Adsorption and Diffusion in Siliceous Zeolites

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C: Surfaces, Interfaces, Porous Materials, and Catalysis 4

First-Principles-Derived Force Fields for CH Adsorption and Diffusion in Siliceous Zeolites Hanjun Fang, Rohan Awati, Salah Boulfelfel, Peter I. Ravikovitch, and David S. Sholl J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b03267 • Publication Date (Web): 24 May 2018 Downloaded from http://pubs.acs.org on May 24, 2018

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The Journal of Physical Chemistry

First-Principles-Derived Force Fields for CH4 Adsorption and Diffusion in Siliceous Zeolites Hanjun Fang,1§ Rohan Awati,1§ Salah E. Boulfelfel,1§ Peter I. Ravikovitch,2 and David S. Sholl1* 1

School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, United States 2

Corporate Strategic Research, ExxonMobil Research and Engineering, 1545 Route 22 East, Annandale, New Jersey 08801, United States

Abstract Most previous studies on development of force fields for molecules in porous materials focus on prediction of adsorption properties. However, accurately reproducing adsorption data is not sufficient to guarantee the accuracy of other properties such as diffusivities. We demonstrate an approach to develop force fields based on periodic first-principles calculations that can accurately predict both adsorption and diffusion properties in crystalline nanoporous materials using CH4 in siliceous zeolites as an example. First, multiple dispersion-corrected density functional theory (DFT) methods were tested for describing CH4 in siliceous chabazite, and the two configurations (CH4 interacting with framework wall and 8-ring window) that are relevant to CH4 adsorption and diffusion were investigated. By comparing with the results from high level random phase approximation (RPA) results, DFT/CC (coupled cluster) was found to be the optimum method for force field development. The DFT/CC-derived force fields that accurately predict both adsorption and diffusion of CH4 in several commonly studied siliceous zeolites are then developed.

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1. Introduction As an increasingly valuable complement to experiment, computational modeling has been used to interpret experimental observations and predict properties ahead of experiment for guest molecules in porous materials such as zeolites, metal-organic frameworks (MOFs), and carbon nanotubes. Firstprinciples quantum mechanical (QM) calculations are capable of accurately determining optimized geometries, binding energies, reaction energy profiles, and electron densities, etc. However, they cannot be readily used to predict macroscopic properties like adsorption isotherms, loading-dependent isosteric heats of adsorption, and molecular diffusivities. Instead, molecular simulations such as Grand Canonical Monte Carlo (GCMC) and Molecular Dynamics (MD) have been widely applied for predicting these properties.1,2 Successful implementation of GCMC and MD simulations requires accurate force fields (FFs) to describe the interactions of guest molecules with porous frameworks. Developing accurate and transferable FFs for adsorbed molecules is challenging. While generic FFs and experimentally-derived FFs work well for many simple systems, they often fail to describe interactions in more complex porous materials.3 Since first-principles QM approaches are capable of accurately predicting intermolecular interactions, deriving FFs from QM data without experimental input is a promising solution. Significant recent progress has occurred in deriving FFs from QM calculations.3-9 We previously used this methodology to develop FFs for adsorption of CO2 in siliceous and cationic zeolites.10-12 This approach uses the fully periodic framework to represent the adsorbent structure and relies on electronic structure calculations for hundreds of adsorption configurations randomly scattered throughout the framework. These FFs accurately predict experimentally observed adsorption properties and show good transferability across different zeolite topologies. In this work, we extend our approach to CH4 in siliceous zeolites. Previous FFs for CH4 and higher alkanes in zeolites have been developed by fitting adsorption isotherms and/or heats of adsorption to experimental data.13,14 However, accurately reproducing adsorption data is not sufficient to guarantee the accuracy of other properties. For example, Jee et al. found that the FFs derived from experimental isotherms for CH4 and CO2 in the silica zeolite DDR cannot accurately describe molecular diffusion in this material.15 This occurs because the adsorption isotherm is dominated by configurations with molecules close to the energy minima, while diffusion is controlled by transition states that would lie at considerably higher energies. Our goal in this work is to develop the first-principles-derived FFs that can accurately predict both adsorption and diffusion properties for CH4 in siliceous zeolites. In section 2, we assess the accuracy of various dispersion-corrected DFT methods by computing adsorption energies of CH4 on siliceous chabazite (Si-CHA), where high-level QM results are already available and can be used for comparison. 2 ACS Paragon Plus Environment

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On the basis of these benchmark calculations, we choose an optimum DFT method to develop FFs that account for CH4–zeolite interactions. To test the accuracy and transferability of the resulting FFs, in section 3 we perform GCMC and MD simulations to predict adsorption and diffusion properties of CH4 in multiple siliceous zeolites and compare the results with the experimental measurements. A comparison between our developed FFs and those used in literature for CH4 diffusion in the siliceous zeolites is also performed. Finally, our conclusions and plans for future work are discussed in section 4.

