Improving Predictions of Gas Adsorption in MetalâOrganic

Article pubs.acs.org/JPCC

Improving Predictions of Gas Adsorption in Metal−Organic Frameworks with Coordinatively Unsaturated Metal Sites: Model Potentials, ab initio Parameterization, and GCMC Simulations Linjiang Chen,† Carole A. Morrison,‡ and Tina Düren*,† †

Institute for Materials and Processes, School of Engineering, and ‡School of Chemistry and EaStCHEM Research School, The University of Edinburgh, King’s Buildings, Edinburgh, EH9 3JL, United Kingdom S Supporting Information *

ABSTRACT: The incorporation of coordinatively unsaturated metal sites (cus’s), also known as open metal sites, into metal− organic frameworks (MOFs), significantly enhances the uptake of certain gases, such as CO2 and CH4, especially at low loadings when fluid−framework interactions play the predominant role. However, due to the considerably enhanced, localized guest interactions with the cus’s, it remains a challenge to predict correctly adsorption isotherms and mechanisms in MOFs with cus’s using grand-canonical Monte Carlo (GCMC) simulations based on generic classical force fields. To address this problem, we carefully investigated several well-established semiempirical model potentials and used a multiobjective genetic algorithm to parametrize them using accurate ab initio data as reference. The Carra− Konowalow potential, a modified Buckingham potential, in combination with the MMSV potential for the cus’s gives not only adsorption isotherms in very good agreement with experiments but also correctly captures the adsorption mechanisms, including adsorption on the cus’s, for CO2 in CPO-27-Mg and CH4 in CuBTC. Moreover, the parameters obtained also give quantitative predictions of CH4 adsorption in PCN-14, another MOF with Cu cus’s, which is an important step for developing transferable force fields that reliably predict adsorption in MOFs with cus’s.

1. INTRODUCTION Metal−organic frameworks (MOFs) are a class of highly porous, crystalline materials that have shown many interesting structural and chemical properties.1−8 Their modular synthesis from metal corner units bridged by organic linkers, together with the possibility of postsynthetic functionalization,9 affords a high degree of tunability and structural diversity. This makes them promising materials for numerous applications including adsorptive storage and separation of gases and liquids,10−16 catalysis,17,18 sensing,19 and biotechnology.20−22 Coordinatively unsaturated metal sites (cus’s), also known as unsaturated metal centers or open metal sites,23−28 have proven to be very important not only for catalytic applications17,18 but also for enhancing the uptake of CO2,23,27,29,30 CH4,23,31,32 and H2,26,33,34 especially at low loadings when host−guest interactions play the predominant role. Computational studies on MOFs have accompanied the experimental efforts since the very beginning. Numerous studies in the literature based on quantum mechanics (QM) or force field (FF) based molecular simulation have showcased the ability of theoretical investigations to complement experimental studies in furthering our understanding of MOFs.35−40 Classical simulations, e.g., Monte Carlo (MC) and molecular dynamics (MD), have evolved into an indispensable tool in studying and characterizing MOFs. In particular, grand-canonical Monte Carlo (GCMC) simulations © 2012 American Chemical Society

are widely used to study adsorption in MOFs, since they can not only produce results directly comparable with experimental results but also provide an insight on the molecular level which is not easily accessible by experiments. These simulations allow calculations on large systems consisting of thousands of atoms at an affordable computational cost.35,38 Molecular simulations usually rely on force fields which are aimed at approximating the total interaction potential of the system with simple analytical functional forms. To date, most molecular simulation studies use the Lennard-Jones (LJ) potential41 with parameters usually taken from generic force fields such as UFF,42 DREIDING,43 and OPLS-AA.44 Although these force fields do surprisingly well for describing adsorption in many MOFs, their applicability has been criticized for describing the interaction with cus’s.30,45−47 In contrast, it has been clearly demonstrated that ab initio methods can describe the interactions with a high level of accuracy, which is of crucial importance for obtaining accurate predictions of adsorption in MOFs with cus’s.45−47 However, their computational cost increases drastically with system size, allowing only the description of small systems (less than 100s of atoms, rather than 1000s by force field-based molecular simulations). Received: June 25, 2012 Revised: August 6, 2012 Published: August 14, 2012 18899

dx.doi.org/10.1021/jp3062527 | J. Phys. Chem. C 2012, 116, 18899−18909

The Journal of Physical Chemistry C

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more complicated, potential energy expressions have emerged.54,58 The additive terms involved in these intermolecular potentials were fitted explicitly to the decomposition of the corresponding ab initio potential energy whenever and wherever possible. Thus these force fields can be expected to provide a more in-depth interpretation of the physics involved in the system. In this contribution, we propose and describe a multiscale simulation strategy for correctly predicting gas adsorption in MOFs with coordinatively unsaturated metal sites. We introduce a systematic, robust protocol for parametrizing some well-established semiempirical model potentials from accurate ab initio reference data. To illustrate our method, two systems were studied, namely CO2 adsorption in CPO-27-Mg23 and CH4 adsorption in CuBTC.24 Both frameworks and their cus’s are illustrated in Figure 1. CPO-27-Mg [Mg2 (2, 5-

