an equation of state or separate bulk-phase simulations. The GCMC simulation technique has been used extensively to calculate adsorption isotherms for gases in MOFs. Adsorption of hydrogen in MOFs has been the focus of many of the simulation studies in the literature.47,51,68,69,75-83 The interest in H2 adsorption is largely a result of experimental claims regarding the potential for MOFs as H2 storage materials.9 Hydrogen exhibits quantum effects at low temperatures and high densities, and therefore, quantum effects must be taken into account when adsorption isotherms are calculated at low temperatures. Path integral Monte Carlo84,85 simulations and Feynman-Hibbs (FH) effective potential methods86,87 have been used to account for H2 quantum effects during adsorption in MOFs at temperatures below 100 K. 3.2. MOF Models. Most adsorption simulations performed to date have assumed that the framework atoms in MOFs are rigid. The framework atoms are fixed at their crystallographic positions, which are usually obtained from X-ray experiments. To date, several general-purpose force fields have been used in MOF adsorption simulations, including the universal force field (UFF),88 DREIDING,89 and optimized potential for liquid simulations all-atom (OPLS-AA)90 force fields. Quantum mechanical calculations have been carried out in some cases in order to develop potentials for specific MOF-adsorbate interactions.47,91 Charges on the framework atoms were included in the calculation of adsorbate-adsorbent interactions for some polar (including quadrupolar) adsorbates.22,23,92 Calculation of the charges on the MOF atoms was previously addressed in section 2.4. Only two simulation studies have considered the effects of sorbent-induced structural changes due to the flexibility of the framework.46,54 In most cases, framework flexibility should not significantly influence the equilibrium adsorption isotherms. For

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example, the MOF known as Zn(bdc)(ted)0.5 (bdc ) 1,4-benzenedicarboxylate, ted ) triethylenediamine) is known to have two different crystal structures, one with the solvent (guest) molecules in place93 and one where the solvent molecules have been removed.94 Hydrogen isotherms for both structures (in the absence of solvent molecules) have been calculated and shown to be almost identical.80 This indicates that slight changes in the MOF structures may not have a large impact on the measured adsorption isotherms, at least for some light gases. The flexibility does however need to be considered when the adsorbent deforms substantially in response to adsorption.46,54,95,96 Potential Models for Adsorbates. Hydrogen is one of the most widely studied adsorbates in MOFs to date.47,51,68,69,75-83 Three different types of fluid-fluid potential models81,97-99 for H2 have been used to study adsorption in MOFs.47,51,68,69,75-83 Spherical 12-6 Lennard-Jones (LJ) models97,98 are the most commonly used, of which the Buch potential97 is known to reproduce the experimental bulk equation of state accurately.79,100 Two-site LJ models have also been used to compute adsorption isotherms.81,82 The potential model of Darkrim and Levesque99 has been used to account for the quadrupole moment of H2 molecules;70,78 this potential consists of a LJ core placed at the center of mass of the molecule and point charges at the position of the two protons and the center of mass. Methane and argon adsorption simulations have been performed using spherical LJ potentials.101-104 Nitrogen adsorption simulations have been performed using the following potential models: a spherical LJ potential,105 a two-site LJ potential,106 and a two-site LJ potential with three charges to represent the quadrupole moment.107 Oxygen adsorption simulations have employed a two-site LJ potential with three charges to represent the O2 quadrupole moment.108 The CO2 potentials used all consist of three LJ sites with charges located on each site to represent its quadrupole moment.107,109,110 The adsorption isotherms for alkanes in MOFs70,111 have been calculated using the TraPPE potential.112 3.3. Simulated Isotherms for Existing MOFs. It is reasonable to assume that if the potential models used in an adsorption simulation are accurate, then the simulations should quantitatively reproduce the experimental adsorption isotherms. There are several issues that should be considered when comparing simulations with experimental data. First, one must be careful to look at a wide pressure range. It is unreasonable to compare simulations with experiments over a very narrow range, e.g., 0-1 bar, and assume that good (or poor) agreement with experiment will continue to high pressure. For example, Yang and Zhong81 have fitted the interaction potential parameters for H2-IRMOF-1 using experimental data up to 1 bar at 77 K. They then predicted the high-pressure adsorption isotherm up to 100 bar.81 In Figure 1, we have compared their prediction with available experimental data from three different groups.13,113,114 It can be seen that simulations overpredict experiments by more than 100% at the highest pressure, even though their low-pressure data are in excellent agreement with experiments. Similar issues apply for temperature effects, where it is best to compare isotherms that span a range of temperatures with experimental data before making definitive claims regarding the accuracy of model potentials. A second issue that is crucial in developing interatomic potentials for adsorption in MOFs is to consider the accuracy of the experimental data with which simulations are compared. For example, as-synthesized MOFs may have defects or trapped residual solvent molecules present in the samples. Liu et al.79

Figure 1. Comparison of the predicted high-pressure H2 adsorption isotherm in IRMOF-1 by Yang and Zhong81 with experiments at 77 K. Circles: simulations by Yang and Zhong.81 The triangles, diamonds, and squares are experimental data from Wong-Foy et al.,13 Panella et al.,113 and Dailly et al.,114 respectively.

Figure 2. Comparison of experimental H2 adsorption isotherms in CuBTC at 77 K from different groups at low pressure, 0 < P < 1 bar. Filled circles, Liu et al.79 (CuBTC-MeOH); filled squares, Rowsell and Yaghi;115 filled down-triangles, Xiao et al.;116 filled stars, Krawiec et al.;117 crosses, Peterson et al.;118 half-filled squares, Wong-Foy et al.;13 half-filled circles, Liu et al.79 (CuBTC-CH2Cl2); filled diamonds, Lee et al.;119 filled up-triangles, Prestipino et al.120

have compared H2 adsorption isotherms at 77 K in CuBTC as measured by different groups, reproduced here as Figures 2 and 3. The amount of gas adsorbed experimentally varies significantly among the experimental reports. This indicates that the purity or integrity of the samples used by different groups can have a significant effect on the measured isotherms. It is important to note that this issue is more challenging to address experimentally for MOFs than in other nanoporous materials such as zeolites, where guest species can be removed simply by calcining samples at high temperatures because MOFs generally have much less stability at high temperatures than zeolites. This discussion highlights the risks associated with developing interatomic potentials based on experimental data from just one material sample, particularly if data are only available for a limited range of physical conditions. To maximize their reliability, interatomic potentials for adsorption in MOFs should be based on experiments from a broad range of physical conditions using data from multiple samples measured in distinct

