Modeling and Visualization of CO2 Adsorption on Elastic Layer

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Modelling and Visualization of CO Adsorption on Elastic Layer-Structured Metal-Organic Framework-11: Toward a Better Understanding of Gate Adsorption Behavior Hideki Tanaka, Shotaro Hiraide, Atsushi Kondo, and Minoru T. Miyahara J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/jp512870p • Publication Date (Web): 13 Apr 2015 Downloaded from http://pubs.acs.org on April 20, 2015

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The Journal of Physical Chemistry

Modelling and Visualization of CO2 Adsorption on Elastic Layer-Structured Metal-Organic Framework11: Toward a Better Understanding of Gate Adsorption Behavior

Hideki Tanaka, a* Shotaro Hiraide,a Atsushi Kondo,b and Minoru T. Miyaharaa* a

Department of Chemical Engineering, Kyoto University, Nishikyo, Kyoto 615-8510, Japan.

b

Tokyo University of Agriculture and Technology, 3-8-1 Harumi, Fuchu, Tokyo 183-8538, Japan

ABSTRACT: Elastic layer-structured metal-organic framework-11 (ELM-11) is a soft porous crystal (SPC) with a 2D square-grid framework [Cu(BF4)2(bpy)2] (bpy = 4,4′-bipyridine) that has attracted attention as a material for CO2 capture and storage because of its gate adsorption properties. Herein, we demonstrate that the structure of CO2-encapsulated ELM-11 at 100 kPa and 273 K can be precisely modelled and visualized by our new structure refinement method, which combines Rietveld analysis of in situ synchrotron X-ray powder diffraction data with molecular simulations. We believe that this is the first study in which the structure of a guest–SPC system

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that exhibits an extensive, complex structural transformation by the gate adsorption was successfully refined by such an approach. The crystallographic data of the open framework structure of ELM-11 enables grand canonical Monte Carlo (GCMC) simulations of CO2 adsorption. The free energy analysis of the gate adsorption phenomenon with the resulting GCMC adsorption isotherm of CO2 provides the precise Helmholtz free energy change of the host framework during the structural transition, which is difficult to access experimentally. Finally, we demonstrate that the temperature dependence of the gate adsorption pressure can be predicted using the Helmholtz free energy change of the host. KEYWORDS: soft porous crystal, gate adsorption, Rietveld analysis, molecular simulation, free energy analysis

1 INTRODUCTION Metal organic frameworks (MOFs) and porous coordination polymers (PCPs), which consist of metal ions and organic linkers, are novel materials that have a number of potential applications such as gas storage, separation, and catalysis.1–6 Soft porous crystals (SPCs),7 which were classified as third-generation PCPs by Kitagawa and co-workers,3,9 possess structural transformability; that is, the crystals exhibit structural deformations induced by various external stimuli such as temperature changes, pressurization, and guest adsorption. The guest-induced structural transition of SPCs typically occurs at a threshold gas pressure and leads to an abrupt increase in the adsorption isotherm, phenomena referred to as ‘gate adsorption’ and ‘breathing.’ The high sensitivity of these materials to gas pressure results mainly from the ability of SPCs to deform by recognizing the shapes and chemical properties (e.g., polarity) of guests. Thus, it is expected that the on-demand synthesis of SPCs with specific gate adsorption properties will open new


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possibilities for highly efficient gas separation processes in the chemical industry. However, at present, the rational design of SPCs for specific applications is still a challenging task, requiring extensive experiment-based screening to optimize the desired properties. Therefore, to predict and design new SPCs with suitable performance, sophisticated thermodynamic modelling of the gate adsorption and breathing phenomenon is required. The osmotic statistical ensemble10 is particularly appropriate for describing adsorption-induced structural transitions when the host framework deforms and changes volume. Coudert et al.10 first developed a thermodynamic description of gate adsorption and breathing phenomena based on the osmotic statistical ensemble and devised an analytical free energy analysis method for estimating the difference in the Helmholtz free energy between the initial and final SPC structures in adsorption-induced structural transitions. This method is simple and useful because it only relies on an experimental adsorption isotherm and enables the classification of the gate adsorption and breathing phenomena. This analytical approach was used to predict the temperature–pressure phase diagram of Xe adsorption on MIL-5311 as well as the pressure phase diagram for the adsorption of a binary mixture of CH4 and CO2 on MIL-53,12 which provided a good description of the experimental data. A more sophisticated thermodynamic description incorporating the adsorption-induced stress exerted on SPCs was then developed, which successfully explained the hysteresis phenomenon experimentally observed during breathing transitions (Xe and CO2 adsorption on MIL-53).13,14 Watanabe et al. performed a free energy analysis of gate adsorption with the aid of grand canonical Monte Carlo (GCMC) simulations and a simple toy model of mutually interpenetrating junglegym (JG) framework structures.15 The calculated free energy landscape elucidated the process of adsorption-induced structural transitions through metastabilized and activated states and provided


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a better understanding of the hysteric phenomena associated with gate adsorption. Their methodology was then applied to various SPCs with interpenetrating JG,16 stacked-layer,17,18 and lozenge-shaped19,20 motifs, which shed light on the nature of the gate adsorption and breathing phenomena. However, despite the progress made by the above-mentioned simulation studies in understanding the fundamental mechanism of structural transitions, the high sensitivity of SPCs to the chemical properties of the guests remains unexplained because the simplified models used in these studies can only mimic the geometrical and physical properties of the SPCs. Several authors have recently performed hybrid osmotic Monte Carlo (HOMC) simulations using all-atom SPC models to investigate the adsorption-induced structural transitions in CO2–MIL-532123

and N2–ZIF-824 systems. However, the authors’ success in capturing the observed breathing and

gate adsorption phenomena has been limited because the HOMC method cannot sample the full phase space, e.g., when adsorbates are densely packed in pores in a pre-transition state. This difficulty can be overcome by the free energy analysis method, which enables the calculation of not only transition states but also activation states. We have conducted a free energy analysis with the aid of GCMC simulations for the Ar–ZIF-8 system and achieved a quantitative understanding of its gate-opening and gate-closing mechanisms.25 However, the successful simulations of CO2– MIL-53, N2–ZIF-8, and Ar–ZIF-8 are largely a result of the preliminarily revealed crystallographic information about the structural transitions of these systems by X-ray diffraction measurements. In many cases, the deformations of SPCs induced by guest adsorption are enormous and complex; the accompanying cracking of their single crystals makes it difficult to determine their framework structures by single-crystal X-ray diffraction. This complicates attempts to simulate gate adsorption phenomena using all-atom SPC models. It is therefore essential to establish a structure refinement method for guest–SPC systems using X-ray powder diffraction (XRPD) data, which