Although density functional theory (DFT) allows the treatment of larger systems on a sound first principle basis, it is still too expensive to be carried out routinely and, more importantly, prone to underestimate some contributions to the intermolecular interaction (e.g., dispersive or van der Waals (vdW)).48−50 Moreover, when the whole adsorption isotherm is of interest, no QM method on its own is practically adequate for the goal. Since both molecular simulation and QM approaches have strong advantages together with critical disadvantages, a multiscale strategy which allows computation on large systems with high accuracy seems a promising and somewhat natural solution for answering the challenges faced in simulating adsorption and diffusion in MOFs with cus’s. To address the issue, we previously45 directly implemented a potential energy surface (PES) calculated by a hybrid DFT/ab initio method in GCMC simulations to predict the adsorption of methane in CuBTC and were able to capture the amount adsorbed as well as (and more importantly) the adsorption mechanism when compared to available experimental results. Most importantly, the interaction with the cus’s was correctly described, which cannot be achieved by any classical force field. While such a direct implementation of ab initio PES in GCMC simulation removes much of the ambiguities introduced by approximating the potential energy with semiempirical model potentials (e.g., LJ, Morse,51 etc.), force fields using simple analytical representations for the potential are more convenient to use and ideally are transferable to other systems thus removing the necessity for expensive ab inito calculations to determine the PES of every new MOF studied. In order to achieve quantitative predictions of adsorption isotherms in MOFs with cus’s when generic force fields fail to do well, some previous studies resorted to scaling or reparameterizing forcefield parameters or partial charges of the framework to match simulation results with experiments.52,53 This parametrization strategy is purely empirical and results in an effective model that is able to reproduce the experimental results to which it has been fitted. The danger of using such “unphysical” parameters was carefully investigated in a recent theoretical study,54 and it was pointed out that the ability to correctly capture the underlying physics of the system as well as the transferability of the parameters to other systems is questionable. In order to accurately describe specific host−guest interactions, which is not restricted to but essential for guest interaction with cus’s, considerable effort has been made to develop ab initio-based force fields.46,47,54−58 In the development of these force fields, QM calculations yielded accurate reference data for parametrization of the chosen potential functional forms. In most of these studies, finite-sized cluster models were adopted to represent the whole frameworks in the QM reference data calculations. This approximation leads to lower computational costs and allows the use of higher level of theory methods (e.g., second-order Møller−Plesset perturbation theory (MP2)59,60) which is crucial when describing intermolecular interactions. A recent report on the development of ab initio force fields for CO2 adsorption in zeolites demonstrates how such a multiscale simulation strategy can also be realized using the periodic structure.61 While these ab initio force fields do share some common ground, they differ in the potential functional forms adopted for describing nonbonded intermolecular interactions. Because of their simplicity, the LJ and Morse potentials are widely used.47,55,57 On the other hand, more sophisticated, physically motivated, but also

Figure 1. Framework structures for CPO-27-Mg (a) and CuBTC (b): white, hydrogen; gray, carbon; red, oxygen; green, magnesium; and brown, copper. Yellow spheres represent the experimental adsorption sites at the cus’s. Note that some of the sites in adjacent cavities are omitted from b for clarity.

dioxidoterephthalate)], also known as Mg\DOBDC or MgMOF-74, has been reported to be one of the best MOFs for selective removal of CO2 under typical flue gas conditions.30,62 The strong affinities of the cus’s toward CO2 and the high density of cus’s present in this MOF are recognized as the main contributors to its outstanding performance. Furthermore, large discrepancies between the simulated CO2 adsorption isotherms based on generic force fields and experimental isotherms were observed for CPO-27-Mg, which were again attributed to the presence of cus’s in this MOF30 thus making this an ideal test case. To demonstrate that our approach is generally applicable to gas adsorption in MOFs with cus’s, we also revisit CH4 adsorption in CuBTC, a system that we simulated previously by implementing an ab initio derived PES directly in GCMC simulations.45

2. METHODOLOGY 2.1. Ab initio Reference Data. To account accurately for the long-range correlation effect of dispersion, a high level ab initio method (e.g., MP2 or coupled cluster) is preferable to a DFT method with purely empirical dispersion correction for force field development. This is currently only achievable for finite-sized, nonperiodic systems. Hence, it is crucial to construct a model cluster that is big enough to represent adequately the most important features of the framework while at the same time ensuring the cluster is small enough to permit manageable computations. The most relevant feature of CPO27-Mg is the square-pyramidal coordination environment of the 18900



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correction to the long-range dispersion interactions.66,68 This method has been previously seen to perform very well for dispersion-dominated systems.58,69,70 The frozen monomer approximation was adopted, employing the B3LYP/Def2TZVPP-optimized geometry of model I and the experimental geometry of CO2 (C−O bond length 1.161 Å; O−C−O bond angle 180°).71 The wave functions were confirmed to have no internal instabilities prior to production of the results. Note that basis set superposition errors were not corrected for following arguments presented in the literature.58,70,72 The model I···CO2 interaction potential was calculated in the gas phase and defined as

open magnesium(II) sites. Therefore, the primary target in constructing a suitable cluster for ab initio calculation was to preserve the electronic structures of the “central”, 5coordinated magnesium(II) site, around which the potential energy surface (PES) was to be sampled. A detailed description for the construction of the model cluster can be found in the Supporting Information (SI). In brief, we first cut along the cdirection of the conventional cell (optimized with a periodic DFT method, see the SI) to get a chain of five consecutive magnesium(II) ions together with the five connecting dioxidoterephthalate anions, as shown in Figure 2a. The

E int = E(model I ···CO2 ) − E(model I) − E(CO2 )

(1)

where E(model I···CO2), E(model I), and E(CO2) are the total energies of the model I···CO2 complex, isolated model I, and isolated CO2 molecule, respectively. A large set of 1158 relative configurations between a CO2 molecule and model I were explicitly evaluated by ab initio calculations to reproduce the PES in the vicinity of the cus. The sampling scheme depicted in Figure 2c, which controls the “approach routes” to the cus, is described by five parameters, r and θ1−θ4, and is discussed in more detail in the SI. For the CuBTC−CH4 system, the ab initio host−guest interaction potential data were taken directly from our previous work where we used the DFT/CC method to obtain the PES for the system. The interested reader is referred to ref 45 for a complete description of the ab initio data calculation and elsewhere for more details on the DFT/CC methodologies.73,74 2.2. Model Potentials. The ab initio interaction energy, as defined in eq 1, is approximated by the sum of electrostatic interaction (Ees) and vdW interaction (EvdW) that are calculated in a pairwise additive way in the proposed force fields as

Figure 2. (a) Repetition of five square-pyramidal cus’s along the cdirection. (b) Model I on which the ab initio calculations were performed. (c) Definition of the relative configurations between a CO2 molecule and the “central” cus. Color code: white, hydrogen; gray, carbon; red, oxygen; green, magnesium; and purple, lithium.