2. Methods 2.1 First-principles Methods for Describing CH4 in Zeolites The accuracy of a first-principles-derived FF is controlled by the accuracy of the QM method upon which it is based.3 Similar to our previous work of FF development for CO2 in zeolites,10 we first performed benchmark calculations using different first-principles QM methods for CH4 in a periodic zeolite structure, aiming to find a QM method that can accurately describe CH4–zeolite interactions with affordable computational cost. The performance of different QM methods is evaluated via the comparison with reliable experimental data or high-level QM results. We chose adsorption of CH4 in Si-CHA (R 3 m space group) as the benchmark system,16 because the computational cost for this material using its primitive unit cell is lower than that of many other zeolites. For this reason, CHA zeolites have been often used for the benchmarking of QM methods.17-23 Among these studies, Göltl et al. investigated the adsorption of CH4 and other small alkanes in purely siliceous and Na-exchanged CHA at different levels of theory, including the standard density functional PBE, dispersion-corrected PBE-D2, vdW-DF, and the random phase approximation (RPA) in combination with the adiabatic-connection fluctuation-dissipation theorem (RPA-ACFDT) using wavefunctions.17 They found that the PBE method underestimates the strength of the interactions between these small alkanes and zeolites, while PBE-D2 and vdW-DF strongly overestimate the adsorption energies. The most accurate description is achieved at the RPA level with HF exchange energies (RPAHF).17 Later, they found similar trends for the small alkanes in protonated CHA. 18-20 The overestimation of adsorption energies using PBE-D2 or -D3 and a variety of vdW-DF approaches has also been observed for CH4 in silicalite, HZSM-5, MOR, ZSM-12, and SAPO-34 zeolites.21,23-25 Although the RPA-HF method performs well for CH4 and other small alkanes in zeolites, the computational cost of this method is still very high for the purpose of FF development, where hundreds of periodic calculations need to be performed. Bludský, Nachtigall, and co-workers proposed the DFT/CC (density functional theory/coupled cluster) method for an accurate description of weakly bound molecular systems.26 This method is based on a correction to DFT, ∆EDFT/CC, defined as the difference between DFT and accurate CCSD(T) interaction energies. The DFT/CC method has been successfully applied to a 3 ACS Paragon Plus Environment


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variety of systems where dispersion interactions are important including adsorption of various molecules on graphene and graphite surfaces,27,28 water in the MOF CuBTC,29 as well as CO2 in proton and alkaline cation exchanged zeolites.30-33 Chen et al. derived an ab initio potential energy surface (PES) for CH4 interacting with MOF CuBTC at the DFT/CC level, then implemented the PES in GCMC simulations, and obtained good agreement between calculations and experiments for adsorption isotherms and adsorption mechanism.34 Recently, Rubeš et al. used DFT/CC-based method for the test on isosteric heats of adsorption of CH4 in several siliceous zeolites, and they found that DFT/CC and DFT/CC-based FF yield accurate isosteric heats of adsorption for most of the zeolites they studied when compared with experimental results.35 In their work, however, prediction of adsorption isotherms and diffusivities was not included. We have previously applied the DFT/CC method in FF development for CO2 in siliceous and cationic zeolites, and the resulting FFs work well for these systems.11,12 In this work, we examine the performance of the DFT/CC method for CH4 in Si-CHA. Based on the work by Bludský et al.,26 we developed CC corrections for CH4 in siliceous zeolite and included the details in Supporting Information. We also evaluated some other recently proposed dispersion-corrected DFT methods such as the Tkatchenko-Scheffler

(DFT-TS)

method,36,37

the

many-body

dispersion

energy

method

(MBD@rsSCS),38,39 and the density-dependent energy correction method (DFT-dDsC)40,41. DFT-TS and DFT-dDsC are similar to DFT-D2, but their dispersion coefficients and damping function are chargedensity dependent, and therefore they account for the influence of the local chemical environment. The MBD@rsSCS method represents a conceptually clean approach for including infinite-order many-body effects in the dispersion energy calculations. We refer the readers to the references for the detailed information about these methods.

2.2 Benchmark Calculations for CH4 in Siliceous Chabazite (Si-CHA) It should be noted that the benchmark studies by Göltl et al. focus on the most energetically stable configurations for CH4 (and other small alkanes) in CHA zeolites, which are relevant for predicting adsorption properties of guest molecules in zeolites.17-20 For reliably predicting diffusion properties, the transition states (TS) through which the guest molecule diffuses from a cage to the neighboring cage or cross the channel also need to be taken into account in the benchmark calculations. For CH4 in Si-CHA, the most energetically stable state is CH4 interacting with the framework wall inside the super-cage,17 while the TS is where CH4 is located near the center of an 8-ring window.15,42 Figures 1a and 1b show these two configurations, respectively. We obtained the optimized geometries of these two states at different levels of theory, including PBE, PBE-D2, PBE-D3, PBE-TS/HI, PBE-MBD@rsSCS, PBE-dDsC, vdW-DF, and vdW-DF2, which have been implemented in the Vienna Ab initio simulation package 4 ACS Paragon Plus Environment