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can be used to perform free energy analyses with the aid of molecular simulations; then, a sophisticated thermodynamic model can be constructed to predict the structural transitions in SPCs. The Rietveld method, a full-pattern least-squares fitting technique which is widely used in powder diffraction structure refinement, minimizes the difference between the experimental and calculated XRPD diagrams.26 However, this method requires a starting structure model, and thus, the prospective determination of the deformed framework structure of the SPC and the configurations of the guest molecules in the framework by a rational method. The combination of the Rietveld method and the maximum entropy method (MEM/Rietveld) can solve this problem and has been applied to several guest–PCP systems (e.g., O2–CPL-1, H2–CPL-1, and C2H2–[Cu2(pzdc)2pyz] systems: pzdc = 2,3-pyrazinedicarboxylate and pyz = pyrazine).27–32 The MEM/Rietveld method is useful but time-consuming because of its self-consistent iterative procedure; moreover, it is difficult to apply when SPCs undergo extensive and complex deformations upon guest adsorption because such changes make construction of the starting model difficult. Therefore, a new structure refinement method suitable for such a system must be developed. Elastic layer-structured metal-organic framework-11 (ELM-11) is an SPC with a 2D square-grid framework [Cu(BF4)2(bpy)2] (bpy = 4,4′-bipyridine) and is the first SPC for which the gate adsorption behavior of a gas was observed.33 This compound shows typical gate adsorption behaviors for several gases34–44 and has attracted particular attention as a new material for CO2 capture and storage. ELM-11 is obtained by the dehydration of {[Cu(bpy)(H2O)2(BF4)2](bpy)} with a 3D interpenetrated framework (pre-ELM-11). It exhibits a 26% increase in the distance between the 2D square-grid layers by encapsulating two CO2 molecules per Cu(BF4)2(bpy)2 at 273 K (hereafter ELM-11 ⊃ 2CO2).38 The structure of pre-ELM-11 was determined by single-crystal X-ray diffraction;45 however the structures of ELM-11 and ELM-11 ⊃ 2CO2 have not yet been


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precisely determined because only XRPD is available for both compounds and they achieve tortuous structural transformations from pre-ELM-11. The present study aims to model and visualize the structure of ELM-11 ⊃ 2CO2 by our new structure refinement method, which combines Rietveld analysis with molecular simulations using in situ synchrotron XRPD data obtained at the BL02B2 beamline of SPring-8, Japan. We then use the obtained structure as the all-atom model for free energy analysis with the aid of GCMC simulations to obtain a better understanding of the gate adsorption behavior of ELM-11.

2 EXPERIMENTAL 2.1 CO2 Adsorption. Pre-ELM-11 was purchased from Tokyo Chemical Industry Co., Ltd. After evacuation at 373 K for 10 h under a pressure of less than 0.1 mPa, the pre-ELM-11 sample was completely transformed into ELM-11, which was structurally confirmed by in situ synchrotron XRPD measurement. The adsorption isotherms of CO2 on ELM-11 at 258, 268, 273, 278, and 283 K were measured with a BELSORP-max instrument (Microtrac Bel) and a cryostat equipped with a two-stage Gifford–McMahon refrigerator.25 The same sample was used for adsorption measurements performed at different temperatures without replacing the sample cell to reduce the experimental error. The cell temperature was kept within ±0.01 K during the adsorption measurements. 2.2 In situ Synchrotron XRPD. The pre-ELM-11 sample was placed in a soda glass capillary measuring 0.4 mm in diameter which was attached to an in situ stainless steel cell using an epoxy adhesive. The sample was then dehydrated in vacuo at 373 K for 10 h. The in situ synchrotron


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XRPD measurement was performed at the BL02B2 beamline of SPring-8 with a large DebyeScherrer-type diffractometer.46 The temperature was maintained at 273 K by a nitrogen gas blower, and 100 kPa CO2 gas (relative pressure P/P0 of 0.0286) was introduced into the capillary using a lab-made gas handling system. The capillary was oscillated by 60° to obtain uniform diffraction intensities. The wavelength of the incident X-rays was 0.079937 nm. 3 METHODS AND SIMULATIONS 3.1 Modelling and Visualization of ELM-11 ⊃ 2CO2. We started from the open framework structure of ELM-11 (structure 1, see Table S1 and Figure S1, Supporting Information) after the gate adsorption of CO2 at 273 K that was determined based on a synchrotron XRPD pattern using EXPO software by Kondo et al.36 However, the structure of 1 does not contain guest CO2 molecules, and the resulting the weighted profile R-factor (Rwp) factor is relatively large (13.45%). We therefore inserted CO2 molecules into 1 and refined the overall structure of ELM-11 ⊃ 2CO2, as described below. 3.1.1 CO2–Host Framework Interaction. The interaction potential between CO2 and the host framework, Uguest, was assumed to be the sum of the Coulombic and Lennard-Jones (LJ) potentials:

U guest = U Coulombic + U LJ U Coulombic = ∑

U LJ =

∑

,

(1)

