Force-Field Prediction of Materials Properties in Metal-Organic

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Letter

On the Force Field Prediction of Materials Properties in Metal Organic Frameworks Peter G. Boyd, Seyed Mohamad Moosavi, Matthew Witman, and Berend Smit J. Phys. Chem. Lett., Just Accepted Manuscript • Publication Date (Web): 23 Dec 2016 Downloaded from http://pubs.acs.org on December 24, 2016

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The Journal of Physical Chemistry Letters

On the Force Field Prediction of Materials Properties in Metal Organic Frameworks Peter G. Boyd,† Seyed Mohamad Moosavi,† Matthew Witman,‡ and Berend Smit∗,†,‡ †Laboratory of Molecular Simulation, Institut des sciences et ingénierie chimiques, École polytechnique fédérale de Lausanne (EPFL), Rue de l’Industrie 17, CH-1951 Sion, Valais, Switzerland ‡Department of Chemical and Biomolecular Engineering, University of California, Berkeley 94720, USA E-mail: [email protected] Phone: +41 21 693 0079 Abstract In this work, MOF bulk properties are evaluated and compared using several force fields on several well-studied MOFs, including IRMOF-1 (MOF-5), IRMOF-10, HKUST1, and UiO-66. It is found that, surprisingly, UFF and DREIDING provide good values for the bulk modulus and linear thermal expansion coefficients for these materials, excluding those which they are not parameterized for. Force fields developed specifically for MOFs including UFF4MOF, BTW-FF and the DWES force field, are also found to provide accurate values for these materials’ properties. While we find that each force field offers a moderately good picture of these properties, noticable deviations can be observed when looking at properties sensitive to framework vibrational modes. This observation is more pronounced upon the introduction of framework charges.

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Due to the nearly limitless range of materials and properties achievable by metal organic frameworks (MOFs), computational researchers have been invaluable in directing efforts towards materials with optimal properties for various applications. 1–4 Current computational resources allow the ability to explore materials properties at a fraction of the time and cost compared with experiment, thus making it an instrumental part of a materials design process. Much of the computational work to date has been focused on gas adsorption properties, where the commonly used fixed-framework approximation is exploited to improve computational efficiency. Here, it is assumed that any framework movement or vibrations will not contribute significantly to the thermodynamically averaged properties, and are simply ignored during calculations. This approximation has been demonstrated to provide relatively accurate results, 5,6 provided the materials do not deviate significantly from their reported crystallographic representations at the thermodynamic conditions studied. There are notable cases where freezing the framework atoms in place is inappropriate, however. For example, where gas adsorption results in significant changes in the lattice organization of the MOF framework atoms 7–9 as evidenced in several ‘breathing’ structures including MIL-53 and DUT-49, 8,10 when modeling the fascinating phenomena of negative thermal expansion (NTE) of these materials, 11,12 or when attempting to accurately model particle diffusion through network pores and small apertures. 13,14 In these cases response of the system to external stimuli with a fully flexible model of the material is necessary. Most of these problems are too large for a DFT approach, however, and so one must resort to modeling properties with empirical force fields, for which there are numerous generalpurpose molecular mechanics engines freely available for academic use. 15–19 In recognition of the need for accurate models to predict the various interesting properties described by the bonding environment within these materials, a number of force fields have recently been developed specifically for MOFs. 12,20–25 The work placed in developing these force fields follow a similar procedure, i.e. fit force field parameters, for instance bond force constants and angle bending terms to accurate data from experiment or ab initio

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calculations, typically at low temperature. The data can take the form of bulk observable properties where force fields are fit to very specific and localized properties, or a more general approach involving a system’s first and second order energetic derivatives. 26,27 Alternatively, rule-based force fields can be used to describe MOF properties. Force fields such as the Universal Force Field (UFF) 28 provide paramters for each atomic type, and mixing rules for these parameters to dictate the strength of local chemical bonds and angle bends. These force fields have the advantage that they can be adaptable to many chemical environments, however at the potential cost to simulation accuracy. It is of importance, therefore, to distinguish if these targeted properties are sensitive to specific force field parameterizations, or if more generalized rule-based force fields can be used. It was shown 29 that good agreement could be obtained between an approximate, yet accurate DFT-based method (DFTB) and UFF, which recently celebrated it’s 24th birthday, and whose intended application was not solid-state porous materials. The motivation of this work is to critically assess two materials properties commonly used to validate new MOF force fields using ‘off the shelf’ force fields as a measure of comparsion. The following will compare the bulk moduli and NTE computed for IRMOF-1 (MOF-5), IRMOF-10, 30 HKUST-1, 31 and UiO-66, 32 MOFs which have been widely studied for various applications, and have been the subjects of specific force field parameterizations. 12,20,21 These MOFs are compared using full descriptions of UFF, 28 DREIDING, 33 UFF4MOF, 21 and the force field by Dubbeldam, Walton, Ellis and Snurr (DWES). 12 We have implemented these force fields in the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), 19 which stands out due to its unprecedented number of features, active development team and helpful albeit sometimes comedic user forum to aid in materials simulations. In addition, a comparison is made with a functional version BTW-FF, 20 however due to some absent energy potentials in LAMMPS, it could not be described in its intended form. The details are discussed further in the article and supporting material. Force fields circumvent expensive ab initio calculations by approximating the electronic