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Figure 3. Comparison of experimental H2 adsorption isotherms in CuBTC at 77 K from different groups for the high-pressure regime, 0 < P < 50 bar. Filled circles, Liu et al.79 (CuBTC-MeOH); filled down-triangles, Xiao et al.;116 filled squares, Panella et al.;113 filled diamonds, Liu et al.;79 (CuBTC-CH2Cl2); filled up-triangles, Wong-Foy et al.13

laboratories whenever this is practical. Systematic efforts to collect experimental data of this kind for representative materials would be of great value for ongoing development of reliable modeling methods. 3.3.1. H2 Adsorption in MOFs. The first reported simulations of H2 in a MOF were those of Kawakami et al.75 They reported simulation results for H2 adsorption in Zn3(bdc)3 at a temperature of 20.28 K and at two pressures, 9.87 × 10-6 and 0.95 atm. They predicted that H2 will completely fill the Zn3(bdc)3 pores, even at the lowest pressure of 9.87 × 10-6 atm. Quantum effects are very important for liquid hydrogen.100,121 Unfortunately, Kawakami et al. ignored quantum effects, making the accuracy of their predictions uncertain. Frost and co-workers76,77 have studied H2 adsorption in MOFs. Their simulation results agree well with the experimental results for IRMOF-1 and IRMOF-8 for pressures up to 1 bar at 77 K.77 They have also studied the relationship between the amount of H2 adsorbed and the heat of adsorption, the surface area, and the pore volume for a variety of different MOFs at 77 K, including IRMOF-1, -4, -6, -7, -8, -10, -12, -14, -15, -16, and -18. They observed that the amount adsorbed can be correlated with the heat of adsorption at low pressures (low H2 coverages), the surface area at intermediate pressures, and the free volume at high pressures, as long as the porous materials have the same framework topology and surface chemistry. Frost and Snurr76 have studied the heat of adsorption required to achieve an acceptable gravimetric H2 density in MOFs by artificially increasing the interaction potential between H2 and linker atoms. The outcome of this calculation agrees with the conclusions of Bhatia and Myers122 regarding the general properties needed in a physisorption material for it to be useful for hydrogen storage; the isosteric heat of adsorption for H2 needs to be 10-15 kJ/mol for H2. This value is far larger than the result that has been demonstrated in any MOF to date, where typical values are between 4 and 10 kJ/mol.78 Sagara et al.47 developed an ad hoc interatomic potential for H2 interaction with IRMOF-1. They calculated the charges on IRMOF-1 atoms and used point charges to represent the quadrupole moment of H2. The simulated H2 adsorption at 77 K overestimated the experiments.123 However, simulated H2 adsorption at 298 K underestimated the findings of experiments.124,125

Garberoglio et al.78 studied H2 adsorption at 77 K in manganese formate, IRMOF-1, and IRMOF-8 for pressures up to 1 bar and compared their results with experiments. They used both the UFF88 and DREIDING force fields89 for H2 adsorption in manganese formate and found that both force fields capture the trends observed in the experiments. We note in passing that the Zn potential from the DREIDING force field89 was used mistakenly in the UFF calculations reported in Figure 4 of ref 78. This resulted in ∼0.3 wt % higher adsorption than if the UFF potential had been used. By using path integral methods to account for the quantum effects in the simulations, results for H2 adsorption agree fairly well with experiments for adsorption in IRMOF-1 and IRMOF-8 up to a pressure range of 1 bar. They found that the H2 potential of Darkrim and Levesque,99 which includes charges on H2 to represent the quadrupole moment, overpredicted the experimental data, especially at low pressures. This overprediction was attributed to enhanced H2-H2 interactions. Thus, the authors recommended against using the Darkrim and Levesque model for H2 adsorption simulations. Garberoglio et al. computed H2 adsorption isotherms in IRMOF-1 and Cu-MMOM at 298 K for pressures up to ∼95 and 50 bar, respectively, and compared with experiments.124,125 The results of these simulations significantly underestimated those observed in corresponding experiments. The reason(s) for this large discrepancy still remains unclear. Garberoglio et al. also predicted the adsorption isotherms for H2 in MOF-2, MOF-3, IRMOF-1, -6, -8, and -14 at 77 and 298 K for pressure up to 100 bar. Based on the results of their predictions, none of the MOFs they have examined are able to meet the U.S. Department of Energy (DOE) targets126 at room temperature as H2 storage materials, especially when it is noted that these are system targets for a complete storage system that includes tanks, heat exchangers and all other balance of plant components. Liu et al.79 have compared simulated H2 adsorption isotherms with experimental isotherms in CuBTC at 77, 87, 175, and 298 K for pressures up to 50 bar. Their simulations at 77 K correctly predict the limiting (high-pressure) capacity when using the FH effective potential to represent quantum effects. Overall, their simulations tend to underestimate experimental results, especially in the low-pressure region. The underestimation could be due to the neglect of charge-quadrupole interactions in their calculations. In a separate paper, Liu et al.80 simulated H2 adsorption in Zn(bdc)(ted)0.5 and compared their calculations with experiments for pressure up to 50 bar at 77 and 298 K. They again included quantum effects at 77 K by using the FH effective potential. They used both UFF and DREIDING potentials to represent the MOF atoms. The simulated adsorption isotherms using these two potentials are slightly different. The experimental adsorption isotherms were bracketed by the simulated adsorption isotherms from the UFF and DREIDING potentials. They have also computed the delivered H2 amount relative to a discharged pressure of 1.5 bar at 77 K and compared the calculated values with those for CuBTC. Although Zn(bdc)(ted)0.5 has larger total adsorption compared with CuBTC, it has a smaller delivered amount of H2 for a discharge pressure of 1.5 bar. This is due to Zn(bdc)(ted)0.5 having a steep adsorption curve in the low-pressure region, meaning that more gas remained in the Zn(bdc)(ted)0.5 than in CuBTC at 77 K and 1.5 bar. They noted that a useful hydrogen storage material should not have too steep an isotherm at low pressures. Yang and Zhong51,81 have studied H2 adsorption in IRMOF1, -8, -18, and -505. They refitted portions of the OPLS-AA force field for the parameters describing the interaction between