,

(2)

qi q j 4πε 0 rij

 σ 12  σ  6  ij ij 4ε ij   −    ,      r r   ij   ij  

(3)


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where qi is the atomic charge; ε0 (= 8.8542 × 10–12 C2N–1m–2) is the vacuum permittivity; rij is the interatomic distance; and σij and εij are the LJ parameters. The Ewald summation method was used to correct the long-range Coulombic interactions with a charge screening constant of 2.0 nm−1 and the reciprocal space sum for k vectors of La/2π|k|, Lb/2π|k|, and Lc/2π|k| ≤ 10 (where La, Lb, and Lc are the lengths of a parallelepiped-shaped cell: La = 3 × a = 4.1103 nm, Lb = 3 × b = 3.3216 nm, and Lc = 2 × c = 3.7462 nm; a, b, and c are the lattice constants of 1). The short range interactions were calculated using a cut-off of 1.6289 nm (< 0.5 Lb). Periodic density functional theory (DFT) calculations (a 1 × 1 × 1 unit cell was chosen) at the GGA-PBE/DNP level were performed using the DMol3 package,47,48 and the atomic charges in the host framework were obtained by Mulliken population analysis. The modified universal force field (UFF),49 with parameters σUFF and αεUFF (see Table S2 and Figure S2, Supporting Information), was applied to the framework atoms to calculate the LJ interaction term. The scaling factor α was determined by the procedure described in Section 3.1.3. The guest-host framework interactions were calculated with the cross parameters,

σgh and εgh, obtained from the Lorentz-Berthelot mixing rules: σgh = (σgg + σUFF)/2 and εgh = (εgg αεUFF)1/2, and were truncated at a distance of 1.6289 nm. The parameters for the CO2–CO2 interaction—the atomic charges, σgg and εgg, and the C–O bond length—were adopted from Chen et al.50 (see Table S3, Supporting Information). 3.1.2 Intra–Host Framework Interaction. The total interaction potential of the host framework, Uhost, can be divided into a bonded term and a non-bonded term, where the latter is the sum of the Coulombic and LJ potentials:

U host = U bonded + U nonbonded = U bonded + U Coulombic + U LJ .

(4)


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In this study, two bond stretching terms (Cu–N and Cu–F), two angle bending terms (N–Cu–N and N–Cu–F), and one bond rotation term between the pyridine rings of bpy (C–C–C–C) were considered as components of the bonded potential, and all remaining degrees of freedom were rigidly constrained. We performed DFT calculations at the PBEPBE/6-31G(d) level using the Gaussian03 package51 for an isolated fragment of ELM-11, Cu(BF4)2(bpy)4, to parameterize each component of the bonded potential. The DFT-optimized BF4 and bpy moieties were first arranged in a symmetric fashion along the three orthogonal axes with their origins at the center of Cu, and then, the overall fragment was optimized with all atoms on the three axes immobilized (see Figure S3, Supporting Information). Further DFT calculations were conducted in a stepwise manner by only varying each bond length and angle of the optimized fragment. The bond rotation term (C– C–C–C) was also parameterized with an isolated bpy molecule in a manner similar to that described above. The same conditions described in Section 3.1.1 were applied for the calculation of the non-bonded term. The LJ interactions of the framework atoms separated by fewer than two bonds, including the coordination bonds, were eliminated in analogy to the potential model for nalkanes.52 Moreover, the Coulombic and LJ interactions between the atoms belonging to the same moieties (BF4 and bpy) were also discarded for the calculation of the non-bonded potential. 3.1.3 Grand Canonical Monte Carlo Simulation. The scaling factor α of the modified UFF was determined such that the theoretical adsorption isotherm of CO2 on the host framework using GCMC simulations fitted the plateau region of the experimental adsorption isotherm of CO2 on ELM-11 at 273 K after gate adsorption. In the GCMC simulations, the framework atoms were immobilized and four trial moves for CO2 (displacement, rotation, creation, and deletion) were made with the same probabilities. The system was equilibrated for 1 × 107 Monte Carlo steps, after which data were collected for another 1 × 107 MC steps. The length of the Markov chain (1 × 107


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steps) corresponds to more than 6 × 104 trials per CO2. The simulation box was constructed with 3 × 3 × 2 unit cells. Periodic boundary conditions were applied in three directions, and the interaction potential between the CO2 molecules was also calculated using the Ewald summation method and the Lorentz-Berthelot mixing rules, as was done for the CO2–host framework interaction described above. The saturated vapor pressures for the CO2 model over the temperature range 248–293 K were determined by Gibbs ensemble Monte Carlo (GEMC) simulations using the code provided by Errington and Panagiotopoulos.53 At each temperature, the system with 1000 CO2 molecules was equilibrated for 5 × 106 MC steps, after which the data were collected for another 1.5 × 107 MC steps. A comparison of the obtained saturated vapor pressure–temperature curve and the corresponding experimental curve is shown in Figure S4, Supporting Information. 3.1.4 Configuration of Adsorbed CO2. The GCMC simulations described in Section 3.1.3 were used to obtain the density distributions of each atom of CO2 in the host framework at 273 K. More than 4 × 104 configurations of the CO2 molecules were collected. We determined the barycentric positions of the CO2 molecule at each possible adsorption site by averaging the obtained distributions of the carbon atom of CO2. The candidate location and orientation of CO2 at the adsorption site were adopted from those of the CO2 molecule sampled by the GCMC simulations that was closest to the determined barycentric position. 3.1.5 Structural Relaxation of ELM-11 ⊃ 2CO2 Model. We performed canonical Monte Carlo (MC) simulations to relax the overall structure of 1 with CO2 (3 × 3 × 2 unit cells) at 273 K. The CO2–host framework, CO2–CO2, and intra-host framework interactions used in the canonical MC simulation are those presented in Sections 3.1.1 and 3.1.2. The configurations of CO2 in the host


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framework determined by the procedure described in Section 3.1.4 were used as the initial configurations for the canonical MC simulations.