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degrees of freedom with a set of fixed functions describing a systems bond, angle, torsion, and long-range potentials. The typical general expression for a force field is shown in equation 1 Etotal =

X

bonds

+

X

Estretch +

X

Etorsion +

X

X

Eout−of −plane

(1)

impropers

dihedrals

+

Ebend

angles

(EvdW + Ecoulomb )

pairs

where a unique functional form for the E’s in equation 1 are provided for each different force field, with accompanying parameters that provide a realistic enenergetic landscape for the bonds, angles, torsions, and pair interactions between atoms. A brief description of the functions used to describe each force field studied in this work are presented in Table 1. For example the Estretch term describing the energy associated with stretching and compressing a bond is described by a spring harmonic term for all of the force fields except for BTW-FF, where a 4th order polynomial term of the form

ij =K2 Rij − R0ij Estretch

2

+ K3 Rij − R0ij

3

+K4 Rij − R0ij

4

(2)

ij is the energy of stretching a bond between two bonded atoms i and j, is used. Here, Estretch

Rij represents the distance between the two atoms and R0ij is the equilibrium bond distance parameter imposed by the force field for two specific types of atoms. In addition, there are 3 other empirical values assigned to this bond potential to ensure the correct behavior. Namely the K2 , K3 , and K4 terms whose values affect the curvature of the bond potential energy surface.

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Table 1: Description of the potentials used in the force fields studied Potential Bond Angle Dihedral Improper torsion Cross terms van der Waals Coulomb

UFF harmonic cosine fourier cosine fourier cosine fourier — Lennard-Jones ewald

DREIDING harmonic/morse harmonic cosine periodic cosine harmonic — L-J/Buck † ewald

BTW-FF UFF4MOF DWES 4th order pol. harmonic harmonic 6th order pol.‡ cosine fourier harmonic fourier cosine fourier periodic cosine 6th order pol.‡ cosine fourier periodic cosine improper-angle pol. — — Buckingham Lennard-Jones Lennard-Jones ewald ewald ewald

†

- DREIDING provides options for functions used in the force field, in this work we have used harmonic and Lennard-Jones for the bond and van der Waals potentials, respectively. ‡ - LAMMPS does not currently possess 6th order polynomial functions. A 4th order polynomial and 2nd order polynomial were used in their stead. †

One should note in Table 1 that in general, BTW-FF uses functions of higher relative complexity, having bond, angle and out-of-plane torsion potentials that contain polynomials of order greater than 2. BTW-FF adopted its potential functions from the Molecular Mechanics 3 (MM3) force field, 34 which was developed to reproduce vibrational and thermodynamic properties of hydrocarbons. Because of the extreme precision required to accurately model these values, the MM3 force field also contains so-called ‘cross-terms’. These terms are included in the form of additional functions between atoms that are two or three bonds apart to accurately model concerted molecular motions (bend-stretch, bend-bend etc.) at finite temperatures. We note that the authors of the BTW-FF do not provide parameters for these cross-terms, despite their presence in the TINKER implementation of BTW, so we have used the original MM3 values in this work. Table 1 is designed to be a reference to the complexity of each force field, and a more detailed discussion of these potentials is presented in the supporting material. We also note that the BTW-FF potentials for the angle-bending and improper torsions could not be faithfully reproduced in LAMMPS, however the energy penalty for these approximations is small, as they only manifest at extreme values for non-equilibrium angles. Further details are provided in Section S.3.3.6 of the supporting material. In all cases studied, we used the atomic positions from the crystallographic information 5