structure was simplified by replacing the dioxidoterephthalate anions with smaller, suitable anions. Substituting the two magnesium atoms at each end of the chain with two lithium atoms (which is commonly done to cap model clusters carved out from MOFs54,55) and saturating all the remaining dangling bonds by hydrogen atoms lead to the final model cluster (denoted as model I) as shown in Figure 2b. Cluster calculations were carried out with the Gaussian 09 program.63 The structure of model I was relaxed at the B3LYP 64/Def2-TZVPP 65 level of theory, with all the magnesium and oxygen atoms belonging to the squarepyramidal cus’s fixed at the periodic DFT optimized positions. Tight convergence criteria (see the SI) were imposed on these geometry optimizations and an ultrafine grid (Integral(UltraFineGrid)) was used for numerical integrations for all calculations (for both geometry optimization and single-point energy). We performed Hirshfeld population analyses on the optimized structures of both the periodic framework and three clusters of different size. From the results shown in Table S1 in the SI, it can be confirmed that even the smallest cluster, model I, is adequate to reproduce the electrostatic features of the cus. Thus all following ab initio calculations discussed are based on model I. To obtain high quality ab initio interaction potentials for the model I···CO2 complex, a double-hybrid density functional with empirical dispersion correction, B2PLYP66-D2,67 was used together with a doubly polarized triple-ζ valence basis set, Def2TZVPP. The B2PLYP-D2 functional adds nonlocal electron correlation effects to a standard hybrid functional by secondorder perturbation theory (MP2) as well as an empirical

E int = Ees + EvdW

(2)

The electrostatic interaction is modeled in the simplest way, which is the atom-centered charge−charge Columbic interaction, defined as 2 1 zizje Ees = 4πε0 rij

(3)

where rij is the distance between atoms i and j, zi and zj are the fractional charges, e is the elementary charge, and ε0 is the vacuum permittivity. Note that for the fitting of ab initio CuBTC−CH4 interaction potential electrostatic interactions were not considered as methane is an almost spherical, apolar molecule. The total energy decomposition defined in eq 2 means that the quality of the partial atomic charges is of crucial importance to achieve a high quality parametrization of the force-field parameters that describe vdW interactions. A comparison of the performance of some of the most widely used partial charge derivation schemes (e.g., CHelpG, MK, RESP, etc.) is not within the scope of this contribution, and the interested reader is directed to critical reviews in the literature.75,76 Taking into account the findings by Sigfridsson and Ryde,75 the point charges used in this work for both model I and the CPO-27-Mg framework (used in the GCMC simulations) were derived using the Merz−Kollman77,78 (MK) method. To eliminate the undesirable rotational dependence observed for the original MK sampling scheme, a much denser grid was used by setting the internal options in the Gaussian 09 program, via IOp(6/41 18901



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applied to the atom pair Mg−C_CO2 (i.e., the carbon atom of the CO 2 molecule) after carefully examining all the configurations sampled and discovering that (1) for interatomic distances smaller than the sum of the vdW radii, the interaction energy for this pair is always positive (i.e., repulsive) and (2) the magnesium(II) site does not favor any configuration with C_CO2 in close contact since both atoms carry a positive charge. Finding an appropriate potential functional form for fitting to the ab initio data for the cus’s is challenging. The relatively strong binding affinity of the adsorbate−cus complex can be explained by enhanced electrostatic interaction due to the local electric field effect of the open metal sites.82,83 There is also clear experimental evidence that the adsorbate−cus distances are considerably smaller than the sum of the corresponding vdW radii,31,82 indicating the enhanced interactions at cus’s originate from the overlap of electrons. From these two observations it follows that the specific interaction with cus’s is short-ranged, which suggests a correct approximation (by the chosen potential functional form) for the strong interaction should comprise a deep potential well at the equilibrium separation as well as a rapid convergence to a dispersiondominated behavior. However, “softness” in the repulsive part of the potential usually comes at the expense of a slow decaying behavior in the attractive region, a behavior that can be observed, for example, for the Morse potential; and a deeper potential well inevitably leads to a large “tail” at long distances, which is also true for the LJ and Buckingham potentials. All these observations motivated us to seek a combined model potential with each “piece” working well in their own range of distances. This would allow a more adequate description of the interaction at cus’s with the desired flexibility. The MMSV (Morse−Morse−spline−van der Waals) and ESMSV (exponential−spline−Morse−spline−van der Waals) potentials are typical examples of such piecewise models that have found wide applications.84−87 In this work, we used the MMSV potential for the cus’s which is given by

= 15, 6/42 = 27, 6/43 = 15). This leads to on average 4043 sampling points per atom for model I, which doubles the recommended density (2000 points per atom).75 The choice of the functional form for fitting the vdW contribution to the ab initio potential energy is found to be of vital importance. Two model potentials are used to approximate the vdW contribution depending on whether the interaction is with the cus’s or not. For atom pairs not involving cus’s (i.e., all atoms except Mg or Cu), the Carra−Konowalow potential,79 a modified Buckingham potential denoted as Buck−CK hereafter, is used: Buck − CK (rij) EvdW

6 ⎞ ⎛ β + 6 ⎞⎛ R eq ⎞ ⎧ ⎪⎛ ⎟⎟ ⎨⎜ 6 ⎟ = Deq ⎜ ⎟⎜⎜ ⎪⎝ β + 6 ⎠ ⎝ β ⎠⎝ rij ⎠ ⎩

⎫ ⎡ ⎛ rij ⎞⎤ ⎪ ⎟⎟⎥ − 1⎬ exp⎢β ⎜⎜1 − ⎪ ⎢⎣ ⎝ R eq ⎠⎥⎦ ⎭

(4)

where Deq is the potential well depth, Req is the location of the minimum potential, and β characterizes the steepness of the exponential repulsion. In general, a Buckingham80 type potential is theoretically better justified than the LJ and Morse potentials because the exponential approximation of short-range repulsion is more realistic from a physical point of view while the interactions at moderate to large separation distances can be better described by a power law of the inverse interatomic distance.81 The original form of the Buckingham potential has a false maximum at small distance, Rmax, and the potential drops to −∞ when rij approaches zero. The common way to correct this behavior in molecular simulation is to introduce a hard sphere potential at small rij, i.e., EvdW = +∞ when rij < Rmax. However, we find a uniform, concise functional form, such as Buck−CK, is more convenient in the parametrization process to avoid possible complications arising from defining Rmax a priori. To keep the number of adjustable parameters down and to keep the type of potential function used as simple as possible, the Buck−CK potential was also