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H2 and the atoms of the framework to match experimental results in the pressure range of 0-1 bar at 77 K. They then predicted the adsorption isotherms for pressures up to 100 bar for temperatures of 77 and 298 K. The interaction potential parameters obtained in this way are MOF dependent; thus, they are not transferrable potentials. The results from this work were shown in Figure 1 as one example where good agreement with experimental data in the low-pressure region (0-1 bar) may not guarantee the accuracy of the adsorption isotherms calculated for the high-pressure region. Jung et al.82 studied H2 adsorption in catenated MOFs, IRMOF-9, -11, and -13 at 77 K up to 1 bar. Catenated MOFs have self-interpenetrating structures. They found that the simulation results of hydrogen adsorption in IRMOF-11 and -13 agree with experimental data well.115,123 However, results calculated in IRMOF-9 overestimate the experimental data.115 The crucial finding of this study is that they showed that linker sites are the dominant sites for adsorption of H2 in catenated MOFs. For noncatenated MOFs, it is believed that sites close to the metal ligand groups are the most attractive sites for adsorption.51,70 Han and co-workers68,69 have studied the adsorption of H2 in IRMOF-1, IRMOF-8, and IRMOF-14. They have developed a force field in part using quantum mechanics results for H2 interactions with the MOFs and then used this force field to calculate the adsorption isotherms. Their simulated isotherms coincidentally agree reasonably well with experiments for IRMOF-1 at pressures of 1, 20, and 50 bar and for IRMOF-8 at a pressure of 1 bar at 77 K.13,123 Simulations overpredicted the experiments by 0.1 wt % for IRMOF-1 at 60 bar and IRMOF-8 at 30 bar at 298 K. We have previously discussed in section 2.4.1, the difficulties in computing weak dispersive interactions of H2/MOF using QM methods; as such, the general accuracy of the force field and such an approach is not expected to be systematic. Garberoglio83 studied H2 adsorption in MOF-related materials known as covalent organic frameworks, COF-102, -103, -105, and -108. He used FH effective potential to represent quantum effects at both 77 and 298 K. It has been shown that FH effective potential overestimates the quantum effects at 298 K.79 Garberoglio found that the amount of H2 adsorbed in COFs is larger than that in IRMOF-1478 by as much as 50%. The amount of H2 adsorbed is slightly larger than 10 wt % at P ∼100 bar in COF-105 and COF-108 at 77 K. However, the amount of H2 adsorbed in all the COFs is only ∼0.8 wt % at P ∼100 bar and 298 K, still far below the U.S. DOE 2010 target of 6 wt % on a system basis.126 Zhang et al.127 have studied the H2 adsorption sites inside IRMOF-1 at 30 K using the so-called “computer tomography for materials” (mCT) method. The mCT method calculates the overall-average distribution of adsorbate molecules in threedimensional space. They found that the strongest adsorption site is near the location of oxygen atoms where three COO groups are joined; this is consistent with experimental observations.14,128 They also calculated H2 adsorption isotherms in IRMOF-1 at 77 K; the simulated isotherms agree well with experiments for pressure up to 1 bar.123 Quantum effects were not taken into account in these studies. 3.3.2. Alkane Adsorption in MOFs. Sarkisov et al.111 predicted the adsorption isotherms for methane, n-pentane, n-hexane, n-heptane, cyclohexane, and benzene in bipyridine molecular squares and IRMOF-1 at 300 K. The adsorption properties of amorphous randomly packed bipyridine molecular squares are very different from their crystalline counterparts.

The randomly packed structures have more pores than the crystalline compound and, therefore, showed higher adsorption at high pressures but lower adsorption at low pressures. The authors noted that an artificial filling of the narrow channels of the bipyridine molecular squares that are kinetically inaccessible can occur in GCMC simulations. This insertion of molecules in kinetically inaccessible pores is a shortcoming of the GCMC method; this effect should be considered when performing GCMC simulations of any porous material that has pores that may be inaccessible to diffusing molecules. Coulombic interactions between the adsorbate and framework atoms were shown to play an important role for benzene adsorption in crystalline bipyridine molecular squares. Du¨ren et al.10 investigated the adsorption properties of IRMOF-1 and -6 for CH4 storage. They compared their results with CH4 adsorption in other materials, including zeolites, MCM-41, and single-walled carbon nanotubes. The simulated adsorption isotherms for CH4 in IRMOF-1 and -6 agree quantitatively with experiments for pressures up to 40 bar at 298 K. Similarly, Du¨ren and Snurr17 studied the influence of the linker molecule on the adsorption of CH4 and n-butane in IRMOF-1, -8, -10, -14, and -16. They concluded that the maximum amount adsorbed increases with increasing pore size, as might be expected. Garberoglio et al.78 studied CH4 adsorption in CuBTC at 295 K and in manganese formate at 195 K for pressure up to 1 bar. The simulated isotherms overestimated experimental studies20 by ∼10% for CH4 in CuBTC. The reason for the difference was attributed to the defects in the experimental CuBTC crystal or the solvent remaining inside the pores after synthesis as indicated by the low pore volume of the sample compared with the ideal crystal.79 The simulated CH4 isotherms in manganese formate do not qualitatively agree with experiments, with the experimental and simulation differing by roughly a factor of 4 at 1 bar.129 Garberoglio83 also computed CH4 adsorption in COF-102, -103, -105, and -108 using both UFF and DREIDING force fields. The amount adsorbed depends significantly on the force field. There is as much as a 20% difference between the amounts adsorbed as calculated by UFF and DREIDING force fields. He found that COF-102 shows the largest CH4 adsorption amount. This material exceeds the DOE target of 180 cm3 (STP)/ cm3 for P ) 35 bar and T ) 298 K.130 Yang and Zhong23,50 studied CH4 adsorption in IRMOF-1 for pressures up to 40 bar and the adsorption of CH4 and C2H6 in CuBTC for pressure up to 1 bar at 298 K. They fitted part of the OPLS-AA force field parameters for CH4 to match experiments, similar to the approach used in their work on H2 and CO2.51,81 Wang131 studied methane adsorption in CuBTC, CPL2, CPL-5, Cu(SiF6)(bpy)2, Cu(GeF6)(bpy)2, and IRMOF-1, -6, -8, -10, and -14 at 298 K for pressures up to 100 bar. He used the same potential parameters for CuBTC and IRMOFs as those obtained by Yang and Zhong.23,50 Following the work of Yang and Zhong,23,50 he refitted some of the OPLS-AA force field parameters for other MOFs to yield better agreement with the experimentally determined adsorption isotherms. He then studied the relationship between the amount CH4 adsorbed and the heat of adsorption, the surface area, and the pore volume. The results he obtained are similar to those of H2 adsorption in MOFs,77 namely, that there is a strong correlation between the amount adsorbed at low, medium, and high coverage, and the heat of adsorption, surface area, and pore volume, respectively. Jiang and Sandler132 have investigated the adsorption isotherms of linear alkanes (CH4-n-hexane) and hexane isomers in IRMOF-1 at 300 K. They found that isosteric heats, Henry

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constants, and adsorption entropies are linearly correlated with the alkane carbon number. They found that long alkanes are preferentially adsorbed the short alkanes at low pressures, whereas the reverse is found at high pressures, and that linear n-hexane adsorbs more than its branched isomer. By comparing with literature results, they found that the amount of pure alkane adsorbed in IRMOF-1 is significantly greater than in a carbon nanotube bundle133 and in silicalite134,135 at 300 K and 104 kPa. Babarao et al.16 have calculated the storage capacity for CH4 in three different crystalline adsorbents, silicalite, C168 schwarzite, and IRMOF-1 at room temperature. They found that IRMOF-1 has the largest adsorption capacity among these three materials. They also compared the simulation results with experiments.10 Simulations agree well with experiments at low pressures and overpredict experiments at higher pressures. The overestimation was attributed to the crystal defects and impurities present in the experimental samples and the inaccuracy of the force fields used in simulations. 3.3.3. CO2 Adsorption in MOFs. Kawakami et al.75 have simulated adsorption of CO2 in Zn3(bdc)3 at 78 K. They used ab initio methods to calculate charge densities on the adsorbent framework and for CO2 molecules. In comparing framework charges computed from three different methods, they found that the values of the charges made a substantial difference for the calculated saturation loading of CO2. The adsorption amounts predicted by simulations were three times larger than observed in experiments. They have attributed this overestimation to the presence of the defects in the experimental samples. Walton et al.136 have calculated the adsorption isotherms of CO2 in IRMOF-1 at 195, 208, 218, 233, 273, and 298 K and compared with experiments. Simulations agree qualitatively with experiments, and they can predict the inflections and steps in the adsorption isotherms. They noted that inclusion of electrostatic interactions between CO2 molecules is required to capture the shape of experimental adsorption isotherms. However, these calculations ignored the contribution due to charges on MOF atoms, which may have an effect on the adsorption isotherms, especially at low pressures.92 Walton et al.136 also predicted the adsorption isotherms of CO2 in IRMOF-3 and MOF-177 at 298 K and found good agreement with experiments. We note that adsorbate-adsorbent electrostatic interactions were found to have a small effect on the adsorption in these calculations.136 In contrast, Yang et al.92 have shown that CO2-MOF electrostatic interactions can account between 10 and 30% of the adsorption for CO2 in several different MOFs at pressures less than 10 bar. The importance of framework charges is smaller at high pressures. Clearly, there is a need to carefully assess the effects of framework-fluid charges on a case-by-case basis. Yang and co-workers22,23,50,92,137 have studied CO2 adsorption in CuBTC, IRMOF-1, -8, -10, -11, -14, and -16, MOF-177, and Mn-MOF. They have refitted the Lennard-Jones energy parameters for selected atoms in four different MOFs by comparing with experimental data for CO2 adsorption in CuBTC, IRMOF1, IRMOF-11, and Mn-MOF. They regressed energy parameters for C and O in the carboxyl group of CuBTC by comparing with experimental data over the 0s1 bar pressure range at a temperature of 295 K.23 They likewise regressed parameters for the phenyl groups in IRMOF-1 and IRMOF-11 using experimental data over a pressure range of 0s40 bar at 298 K.50,92 For Mn-MOF they used experimental data covering the 0s1 bar pressure range at 195 K92 to fit C and O parameters. As mentioned in section 3.2, regressing parameters over a narrow pressure and temperature range may lead to parameters that have poor predictive capabilities. In addition, the experi-