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(VASP).43,44 Currently RPA-HF method cannot be used for calculating atomic forces, and therefore cannot readily be used for geometrical optimization. The RPA-HF energies were on the basis of the geometries optimized at other levels of theory. The same is true for the DFT/CC method. The results are summarized in Table 1, including the geometrical parameters and adsorption energies (∆Eads) at different levels of theory. The difference in energy between the two configurations (∆∆Eads) can be viewed as the enthalpic contribution to the diffusion barrier. The results from Göltl et al. for CH4 interacting with framework wall inside the super-cage are also included in Table 1 for validation purpose.17 Our results are generally consistent with theirs. Some deviation exists for both the nearest atomic distances and adsorption energies, and this is probably because of minor differences in the local minimum states in the two sets of calculations. The adsorption energies (∆Eads) from RPA-HF are similar among different optimized geometries, in the range of –12.1 to –14.7 kJ/mol for CH4 in the super-cage, and –0.2 to –2.2 kJ/mol in the 8-ring window. For the diffusion barriers (∆∆Eads), the difference is even smaller, within 1 kJ/mol. Previous studies indicate that caution must be used in comparing the calculated adsorption energies of guest molecule on zeolites with experimentally measured heats of adsorption.10,19,45 The QM calculations only consider the global or local minimum configurations of guest molecules, while experimental heats of adsorption are an average of all possible configurations of guest molecules in the pore, even at low loading, because of thermal effects. A more straightforward way to evaluate the accuracy of the DFT methods would be to compare the DFT results with those from higher-level QM methods. In this case, the results from the RPA-HF method, which has been demonstrated to reliably describe adsorption of CH4 and other short-chain alkanes in CHA zeolites, can be used as the reference values.17-19 As expected, PBE significantly underestimates adsorption energies for CH4 in both the supercage and 8-ring window. PBE-D2, PBE-D3, PBE-MBD@rsSCS, PBE-dDsC, vdW-DF, and vdW-DF2 overestimate adsorption energies for both configurations. PBE-TS/HI performs well for CH4 in the 8-ring window, but overestimates the adsorption energy for CH4 in the super-cage. It is interesting that the diffusion barriers predicted from PBE-D3, PBE-MBD@rsSCS, PBE-dDsC, and vdW-DF2 are close to those predicted from RPA-HF, with differences within 2~3 kJ/mol. DFT/CC gives adsorption energies in range of –16.4 to –17.2 kJ/mol for CH4 in the super-cage, and –4.3 to –5.7 kJ/mol for CH4 in the 8-ring window, which indicate that the DFT/CC energies are not sensitive to the methods used in geometry optimizations. Our results for CH4 in the super-cage are close to that from Rubeš et al, which is –16.8 kJ/mol at the DFT/CC level of theory for CH4 in Si-CHA.35 When compared with the RPA-HF results, DFT/CC overestimates adsorption energies by 3-4 kJ/mol for both CH4 configurations. The diffusion barriers predicted from DFT/CC, however, are almost identical to those from RPA-HF. These benchmark 5 ACS Paragon Plus Environment


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calculations indicate that DFT/CC gives good agreement compared to RPA-HF. Considering the trade of between accuracy and computational cost, DFT/CC was used in following force field development.

Figure 1: Two adsorption configurations of CH4 in siliceous CHA: (a) in the super-cage, and (b) in the 8ring window. They are viewed along two directions. C, H, Si, and O atoms are depicted as gray, white, dark cyan, and red spheres, respectively. For clearer visualization, the atoms of CH4 and framework atoms that are close to CH4 are represented by ball-and-stick model, while the rest atoms by line model.