Figure 1. Part of the simulation cell of ELM-11 ⊃ 2CO2 for the canonical MC method (1 × 1 × 1 unit cell). The translucent atoms are those produced by symmetry operations.

Kondo et al. reported that the ELM-11 ⊃ 2CO2 structure had the symmetry of space group C2/c (No. 15).36 We confirmed this assignment by a satisfactory fit to our synchrotron XRPD pattern by the Le Bail method using the RIETAN-FP54 software package (Figure S5 and Table S4, Supporting Information). This suggests that the ELM-11 ⊃ 2CO2 structure is crystalline even though the thermal fluctuation of adsorbed CO2 should be relatively large at 273 K. Several trial moves based on the symmetry of the space group were performed in the canonical MC simulations. The symmetry axes and points in the ELM-11 ⊃ 2CO2 structure (1 × 1 × 1 unit cell) are shown in Figure 1. The MC moves are as follows: (i) rotation of bpy I about the center of symmetry located between the pyridine rings; (ii) translation of the center of mass of bpy II along the twofold axis (C2), rotation of bpy II about the C2 axis, and bond rotation (C–C–C–C torsion) between the pyridine rings of bpy II; (iii) translation of the center of mass of BF4 and rotation of BF4; and (iv) translation of the center of mass of CO2 and rotation of CO2. The pyridine ring, BF4, and CO2 were


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treated as rigid bodies, and the Cu atom was immobilized during the simulation. The system was equilibrated for 1 × 106 MC steps, and the configuration with the lowest total potential energy was collected over another 1 × 106 MC steps for use as the initial structure for the Rietveld analysis. 3.1.6 Rietveld Analysis. The initial ELM-11 ⊃ 2CO2 structure obtained by the canonical MC simulation (Section 3.1.5) was refined by the Rietveld method using the PDXL (Rigaku Corp., Japan)55 and RIETAN-FP54 software packages. The peak profile was approximated by a split pseudo-Voigt function, and soft constraints were imposed on all bond lengths and bond angles during refinement. The scattering of H was taken into account by attaching the H atoms to the bpy molecules, but the H atom parameters were not refined. The site occupancy of the CO2 molecule was set to 1.0 according to the experimental adsorption data obtained at P/P0 = 0.0286 and 273 K. 3.2 Free Energy Analysis for Gate Adsorption. The osmotic free energy of the system, ΩOS, can be expressed as:10

(

)

(

)

Ω OS N host , µ , P, T = F host N host ,V , T + PV + Ω guest (µ ,V , T ) ,

(5)

where Nhost represents the number of host framework atoms, µ is the chemical potential of the adsorbed guest and the external gas, P is the external gas pressure at µ, T is the temperature, Fhost is the Helmholtz free energy of the host, V is the volume of the host, and Ωguest is the grand potential of the guest. The grand potential can be calculated by integrating an adsorption isotherm of the guest, Nguest, over a virtual fixed-host framework: Ω guest (µ , V , T ) = − k BTN guest (µid , V , T ) −

∫

µ

µ id

N guest (µ ′, V , T ) dµ ′ ,

(6)


12

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where kB is the Boltzmann constant. The first term on the right-hand side is the grand potential at a sufficiently small chemical potential, µid. The change in ΩOS due to the deformation of the host framework from the closed structure i to the open structure k after gate adsorption is given by

(

)

(

Ω OS N host , µ , P, T − Ω iOS N host , µ , P, T k

(

)

(

)

)

= Fkhost N host ,Vk , T − Fi host N host ,Vi , T + P(Vk − Vi ) .

(7)

(µ ,Vk , T ) − Ωiguest (µ ,Vi , T ) + Ω guest k

When the grand potential of the closed structure is zero independently of µ because of the absence of guest adsorption, eq. 7 can be rewritten as a function of µ:

(µ ) , ∆Ω ikOS (µ ) = ∆Fikhost + P(µ )∆Vik + Ω guest k

(8)

where ∆Fikhost is the Helmholtz free energy change required to deform the host from structure i to k in vacuo and ∆Vik is the volume change of the host. The right-hand side of eq. 8 should be zero at the equilibrium gate adsorption, and the P∆Vik term is negligible in most cases. Specifically, if ∆Fikhost and Ωkguest are known, the chemical potential (pressure) of the gate-opening at which ∆ΩikOS becomes zero can be specified. However, it would be difficult to evaluate both free energies by calorimetric experiment alone, as first noted by Coudert et al.,10 because the exothermic heat of adsorption and endothermic heat from the deformation of the host cannot be separately measured. We therefore determined ∆Fikhost and Ωkguest by the following procedure. We started from the ELM-11 ⊃ 2CO2 structure refined by the Rietveld analysis (Section 3.1.6). Using the open framework structure of ELM-11, we determined the final CO2-host framework interaction potential using the same procedure as that described in Sections 3.1.1 and 3.1.3. A ‘fictitious’ adsorption isotherm of CO2 on the open framework of ELM-11 at 273 K was obtained