⎧ ⎧ ⎡ ⎛ ⎫ ⎡ ⎛ r ⎞⎤ r ⎞⎤⎪ ⎪ ⎪ ⎨ ⎢α1⎜1 − ij ⎟⎥ − 2exp⎢ α1 ⎜1 − ij ⎟⎥⎬ exp D eq ⎪ ⎪ ⎢ ⎜ ⎢⎣ 2 ⎜⎝ R eq ⎟⎠⎥⎦ R eq ⎟⎠⎥⎦⎪ ⎭ ⎪ ⎩ ⎣ ⎝ ⎪ ⎧ ⎡ ⎛ ⎫ ⎡ ⎛ ⎪ ⎪ rij ⎞⎤ r ⎞ ⎤⎪ α MMSV ⎟⎟⎥ − 2exp⎢ 2 ⎜⎜1 − ij ⎟⎟⎥⎬ (rij) = ⎨ Deq ⎨exp⎢α2⎜⎜1 − EvdW ⎢⎣ 2 ⎝ R eq ⎠⎥⎦ R eq ⎠⎥⎦⎪ ⎪ ⎪ ⎩ ⎢⎣ ⎝ ⎭ ⎪ ⎪b + (r − R ){b + (r − R )[b + (r − R )b ]} ij 1 2 ij 2 3 ij 1 4 ⎪ 1 ⎪ −6 ⎩−C6rij

where Deq, Req, and rij have the same meanings as in eq 4; α1 and α2 are the stiffness parameters; and C6 is the dispersion constant which is also fitted in the parametrization (as opposed to being determined independently or experimentally). The joining points R1 and R2 and the spline-function parameters b1−b4 were not independently adjusted in the fitting procedure but obtained algebraically. R1 is the inflection point (maximum force) of the Morse function, and R2 is fixed at 1.4Req, following common practice.84 Relaxing this constraint on R2 did not lead to any significant improvement in the fitting. The splinefunction parameters b 1 −b 4 were fixed by smoothness

for 0 ≤ rij ≤ R eq

for R eq ≤ rij ≤ R1 for R1 ≤ rij ≤ R 2 for R 2 ≤ rij < ∞

(5)

conditions at the joining points, i.e., eq 5 and its first derivatives are continuous at every point. The exact expressions to determine the values of R1 and R2 and b1−b4 are given in Table S3 in the SI. The seemingly complicated MMSV potential function thus has only five parameters to be determined in the parametrization, namely Deq, Req, α1, α2, and C6. We emphasize that the strong interactions between the fluid molecules and the cus’s of both MOFs studied here are due to physisorption and are well away from forming a covalent bond,62,82 which is a prerequisite for using a purely nonbonded intermolecular force field. Despite the interaction energy at the 18902



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S2 in the SI. The charges for CO2 were chosen to be −0.35 for O_CO2 (i.e., oxygen atom of the CO2 molecule), in order to be consistent with the TraPPE92 force field used for describing CO2−CO2 interactions in the GCMC simulations. To calculate model I···CO2 interactions, the MMSV potential was used for Mg−O_CO2, with all other interactions calculated by the Buck−CK potential except for those between the CO2 molecule and the Li atoms which were used for capping the dangling bonds in model I. Since Li atoms are not present in the actual CPO-27-Mg framework and no configurations with CO2 being close to Li were sampled for the model I···CO2 complex (see the SI), the Li−O_CO2 and Li−C_CO 2 interactions were calculated using the standard (12−6) LJ potential and the equilibrium distances (Req) were fixed at the values taken from the UFF (using TraPPE for CO2) while the potential well depths (Deq) were allowed to vary but acting merely as an error term in the fitting procedure. The two Deq values for Li−CO2 are omitted from Table 1 to avoid confusion but are given in Table S4 in the SI for completeness. This definition of intermolecular interactions between model I and CO2 leads to 44 free parameters to be adjusted in the fitting procedure (plus the two Li parameters), and the resulting forcefield parameters are summarized in Table 1. The force-field parameters presented in Table 1 yield a very good fit to the whole range of ab initio reference data. Despite the 1065 interaction energies spanning a range from ca. −10 to +5 kcal/mol, the root-mean-square deviation (rmsd) between the force field and the ab initio data is only 0.33 kcal/mol in the whole range and 0.26 kcal/mol in the range up to +1 kcal/mol which is the most important range to describe adsorption in this MOF. A comparison of the model I···CO2 interaction energies given by the B2PLYP-D2/Def2-TZVPP calculations and the corresponding force-field predictions is given in Figure S2a in the SI. A more detailed picture of the performance of the force field can be obtained from Figure 4. In Figure 4a−c, the approach route of a CO2 molecule to the central magnesium(II) site is shown with different orientations of CO2 molecules. In all cases, the ab initio data is very well reproduced. Figure 4d−f shows examples of CO2 approaching other atoms than Mg, and it can be seen that the force field performs equally well. The force field was further validated by 50 “blind” tests in order to examine how well the PES from the ab initio calculations is reproduced by our force-field parameters. Additionally, we performed periodic DFT calculations on the whole framework structure to exclude adverse effects that could arise from the cluster approach used. Full details are given in the SI. 3.2. Force Field for CuBTC−CH4. In order to demonstrate that our approach is not restricted to CO2 adsorption in CPO27-Mg, we followed the same procedure to get force-field parameters for CH4 in CuBTC, with three main differences. First, both the ab initio calculations and the parametrization were performed with the periodic CuBTC structure. Note that the ab initio CuBTC−CH4 potential energy data were taken directly from our previous work45 where we used the DFT/CC method to obtain the PES and no additional DFT/CC calculations were performed for the system in this work. Second, the methane molecule was described as a united-atom in the force field; that is, one methane molecule was represented by a single sphere. And finally, no electrostatic interaction was taken into account as methane molecule is almost spherical and apolar. The MMSV potential was used for Cu−CH4 interactions with all the other framework atoms interacting with a CH4 molecule described by the Buck−CK