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Table 1: Adsorption energies (in kJ/mol), ∆Eads, of one CH4 molecule in siliceous CHA calculated at different levels of theory, and the nearest distance (in Å), Rmin (C–Si), between the carbon atom of CH4 and silicon atoms of zeolite. The adsorption configurations are shown in Figure 1. The energy difference from the super-cage to the 8-ring, ∆∆Eads, is also listed. When a geometry was obtained from optimization at a different level of theory, the functional used for optimization is given in parentheses. Rmin (C–Si) ∆Eads ∆∆Eads Super-cage 8-Ring Super-cage 8-Ring PBE 4.44 (4.25)a 3.84 -2.9 (-2.4)a 21.2 24.1 a PBE-D2 3.99 (4.15) 3.79 -21.3 (-18.3)a -12.0 9.3 PBE-D3 4.38 3.81 -22.7 -8.7 14.0 PBE-TS/HI 4.21 3.81 -22.8 0.4 23.2 PBE-MBD@rsSCS 4.20 3.81 -22.1 -9.8 12.3 PBE-dDsC 4.21 3.79 -25.8 -12.4 13.4 vdW-DF 4.26 (4.27)a 3.86 -32.6 (-33.2)a -7.4 25.2 vdW-DF2 4.22 3.83 -23.9 -9.3 14.6 DFT/CC (PBE geo.) -16.4 -4.8 11.6 DFT/CC (PBE-D2 geo.) -17.0 -4.4 12.6 DFT/CC (PBE-D3 geo.) -16.6 -4.3 12.3 DFT/CC (vdW-DF geo.) -17.0 -4.8 12.3 DFT/CC (vdW-DF2 geo.) -17.2 -5.7 11.5 RPA-HF (PBE geo.) -12.1 (-14.0)a -0.2 11.9 RPA-HF (PBE-D2 geo.) -14.4 (-8.2)a -1.7 12.7 RPA-HF (PBE-D3 geo.) -14.3 -1.5 12.8 a RPA-HF (vdW-DF geo.) -14.7 (-14.5) -2.2 12.5 RPA-HF (vdW-DF2 geo.) -12.6 -0.6 12.0 a

the values in parentheses are from reference17

2.3. Force Field Model and Computational Method It is important to use a CH4–CH4 potential that correctly captures the phase behavior of pure CH4, so we used the TraPPE potential,46 which was developed for this purpose. In order to fully specify the energy of adsorbed molecules, we only need to define the CH4–zeolite interactions. In previous studies of CH4 in zeolites, FF parameters are often derived by fitting isotherms to experimental data, and CH4 molecule is treated as the united-atom (UA) model, where the carbon atom and its bonded hydrogen atoms are grouped to form one unit. In this case no Coulomb interactions are included between CH4 and the zeolite. It is also relatively common to include only vdW interactions with framework oxygen atoms, and to assume that interactions with silicon atoms are included through the effective interaction potential with O atoms.14,47 The UA model for CH4 would be a good approximation to simulate molecular systems in which the intermolecular motion is much more important than the intramolecular motion. Treating the vdW interaction from silicon atoms through the effective potential with oxygen atoms is reasonable since silicon atoms are screened by the bulkier oxygen atoms. To test these two approximations, we tested two kinds of FFs for CH4 in siliceous zeolites as illustrated in Figure 2. One uses a UA model for CH4 and includes only vdW interactions between CH4 7 ACS Paragon Plus Environment


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and framework oxygen atoms (Figure 2a). The other uses a rigid all-atom (AA) model with atomic charges for each atom of CH4 molecule and includes vdW and Coulombic interactions with both silicon and oxygen atoms between CH4 and zeolite (Figure 2b). The geometry of CH4 in the AA model was optimized using PBE-D2.

Figure 2: Two models used in force field development for CH4 in siliceous zeolites: (a) the united-atom (UA) model without atomic charges is for CH4, with only oxygen framework atoms being explicitly included for vdW interactions between CH4 and zeolite, and (b) the all-atom (AA) model with atomic charges is for CH4, and both silicon and oxygen framework atoms are explicitly included for van der Waals (vdW) and Coulomb interactions between CH4 and zeolite

When the AA model is used, we assume the interactions between each atom in CH4 and a zeolite atom are represented by pairwise vdW and Coulombic interactions,

EFF ( Rij ) = EvdW + ECoul = s12

C6ij qi q j C12ij − s + 6 Rij12 Rij6 Rij

(1)

where Rij is the distance between atoms i and j, C6ij and C12ij are the attractive and repulsive coefficients, qi and qj represent the charges for atoms i and j, respectively, and s6 and s12 are global scaling factors that are fitted to allow the closest correspondence between the first-principles results and the classical FF in a least-squares sense. C6ij values were adopted from Grimme’s work,48 and C12ij were determined by a simple relation we used before10

C12ij ( R0i + R0j )6 = C6ij 2

(2)


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where R0i and R0j are the vdW radii of atoms i and j from Grimme et al.48 Table 2 gives the C12ij and C6ij coefficients for each cross-species interaction between CH4 and Si-CHA. The Coulomb interactions were treated by a point charge model employing density derived electrostatic and chemical (DDEC3) charges for the atoms of zeolite framework and CH4 molecule.49-51 When the UA model is used, the Coulomb term in eq. (1) is not included. In the FF fitting, the residual standard deviation (RSD) is minimized, where n

∑(E

k FF

k − EDFT / CC )

2

k

RSD =

(3)

n−2

k k Here EFF is the interaction energy calculated at the FF level for CH4 configuration k, EDFT / CC is the

interaction energy calculated at the DFT/CC level, and n is the number of configurations in FF fitting dataset. The mean deviation (MD) is also calculated after the parameterization, n