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files provided by the Cambdridge Structural Database (CSD). 35,36 Some of the modern MOFcentric force fields do not encompass the entire set of structures studied here, rendering comparison impossible. For example, the DWES force field contains parameters for IRMOF1 and IRMOF-10, but not HKUST-1 or UiO-66 and thus properties for these neglected materials cannot be computed. The computed bulk moduli are presented in Table 2. These values were computed from a procedure where the lattice parameters were isotropically scaled and the atomic positions minimized. With a few exceptions, this gave a smooth energy - volume curve to provide good fits to the Murnaghan equation of state 37 shown in equation 3. This equation was chosen for its relative simplicity, and considering the imposed deviations in volume do not stray far from equilibrium, more complex equations of state were deemed unnecessary. B0 V E = E0 + B′

"

′ V0 B V (B ′ − 1)

+1

#

(3)

One of the most striking features of Table 2 is that all of the force fields predict the same ranking in increasing order of bulk modulus. Moreover, with the exception of the bulk moduli computed for UiO-66, most values lie within ± 5 GPa of DFT or experimentally observed values. This deviation may appear large; however, considering the variability in bulk moduli for HKUST-1 can range from 25 to 35 GPa from DFT calculations at different levels of theory, 38,39 the bulk moduli computed by these force fields are well within the range of acceptable values. The first column in Table 2 showing the values reported from the LAMMPS implementation of BTW-FF demonstrates the close agreement with the values reported in the original article by Bristow et al. 20 as all are within 2 GPa of the original values. Discrepancies in these values can be attributed to the subtle differences in the BTW force field implementations between TINKER and LAMMPS discussed above. It is remarkable that simple force fields such as DREIDING can reproduce the bulk moduli for these MOFs, which uses a single force constant for all bonds of the same order, regardless of the chemical species of its 6


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atoms. Likewise UFF, which wasn’t designed for simulations of nano-porous materials, can reproduce the bulk moduli trends and values. We note that the story changes significantly when charges are introduced to each framework and the bulk moduli re-computed using the UFF, UFF4MOF, and DREIDING force fields. We have presented the bulk moduli using different charge derivation schemes in Section S.6 of the supporting information, where the values can deviate up to 18 GPa for the same MOF using methods that obtain partial atomic charges from DFT calculations. While each of these periodic table covering force fields do not provide partial charges for their atom types, it seems clear that the introduction of charges yields worse agreement with experimental materials properties. 33 We note that the parameters for the original Zr and Cu types in UFF 40 are not designed to reproduce the square planar and square antiprismatic geometries in HKUST-1 and UiO66, respectively. However an ad hoc adjustment of these values to support the MOF metal coordination geometries yields good agreement with literature values for the bulk moduli, improving upon those values reported for BTW-FF. The adjustment, which fits the original force constants to the existing coordination geometries in each crystal, is discussed in detail in the supporting information. It is instructive to investigate the major contributions to the bulk modulus from each of the energy terms arising from the force field functions. Fig. 1 shows, for each MOF, the second derivative values arising from the various force field and functional terms, whose Table 2: Bulk Modulus values computed from different force fields. Units in GPa. MOF IRMOF-1 IRMOF-10 HKUST-1 UiO-66

BTW-FF (ref 20) UFF UFF4MOF 13.6 (11.95) 14.5 16.8 9.0 (8.25) 7.6 10.4 23.9 (25.05) 28.7 29.4 27.1 (27.15) 42.4 —

DREIDING 22.0 9.7 31.1 —

a - Refs 24,39,41–46 b - Refs 47,48 c - Refs 38,39 d - Ref 46

7


DWES 17.5 8.1 — —

DFT/exp 15.3 – 18.5 a 6.0,9.09 b 24.5 – 34.66 c 41.0 d


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magnitudes are directly proportional to their bulk moduli. It is clear that in most cases, the bonding function is the primary contributor to the bulk modulus. Notably the nonbonded interactions dominate the bulk modulus contribution for IRMOF-1 with DWES force field. This arises due to the force field’s lack of bonds between Zn(II) ions and the nearby benzene-dicarboxylate ligands, effectively dislocating the structure from a continuous network of bonding. The replacement of the directionally dependent bonding terms with the isotropic form of the non-bonded functions can be expected to provide similar bulk moduli, since the bulk modulus measures the response to uniform hydrostatic pressure imposed on the system. It is likely, therefore, that more significant differences will arise when looking at the individual elements of the stress tensor, where the directional dependence of the potential energy surface will have more of an impact. This is evidenced by the disagreement between elastic constants computed for IRMOF-1, reported in Section S.7 of the supporting information. Interestingly, the BTW-FF predicted bulk modulus for UiO-66 comes from a difference between angle bending and non-bonded interactions. These contributions arise from the presence of atomic charges in the system and the subsequent distortions that occur from relaxing the atomic positions when the cell shape is changed. We add here that providing charges to the force fields UFF, UFF4MOF, and DREIDING cause erratic bulk modulus values in these materials due to the unpredictable behaviour of charge interactions in these materials. The details of charge assignment and observed results are left for the supporting material.