cus’s being very high, and the equilibrium distance between the two interacting atoms being considerably smaller than the sum of the corresponding vdW radii, experimental studies have confirmed that the adsorption involved in both systems is fully reversible.23,31 2.3. Force Field Parametrization Strategy. To fit the above proposed model potentials to the ab initio reference data, we used a genetic algorithm88 (GA) because of the nonlinear features of these functional forms. In brief, GAs are heuristic search techniques inspired by the biological process of evolution by means of natural selection. Using mathematical operations that mimic the three biological functions of selection, crossover, and mutation, GAs operate on a dynamic population of potential solutions and generate progressively improved approximations to a solution. GAs are efficient for function minimization in a complex search landscape with possibly strongly correlated adjustable parameters, which is usually the case in force field parametrization.89 Details can be found elsewhere.90 The GA implementation in this work is a multiobjective minimization91 that attempts to create a set of Pareto optima for two objective functions. Details about the objective functions used, GA setup, and minimization procedure are given in the SI.

3. RESULTS AND DISCUSSION 3.1. Force field for CPO-27-Mg−CO2. In total, 1158 ab initio calculations at the B2PLYP-D2/Def2-TZVPP level of theory were carried out with different configurations of model I···CO2, and 1065 of them were used in the force field parametrization, while high energy (>5 kcal/mol) configurations were excluded. The reason for this is that these configurations have negligible influence on adsorption at moderate temperatures (i.e., 278, 298, and 343 K as being investigated in this work) and at low pressures (i.e., up to atmospheric pressure), which is of interest in this work. This large training set allowed us to define the atom types for model I in an explicit way, i.e., in accordance to their hybridizations and coordination environments, without risking overfitting the model, which can happen when the number of adjustable parameters exceeds (or is too large relative to) the number of data points to be modeled. Eight atom types were defined for model I, as shown in Figure 3. In fitting the force field, the partial atomic charges for model I were calculated by the MK method and are presented in Table

Figure 3. Atom types for model I (left) and their corresponding positions in the organic linker of the CPO-27-Mg framework (right); only fragments of the structures are shown with the rest omitted for clarity. 18903



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Table 1. Force-Field Parameters for CPO-27-MgCO2 atom type i Deq (kcal/mol) Req (Å) β Deq (kcal/mol) Req (Å) β

Mg

O1

0.182 3.252 6.665 n/a n/a n/a

O2

C1

0.099 3.446 5.614

0.098 3.343 7.542

0.102 3.518 5.175

0.101 3.379 8.782 Mg−O_CO2b

C_CO2a 0.095 3.618 7.224 O_CO2 0.100 3.452 5.300

C2

C3

H

0.096 3.597 7.501

0.098 3.462 5.910

0.047 2.965 5.376

0.101 3.634 7.855

0.096 3.589 5.549

0.048 3.067 5.343

Deq (kcal/mol)

Req (Å)

α1

α2

C6 [kcal/(mol Å−6)]

0.777

2.658

10.303

11.888

253.925

a

The Buck−CK potential cross-terms for atom type i−C_CO2, followed by the cross-terms for O_CO2. bThe MMSV potential cross-terms for interactions between magnesium(II) sites and O_CO2.

Figure 4. Comparison of the model I···CO2 interaction potentials calculated with the B2PLYP-D2/Def2-TZVPP method (red circle) and the force field (blue line) for the different relative configurations shown in the insets. The arrows indicate the direction of the CO2 molecule moving away from model I.

potential. Six atom types were defined, as shown in Figure 5, which leads to a total of 20 parameters to be fitted using ∼1000 ab initio data points. The resulting force-field parameters, listed in Table 2, give an rmsd value of 0.37 kcal/mol for the interaction energy ranging from ca. −5 to +3 kcal/mol. In spite of the presence of open metal sites in the CuBTC framework, the most attractive adsorption sites for methane at 77 K were determined experimentally31 to be the tight space encapsulated by the four neighboring BTC (BTC = 1,3,5benzene-tricarboxylate) ligands. We have shown previously that the correct prediction of CH4 adsorption at 77 K requires an accurate description of the host−guest potential energy associated with the different adsorption sites.45 Unlike for QM methods that treat interactions in an explicit manner, this is a challenge for force fields using simple functional forms and

therefore a very good test of the functional form chosen and the parameters fitted. We thus fitted the Morse and Mie41,93 potentials to the ab initio data for CuBTC−CH4 as well. The Mie potential is an LJ-type potential with adjustable repulsive (λr) and attractive (λa) exponents and is given by Mie EvdW (rij)

⎡⎛ ⎞ λ r ⎛ ⎞ λ a ⎤ σ σ = ΩDeq ⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠

λa /(λr − λa)⎤ ⎡ λr ⎛ λr ⎞ ⎥ with Ω = ⎢ ⎜ ⎟ ⎢ λr − λa ⎝ λa ⎠ ⎥ ⎣ ⎦

(6)

where σ is the position at which the potential is zero. Ω ensures the minimum potential is −Deq at the equilibrium distance. The 18904



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reason for using the Mie potential instead of the LJ potential was to make sure the comparisons were done among model potentials all having certain extents of flexibility in adjusting the repulsive and attractive parts to better fit the ab initio data. To illustrate the difference between the CuBTC−CH4 potential energy surfaces derived from the different methods, contour plots for the (200) planes (Miller indices), which encompass adsorption site C (the cus’s) and site B (close to the corner of two neighboring BTC-ligands connected by the copper ions), are given in Figure 6. Note that the lower (i.e., more negative) the potential energy, the stronger the interaction. The differences are very apparent. In our previous work, we showed that the strong interaction at cus’s (site C) was correctly captured by the DFT/CC method,45 and Figure 6a further confirms that the enhanced interaction, arising from the local electric field effects due to the open copper(II) site, is very short-ranged. In contrast to this, the UFF force field which is based on a (12−6) LJ potential and was chosen here to represent the performance of generic force fields completely fails to capture the interaction of the cus’s. By comparing the differences between Figure 6b, d, and e, the importance of carefully choosing an appropriate functional form for cus’s is further confirmed. All three force fields were fitted independently to the ab initio data, and they all reproduce the strong interaction at the cus’s (compared to the UFF (Figure 6c), where cus’s are completely missed). However, only the force field presented in Table 2 is able to preserve the anisotropic features of the potential energy surface around the copper paddle wheels, although this feature is slightly less pronounced using our force-field parameters than in the original DFT/CC data. Notably, the parameters derived for both the Morse potential and the Mie potential result in a much stronger interaction for site B, which is close to the corner of two neighboring BTC ligands connected by copper(II). This is not surprising given the geometrical arrangements of these sites