∑( E MD =

k FF

k − EDFT / CC )

k

n

(4)

The RSD and MD can give an overall evaluation of the performance of the fitted FF in reproducing the QM data. We used the same primitive Si-CHA unit cell as the benchmark section for force field development. The unit cell was first fully optimized at the PBE-D2 level, which gives lattice constants of a = b = c = 9.333 Å and α = β = γ = 94.34°, close to the experimentally determined data, a = b = c = 9.229 Å and α = β = γ = 94.3°.16 DFT/CC calculations were performed with a loading of one CH4 per unit cell. To generate CH4 configurations in FF fitting dataset, we applied NVT MC (N = 1, T = 300 K, and AA model for CH4) simulations based on the 3×3×3 extended supercell. We observed that the ordinary NVT MC technique only leads to energetically favorable configurations for CH4 in the zeolite framework that are relevant to prediction of adsorption properties. As mentioned above, the energetically unfavorable configurations where CH4 sits inside 8-ring windows are critical for describing diffusion behaviors. To effectively generate configurations of CH4 in 8-ring windows, we firstly found the center of each supercage within the supercell of Si-CHA, and during the NVT MC simulations we blocked these centers using spheres of radius of 4, 3, 2, 1, and 0 Å, respectively. This way helps to make CH4 towards 8-ring windows, and configurations of CH4 in both super-cages and 8-ring windows can be obtained (see Figure S3 in Supporting Information). For each blockage radius, the same number of CH4 configurations was randomly chosen from the NVT MC snapshots. We generated CH4 configurations and derived FF parameters through two iterations. In the first iteration, the ClayFF parameters52 were used for the zeolite atoms (O and Si) and the TraPPE parameters46 9 ACS Paragon Plus Environment


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and DDEC3 charges for the atoms of CH4. Lorentz-Berthelot mixing rules were applied for the LennardJones for cross interacting species between CH4 and zeolite. A total of 300 configurations were chosen from the NVT MC snapshots and used in the first iteration of force field fitting. The fitted FF parameters were then used in in the second iteration following the same procedure. Then a total of 1,000 configurations were included to refine the force field parameters. Further iterations did not influence the final FF parameters. The final FF parameters using AA and UA models are summarized in Table 3. For simplicity, we will refer to the two FFs derived in this way as CCFF_AA and CCFF_UA. It is useful to note that the number of independent fitting parameters in the two FFs is the same (s6 and s12 in eq. (1)), despite the difference in the functional form of the FFs. We have tested another set of blocking spheres (4.0, 3.5, 3.0, 2.5, 2.0, 1.5, 1.0, 0.5, and 0.0 Å). The interval of adjacent spheres is smaller, and found the final fitted force field parameters change by within 1% and 2% for for UA and AA models, respectively, and these changes would not significantly influence the adsorption and diffusion properties. Table 2: Attractive and repulsive coefficients (C6ij and C12ij) and the sum of van der Waals radii (R0i + R0j) for each cross species between CH4 and siliceous zeolites. Cross species C12ij C6ij R 0i + R 0j 12 -1 6 -1 (Jnm mol ) (Jnm mol ) (Å) AA model UA model Si–C Si–H Oz–C Oz–H

Oz– CH4

2.031×10-3 2.287×10-4 2.637×10-4 2.590×10-5

Table 3: CCFF_AA and CCFF_UA parameters for CH4 in siliceous zeolites. Cross species ε/kB (K) σ (Å) CCFF_AA Si–C 33.98 3.845 Si–H 24.15 3.298 Oz–C 19.88 3.391 Oz–H 16.17 2.844 CCFF_UA Oz–CH4 109.76 3.416

4.019 1.137 1.107 0.313

3.168 2.717 2.794 2.343

Charge (e) Si (2.2124) Oz (-1.1052) C (-0.516) H (0.129)

2.3. Force Field Fitting A detailed comparison of the interaction energies predicted using CCFF_AA and CCFF_UA and the corresponding energies at the DFT/CC level is shown in Figure 3. When the AA model is used, the 1000 DFT/CC calculations span a range of adsorption energies, from -17 to 7 kJ/mol, and the CCFF_AA interaction energies are reasonably consistent with the DFT/CC results (Figures 3a and 3b). Some