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by GCMC with the host framework atoms immobilized (the simulation procedure is the same as that described in Section 3.1.3), and the grand potential Ωkguest was calculated by integrating the GCMC isotherm according to eq. 6. The Helmholtz free energy change of the host ∆Fikhost was then determined by shifting the Ωkguest profile such that the ∆ΩikOS value became zero at the experimental gate adsorption pressure at 273 K (the P∆Vik term was neglected). The experimental adsorption isotherm of CO2 on ELM-11 at 273 K shows a hysteresis loop corresponding to gate adsorption. In our previous work, we found that the desorption branch is close to the thermodynamic equilibrium transition pressure and that the adsorption branch originates from the spontaneous transition from a metastable state, based on the free energy analysis for the simplified SPC model with a stacked-layer structure.17 We therefore ascribe the experimental desorption branch to ‘gate adsorption’ under the thermodynamic equilibrium conditions considered in this study. Coudert et al. originally proposed that ∆Fikhost could be evaluated by fitting a Langmuir isotherm as the fictitious isotherm to a plateau region of the experimental isotherm after gate adsorption.10 Their method is simple and useful when the structure of the open framework is unknown, but the ∆Fikhost value obtained by their method is only approximate because of the limited region over which the Langmuir isotherm is fitted. On the other hand, our method, in which the ∆Fikhost value is evaluated from the GCMC isotherm, should be more precise and accurate if the exact structure of the open framework is available. In this instance, if the open framework structure and the Helmholtz free energy change of the host are nearly independent of temperature over a narrow temperature region, it should be possible to predict the gate adsorption pressure at any temperature in the limited region by calculating the GCMC isotherm at the corresponding temperature. We tested this hypothesis by comparing our simulation results with the experimental data obtained at 258, 268, 278, and 283 K.


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Figure 2. Comparison between the adsorption isotherms of CO2 on 1 at 273 K simulated by GCMC with four scaling factors and the experimental data for ELM-11 (desorption) at 273 K.

4 RESULTS AND DISCUSSION 4.1 Tentative Interaction Parameters. The atomic charges in the framework of 1 determined by the periodic DFT calculations and Mulliken population analysis are tabulated in Table S2, Supporting Information. Figure 2 shows the adsorption isotherms of CO2 on 1 at 273 K simulated by GCMC with the determined atomic charges and the modified UFF. The GCMC isotherm obtained without modification of the UFF (scaling factor α = 1) shows a steep rise at low pressure and a greater total adsorption of CO2 than that obtained experimentally, which suggests that the UFF overestimates the guest-host framework interaction, as reported in previous studies.25,26 Decreases in the scaling factor lead to reductions in the adsorption amount, and the best fit to the plateau region of the experimental isotherm is obtained at α = 0.68. The bonded potentials [bond stretching (Cu–N and Cu–F), angle bending (N–Cu–N and N–Cu–F), and bond rotation between the pyridine rings of bpy (C–C–C–C)] determined by the DFT calculations of the Cu(BF4)2(bpy)4 cluster are shown in Figs. S6–S8, Supporting Information.


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Figure 3. (a) Distribution of CO2 in 1 (monomer unit) obtained by GCMC at 273 K. Translucent red and gray represent the distribution of oxygen and carbon atoms of CO2, respectively. Four CO2 molecules show the barycentric positions of the distribution at sites A and B; (b) 1A ⊃ 2CO2; (c) 1B ⊃ 2CO2.

Notably, the DFT calculations indicate the presence of a Jahn-Teller distortion which makes the Cu–F equilibrium bond length larger than that of Cu–N (Figure S6, Supporting Information). 4.2 Configuration of Adsorbed CO2. Figure 3a depicts the distribution of each atom of CO2 in 1 (monomer unit: Cu(BF4)2(bpy)2) obtained by GCMC at P/P0 = 0.0286 and 273 K. The distribution suggests that there are two types of adsorption sites (A and B) in the open framework of 1; site A was confirmed to have a slightly stronger potential field than site B. The four CO2 molecules illustrated in Figure 3a are located at the barycentric positions of the distribution at each site. However, as observed experimentally, only two CO2 molecules (not four) can be accommodated in the open framework at 273 K. Moreover, given the steric hindrance between adsorbates, two CO2 molecules cannot occupy sites A and B simultaneously, although a combination of sites A


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Figure 4. ELM-11 ⊃ 2CO2 structures relaxed by the canonical MC at 273 K: (a) 2A ⊃ 2CO2 and (b) 2B ⊃ 2CO2. (c) Rietveld refined structure of 3 ⊃ 2CO2 obtained using 2B ⊃ 2CO2 as a starting structure.

and A or sites B and B is permitted. Therefore, we constructed two structure models wherein two CO2 molecules occupy either only sites A or only sites B in 1 (hereafter designated as the 1A ⊃ 2CO2 and 1B ⊃ 2CO2 models, respectively), as shown in Figs. 3b and 3c. 4.3 Structural Relaxation of ELM-11 ⊃ 2CO2 Model. The overall structures of 1A ⊃ 2CO2 and 1B ⊃ 2CO2 were relaxed by the canonical MC at 273 K, and the obtained structures (hereafter 2A ⊃ 2CO2 and 2B ⊃ 2CO2, respectively) are shown in Figs. 4a and 4b, respectively. The total potential energies of the two models were significantly reduced after structural relaxation [–866 kJ/mol-monomer for 2A ⊃ 2CO2 and –870 kJ/mol-monomer for 2B ⊃ 2CO2]. The 2B ⊃ 2CO2 structure is slightly more stable than the 2A ⊃ 2CO2 structure because of the stronger framework– CO2 interaction; however, the CO2 configurations of 2A ⊃ 2CO2 and 2B ⊃ 2CO2 are completely different from one another, which suggests that the potential energy surface of the ELM-11 ⊃ 2CO2 system has at least one large energy barrier between the minima corresponding to the 2A ⊃ 2CO2 and 2B ⊃ 2CO2 structures.


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Figure 5. Rietveld refinement pattern of ELM-11 ⊃ 2CO2 at P/P0 = 0.0286 and 273 K obtained using 2B ⊃ 2CO2 as a starting structure. The bottom panel shows the residual error.