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Table 3: Linear thermal expansion coefficients computed with different force fields. Units −1 −6 are in 10 · K . MOF BTW-FF (ref 20) IRMOF-1 -2.9 (-5.27) IRMOF-10 -5.4 (-8.11) HKUST-1 -3.1 (-3.18) UiO-66 -3.1 (-1.04)

UFF UFF4MOF DREIDING DWES exp -13.0 -26.2 -10.6 -18.9 -12.0 – -16.0a -15.2 -16.9 -16.0 -18.2 — -4.1b -12.0 -11.1 -4.0 — — -8.4 — — —

a - Refs 49,52,53 b - Ref 51

made in this case, as they share both bond topologies and force field potentials (see Table 1). The 13.2 MK-1 difference in IRMOF-1 NTE is attributed to the smaller magnitude of the bonding force constants (40-50 kcal·mol−1 ·Å−2 ) for the metal ions in UFF4MOF. This translates to a larger NTE observed with UFF4MOF due to the prevalence of higher magnitude vibrations in the cell, as these modes are more thermally accessible due to the smaller bond force constants of the metal - oxygen bonds. The force fields can yield differences of more than 100% of the negative thermal expansion coefficients, which is exacerbated when partial atomic charges are included in UFF, UFF4MOF and DREIDING parameterizations (see Section S.5 of the supporting information for details). Here it is clear that this materials property is more sensitive to the force field parameterization, and that each materials’ soft vibrational modes are significantly influenced by both bonded and non-bonded interactions. While UFF4MOF appears to overpredict the negative thermal expansion of IRMOF-1, many of these values agree within ± 10 10−6 · K−1 , but without sufficient experimental data it is difficult to ascertain the accuracy

of these calculations.

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SBUs in MOFs for unambiguous assignment of correct atom types and bond orders for each force field. The Paddlewheel motif appears to be the most dominant coordination chemistry of those in Fig 2 in the CoRE database, consisting of 7.7% of the total. Of this 7.7%, roughly 34% are Zn paddlewheels and 54% are of the copper variety. Note that there are a significant number of duplicate structures found in the CSD, as was reported recently, 57 thus 7.7% is a generous measure of the coverage of paddlewheels in the CoRE database. This result suggests that that further efforts must be directed towards developing a force field that governs a wider variety of periodic lattice materials with differing metal - ligand coordinaton geometries.

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in these calculations is the bonding topology. Likewise, the negative trend of the linear NTE coefficient for each MOF was captured by all of the aforementioned force fields, however with differences of up to 25 MK-1 . Here, subtle interactions between force field parameters can give rise to different linear thermal expansion coefficients, suggesting that this is a more stringent test for a force fields parameterization. Because the negative expansion of these materials depends on specific vibrational modes of the ligands, 49 it is likely that comparing each force field’s vibrational frequencies will yield more pronounced differences. This will certainly affect properties that are more sensitive to vibrational modes, such as the induced breathing observed in the MIL-53 series of MOFs and DUT-49, 8,10 as well as the temperatureinduced transitions observed in functionalized MOFs. 58 It was recently demonstrated that an accurately parameterized force field could qualitatively reproduce this phenomena, 59 however it remains to be seen if more generalized force fields can be developed that cover a larger range of MOF materials. Each force field studied in this work has been collected into a Python program which is available for at https://github.com/peteboyd/lammps_interface. This code will read in MOF files in the crystallographic information file (CIF) format and enumerate all bonds, angles, dihedrals, improper torsion, and pair interactions of the structure and apply the appropriate force field parameters to each term. The resulting information is printed as a LAMMPS input file to encourage the study and comparison of these force fields in the academic community.

Acknowledgement PGB and SMM would like to thank Dr. Davide Tiana for helpful discussions with the BTW Force Field, and PGB would like to thank Dr. Thomas Daff for helpful discussions on force field implementations using the Python programming language. This project has received funding from the European Research Council (ERC) under the European Union’s Horizon

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2020 research and innovation programme (grant agreement No 666983, Magic) for PGB and BS, MW received support from the Center for Gas Separations Relevant to Clean Energy Technologies, an Energy Frontier Research Center funded by the DOE, Office of Science, Office of Basic Energy Sciences under award DE-SC0001015, and SMM was supported by the Deutsche Forschungsgemeinschaft (DFG, priority program SPP 1570).