mental results of Wang et al.,20 which were used to parametrize the force field for CuBTC,23 may be inaccurate. Liu et al.79 have shown that the CuBTC material synthesized by Wang et al.20 has a much lower pore volume compared with the ideal crystal and with experimental pore volumes from carefully prepared CuBTC samples.79 This indicates that the amount of CO2 adsorbed in CuBTC obtained by Wang et al.20 could be artificially low. Thus, using these experimental CO2 adsorption results to refit the potential parameters23 could be problematic. Yang et al.92 studied the effects of the heat of adsorption at low pressure, accessible surface area, and free volume on the amount of CO2 adsorbed in various MOFs using the potential parameters they regressed from experimental data. They found that the amount of CO2 adsorbed in MOFs at low pressures is correlated to the heat of adsorption. At moderate pressures, P ∼30 bar, the uptake of CO2 is related to both the accessible surface area and free volume. Yang et al.92 have also investigated the effect of framework charges in MOFs on the amount CO2 adsorbed in IRMOF-14, IRMOF-17, and MOF-177 at 298 K. They found that the electrostatic interactions between MOF atoms and CO2 enhance the amount CO2 adsorbed by ∼20-30% in the low-pressure regime. At high pressures, charges enhance the amount of CO2 adsorbed by less than 3% compared with the uncharged framework. As they did for CH4, Babarao et al.16 calculated the storage capacity for CO2 on silicalite, C168 schwarzite, and IRMOF-1 at room temperature. The adsorption capacity in IRMOF-1 is substantially larger than that in the other two materials, as was the case for CH4.16 Their simulated adsorption isotherms agree with experiments on IRMOF-1 at low pressures and slightly overestimate experiments at higher pressures.11 Ramsahye et al.46 have studied CO2 adsorption in a hybrid metal-organic framework material, MIL-53(Al). This structure has hydroxyl groups (µ2-OH groups) located at the metaloxygen-metal links. They used the charges computed from DFT in conjunction with a three-site model for CO2110 to perform GCMC simulations to calculate isotherms and the enthalpies of adsorption in the two different structures of MIL-53(Al). These two structures, namely, the narrow-pore (MIL-53np(Al)) and large-pore (MIL-53lp(Al)) forms, have the same chemical composition but different pore width of 8.3 and 13.8 Å, respectively. The simulated enthalpies of adsorption at low coverages in MIL-53np(Al) agree well with the experimental results obtained by microcalorimetry in the low-pressure region, while the simulated enthalpies of adsorption in MIL-53lp(Al) agree with experimental results obtained at high pressures. This outcome is consistent with the existence of a structural transition from the narrow-pore form to the large-pore form during the CO2 adsorption process in MIL-53(Al). Ramsahye et al. calculated CO2 adsorption isotherms at 303 K in the two structures of MIL-53(Al) for pressure up to 30 bar. They have shown that the experimental isotherm of MIL-53(Al) is made up of contributions from the large- and narrow-pore forms of MIL-53(Al). They proposed that the interaction between CO2 and the µ2-OH groups in MIL-53(Al) is the governing factor for the structure transition. Ramsahye et al.46 also calculated the adsorption isotherm for CO2 in MIL-47(V) at 303 K for pressures up to 20 bar. The simulations overestimate experiments, most probably due to only a partial removal of solvent molecules in the experimental structure. 3.3.4. N2, O2, and Ar Adsorption in MOFs. Kawakami et al.75 have studied N2, O2, and Ar adsorption in Zn3(bdc)3. The Ar adsorption isotherm was computed at its boiling temperature, 87.28 K, for pressures at 9.87 × 10-6 and 0.95 atm. They have

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compared the simulated N2 adsorption isotherm at 77 K with experimental data for pressures up to 1 atm. Simulated data were observed to be 1.7 times larger than experimental data. In their simulations, they treated O2 as a magnetic radical species with S ) 1 spin per molecule to study its magnetic properties when adsorbed in MOF pores. They found that O2 magnetic chains may form due to the confinement of the O2 position and orientation by the Zn3(bdc)3 pores. Vishnyakov et al.104 have calculated adsorption isotherms for Ar in CuBTC at 87 K. They adjusted the force fields in their simulations to provide results matching with the experimentally measured Henry’s constant. They have investigated four different potential models to represent the Ar-Ar and Ar-MOF interactions. Among the force fields they studied, the UFF gave the most reasonable agreement with experiment. We note that their calculations mistakenly used the potential parameters for Ni in place of that for Cu. As part of their work, they identified the most favorable adsorption sites and studied the sequence in which the pores in CuBTC filled with increasing pressure. Dubbeldam et al.70 have simulated N2 and Ar adsorption in IRMOF-1 at 78 K. They scaled down the adsorption isotherms by a factor of 0.725 to match the experimental data. They have studied the adsorption sites for N2 and Ar in IRMOF-1. They showed that the positions and occupations of the adsorption sites of N2 and Ar match well with experiments.14 At low temperatures, such as 30 K, the molecules are localized around their crystallographic sites, while at room temperature the molecules are spread throughout the pore volume. They found that the dominant adsorption site for small molecules (including the species Ar, N2, CO2, H2, CH4, C2H6, and C3H8) is the site nearest the Zn4O cluster of the big cage where the linkers point outward. Walton and Snurr138 predicted adsorption isotherms for N2 in IRMOF-1, -6, -10, -14, -16, and -18. The BET surface areas obtained using the simulated adsorption isotherms agree very well with the accessible surface areas139 calculated from crystal structures. They concluded that, by carefully choosing the pressure range, BET theory can be used to characterize the surface areas of the MOF materials. Yang et al.22 simulated the adsorption of N2 and O2 in CuBTC at 295 K for pressures up to 1 bar and compared with experiments. Using the same approach as for H2 adsorption in MOFs51,81 as discussed in section 3.2.1, they adjusted the adsorbate-MOF interaction parameters to obtain good agreement with the experimental adsorption isotherms. They then used these potentials to predict the adsorption isotherms for CO2/ N2/O2 mixtures (see section 4 for discussion). Garberoglio et al.78 calculated Ar adsorption in CuBTC at 87 K and in manganese formate at 78 K. Simulations agreed very well with experiments for Ar adsorption in CuBTC in the low-pressure regime but overestimated the amount adsorbed at high pressures by ∼30%. For Ar adsorption in manganese formate, the simulated adsorption capacity is a factor of ∼50 larger than experimental value. The authors suggested that because the experimental temperature is below the triple-point temperature of Ar (Ttr ) 83.8 K), the discrepancy may be due to the formation of bulklike argon clusters on the surface of the adsorbent, which kinetically prevents the entry of Ar into the sample. Liu et al.79 calculated N2 adsorption isotherms at 77 K in CuBTC to obtain the surface area and pore volume to compare with the experiments. They found very good agreement with experimentally measured values from CuBTC activated by a novel method,79 but also noted poor agreement with experimental values from some other groups using a more harsh