Figure 5. Fragment of the CuBTC framework showing two adjacent copper(II) cus’s and four connecting BTC ligands. Atom types defined in the force field are shown except that for copper which corresponds to the brown spheres. Experimental adsorption sites31 are represented by colored spheres: site A (blue) is located at the center of the cage window; site B (green) is close to the corner of two neighboring BTC ligands connected by copper(II) ions; and site C (yellow) is located close to the open copper(II) site.

Table 2. Force-Field Parameters for CuBTC−CH4 atom type i Deq (kcal/mol) Req (Å) β

O 0.123 3.874 7.300

C1 0.123 4.062 4.750 Cu−CH4b

C2

C3

H

CH4a 0.115 4.085 4.365

0.121 4.081 4.197

0.074 3.372 4.156

Deq (kcal/mol)

Req (Å)

α1

α2

C6 [kcal/(mol Å−6)]

1.500

3.023

11.098

11.098

246.173

a

The Buck−CK potential cross-terms for atom type i−CH4; the methane molecule was modeled as a single sphere using the unitedatom approach. bThe MMSV potential cross-terms for interactions between copper(II) sites and CH4.

Figure 6. Contour plots of the potential energy between a methane molecule and the CuBTC framework on the (200) plane derived from the different methods: (a) DFT/CC,45 (b) force field presented in Table 2, (c) UFF, (d) force field using the Morse potential, and (e) force field using the Mie potential. Adsorption sites B and C (at the cus’s) are labeled. The white space corresponds to the CuBTC framework. 18905



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around the cus (see Figure 5; sites A, B, and C are ∼4.8, 5.1, and 3.1 Å from the copper(II) site, respectively). In all the potential functions examined here, as well as most semiempirical model potentials, the nonbonded monopole− monopole interactions are only distance-dependent. Since no angular dependence of the monomers are considered in these force fields, site B can benefit from the strong interactions created by the two deep potential wells surrounding each copper(II) site, though it does not actually face the cus’s. On the basis of these observations, we note that in future force field development explicitly accounting for angular dependence in the functional forms may lead to improvements in describing the interactions at cus’s. 3.3. GCMC Simulations. To validate our force fields on their capability of correctly capturing adsorption mechanisms, we computed gas adsorption isotherms using GCMC simulation and compare the results from our force-field parameters with experimental data as well as the UFF-based simulations. All GCMC simulations were carried out with a locally modified version of the multipurpose simulation code MUSIC.94 Details of the simulation setups can be found in the SI, and details of the method are given elsewhere.95 With the force-field parameters listed in Table 1, we studied the CO2 adsorption in CPO-27-Mg at different temperatures. The simulated CO2 adsorption isotherms using the parametrized force field and the UFF for comparison are shown in Figure 7. Experimentally, the CPO-27-Mg MOF has been shown to take up impressive amounts of CO2 at ambient temperatures up to atmospheric pressure.23,27,30,62 However, it is clear from Figure 7a that the GCMC simulation based on the UFF can not correctly predict this significant uptake at the low pressures. Large discrepancies were also observed in the work of Yazaydın et al.,30 where the DREIDING force field together with the UFF for Mg atoms were used. In contrast, the simulations based on our force field predicted the CO2 adsorption in good agreement with the experiments. The overestimations may be partly explained by the quality of the experimental sample as the simulations are carried out in infinite, perfect, and fully activated crystals. When the experimental adsorption isotherm at 298 K is scaled by a factor of 1.1, which is the ratio between the theoretical39 (1733 m2/g using a nitrogen probe with a diameter of 3.681 Å) and experimental23 BET (1542 m2/g) surface areas, we find almost quantitative agreement with the experimental data. Our force field is able to predict quantitatively the uptake of CO2 not only for 298 K but also for 278 and 343 K as illustrated in Figure 7b. The simulations not only reproduce the general trends of the experimental adsorption isotherms but also the inflection in the isotherm23 which occurs when one CO2 molecule is adsorbed per magnesium(II) site. In line with this good prediction of the adsorption isotherms, the calculated initial isosteric heat of adsorption (Qst, definition and calculation details are in the SI) of 9.5 kcal/mol at 298 K is also in good agreement with experimental values in the literature, 9.3 kcal/mol,62 10.0 kcal/mol,23 and 11.2 kcal/mol.27 Moreover, in the simulation, the first CO2 molecules are exclusively adsorbed at the open magnesium(II) sites in an endon fashion at low loadings, which is also in line with the experimental findings.82,96 At a loading of ∼0.75 adsorbed CO2 per magnesium(II) site at 298 K, the simulated distance between the Mg atom and the nearby oxygen of the adsorbed CO2 molecule varies between 2.3 and 2.8 Å with the angle of Mg−O_CO2−C_CO2 between 120° and 150°. These values

Figure 7. CO2 adsorption isotherms for CPO-27-Mg. (a) Adsorption isotherms at 298 K. The scaled experimental isotherm was obtained by multiplying the corresponding experimental results by 1.1, the ratio between the simulated and experimental surface areas. (b) Comparison between experimental (closed symbols) and simulated (open symbols) adsorption isotherms at 278 (blue triangle), 298 (red circle), and 343 K (black square). Note that the isotherms are represented on a logarithmic pressure axis to better show the adsorption behavior at low pressure and that the isotherms shown are unscaled isotherms. Experimental data were taken from ref 23.