4.4 Rietveld Analysis. We first applied Rietveld fitting to the synchrotron XRPD data using the 2A ⊃ 2CO2 and 2B ⊃ 2CO2 structures as the input, but only refined the parameters of the profile function. The values obtained for Rwp as the reliability factor of the Rietveld fitting were 8.37% for 2A ⊃ 2CO2 and 4.36% for 2B ⊃ 2CO2, which suggest that the 2B ⊃ 2CO2 structure is a suitable starting structure model (see Figs. S9 and S10, Supporting Information). This conclusion is also supported by the fact that the total potential energy of 2B ⊃ 2CO2 obtained after the canonical MC is lower than that of 2B ⊃ 2CO2, as mentioned in Section 4.3. We therefore conducted the Rietveld refinement using the 2B ⊃ 2CO2 structure and obtained a reliable structure for ELM-11 ⊃ 2CO2 (hereafter, the 3 ⊃ 2CO2 model), which is shown in Figure 4c. In the Rietveld refinement, partial profile relaxation was applied for the 021, 202, 020, 204, 130, and 131¯ reflections.57 Moreover, the anisotropic atomic displacement parameters were also refined to take into account of the thermal fluctuation of adsorbed CO2 molecules, which should be larger than that of the host framework. The resulting Rietveld refinement pattern is shown in Figure 5, and the crystallographic parameters are tabulated in Table 1, Table S5, and Table S6, Supporting Information. We also performed the


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MEM analysis of the synchrotron XRPD pattern using the Dysnomia software package,58 and the result is shown in Figure 6. The obtained MEM charge density of CO2 is consistent with the Rietveld-refined structure at the atomic level, which demonstrates the reliability of the Rietveld analysis. The final Rwp factor was 2.32%; hence, it is clear that our Rietveld analysis leads to a significant improvement in the Rwp value relative to that obtained by Kondo et al., 13.45%.36 The improvement in the Rietveld fitting can be attributed not only to the incorporation of the adsorbed CO2 molecules but also to the refinement of the host framework itself. For example, the orientation of the pyridine rings of bpy was considerably altered by the structural relaxation with the canonical MC simulation and the subsequent Rietveld refinement, as demonstrated in Figure S11, Supporting Information. Table 1. Crystal data for ELM-11 ⊃ 2CO2 T [K] P (CO2) [kPa]

273 100

formula crystal system

CuB2C20N4H16F8・2CO2 monoclinic

space group a [nm]

C2/c (No. 15) 1.36851(6)

b [nm] c [nm]

1.10446(3) 1.87175(6)

β [deg] V [nm3]

95.687(3) 2.8157(2)

Z Rwp

4 0.02316

Rp

0.01561

RI

0.04029

S

2.353

Figure 6. MEM charge density map of ELM-11 ⊃ 2CO2 at P/P0 = 0.0286 and 273 K and the Rietveld-refined 3 ⊃ 2CO2 structure. The equi-density level is 1000 e nm−3.


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Figure 7. Detailed configuration of the CO2 molecule in the 3 ⊃ 2CO2 structure.

4.5 Refined Structure of ELM-11 ⊃ 2CO2 and Final Interaction Parameters. The configuration of the CO2 molecule in the 3 ⊃ 2CO2 structure is shown in detail in Figure 7. Notably, the CO2 molecule is located less than 0.3 nm from two BF4– anions, indicating relatively strong interactions between the species. We therefore conducted dispersion-corrected DFT (DFT-D59) calculations for 3 ⊃ 2CO2 (except for the dispersion correction, the calculation details are the same as those described in Section 3.1.1). The binding energies were corrected for the basis set superposition error (BSSE) using the counterpoise method.60 The CO2–host framework interaction obtained from the DFT-D calculations is –33.7 kJ/mol-CO2, which is indeed stronger than the intermolecular interaction for solid CO2 (–25 kJ/mol-CO2 at 0.1 MPa and 195 K). The point to be emphasized here is that the CO2–host framework interaction potential determined in this study


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Figure 8. Electrostatic potential map of the 3 ⊃ 2CO2 structure obtained from (a) calculations using the Mulliken charges and the atomic charges of the CO2 model and (b) DFT calculations.

Figure 9. (a) Adsorption isotherm of CO2 on 3 at 273 K simulated by GCMC with the scaling factor α = 0.74 together with the experimental data for ELM-11 (desorption) at 273 K. (b) The guest grand thermodynamic potential Ωkguest calculated by integrating the fictitious GCMC isotherm on 3 at 273 K and the osmotic free energy change of the system ∆ΩikOS.

cannot be measured calorimetrically because only the net heat, which is the sum of the exothermic heat of adsorption and the endothermic heat from the deformation of the host, would be obtained. We also evaluated the total potential energy of 2B ⊃ 2CO2 by DFT-D and found that the total potential energy of 3 ⊃ 2CO2 was lower than that of 2B ⊃ 2CO2 by 520 kJ/mol-monomer, which validates our Rietveld refinement. The final atomic charges in the framework of 3 were determined by periodic DFT calculations and a Mulliken population analysis and are tabulated in Table S7, Supporting Information. It is often claimed that Mulliken population analysis has the disadvantage of depending strongly on the basis set used.61,62 We therefore tested the applicability of the atomic charges obtained by Mulliken population analysis in this study. Figure 8a shows the electrostatic potential map calculated by the


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Mulliken charges and the atomic charges of the CO2 model using the 3 ⊃ 2CO2 structure. The appearance of the electrostatic potential map is different from the direct output of the DFT calculation (Figure 8b). From a methodological standpoint, this is a natural result of the effective atomic charges (in reality, all atomic nuclei have positive charges) and is not unique to calculations involving Mulliken charges. The value of the electrostatic interaction potential between CO2 and the host framework, ue, calculated using the Mulliken charges and the atomic charges of the CO2 model was –8.10 kJ/mol-CO2, whereas the BSSE-corrected ue (the ‘true value’) from the DFT calculations was –8.99 kJ/mol-CO2. The good agreement between the two calculations suggests that the Mulliken charges determined in this study are applicable to the ELM-11 ⊃ 2CO2 system. Figure 9a shows the adsorption isotherm of CO2 on 3 at 273 K simulated by GCMC with the Mulliken charges and the modified UFF. The scaling factor, α, for the energy parameter of the UFF was re-determined such that the GCMC isotherm provided the best fit to the plateau region of the experimental isotherm. The resulting α value was 0.74, which is slightly higher than the tentative value (α = 0.68). The distribution of the CO2 carbon atoms in 3 obtained by GCMC at 273 K is shown in Figure 10. The distribution is drawn for CO2 with an existence probability of 70%, and it is found in an ellipsoidal region with approximate dimensions of 0.09 nm × 0.13 nm × 0.24 nm. The CO2 distribution obtained by GCMC is in good agreement with the configuration of adsorbed CO2 determined by the Rietveld refinement, which supports the validity of the final potential parameters for the CO2–host framework interaction. Moreover, the result suggests that the thermal fluctuation of the adsorbed CO2 molecules should be larger than that of the host; however, they are strongly confined and arranged in the narrow voids of the host framework even at 273 K.