activation procedure. They concluded that activation can have a profound impact on the properties of CuBTC. They also compared simulated N2 isotherms at 253 and 298 K with experiments for pressures up to a maximum of 60 bar. The simulations underestimated the experimental N2 adsorption data; this may be attributed to ignoring the charge-quadrupole interactions of N2 and the framework atoms. Liu et al.79 also compared simulated Ar adsorption isotherms at 298 and 356 K with experiments for pressures up to 60 bar. The results of these simulations agreed very well with experiments at 298 K but overestimated experiments at 356 K. Krungleviciute et al.140 performed adsorption simulations for Ar in CuBTC at 87 K and compared with their own experiments. Their simulated adsorption isotherms significantly overpredicted the amount adsorbed obtained from experiments. They therefore scaled the simulation results, multiplying by a factor of 0.625 to match the experimental results. The experimentally measured pore volume of their CuBTC material is much smaller than that reported by Liu et al.79 Thus, the poor agreement between their simulations and experiments is due, at least partially, to synthesis and activation procedures used experimentally for their material. Garberoglio83 simulated Ar adsorption in COF-102 and COF103 at 87 K using both UFF and DREIDING force fields and compared with experiments. Simulations overestimated experiments by ∼25% upon saturation and performed worse at lower pressures. The author mentioned that the discrepancy could be due to a number of effects, including inaccuracy in solid-fluid interaction, an unknown structure change at high loadings, or imperfections in the materials. 3.4. Predictions of New Materials from Simulations. The simulations reviewed in section 3.2 were performed for existing MOFs, with structures determined from experiments. One of the uses of atomically detailed modeling is to predict the behavior of materials that have not yet been synthesized. In this section, we discuss simulations on hypothetical materials that have yet to be synthesized. Du¨ren et al.10 stated that the ideal material for CH4 storage should have a large accessible surface area, high free volume, low framework density, and strong energetic interactions. However, changing one of these parameters might negatively affect another parameter and therefore decrease the amount adsorbed. Du¨ren et al.10 used insights from simulations along with their heuristics for an ideal sorbent to design three new IRMOF materials. One of the materials IRMOF-993, which uses 9,10-anthracenedicarboxylate as linker molecule, was predicted to have higher uptake of CH4 than IRMOF-6 by 23-36%. This material, IRMOF-993, has a much higher butane/methane selectivity compared with IRMOF-1.17 In addition to their calculations of H2 adsorption in existing MOFs, Han et al.69 studied the adsorption of H2 in a new set of MOFs, including MOF-C6, MOF-C10, MOF-C16, MOF-C22, and MOF-C30. These MOF materials have vertices composed of M4O(CO2)6 clusters (where M ) Zn, Be, or Mg) that link the organic aromatic units to form a cubic cage structure. They developed force fields using quantum mechanics calculations for H2-MOFs and then used this force field to calculate adsorption isotherms. They found that Mg-based materials have higher H2 adsorption energies than the Zn-based materials. The amount of H2 adsorbed in the hypothetical Mg-based MOFs is predicted to be larger than in corresponding Zn-based MOFs. Han and Goddard68 have studied the effect of doping Li in MOF-C6, -C10, -C16, -C22, and -C30 using first-principle calculations. They found that Li atoms prefer to bind at the centers of the hexagonal aromatic rings and that Li atoms on

2364 Ind. Eng. Chem. Res., Vol. 48, No. 5, 2009 Table 4. Summary of Molecular Simulations of Mixture Adsorption in MOFsa authors Du¨ren and Snurr

MOF 17

adsorbed mixture

IRMOF-1, IRMOF-8, IRMOF-10, IRMOF-14, IRMOF-16

C4H10/CH4

Yang and Zhong50

IRMOF-1, CuBTC

Jiang and Sandler132

IRMOF-1

CH4/H2 CO2/H2 CO2/CH4 CO2/CH4/H2 C1/C2/C3/nC4/nC5 nC5/iC5/neoC5

Wang et al.15,137

CuBTC Mn-MOF

Babarao et al.16

IRMOF-1

Yang et al.22

CuBTC

CO2/CO C2H4/CO2 C2H4/C2H6 CO2/CH4 CO2/C2H6 CO2/CH4/C2H6 CO2/CH4 CO2/O2 CO2/N2 CO2/N2/O2

bulk-phase conditions T ) 298 K P ) 0.01, 0.1 MPa equimolar and other bulk-phase compositions T ) 298 K P ) 0-5 MPa various bulk-phase compositions T ) 300 K f ) 0.0001-10 MPa equimolar and other bulk phase compositions T ) 298 K P ) 0-5 MPa equimolar bulk-phase composition T ) 298 K P ) 0-2 MPa equimolar and other bulk phase compositions T ) 300 K P ) 0.001-7 MPa equimolar bulk phase T ) 298 K P ) 0-5 MPa equimolar and other bulk-phase compositions

a For calculations reported in terms of ideal gas pressures, the pressure range, P, is indicated. For calculations reported in terms fugacities, the fugacity range, f, is indicated.