Supporting Information Available • supporting_information.pdf: Discussion on implementation of force fields. • lammps_input_files.zip: archived file containing LAMMPS inputs for IRMOF-1, IRMOF10, HKUST-1, and UIO-66 for all the force fields studied in this work. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (1) Haldoupis, E.; Nair, S.; Sholl, D. S. Finding MOFs for Highly Selective CO2/N2 Adsorption Using Materials Screening Based on Efficient Assignment of Atomic Point Charges. J. Am. Chem. Soc. 2012, 134, 4313–4323. (2) Haldoupis, E.; Nair, S.; Sholl, D. S. Efficient Calculation of Diffusion Limitations in Metal Organic Framework Materials: A Tool for Identifying Materials for Kinetic Separations. J. Am. Chem. Soc. 2010, 132, 7528–7539. (3) Wilmer, C. E.; Farha, O. K.; Bae, Y.-S.; Hupp, J. T.; Snurr, R. Q. Structure-Property Relationships of Porous Materials for Carbon Dioxide Separation and Capture. Energy Environ. Sci. 2012, 5, 9849–9856. (4) Wilmer, C. E.; Leaf, M.; Lee, C. Y.; Farha, O. K.; Hauser, B. G.; Hupp, J. T.;

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Snurr, R. Q. Large-Scale Screening of Hypothetical Metal–Organic Frameworks. Nat. Chem. 2012, 4, 83–9. (5) Dubbeldam, D.; Calero, S.; Vlugt, T. J. H.; Krishna, R.; Maesen, T. L. M.; Smit, B. United Atom Force Field for Alkanes in Nanoporous Materials. J. Phys. Chem. B 2004, 108, 12301–12313. (6) García-Sánchez, A.; Dubbeldam, D.; Calero, S. Modeling Adsorption and Self–Diffusion of Methane in LTA Zeolites: The Influence of Framework Flexibility. J. Phys. Chem. C 2010, 114, 15068–15074. (7) Kitaura, R.; Fujimoto, K.; Noro, S.-i.; Kondo, M.; Kitagawa, S. A Pillared-Layer Coordination Polymer Network Displaying Hysteretic Sorption: [Cu2(pzdc)2(dpyg)]n (pzdc= Pyrazine-2,3-dicarboxylate; dpyg=1,2-Di(4-pyridyl)glycol). Angew. Chem., Int. Ed. Engl. 2002, 41, 133–135. (8) Serre, C.; Millange, F.; Thouvenot, C.; Noguès, M.; Marsolier, G.; Louër, D.; Férey, G. Very Large Breathing Effect in the First Nanoporous Chromium(III)-Based Solids: MIL-53. J. Am. Chem. Soc. 2002, 124, 13519–13526. (9) Serre, C.; Millange, F.; Surblé, S.; Férey, G. A Route to the Synthesis of Trivalent Transition–Metal Porous Carboxylates with Trimeric Secondary Building Units. Angew. Chem., Int. Ed. Engl. 2004, 43, 6285–6289. (10) Krause, S.; Bon, V.; Senkovska, I.; Stoeck, U.; Wallacher, D.; Többens, D. M.; Zander, S.; Pillai, R. S.; Maurin, G.; Coudert, F.-X.; Kaskel, S. A Pressure-Amplifying Framework Material with Negative Gas Adsorption Transitions. Nature 2016, 532, 348–352. (11) Han, S. S.; Goddard, W. A. Metal–Organic Frameworks Provide Large Negative Thermal Expansion Behavior. J. Phys. Chem. C 2007, 111, 15185–15191.

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(12) Dubbeldam, D.; Walton, K. S.; Ellis, D. E.; Snurr, R. Q. Exceptional Negative Thermal Expansion in Isoreticular Metal–Organic Frameworks. Angew. Chem., Int. Ed. Engl. 2007, 119, 4580–4583. (13) Camp, J. S.; Sholl, D. S. Transition State Theory Methods To Measure Diffusion in Flexible Nanoporous Materials: Application to a Porous Organic Cage Crystal. J. Phys. Chem. C 2016, 120, 1110–1120. (14) Zimmermann, N. E. R.; Jakobtorweihen, S.; Beerdsen, E.; Smit, B.; Keil, F. J. InDepth Study of the Influence of Host-Framework Flexibility on the Diffusion of Small Gas Molecules in One-Dimensional Zeolitic Pore Systems. J. Phys. Chem. C 2007, 111, 17370–17381. (15) Todorov, I. T.; Smith, W.; Trachenko, K.; Dove, M. T. DL_POLY_3: New Dimensions in Molecular Dynamics Simulations via Massive Parallelism. J. Mater. Chem. 2006, 16, 1911–1918. (16) Hess, B.; Kutzner, C.; van der Spoel, D.; Lindahl, E. GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. J. Chem. Theory Comput. 2008, 4, 435–447. (17) Gale, J. D.; Rohl, A. L. The General Utility Lattice Program ( GULP ). Mol. Simul. 2003, 29, 291–341. (18) Dubbeldam, D.; Calero, S.; Ellis, D. E.; Snurr, R. Q. RASPA: Molecular Simulation Software for Adsorption and Diffusion in Flexible Nanoporous Materials. Mol. Simul. 2015, 42, 81–101. (19) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1–19.