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deviations between CCFF_AA and DFT/CC energies exist, especially when the CH4 molecule is located near the center of 8-ring windows of Si-CHA (Figure 3c). The CCFF_AA interaction energies for 99.5% (100%) of the CH4 configurations have deviations within ±4 (±8 kJ/mol) of the DFT/CC energies. The RSD and MD between the FF and the DFT/CC results are 0.9 and 0.04 kJ/mol for the AA model, respectively. When the UA model is used, a larger deviation between CCFF_UA and DFT/CC energies is observed than that from the AA model (Figure 3d). This is not surprising since stronger approximations are made in the UA model to describe CH4 than that of the AA model. For the most energetically favorable configurations (Figure 3e), CCFF_UA underestimates the interaction energies by about 2 kJ/mol compared to the DFT/CC results, and deviation increases to 7 or -8 kJ/mol when the CH4 molecule is located near the center of 8-ring windows (Figure 3f). The CCFF_UA interaction energies for 94.7% (99.8%) of the CH4 configurations have deviations within ±4 (±8 kJ/mol) of the DFT/CC energies. Overall, RSD and MD between the FF and the DFT/CC results are 1.4 and 0.01 kJ/mol for the UA model, respectively. We also checked CCFF_AA and CCFF_UA in calculating the adsorption energies of the two configurations of CH4 in Si-CHA as shown in the benchmark calculations (section 2.2). During the calculation, the position of CH4 was optimized, while the framework of Si-CHA was fixed to the PBE-D2 minimized geometry. The results are summarized in Table 4. Both the CCFF_AA and CCFF_UA perform well in predicting the adsorption energies and diffusion barriers compared with the results using DFT/CC (Table 1). Geometrical parameters are also predicted well using the two FFs when compared to the results at the different levels of DFT.

Table 4: Adsorption energies (in kJ/mol), ∆Eads, of one CH4 molecule in siliceous CHA calculated by the developed force fields, and the nearest distance (in Å), Rmin (C–Si), between the carbon atom of CH4 and silicon atoms of zeolite. The adsorption configurations are shown in Figure 1. The energy difference from the super-cage to the 8-ring, ∆∆Eads, is also listed. Rmin (C–Si) ∆Eads ∆∆Eads Super-cage 8-Ring Super-cage 8-Ring CCFF_AA 4.13 3.92 -17.4 -5.7 11.7 CCFF_UA 4.26 3.94 -15.6 -1.7 13.9


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Figure 3: Force field fitting results for CH4 in siliceous CHA: (a, d) Comparison of the interaction energies of CH4 in siliceous CHA zeolite for the CCFF and DFT/CC, (b, e) the difference in interaction energies (ECCFF –EDFT/CC) as a function of EDFT/CC, (c, f) ECCFF –EDFT/CC as a function of the nearest interatomic distance between the carbon atom of CH4 and the center of 8-membered ring window. (a, b, and c) are for the all-atom (AA) model, and (d, e, and f) for the united-atom (UA) model.


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3. Results and Discussion 3.1 Prediction of Adsorption Properties To examine the applicability of the FFs developed above, we compared adsorption properties predicted using CCFF_AA and CCFF_UA with experimental adsorption data for several siliceous zeolites. Adsorption isotherms and isosteric heats of adsorption were predicted computationally using standard GCMC methods (see Supporting Information). We emphasize that our calculated results come from our first-principles derived FFs and are not fitted to experimental data in any way. We first discuss results for CH4 adsorption in siliceous CHA, the zeolite on which the FF development is based. The simulated and experimental isotherms are shown in Figure 4a. The simulation results using CCFF_AA and CCFF_UA at 301 K are close each other, and in good agreement with the experimental isotherms from three different groups.53-55 The isosteric heats of adsorption at zero loading are predicted to be 17.7 and 17.0 kJ/mol for CCFF_AA and CCFF_UA (Figure 4b), respectively, which are accordance with the experimental result from Pham and Lobo.55 Our simulation results are also close to the experimental result (16.8 kJ/mol) obtained by Rubeš et al.35 To examine the transferability of our force fields, we performed GCMC simulations of CH4 in several other zeolites. Figures 4c and 4d show the isotherms and heats of adsorption for ITQ-29 (siliceous LTA). The agreement between the simulations and experiments is good for isotherms in Si-LTA, with some slight deviations compared to the work from Hedin et al.53 Considering the variations between experimental results from different groups, the predictions based on our method are good. The heats of adsorption of CH4 in ITQ-29 at all loadings are similar to each other with the two FFs and they are generally lower by about 2 kJ/mol compared with the experimental data from Palomino et al.56 Figure 5 shows the results for CH4 in siliceous MFI, which is an extensively studied system in experiment. The agreement between the simulations and experiments is excellent for isotherms at all the temperatures and pressures studied in this work (Figures 5a, 5b, and 5c). The deviation for heats of adsorption is within 2 kJ/mol compared with the experimental data from Sun et al.57 and Dunne et al (Figure 5d).58 DDR is another commonly studied zeolite. The comparison of our simulated and experimental data for CH4 in DDR is shown in Figure 6. CCFF_AA and CCFF_UA perform well for predicting isotherms at 195 K (Figure 6a), but slightly underestimate loadings at higher temperatures if compared with the experimental results from Bergh et al.59 When we include the experimental data from Himenno et al. in comparison,60 the agreement is excellent for both isotherms and heats of adsorption (Figures 6b and 6c). Based on the validation results for CH4 in these zeolites, the FF transferability with respect to adsorption isotherms is good.