adjacent aromatic rings are preferentially sited on opposite sides of the rings. They obtained effective binding energies of 16.7 kJ/mol for H2 bindings to aromatic rings due to the presence of Li. This is significantly higher than the binding energy on the undoped MOF. They predicted that Li-doped MOFs would have H2 uptake close to the 2010 DOE target130 near ambient temperatures. Zhang et al.127 have designed five new MOF materials by replacing the organic linker of IRMOF-1. They denoted these new MOFs as MOF-d1, -d2, -d3, -d4, and -d5. They replaced bdc with oxalate for MOF-d1 and introduced halogen atoms on to the edges of bdc to create MOF-d2, -d3, -d4, and -d5. The amounts adsorbed for all these newly designed MOFs were significantly improved compared with IRMOF-1 due to the introduction of strongly electronegative atoms in the linker. However, none of these materials showed a significant enough increase to make them viable for vehicular hydrogen storage materials. We note that none of these hypothetical structures were reoptimized after changes were made to the linker; the lattice parameters of the parent structure were retained. 4. Molecular Simulation of Adsorbed Mixtures in MOFs Although experimental measurement of single-component adsorption in MOFs (and other porous materials) is straightforward, assessing adsorption of molecular mixtures is much more involved and time-consuming.19,20,124,141 Knowledge of mixture adsorption isotherms is important for any application envisioned for MOFs that relies on selective adsorption of one species relative to other species. Molecular simulations can play a useful role in this area because once a molecular model describing single-component adsorption is available, performing simulations to probe mixture adsorption is only slightly more complicated than the initial single-component simulations. Molecular simulations have been widely applied to study mixture adsorption in other nanoporous materials.133,142-145 A number of groups have now investigated mixture adsorption in MOFs using molecular simulations. Some of the main aspects of these calculations are summarized in Table 4. One cautionary note in interpreting these results is that simulation results are typically reported in terms of pressure for an ideal gas bulk

phase. For systems where deviations from ideality in the bulk phase would be expected, pressures that are reported in this way should more precisely be defined as fugacities and an appropriate bulk-phase equation of state should be used to relate the conditions of the simulation to true physical conditions. One theme within simulations of mixture adsorption in MOFs has been to compare the adsorption selectivity of MOFs to other nanoporous materials. Jiang et al.132 examined mixture adsorption of C1-n-C5 linear alkanes and mixture adsorption of C5 isomers in IRMOF-1, silicalite (a prototypical silica zeolite), and a (10,10) carbon nanotube. Qualitatively, the outcome in each material is similar to the well-known result for zeolites: enthalpy effects dominate at low pressures, favoring long-chain alkanes over smaller molecules and straight-chain molecules over branched molecules, while at high pressure entropy effects can become important, favoring adsorption of smaller linear alkanes over longer linear species. Because of the greater free volume in IRMOF-1, this material was found to have a larger adsorption capacity than silicalite or the carbon nanotube. The adsorption selectivity of IRMOF-1, however, was calculated to be less than the other two materials. Babarao et al.16 performed similar simulations for mixture adsorption of CO2 and CH4 in IRMOF-1, silicalite, and C168 schwarzite, a nanoporous carbon with a well-defined crystal structure. At room temperature and pressures under 10 kPa, the selectivity for CO2 from an equimolar CO2/CH4 mixture was calculated as 2, 2.4, and 5 for IRMOF-1, silicalite, and C168 schwarzite, respectively. Another application of simulations of mixture adsorption is of course to predict the properties of specific MOFs for particular separations of interest. Yang and co-workers22 performed GCMC simulations on the adsorption-based separation of CO2 in CuBTC from mixtures of CO2/N2/O2 representative of flue gas. They found a CO2 selectivity value of 20 from CO2/N2/O2 mixture at room temperature and a total pressure of 5 MPa. Wang and co-workers15 used simulations of mixtures to consider whether CuBTC could be useful for purification of carbon monoxide, capture of carbon dioxide, and separation of olefin/ paraffin mixtures. For equimolar mixtures, the selectivity of CO2 from CO is found to be ∼25 at a total pressure of 5 MPa,

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whereas the selectivity of C2H4 from CO2 was ∼2 under the same conditions. Perhaps the most productive use of simulations of mixture adsorption is to compare the performance of multiple MOFs. Du¨ren and Snurr17 assessed the suitability of five different IRMOF materials as adsorbents for the separation of hydrocarbons and used their results to suggest a new MOF structure more promising than existing materials. In these IRMOFs, the selectivity of butane over methane increased with decreasing cavity size and with increasing number of carbon atoms in the framework and, therefore, with increasing interaction between the sorbate molecules and the framework. The adsorption selectivities predicted for these materials are similar to those that are known experimentally for silica zeolites and activated carbon.17 Yang and Zhong used simulations to investigate the separation characteristics of IRMOF-1 and CuBTC for mixtures of CO2, CH4, and H2. These calculations are a useful example of how adsorption selectivities can vary as the structure of the adsorbent is changed. The adsorption selectivity of CH4 from an equimolar CH4/H2 mixture at room temperature and at a pressure of 5 MPa was found to be ∼6 and ∼12 in IRMOF-1 and CuBTC, respectively. For IRMOF-1, the selectivity of CH4 was nearly pressure independent. On the other hand, for CuBTC the selectivity of methane decreases quickly at low pressures. 4.1. Applications of Ideal Adsorbed Solution Theory (IAST) to Mixture Adsorption in MOFs. A variety of mathematical tools of varying complexity exist to predict the properties of adsorbed mixtures in nanoporous materials without requiring direct measurement or simulation of mixture adsorption.146 If the concentration of all adsorbed species is low, for example, the adsorption selectivity is simply the ratio of Henry’s constants for each adsorbing species as a single component. At nondilute adsorbate concentrations, mixing theories such as IAST can be used to make predictions for multicomponent adsorption equilibrium using only data from single-component experiments or simulations.147 In our view, perhaps the most important application of molecular simulations of mixture adsorption in MOFs is to test whether IAST is accurate for the mixtures of interest. If IAST is found to be accurate for a particular class of adsorbates and adsorbents, then further detailed calculations of mixture equilibria are unnecessary to assess adsorption selectivity. In almost all examples where molecular simulations of mixture adsorption in MOFs have been compared to IAST, the predictions of IAST have been found to be accurate. These comparisons include Yang and Zhong’s examination of CH4/ H2 and CO2/CH4 mixtures in IRMOF-1,50 the similar calculations of Babarao and co-workers16 for CO2/CH4 mixture in the same material, the results of Yang and co-workers22 for CO2/ N2 and CO2/O2 mixtures in CuBTC, and calculations by Keskin et al. for CH4/H2 mixtures in CuBTC.148 Only one example has been reported for which IAST does not give accurate results; Yang and Zhong showed that IAST gave poor results for CO2/ H2 mixtures in CuBTC. The discrepancy observed for this mixture was attributed to the constituents of the CO2/H2 mixture, which differ in both size and strength of the physical interaction with MOF atoms. Developing a detailed mechanistic understanding of the limitations of IAST for this example would be useful for assessing what other adsorbed mixtures might behave in a similar way. The results described above support the idea that IAST will generally give accurate predictions for the mixture adsorption of many light gases in MOFs. When this situation occurs, further