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(20) Bristow, J. K.; Tiana, D.; Walsh, A. Transferable Force Field for Metal–Organic Frameworks from First-Principles: BTW-FF. J. Chem. Theory Comput. 2014, 10, 4644–4652. (21) Addicoat, M. A.; Vankova, N.; Akter, I. F.; Heine, T. Extension of the Universal Force Field to Metal–Organic Frameworks. J. Chem. Theory Comput. 2014, 10, 880–891. (22) Bureekaew, S.; Amirjalayer, S.; Tafipolsky, M.; Spickermann, C.; Roy, T. K.; Schmid, R. MOF-FF - A Flexible First-Principles Derived Force Field for Metal–Organic Frameworks. Phys. Status Solidi B 2013, 250, 1128–1141. (23) Sun, Y.; Sun, H. An All-Atom Force Field Developed for Zn4O(RCO2)6 Metal Organic Frameworks. J. Mol. Model. 2014, 20, 2146. (24) Tafipolsky, M.; Schmid, R. Systematic First Principles Parameterization of Force Fields for Metal–Organic Frameworks using a Genetic Algorithm Approach. J. Phys. Chem. B 2009, 113, 1341–1352. (25) Zhao, L.; Yang, Q.; Ma, Q.; Zhong, C.; Mi, J.; Liu, D. A Force Field for Dynamic Cu-BTC Metal–Organic Framework. J. Mol. Model. 2011, 17, 227–234. (26) Vanduyfhuys, L.; Vandenbrande, S.; Verstraelen, T.; Schmid, R.; Waroquier, M.; Van Speybroeck, V. QuickFF: A Program for a Quick and Easy Derivation of Force Fields for Metal–Organic Frameworks from Ab Initio Input. J. Comput. Chem. 2015, 36, 1015–1027. (27) Vanduyfhuys, L.; Verstraelen, T.; Vandichel, M.; Waroquier, M.; Van Speybroeck, V. Ab Initio Parametrized Force Field for the Flexible Metal–Organic Framework MIL53(Al). J. Chem. Theory Comput. 2012, 8, 3217–3231. (28) Rappé, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. UFF, A Full Periodic Table Force Field for Molecular Mechanics and Molecular Dynamics Simulations. J. Am. Chem. Soc. 1992, 114, 10024–10035. 18


Page 18 of 33

Page 19 of 33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(29) Garberoglio, G.; Taioli, S. Modeling Flexibility in Metal–Organic Frameworks: Comparison Between Density-Functional Tight-Binding and Universal Force Field Approaches for Bonded Interactions. Microporous Mesoporous Mater. 2012, 163, 215–220. (30) Eddaoudi, M.; Kim, J.; Rosi, N. L.; Vodak, D. T.; Wachter, J.; O’Keeffe, M.; Yaghi, O. M. Systematic Design of Pore Size and Functionality in Isoreticular MOFs and Their Application in Methane Storage. Science 2002, 295, 469–472. (31) S-Y Chui, S.; M-F Lo, S.; H Charmant, J. P.; Guy Orpen, A.; Williams, I. D. A Chemically Functionalizable Nanoporous Material [Cu 3 (TMA) 2 (H 2 O) 3 ] n. Science 1999, 283, 1148–1150. (32) Cavka, J. H.; Jakobsen, S.; Olsbye, U.; Guillou, N.; Lamberti, C.; Bordiga, S.; Lillerud, K. P. A New Zirconium Inorganic Building Brick Forming Metal Organic Frameworks with Exceptional Stability. J. Am. Chem. Soc. 2008, 130, 13850–13851. (33) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. DREIDING: A Generic Force Field for Molecular Simulations. J. Phys. Chem. 1990, 94, 8897–8909. (34) Allinger, N. L.; Yuh, Y. H.; Lii, J. H. Molecular Mechanics. The MM3 Force Field for Hydrocarbons. 1. J. Am. Chem. Soc. 1989, 111, 8551–8566. (35) Groom, C. R.; Allen, F. H. The Cambridge Structural Database in Retrospect and Prospect. Angew. Chem., Int. Ed. Engl. 2014, 53, 662–671. (36) Allen, F. H. The Cambridge Structural Database: A Quarter of a Million Crystal Structures and Rising. Acta Crystallogr., Sect. B: Struct. Sci. 2002, 58, 380–388. (37) Murnaghan, F. D. The Compressibility of Media under Extreme Pressures. Proc. Natl. Acad. Sci. U.S.A. 1944, 30, 244–247.