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Figure 4. Comparison of simulated (CCFF_AA and CCFF_UA) and experimental adsorption isotherms and heats of adsorption of CH4 in siliceous CHA (a and b), and ITQ-29 (siliceous LTA) (c and d). The experimental data are from Hedin et al.,53 Maghsoudi et al.,54 Pham et al.,55 and Palomino et al.56 Lines are drawn to guide the eye.


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Figure 5. Comparison of simulated (CCFF_AA and CCFF_UA) and experimental adsorption isotherms and heats of adsorption of CH4 in siliceous MFI. The experimental data are from Zhu et al.,61 Sun et al.,57 and Dunne et al.58 Lines are drawn to guide the eye.



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Figure 6. Comparison of simulated (CCFF_AA and CCFF_UA) and experimental adsorption isotherms and heats of adsorption of CH4 in siliceous DDR. The experimental data are from Himeno et al.60 and Bergh et al.59 Lines are drawn to guide the eye.


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We have also checked the influence of the first-principles method on the performance of FFs. The effect of QM method is significant. For instance, while the FFs derived from DFT/CC work well for CH4 in CHA and ITQ-29, the ones derived from DFT-D2 overestimate the isotherms and heats of adsorption (Figure S4 in Supporting Information). This is different from the case of CO2, where the FFs derived from both DFT/CC and DFT-D2 give similar results.10,11 The difference in performance of DFT/CC and DFT-D2 for CH4 and CO2 in zeolites observed from our studies is consistent with that from Bludský and co-workers.30,35,62 This is probably because CH4 in zeolites is dispersion dominated and far more sensitive to force field van der Waals parameters compared to CO2 in zeolites, where both dispersion and electrostatic interactions dominate.

3.2 Prediction of Diffusion Properties To examine the applicability of the FFs for predicting diffusion properties, we performed standard MD simulations for CH4 in Si-CHA and Si-LTA zeolites, calculated self-diffusion coefficients,63 and compared them with experimental data obtained by Hedin et al. using pulsed field gradient (PFG) NMR.53 These two zeolites include 8-ring windows, through which CH4 molecules diffuse from cage to cage. It has been shown that for 8-ring zeolites, the flexibility of framework would have influence on molecular diffusion, so we tested both rigid and flexible frameworks. The modified Hill-Sauer FF from our recent work was used to account for flexibility of the zeolites,64 since it improves the description of pore sizes and framework flexibility in small pore zeolites relative to the original Hill-Suer FF.65 Because the atomic charges of the framework in our CCFF_AA are not consistent with those from Hill and Sauer FF,65 we only investigate flexible framework when using the CCFF_UA. Our MD simulations were performed using LAMMPS,66 and further details are given in the Supporting Information. The results for ITQ-29 are reported in Table 5. The experimental diffusion coefficient for CH4 in ITQ-29 was measured at the loading of 0.4 molecules per cage.53 To get better statistics, in simulations we calculated the diffusion coefficients at infinite dilution and the loading of 1 molecule per cage, and we expect that the simulated results should provide the lower and upper bounds for the result with the actual fractional loading (see section S3.2 in Supporting Information). As is seen, both CCFF_AA and CCFF_UA with rigid framework do a good job in predicting the diffusion coefficients when compared with the experimental data. When flexibility is taken into account, slightly better agreement is achieved, although the influence of flexibility is not significant for this case. Table 6 summarizes the results for siliceous CHA. CCFF_AA and CCFF_UA with rigid framework underestimate the diffusion coefficients compared to experimental data, but the values are in the same order of magnitude. When flexibility is taken into account, CCFF_UA performs better compared with the result using rigid framework. The 8-ring window sizes of Si-CHA and Si-LTA are 3.70 × 4.17 Å 17 ACS Paragon Plus Environment


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and 4.00 × 4.22 Å, respectively,53 and the kinetic diameter of CH4 is 3.8 Å.67 Our previous studies show that the framework flexibility plays a crucial role when the size of the diffusing molecule approaches the size of the window.42,63 The window size of Si-CHA is more comparable to the kinetic diameter of CH4 than that of Si-LTA, and therefore the influence of framework flexibility is more significant for CH4 in Si-CHA than in Si-LTA. Multiple previous FFs have been developed for adsorption of CH4 in zeolites, and their performance for predicting adsorption properties is generally satisfactory.13,14,47,68-83 Here we checked their performance for predicting diffusion properties by calculating self-diffusion coefficients for CH4 in ITQ-29 and CHA at 300 K. The details about the FFs we used are summarized in Table S10 in Supporting Information. Since some of these FFs predict slow diffusion (less than 10-12 m2/s) that is beyond the time scale of standard MD, dynamically-corrected transition state theory (dcTST) method was used for these simulations.84-86 In dcTST simulations the loading of CH4 was at infinite dilution, and flexibility of framework was taken into account as described above. More details about dcTST are given in the section S3.3 in Supporting Information. Figure 7 summarizes the results of simulated self-diffusion coefficients as a function of the FF parameter, σLJ (Å) of CH4-Oz, for the various FFs we tested. It can be seen that the predicted selfdiffusion coefficients using different FFs differ by 8 and 10 orders of magnitude for ITQ-29 and CHA, respectively. The numerical values are reported in Table S11 in Supporting Information. By comparing with experimental data from Hedin et al.,53 most of earlier FFs that were developed to reproduce experimental adsorption do not perform reliably for predicting diffusivities. Our CCFF_AA and CCFF_UA stand out in the comparison. This is a striking example of how fitting a FF to only adsorption data can give predictions that are highly inaccurate for predicting molecular diffusion.