simulations of adsorbed mixtures will frequently not be necessary. We strongly recommend that evaluating the applicability of IAST be a routine part of any set of simulations probing mixture adsorption in MOFs, since a relatively small number of calculations will in many cases provide sufficient information to completely characterize the mixtures of interest. It would of course be worthwhile to understand the physical origins of strong deviations from IAST in examples where this outcome is observed so that deviations in similar future examples can be anticipated. It is well-known from comparison with experimental data for other porous materials that IAST frequently does not perform well for mixtures where the adsorbed components differ strongly in size, polarity, or both,146 so it is reasonable to expect that similar issues will also occur in MOFs. Applying IAST does require that single-component adsorption data are available over a wide range of adsorbate loadings. Variants of standard GCMC simulations that remove some of the uncertainty associated with fitting single-component isotherms to a limited set of state points are available,50,149 although these methods have not been applied to MOFs to date. 5. Molecular Simulations of Adsorbate Transport in MOFs In many potential applications of nanoporous materials, the transport rates of molecules inside the material’s pores are important. In equilibrium-based separations such as pressure swing adsorption, transport rates define limits on the cycle times that can be achieved. In these cases, molecular transport rates are mainly important if they are very slow. In other applications such as membrane-based separations, however, the relative transport rates of molecules inside the material of interest are crucial in determining the overall performance of a material. Because accurate characterization of molecular transport inside nanoporous materials using experiments is much more challenging than direct measurements of single-component adsorption equilibria,1 very little is currently known about molecular diffusion in MOFs. Almost all the information that is currently available about this topic has come from molecular simulations. To discuss molecular diffusion inside nanoporous materials, it is important to dispel the notion that a single diffusion coefficient can describe mass transport under all circumstances. Multiple reviews of the various mathematically distinct diffusion coefficients that are associated with various physical situations describe this topic in detail.150-152 For diffusion of a single adsorbed component, the two most common quantities to consider are the self-diffusion coefficient, which quantifies motion of a single molecule, and the transport diffusion coefficient, which describes net mass transfer in the presence of a concentration gradient in the adsorbed species. Selfdiffusivity describes the motion of individual tagged particles, and it is related to the mean squared displacement of tagged particles by an Einstein relation. The transport diffusivity is defined as the proportionality constant relating a macroscopic flux to a spatial concentration gradient in Fick’s law.153 The transport diffusion coefficient is frequently expressed in terms of a third diffusion coefficient, the corrected diffusion coefficient, and a term associated with curvature in the adsorption isotherm. Well-developed simulation methods exist to measure all three diffusion coefficients from MD simulations.152,154,155 Because the self-diffusivity is easier to obtain from MD than the other diffusion coefficients, it is often the only diffusion coefficient that is examined in simulation studies. The first two simulation studies of molecular diffusion in MOFs were by Sarkisov et al.111 and Skoulidas.156 Sarkisov et

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al. focused on the self-diffusion of a variety of different adsorbates, mainly at dilute concentrations. Specifically, they simulated methane, n-pentane, n-hexane, and n-heptane in IRMOF-1 at 300 K. Skoulidas simulated the loading-dependence of the self, corrected, and transport diffusivities of Ar in CuBTC at room temperature. The self, corrected, and transport diffusivities are all functions of concentration, and they are only equal in the limit of dilute concentrations. In extreme cases, the self and transport diffusivities can vary by orders of magnitude.157,158 Skoulidas and Sholl153 subsequently reported similar loadingdependent self, corrected, and transport diffusivities for Ar, CH4, CO2, N2, and H2 in IRMOF-1 and Ar in MOF-2, MOF-3 and CuBTC. An interesting outcome from these initial simulations was that the calculated diffusivities were similar in magnitude to those for similar species in silica zeolites. Superficially, this observation may seem counterintuitive because of the substantial difference in pore size and volume between IRMOF-1 and typical zeolites. Skoulidas and Sholl153 noted that, under most conditions, adsorbed molecules in large-pore materials such as IRMOF-1 are confined to a relatively narrow region in the vicinity of the pore walls. This means that the effective “width” of the region in which the adsorbed molecule actually moves during diffusion is similar in dimension to the subnanometerlength scales that exist inside zeolite pores. Furthermore, the atomic-scale roughness of the potential energy surface defined by the MOF pore walls is quite similar to that for typical zeolites. This argument strongly suggests that the magnitude of diffusion coefficients for simple molecules inside MOFs should generically be similar to those for chemically simple zeolites. Materials are known in which very smooth pore walls result in extremely rapid molecular diffusion,152,157 but this outcome is unlikely to occur in any MOF. Jhon et al.159 used MD simulations to measure the selfdiffusivity of methane in alkoxy-functionalized IRMOFs. Their results for IRMOF-1 were in good agreement with earlier simulations.111,153 When longer alkoxy chains were substituted into IRMOF-1, a decrease in the self-diffusivity was observed, as might be expected. Yang and Zhong81 used MD to calculate the self-diffusivity of H2 in IRMOF-1, -8, and -18. The diffusion of H2 in IRMOF-18 was found to be slower than in the other two materials, an effect ascribed to the pendant CH3 groups present in IRMOF-18. The low-temperature diffusion coefficients for H2 predicted by these calculations were quite similar to previous reports of H2 diffusion in zeolites, with diffusion coefficients at 77 K of ∼10-8 m2/s.160,161 Liu et al.80 performed MD simulations to compute self and transport diffusivities of H2 in [Zn(bdc)(ted)0.5] at both 77 and 298 K over a range of pore loadings, and they concluded that the diffusivities of H2 in this structure are comparable to H2 diffusivities in IRMOF-1 at 298 K. Most of the studies78,80,81,111,153,156 in the literature excluded the lattice dynamics by freezing the experimental geometry of the framework when calculating pure gas diffusion in MOFs. Amirjalayer et al.162 used an extended force field to predict the self-diffusion of benzene in both rigid and flexible MOF-5 via MD simulations and concluded that a rigid MOF lattice gives a higher diffusion coefficient than a flexible lattice. When the lattice motion was included, the self-diffusivity of benzene is predicted to be 2.49 × 10-9 m2/s by Amirjalayer et al.162 This value was within accuracy comparable to uncertainty in corresponding experimental measurements of Stallmach et al.163 (2.0 × 10-9 m2/s). Furthermore, they calculated the activation energies for the diffusion of benzene in both rigid and flexible

MOF-5 and argued that the calculated value for the flexible framework appears reasonable whereas the value for the rigid model is too low to be physically reasonable. Thus, this work concluded that including the flexibility of lattice leads to a deeper insight into the mechanism of molecular transport, which is helpful for design of MOF systems. However, it is difficult to speculate on the generic effect of framework flexibility on adsorbate mobility; therefore, future studies examining this point will be valuable. Recently, a few studies considering the flexibility effects in MOFs from a modeling perspective have appeared in the literature. Dubbeldam et al.164 used a flexible force field to predict negative thermal expansion of IRMOF-1, -10, and -16. Greathouse and Allendorf developed a flexible force field to model the interaction of water with IRMOF-1165 and later reported a series of MD simulations of several adsorbed hydrocarbons to validate this flexible force field for IRMOF1.166 One of the challenges in understanding diffusion of adsorbed molecules in MOFs is the lack of experimental data on diffusion in MOFs. Only one experimental study to date has assessed molecular diffusion in an MOF. Stallmach et al.163 used pulsed field gradient NMR to measure the self-diffusivity of methane, ethane, n-hexane, and benzene in MOF-5. The n-hexane selfdiffusivity observed experimentally agreed well with the value reported in an earlier MD study,111 whereas the experimentally measured methane self-diffusion coefficient was a factor of ∼6 higher than the value reported in an MD simulation.111,153 It is important to note in this context that diffusion coefficients in nanoporous materials can vary over multiple orders of magnitude as different materials are considered,152,157 so while the difference between simulation and experiment for this example is clear, it does not represent a disastrous failure of the simulations. The complications discussed previously in relation to interpreting experimental adsorption data, that is the role of residual solvent and lattice defects, are also likely to be important in measurements of diffusion in MOFs. Because the experimental data discussed above is limited, it is simply not possible to assess the potential role of these effects in the extant experimental data. A useful future direction in this area would be for comparisons to be made between experiments and simulations using MOFs for which good agreement has been observed between multiple experimental groups for adsorption properties and where intermolecular potentials have been validated against this adsorption data. Understanding multicomponent diffusion in MOFs is essential to predict the possible utility of MOFs in chemical separations based on mass transport of adsorbed species. Measuring mixture diffusion in nanoporous materials experimentally is challenging; thus, molecular simulations have a useful role to provide detailed information about transport rates of mixtures in these materials. Since these simulations are computationally demanding, information on multicomponent diffusivity in MOFs is still lacking. Recently, we presented the first examination of diffusion of a binary mixture in CuBTC using molecular simulations.148 Specifically, we examined adsorption and diffusion of H2/CH4 mixtures in CuBTC and tested several correlations that have been proposed previously to predict mixture transport and adsorption properties in nanoporous materials167,168 using the data obtained from simulations. The main conclusion from these calculations was that for H2/CH4 mixtures in CuBTC it is possible to predict mixture properties from single-component data with a high degree of accuracy.