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(38) Chapman, K. W.; Halder, G. J.; Chupas, P. J. Guest-Dependent High Pressure Phenomena in a Nanoporous Metal–Organic Framework Material. J. Am. Chem. Soc. 2008, 130, 10524–10526. (39) Lukose, B.; Supronowicz, B.; St. Petkov, P.; Frenzel, J.; Kuc, A. B.; Seifert, G.; Vayssilov, G. N.; Heine, T. Structural Properties of Metal–Organic Frameworks Within the Density-Functional Based Tight-Binding Method. Phys. Status Solidi B 2012, 249, 335–342. (40) Rappé, A. K.; Goddard, W. A. Charge Equilibration for Molecular Dynamics Simulations. J. Phys. Chem. 1991, 95, 3358–3363. (41) Graham, A. J.; Allan, D. R.; Muszkiewicz, A.; Morrison, C. A.; Moggach, S. A. The Effect of High Pressure on MOF-5: Guest-Induced Modification of Pore Size and Content at High Pressure. Angew. Chem., Int. Ed. Engl. 2011, 50, 11138–11141. (42) Samanta, A.; Furuta, T.; Li, J. Theoretical Assessment of the Elastic Constants and Hydrogen Storage Capacity of Some Metal–Organic Framework Materials. J. Chem. Phys. 2006, 125 . (43) Mattesini, M.; Soler, J. M.; Yndurain, F. Ab Initio Study of Metal–Organic Framework5 Zn4O(1,4-benzenedicarboxylate)3: An Assessment of Mechanical and Spectroscopic Properties. Phys. Rev. B 2006, 73, 094111. (44) Bahr, D. F.; Reid, J. A.; Mook, W. M.; Bauer, C. A.; Stumpf, R.; Skulan, A. J.; Moody, N. R.; Simmons, B. A.; Shindel, M. M.; Allendorf, M. D. Mechanical Properties of Cubic Zinc Carboxylate IRMOF-1 Metal–Organic Framework Crystals. Phys. Rev. B 2007, 76, 184106. (45) Greathouse, J. A.; Allendorf, M. D. Force Field Validation for Molecular Dynamics Simulations of IRMOF-1 and Other Isoreticular Zinc Carboxylate Coordination Polymers. J. Phys. Chem. C 2008, 112, 5795–5802. 20