are in good agreement with the neutron diffraction experiments performed at 20 K, where the corresponding distance and angle were found to be 2.3 Å and 129°, respectively, for the same loading.96 This further confirms that the proposed force field provides a correct description of the adsorption mechanism on the molecular level. Methane adsorption isotherms in CuBTC obtained from both DFT/CC-PES and force field-based simulations at 77 K are shown in Figure 8 together with the experimental results. The most significant feature of the experimental isotherm is the step at a loading of 85 molecules per unit cell, which was experimentally determined to be the filling of the 88 favorable adsorption sites of which the cus’s constitute 48.31 Our previous work showed that GCMC simulations based on the DFT/CC-PES were able not only to accurately describe the interactions with the cus’s, as well as with all other adsorption sites, but also correctly capture the adsorption mechanisms for a wide range of temperatures and pressures.45 In Figure 8a, an almost quantitative agreement between the isotherms predicted by the DFT/CC-PES and the force field is observed, which confirms the accuracy of the force field in reproducing the PES as described by the DFT/CC method. More noteworthy, the significance of the potential functional form chosen is re18906



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Figure 9. Comparison of the absolute methane adsorption isotherms for PCN-14 between the force field-based GCMC simulation results (open symbols) and the experimental results (closed symbols) at 240 (green diamond), 270 (blue triangle), 280 (red circle), and 290 K (black square). The force-field parameters used are shown in Table 2, and the experimental results are taken from ref 97.

predicting methane adsorption in PCN-14 achieved by using our force field when compared to the UFF-based simulation results as shown in Figure S5 in the SI. On the basis of these promising observations, we foresee that, in comparison to generic classical force fields, the proposed parameters may also deliver an improved description of the Cu−CH4 interaction for other MOFs consisting of Cu2(OOCR)4 paddle wheels and might do reasonably well for open copper(II) sites in different coordination environments.

Figure 8. Methane adsorption isotherms for CuBTC at 77 K. (a) Comparison of simulated isotherm based on the proposed force field with the isotherms from the DFT/CC-PES-based simulation and experiments. (b) Comparison of simulated isotherms using different potential models. Experimental data were taken from ref 31.

4. CONCLUSIONS In order to improve the description of the interaction between gas molecules and MOFs with coordinatively unsaturated metal sites, we have studied two systems, namely CO2 adsorption in CPO-27-Mg and CH4 adsorption in CuBTC. Several model potentials were carefully compared and the MMSV and BuckCK potentials were chosen for describing the framework-fluid interactions. On the basis of the accurate ab initio reference data, the force fields were parametrized using a multiobjective genetic algorithm and were subsequently validated through extensive comparisons between the force field-based simulation results and experimental data available in the literature. In both cases, the adsorption isotherms are in very good agreement with experiments, and more importantly, the interactions at the cus’s as well as the overall adsorption mechanisms in the frameworks are captured correctly. Using the force-field parameters developed for the CuBTC−CH4 system, CH4 adsorption in another Cu-MOF, PCN-14, can be predicted quantitatively for different temperatures. These results are promising in terms of developing force-field parameters that are transferable to other MOFs. However, more high quality adsorption data, ideally measured at low temperatures to capture the adsorption mechanism in more detail in MOFs with Cu and Mg cus’s, is necessary to judge how widely transferable these parameters are. Furthermore, the proposed bottom-up methodology of combining the advantages of both ab initio methods and GCMC simulation holds promise for correctly describing the

emphasized by the comparison of the adsorption isotherms in Figure 8b. Neither the Morse potential nor the Mie potential correctly predicts the adsorption isotherm. While the strong interaction at the cus’s was captured, the simulations based on these two force fields predicted the filling of site B at much lower pressures, leading to a more rapid saturation of methane inside the framework. This was expected since neither of the force fields correctly distinguished the relative strengths of sites B and C (at the cus’s), which is evident in Figure 6d and e. In contrast to standard generic force fields, such as UFF and DREIDING that are generally considered to be transferable, it is unclear a priori if force fields developed from ab initio calculations on a particular system are transferable to other systems. We therefore computed methane adsorption isotherms for PCN-1497 at different temperatures using the forcefield parameters presented in Table 2. Both CuBTC and PCN14 consist of Cu2(OOCR)4 paddle wheels, but the two structures differ in the bridging organic ligands, i.e., 1,3,5benzene-tricarboxylate for CuBTC and 5,5'-(9,10anthracenediyl)di-isophthalic for PCN-14, resulting in different framework topologies. Despite the structural diversity of adsorption sites in PCN-14, the force field parametrized for CuBTC yields very good agreement with the experimental isotherms for all the temperatures investigated, as shown in Figure 9, demonstrating that the force field provides an excellent description of the interactions between methane and PCN-14. More encouraging is the significant improvement in 18907