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Figure 10. Distribution of carbon atoms of CO2 with existence probability of 70% in 3 obtained by GCMC at P/P0 = 0.0286 and 273 K, and configuration of adsorbed CO2 obtained by Rietveld refinement.

4.6 Free Energy Analysis for Gate Adsorption. The guest grand thermodynamic potential Ωkguest was calculated by integrating the fictitious GCMC isotherm of 3 at 273 K and is shown in Figure 9b. The Helmholtz free energy change of the host ∆Fikhost was then determined to be 12.21 kJ/molmonomer by shifting the Ωkguest profile such that the osmotic free energy change ∆ΩikOS became zero at the experimental gate adsorption pressure of P/P0 = 7.16 × 10−3 at 273 K. It should be noted that the ∆Fikhost value, as well as the CO2–host framework interaction potential, cannot be directly determined by experiment, but can only be precisely assessed by our approach using the free energy analysis method that combines experiment and GCMC simulations. We also tested the analytical approach developed by Coudert et al.10 which evaluates ∆Fikhost by fitting a Langmuir isotherm to the plateau region of the experimental isotherm after gate adsorption. The obtained


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Figure 11. Top panels: ∆ΩikOS profile obtained as a sum of ∆Fikhost and Ωkguest profile calculated by integrating the fictitious GCMC isotherm of CO2 on 3. Bottom panels: GCMC isotherm of CO2 on 3, the experimental data for ELM-11 (desorption), and theoretically predicted gate adsorption isotherm at (a) 258, (b) 268, (c) 278, and (d) 283 K.

∆Fikhost value was 8.57 kJ/mol-monomer, which suggests that Coudert’s approach can provide a reasonable approximation of ∆Fikhost. Figure 11 shows the ∆ΩikOS profiles obtained as the sum of ∆Fhost = 12.21 kJ/mol-monomer and the Ωkguest profiles calculated by integrating the fictitious GCMC isotherms of CO2 on 3 at 258, 268, 278, and 283 K. The experimental gate adsorption pressure increased three-fold with a small change in temperature (258–283 K). Gate adsorption should occur when the osmotic free energy change becomes zero. The estimated gate adsorption pressures are thus 11.2, 19.6, 32.4, and 42.3 kPa at 258, 268, 278, and 283 K, respectively, which are in reasonable agreement with the experimental data (13.4, 19.1, 28.5, and 36.5 kPa, respectively: the middle point of the gate adsorption step). As mentioned above, the ∆Fikhost value at 273 K was determined by the fitting such that the osmotic free energy change ∆ΩikOS became zero at the experimental gate adsorption


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pressure, however, it is not just a fitting parameter but is an important quantity governing the gate adsorption property, which was derived from the thermodynamic model (eq. 8). The reasonable agreement between the experimental and predicted gate adsorption pressures at different temperatures demonstrates the validity of the thermodynamic model and the determined ∆Fikhost value at 273 K (12.21 kJ/mol-monomer). The errors between the predicted and experimental gate adsorption pressures at each temperature are less than 16%. The prediction accuracy of our model should be sufficient for engineering use, and we believe that the model will provide a useful tool for the rational design of SPCs for specific applications. However, further consideration is required with respect to the systematic deviation of the predicted gate adsorption pressure from the experimental pressure. Neglecting the temperature dependence of ∆Fikhost is the most probable cause for the systematic error. Namely, our results suggest that the entropy change of the host, ∆Sikhost, should be taken into account. We therefore estimated ∆Sikhost from the errors between the predicted and experimental gate adsorption pressures in the range from 258 K to 283 K and the following thermodynamic relationship:

∆Fikhost (T ) = ∆U ikhost (T ) − T∆S ikhost (T ) ≈ ∆uikhost − T∆S ikhost ,

(9)

where ∆Uikhost and ∆uikhost are changes in the internal and potential energies of the host, respectively. In eq. 9, the temperature dependence of the potential energy and entropy of the host are neglected. The obtained ∆Sikhost value was 56 kJ/mol·K-monomer, and by taking into account the entropy change, the errors between the predicted and experimental gate adsorption pressures decreased to less than 5.2% in the temperature range 258–283 K. The details of the temperature dependent model will be discussed elsewhere.


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5 CONCLUSIONS The structure of ELM-11 ⊃ 2CO2 was determined by our new structure refinement method, which combines Rietveld analysis with molecular simulations using in situ synchrotron XRPD data. We succeeded in modelling and visualizing the structure of ELM-11 ⊃ 2CO2; to the best of our knowledge, this is the first report in which the structure of a guest–SPC system demonstrating an extensive and complex structural transformation was refined by the Rietveld method with the aid of molecular simulations. Our structure refinement method should also be useful for many SPCs which exhibit tortuous structural transformations due to guest adsorption. The crystallographic parameters and force field of the open framework structure of ELM-11 enabled GCMC simulations with an all-atom model. We thus performed a free energy analysis for gate adsorption using the GCMC isotherm and obtained the precise Helmholtz free energy change of the host at 273 K, which is difficult to access experimentally. We also confirmed that the temperature dependence of the gate adsorption pressure could be predicted using the Helmholtz free energy change of the host, which allows a better understanding of the gate adsorption phenomenon. The future challenge is to understand the process of adsorption-induced structural transitions in SPCs through metastabilized and activated states, which cause hysteresis phenomena. Several related investigations, including studies on the structural determination of dehydrated ELM-11 by Rietveld analysis, in situ measurements of CO2 adsorption on ELM-11, and free energy analysis combined with molecular simulations, are now in progress.