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Table 5: Self-diffusion coefficients (m2/s) for CH4 in ITQ-29 (siliceous LTA) at 301 K, calculated using CCFF_AA and CCFF_UA with rigid and flexible frameworks. Standard Molecular Dynamics Exp. dataa Loading Infinite dilution 1.0 0.4 (molecule/cage) -10 -10 CCFF_AA (1.24 ± 0.25) × 10 (2.09 ± 0.53) × 10 (rigid framework) -10 -10 -10 CCFF_UA 1.42 × 10 (1.45 ± 0.34) × 10 (1.48 ± 0.54) × 10 (rigid framework) -10 -10 CCFF_UA (1.44 ± 0.29) × 10 (1.49 ± 0.26) × 10 (flexible framework) a Hedin et al. PFG-NMR.53 Table 6: Self-diffusion coefficients (m2/s) for CH4 in siliceous CHA at 301 K, calculated using CCFF_AA and CCFF_UA with rigid and flexible frameworks. Standard Molecular Dynamics Exp. dataa Loading Infinite dilution 1.0 0.4 (molecule/cage) -11 -11 CCFF_AA (0.27 ± 0.04) × 10 (0.57 ± 0.13) × 10 (rigid framework) -11 -11 -11 CCFF_UA 1.07 × 10 (0.35 ± 0.06) × 10 (0.63 ± 0.15) × 10 (rigid framework) -11 -11 CCFF_UA (0.49 ± 0.07) × 10 (0.96 ± 0.12) × 10 (flexible framework) a Hedin et al. PFG-NMR.53



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Figure 7: CH4 self-diffusion coefficients at infinite dilution and 300 K in flexible zeolite ITQ-29 (black circles) and CHA (red squares) computed using CCFF (UA: filled symbols, AA: hashed symbols) and compared to 15 other force fields from literature (see Tables S10 and S11 in Supporting Information for details). Hedin et al.53 experimental self-diffusion coefficients are shown as dashed lines.

4. Conclusions We have developed first-principles-derived force fields for CH4 in siliceous zeolites that can accurately predict both adsorption and diffusion properties. Two models are tested for CH4 and zeolites. One uses a united-atom (UA) model for CH4 and includes only vdW interactions between CH4 and framework oxygen atoms. The other uses a rigid all-atom (AA) model with atomic charges for each atom of CH4 molecule and includes vdW and Coulombic interactions with both silicon and oxygen atoms between CH4 and zeolite. The results show that the first model that has stronger approximation performs similarly as the second model in predicting both adsorption and diffusion properties. The developed force fields show good transferability among different topologies. The force fields derived from DFT/CC method work well for CH4 in siliceous zeolites, while the ones derived from DFT-D2 method overestimate the isotherms and heats of adsorption. This observation is different from that of CO2 in 20 ACS Paragon Plus Environment

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siliceous zeolites, where the force fields derived from DFT/CC and DFT-D2 give similar results. Finally, a comparison between our force fields and those in literature indicate that most of earlier force fields that were developed to reproduce experimental adsorption do not perform reliably for predicting diffusivities of CH4 in silica zeolites. The extension of the methodology to higher hydrocarbon molecules and cationic zeolites is undergoing.



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ASSOCIATED CONTENT Supporting Information Detailed description of DFT/CC method for CH4 in zeolite, periodic DFT calculations, and classical simulations.

AUTHOR INFORMATION Corresponding Authors [email protected] Author Contributions §

These authors contribute equally to this work

ORCID iD Hanjun Fang: 0000-0002-7125-6404 Salah E. Boulfelfel: 0000-0003-1412-1826 Rohan Awati: 0000-0001-9361-0622 David S. Sholl: 0000-0002-2771-9168

Notes The authors declare no competing financial interests.

ACKNOWLEGMENTS HF, RA, SB, and DSS acknowledge funding from ExxonMobil Research and Engineering. We thank Preeti Kamakoti and Lucas Koziol for helpful discussions.


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Adsorption and Diffusion in Siliceous Zeolites

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