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(8) Almeida Paz, F. A.; Klinowski, J.; Vilela, S. M. F.; Tome, J. P. C.; Cavaleiro, J. A. S.; Rocha, J. Chem. Soc. Rev. 2012, 41 (3), 1088−1110. (9) Cohen, S. M. Chem. Rev. 2011, 112 (2), 970−1000. (10) Czaja, A. U.; Trukhan, N.; Muller, U. Chem. Soc. Rev. 2009, 38 (5), 1284−1293. (11) Sumida, K.; Rogow, D. L.; Mason, J. A.; McDonald, T. M.; Bloch, E. D.; Herm, Z. R.; Bae, T.-H.; Long, J. R. Chem. Rev. 2011, 112 (2), 724−781. (12) Li, J.-R.; Sculley, J.; Zhou, H.-C. Chem. Rev. 2011, 112 (2), 869− 932. (13) Shah, M.; McCarthy, M. C.; Sachdeva, S.; Lee, A. K.; Jeong, H.K. Ind. Eng. Chem. Res. 2011, 51 (5), 2179−2199. (14) Suh, M. P.; Park, H. J.; Prasad, T. K.; Lim, D.-W. Chem. Rev. 2011, 112 (2), 782−835. (15) Liu, J.; Thallapally, P. K.; McGrail, B. P.; Brown, D. R.; Liu, J. Chem. Soc. Rev. 2012, 41 (6), 2308−2322. (16) Wu, H.; Gong, Q.; Olson, D. H.; Li, J. Chem. Rev. 2012, 112 (2), 836−868. (17) Yoon, M.; Srirambalaji, R.; Kim, K. Chem. Rev. 2011, 112 (2), 1196−1231. (18) Ranocchiari, M.; Bokhoven, J. A. v. Phys. Chem. Chem. Phys. 2011, 13 (14), 6388−6396. (19) Kreno, L. E.; Leong, K.; Farha, O. K.; Allendorf, M.; Van Duyne, R. P.; Hupp, J. T. Chem. Rev. 2011, 112 (2), 1105−1125. (20) McKinlay, A. C.; Morris, R. E.; Horcajada, P.; Férey, G.; Gref, R.; Couvreur, P.; Serre, C. Angew. Chem., Int. Ed. 2010, 49 (36), 6260−6266. (21) Della Rocca, J.; Liu, D.; Lin, W. Acc. Chem. Res. 2011, 44 (10), 957−968. (22) Horcajada, P.; Gref, R.; Baati, T.; Allan, P. K.; Maurin, G.; Couvreur, P.; Férey, G.; Morris, R. E.; Serre, C. Chem. Rev. 2011, 112 (2), 1232−1268. (23) Dietzel, P. D. C.; Besikiotis, V.; Blom, R. J. Mater. Chem. 2009, 19 (39), 7362−7370. (24) Chui, S. S. Y.; Lo, S. M. F.; Charmant, J. P.; nbsp, H; Orpen, A. G.; Williams, I. D. Science 1999, 283 (5405), 1148−1150. (25) Dincă, M.; Long, J. R. J. Am. Chem. Soc. 2007, 129 (36), 11172− 11176. (26) Zhou, W.; Wu, H.; Yildirim, T. J. Am. Chem. Soc. 2008, 130 (46), 15268−15269. (27) Caskey, S. R.; Wong-Foy, A. G.; Matzger, A. J. J. Am. Chem. Soc. 2008, 130 (33), 10870−10871. (28) Sumida, K.; Horike, S.; Kaye, S. S.; Herm, Z. R.; Queen, W. L.; Brown, C. M.; Grandjean, F.; Long, G. J.; Dailly, A.; Long, J. R. Chem. Sci. 2010, 1 (2), 184−191. (29) Llewellyn, P. L.; Bourrelly, S.; Serre, C.; Vimont, A.; Daturi, M.; Hamon, L.; De Weireld, G.; Chang, J.-S.; Hong, D.-Y.; Kyu Hwang, Y.; Hwa Jhung, S.; Férey, G. r. Langmuir 2008, 24 (14), 7245−7250. (30) Yazaydın, A. O. z. r.; Snurr, R. Q.; Park, T.-H.; Koh, K.; Liu, J.; LeVan, M. D.; Benin, A. I.; Jakubczak, P.; Lanuza, M.; Galloway, D. B.; Low, J. J.; Willis, R. R. J. Am. Chem. Soc. 2009, 131 (51), 18198− 18199. (31) Getzschmann, J.; Senkovska, I.; Wallacher, D.; Tovar, M.; Fairen-Jimenez, D.; Düren, T.; van Baten, J. M.; Krishna, R.; Kaskel, S. Microporous Mesoporous Mater. 2010, 136 (1−3), 50−58. (32) Chowdhury, P.; Bikkina, C.; Gumma, S. J. Phys. Chem. C 2009, 113 (16), 6616−6621. (33) Sumida, K.; Her, J.-H.; Dincă, M.; Murray, L. J.; Schloss, J. M.; Pierce, C. J.; Thompson, B. A.; FitzGerald, S. A.; Brown, C. M.; Long, J. R. J. Phys. Chem. C 2011, 115 (16), 8414−8421. (34) Mallick, A.; Saha, S.; Pachfule, P.; Roy, S.; Banerjee, R. J. Mater. Chem. 2010, 20 (41), 9073−9080. (35) Düren, T.; Bae, Y.-S.; Snurr, R. Q. Chem. Soc. Rev. 2009, 38 (5), 1237−1247. (36) Keskin, S.; Liu, J.; Rankin, R. B.; Johnson, J. K.; Sholl, D. S. Ind. Eng. Chem. Res. 2008, 48 (5), 2355−2371. (37) Tafipolsky, M.; Amirjalayer, S.; Schmid, R. Microporous Mesoporous Mater. 2010, 129 (3), 304−318.

enhanced interactions at cus’s in molecular simulation of adsorption. A straightforward application of this protocol is to extend it to the isostructural analogues of CPO-27-Mg, i.e., CPO-27-M (MCo, Ni, Fe, etc.). This series of MOFs have been identified as promising candidates in various applications and generic force field based simulations cannot correctly describe the interactions with the cus’s.30 We expect the parameters for the linker to remain the same while more ab initio calculations are required to parametrize the metals and their immediate environment. Last but not least, we emphasize that the choice of model potentials, or potential functional forms to be specific, has a critical influence on the accuracy of the predictions of adsorption in MOFs with cus’s. Potentials like the LJ and Morse potentials are simple and widely adopted in majority of the existing force fields and they will undoubtedly continue to play an important role in molecular simulation. Nevertheless, the correct description of adsorption at coordinatively unsaturated metal sites requires more complicated potentials and our work is only a first step for deriving reliable and hopefully transferable force fields for this purpose.

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ASSOCIATED CONTENT

S Supporting Information *

Computational details about the construction of the model cluster for the CPO-27-Mg−CO2 system. Sampling scheme for generating the relative model I···CO2 configurations. Formulas for determining the joining points and spline-function parameters of the MMSV model potential. Details about the validation of the force field derived for the CPO-27-Mg−CO2 system. Methane adsorption isotherms for PCN-14 MOF at 240, 270, 280, and 290 K. Detailed information on the objective functions used in the force field parametrization, the genetic algorithm implementation, and the minimization procedure. GCMC simulation details, generic force-field parameters for the MOF, CO2, and CH4 atoms, and partial atomic charges for the CPO-27-Mg framework. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Lukás ̌ Grajciar and Petr Nachtigall for very helpful discussions and the EPSRC for funding (EP/G062129/1). This work made use of the EaSTCHEM Research Computing Facility (http://www.eastchem.ac.uk/rcf) and the Edinburgh Compute and Data Facility (ECDF) (http://www.ecdf.ed.ac. uk).

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REFERENCES

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