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ASSOCIATED CONTENT Supporting Information Crystal data and snapshots of ELM-11 after gate adsorption of CO2 adopted from Kondo et al.;36 interaction parameters from the UFF and atomic charges from Mulliken population analysis for the ELM-11 framework; interaction parameters for a CO2 molecule; snapshot of the isolated fragment of ELM-11 (Cu(BF4)2(bpy)4) used for the DFT calculations; saturated vapor pressure– temperature curve of CO2 obtained from the GEMC simulations; Le Bail fitting for the XRPD pattern of ELM-11 ⊃ 2CO2 and obtained crystal data; bonded potentials determined by the DFT calculations for the Cu(BF4)2(bpy)4 cluster; Rietveld refinement patterns (only profile fitting) of ELM-11 ⊃ 2CO2 obtained using 2A ⊃ 2CO2 and 2B ⊃ 2CO2 as the starting structures; snapshot of the Rietveld-refined structure of ELM-11 ⊃ 2CO2; atomic coordinates of ELM-11 ⊃ 2CO2. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author E-mail: [email protected] E-mail: [email protected] Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was financially supported by a Grant-in-Aid for Scientific Research (B) 24360318, a Grant-in-Aid for Young Scientists (A) 25709074, a Grant-in-Aid for Challenging Exploratory


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Research 26620060, and JST, CREST. The synchrotron radiation experiments were performed at the BL02B2 beamline of SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (Proposal No. 2014A1317). H. T. thanks Prof. Katsumi Kaneko, Prof. Hirofumi Kanoh, and Dr. Hiroshi Kajiro for fruitful discussions. REFERENCES (1) Yaghi, O. M.; Li, H. Hydrothermal Synthesis of a Metal-Organic Framework Containing Large Rectangular Channels. J. Am. Chem. Soc. 1995, 117, 10401–10402. (2) Yaghi, O. M.; Li, G.; Li, H. Selective Binding and Removal of Guests in a Microporous Metal–organic Framework. Nature 1995, 378, 703–706. (3) Kitagawa, S.; Kondo, M. Functional Micropore Chemistry of Crystalline Metal ComplexAssembled Compounds. Bull. Chem. Soc. Jpn. 1998, 71, 1739–1753. (4) Kondo, M.; Fujimoto, K.; Okubo, T.; Asami, A.; Noro, S.; Kitagawa, S.; Ishii, T.; Matsuzaka, H. Novel Extended Linear Structure of Decavanadate Anions Linked by Bis(4Pyridinium)Disulfide(H2dpds), {(H2dpds)2[V10O26(OH)2]･10H2O}n. Chem. Lett. 1999, 291–292. (5) James, S. L. Metal-Organic Frameworks. Chem. Soc. Rev. 2003, 32, 276–288. (6) Férey, G. Hybrid Porous Solids: Past, Present, Future. Chem. Soc. Rev. 2008, 37, 191–214. (7) Horike, S.; Shimomura, S.; Kitagawa, S. Soft Porous Crystals. Nat. Chem. 2009, 1, 695– 704. (8) Kitagawa, S.; Uemura, K. Dynamic Porous Properties of Coordination Polymers Inspired by Hydrogen Bonds. Chem. Soc. Rev. 2005, 34, 109–119. (9) Kitagawa, S.; Kitaura, R.; Noro, S. Functional Porous Coordination Polymers. Angew. Chem. Int. Ed. Engl. 2004, 43, 2334–2375. (10) Coudert, F.-X.; Jeffroy, M.; Fuchs, A. H.; Boutin, A.; Mellot-Draznieks, C. Thermodynamics of Guest-Induced Structural Transitions in Hybrid Organic-Inorganic Frameworks. J. Am. Chem. Soc. 2008, 130, 14294–14302. (11) Boutin, A.; Springuel-Huet, M.-A.; Nossov, A.; Gédéon, A.; Loiseau, T.; Volkringer, C.; Férey, G.; Coudert, F.-X.; Fuchs, A. H. Breathing Transitions in MIL-53(Al) Metal-Organic Framework upon Xenon Adsorption. Angew. Chem. Int. Ed. Engl. 2009, 48, 8314–8317. (12) Coudert, F.-X.; Mellot-Draznieks, C.; Fuchs, A. H.; Boutin, A. Prediction of Breathing and Gate-Opening Transitions upon Binary Mixture Adsorption in Metal-Organic Frameworks. J. Am. Chem. Soc. 2009, 131, 11329–11331. (13) Neimark, A. V.; Coudert, F.-X.; Boutin, A.; Fuchs, A. H. Stress-Based Model for the Breathing of Metal−Organic Frameworks. J. Phys. Chem. Lett. 2010, 1, 445–449. (14) Neimark, A. V; Coudert, F.-X.; Triguero, C.; Boutin, A.; Fuchs, A. H.; Beurroies, I.; Denoyel, R. Structural Transitions in MIL-53 (Cr): View from Outside and Inside. Langmuir 2011, 27, 4734–4741. (15) Watanabe, S.; Sugiyama, H.; Adachi, H.; Tanaka, H.; Miyahara, M. T. Free Energy Analysis for Adsorption-Induced Lattice Transition of Flexible Coordination Framework. J. Chem. Phys. 2009, 130, 164707. (16) Sugiyama, H.; Watanabe, S.; Tanaka, H.; Miyahara, M. T. Adsorption-Induced Structural


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Modeling and Visualization of CO2 Adsorption on Elastic Layer

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