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6. Conclusion and Outlook In this review, we have examined applications of atomistic simulations to metal-organic framework materials. As is evident from the volume of literature we have cited, this area is growing rapidly. To conclude, we list what we feel are the main challenges and opportunities for using simulations to contribute to the development of practical applications of MOFs. We begin with the challenges: 1. Quantum mechanical methods can give accurate structural information about MOFs. The opportunities that exist to use this capability to consider new structure have not yet been widely explored; most work to date has focused on comparing quantum mechanical structural information with data that is already readily available from experiments. 2. The use of quantum mechanical calculations either to directly characterize physisorption of molecules in MOFs or to provide point charges for classical force fields is faced with several challenges. Multiple papers have used density functional theory calculations to examine the weak interactions of H2 with MOFs, but this QM approach is well-known to not describe van der Waals interactions accurately, so it is unclear that these calculations give anything other than qualitative information. QM calculations have been useful in defining point charges, but it is important to note that no unique way to accomplish this task exists, and different charge decomposition methods can give rather different results (see Table 1). 3. The development of accurate classical interatomic potentials for describing adsorption in MOFs remains challenging. Strong variations among different experimental measurements of adsorption in what is nominally the same material have been reported (see Figure 1) due to complications arising from residual solvent from the synthesis of a MOF being present in the materials’ pores. Careful judgment should be used by modelers before investing significant efforts in adapting intermolecular potentials to any one adsorption experiment. From the modeling perspective, it is important to use adsorption data from a broad range of conditions to parametrize potentials whenever this is practical. Efforts to test and improve the transferability of potential among related families of MOFs will have great value. 4. Most (although not all) simulations of molecular adsorption and diffusion in MOFs approximate the MOF as a rigid structure. This assumption creates tremendous savings in computational effort. Nevertheless, careful studies that establish when this approach is viable would be useful. 5. Atomistic simulations typically make no predictions about the long-term stability of MOFs. The stability of these materials is a serious issue in practical applications. Some recent efforts have begun to use atomistic modeling to understand the mechanism of water-induced decomposition of IRMOF-1.165 Using the methods developed in this work to consider the stability of other MOFs may be useful, although it is likely that this issue is more straightforward to address experimentally. To aid the development of MOFs for real applications it would be very helpful if experimental reports of new syntheses explicitly included information on stability with respect to simple parameters such as temperature and humidity. The most significant opportunities that exist for atomistic modeling of MOFs lie in areas where experiments for some property of interest are challenging, not in reiterating properties that have already been addressed experimentally. Several examples of this idea include the following: 1. Atomistic simulations can be used to test hypothetical structures for particular applications if the metric describing the

performance of a material for the application can be directly calculated. A good example of initial success in this area is the work of Snurr and co-workers on designing materials with large adsorption capacities for methane.10 2. Thermal transport in adsorbents is important in fixed-bed adsorption applications. Molecular simulations may be able to play a useful role in predicting the heat-transfer properties of MOFs. 169,170 3. Charactering the adsorption of chemical mixtures in MOFs (or other porous materials) is tedious experimentally. Relatively routine applications of GCMC simulations, however, allow mixture adsorption to be assessed efficiently once a force field for the adsorbing components is defined. We do not, however, advocate extensive GCMC simulations of mixture adsorption as a path forward in this topic. As we described above, most examples of mixture adsorption in MOFs to date can be accurately predicted using ideal adsorbed solution theory based on single-component adsorption data. We suggest that, in any consideration of mixture adsorption using simulations, the accuracy of IAST first be considered by comparing its predictions with a small number of GCMC mixture simulations. If IAST is found to be accurate, then no further mixture simulations are required. An interesting direction in this area will be to consider the applicability of simple mixing theories like IAST as mixtures that are more chemically complex than the relatively simple mixtures that have been examined to date are used. 4. The development of quantitative information about molecular diffusion in MOFs is only just beginning. Detailed characterization of diffusion in MOFs will be helpful for considering possible applications of MOFs such as membranebased separations where molecular transport rates are crucial.18 One important avenue in advancing the ability to simulate diffusion in MOFs will be to make careful comparisons with experimental measurements in materials that are known to give unambiguous results when characterized by adsorption. A second direction where simulation is likely to play a crucial role is in understanding mixture diffusion in MOFs. The small amount of data that is available on this topic suggests that mixing theories that use single-component information to predict mixture properties can yield accurate results for at least simple chemical mixtures in MOFs.148 Acknowledgment S.K. and D.S.S. acknowledge partial support from the National Science Foundation through Grants CTS-0413027 and CTS-0556831. J.L., R.B.R., and J.K.J. acknowledge funding from the U.S. Department of Energy through the National Energy Technology Laboratory under Grant 41817M203841817M2000. Literature Cited (1) Ka¨rger, J.; Ruthven, D. Diffusion in Zeolites and Other Microporous Materials; John Wiley & Sons: New York, 1992. (2) Chen, N. Y.; Degnan, T. F.; Smith, C. M. Molecular Transport and Reaction in Zeolites: Design and Application of Shape SelectiVe Catalysis; John Wiley & Sons: New York, 1994. (3) Davis, M. E. Ordered Porous Materials for Emerging Applications. Nature 2002, 417, 813. (4) James, S. J. Metal Organic Frameworks. Chem. Soc. ReV. 2003, 32, 276. (5) Kitagawa, S.; Kitaura, R.; Noro, S. Functional Porous Coordination Polymers. Angew. Chem., Int. Ed. 2004, 43, 2334. (6) Rosseinsky, M. J. Recent Developments in Metal-Organic Framework Chemistry: Design, Discovery, Permanent Porosity and Flexibility. Microporous Mesoporous Mater. 2004, 73, 15.

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ReceiVed for reView April 23, 2008 ReVised manuscript receiVed June 17, 2008 Accepted June 27, 2008 IE800666S