Page 20 of 33

Page 21 of 33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(46) Wu, H.; Yildirim, T.; Zhou, W. Exceptional Mechanical Stability of Highly Porous Zirconium Metal–Organic Framework UiO-66 and its Important Implications. J. Phys. Chem. Lett. 2013, 4, 925–930. (47) Kuc, A.; Enyashin, A.; Seifert, G. Metal–Organic Frameworks: Structural, Energetic, Electronic, and Mechanical Properties. J. Phys. Chem. B 2007, 111, 8179–8186. (48) Yang, L.-M.; Ravindran, P.; Vajeeston, P.; Tilset, M. Ab Initio Investigations on the Crystal Structure, Formation Enthalpy, Electronic Structure, Chemical Bonding, and Optical Properties of Experimentally Synthesized Isoreticular Metal–Organic Framework-10 and its Analogues: M-IRMOF-10 (M = Zn, Cd, Be, Mg, Ca, Sr and Ba). RSC Adv. 2012, 2, 1618–1631. (49) Lock, N. et al. Scrutinizing Negative Thermal Expansion in MOF–5 by Scattering Techniques and Ab Initio Calculations. Dalton Trans. 2013, 42, 1996–2007. (50) Cliffe, M. J.; Hill, J. A.; Murray, C. A.; Coudert, F.-X.; Goodwin, A. L. DefectDependent Colossal Negative Thermal Expansion in UiO-66(Hf) Metal–Organic Framework. Phys. Chem. Chem. Phys. 2015, 17, 11586–11592. (51) Wu, Y.; Kobayashi, A.; Halder, G. J.; Peterson, V. K.; Chapman, K. W.; Lock, N.; Southon, P. D.; Kepert, C. J. Negative Thermal Expansion in the Metal–Organic Framework Material Cu 3(1,3,5-benzenetricarboxylate)2. Angew. Chem., Int. Ed. Engl. 2008, 47, 8929–8932. (52) Lock, N.; Wu, L.-Y.; Christensen, M.; Cameron, L. J.; Peterson, V. K.; Bridgeman, A. J.; Kepert, C. J.; Iversen, B. B. Elucidating Negative Thermal Expansion in MOF-5. J. Phys. Chem. C 2010, 114, 16181–16186. (53) Zhou, W.; Wu, H.; Yildirim, T.; Simpson, J. R.; Walker, A. R. H. Origin of the Exceptional Negative Thermal Expansion in Metal–Organic Framework-5 Zn4O(1,4benzenedicarboxylate)3. Phys. Rev. B 2008, 78, 054114. 21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(54) Chung, Y. G.; Camp, J.; Haranczyk, M.; Sikora, B. J.; Bury, W.; Krungleviciute, V.; Yildirim, T.; Farha, O. K.; Sholl, D. S.; Snurr, R. Q. Computation-Ready, Experimental Metal–Organic Frameworks: A Tool to Enable High-Throughput Screening of Nanoporous Crystals. Chem. Mater. 2014, 26, 6185–6192. (55) Horcajada, P.; Surble, S.; Serre, C.; Hong, D.-Y.; Seo, Y.-K.; Chang, J.-S.; Greneche, J.M.; Margiolaki, I.; Ferey, G. Synthesis and Catalytic Properties of MIL–100(Fe), an Iron(III) Carboxylate with Large Pores. Chem. Commun. 2007, 27, 2820–2822. (56) Millange, F.; Serre, C.; Férey, G. Synthesis, Structure Determination and Properties of MIL-53as and MIL-53ht: The First Cr(III) Hybrid Inorganic-Organic Microporous Solids: Cr(III)(OH)O2C-C6H4-CO2HO2C-C6H4-CO2H. Chem. Commun. 2002, 822– 823. (57) Nazarian, D.; Camp, J. S.; Sholl, D. S. A Comprehensive Set of High–Quality Point Charges for Simulations of Metal–Organic Frameworks. Chem. Mater. 2016, 28, 785– 793. (58) Henke, S.; Schneemann, A.; Fischer, R. A. Massive Anisotropic Thermal Expansion and Thermo-Responsive Breathing in Metal–Organic Frameworks Modulated by Linker Functionalization. Adv. Funct. Mater. 2013, 23, 5990–5996. (59) Alaghemandi, M.; Schmid, R. Model Study of Thermoresponsive Behavior of Metal– Organic Frameworks Modulated by Linker Functionalization. J. Phys. Chem. C 2016, 120, 6835–6841.

22


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The Journal of Physical Chemistry Letters IRMOF-1 0.6 1e 4

0.5 0.4 0.3 0.2 0.1 0.0 0.1

Energy function

pair

per impro


UiO-66

angle

4 1e 4 3 2 1 0 1 2 3 4

bond

pair

impro

per

HKUST-1

Energy function

IRMOF-10

torsio n

BTW-FF UFF UFF4MOF DREIDING DWES

angle

bond

E · V−2 (kcal·Å −6 ) 2

E · V−2 (kcal·Å −6 )

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

torsio n

2.5 1e 4 2.0 1.5 1.0 0.5 0.0 0.5 3.0 1e 4 2.5 2.0 1.5 1.0 0.5 0.0 0.5

Page 25 of 33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Paddlewheel - 7.70 % M4 O - 1.20 % M3 O - 0.80 % M-pillar - 1.60 % M6 O8 - 0.04 % other - 88.66 %


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7

E4bend Fourth Order E6bend Sixth Order

6

bend

%Error ((1 − EE46bend ) × 100)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33


Percent Error Histogram θ − θ0 Extreme Observed

5 4 3 2 1 0 30

20

10

0 θ − θ0 (degrees)

10


20

30

0.45 0.40 0.35 0.30 0.25 0.20 0.15 0.10 0.05 0.00 12 10 8 6 4 2 0

HKUST-1

1.2 1.0 0.8 0.6 0.4 0.2 0.0 0.2 0.4

Length Deviation (Å)

RMSD all atoms cell parameter a Minimization cycles

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UIO-66

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.1 0.2 800

Length Deviation (Å)

RMSD (Å)

RMSD (Å)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

IRMOF-1The Journal of Physical Chemistry Letters IRMOF-10

0

100 200 300 400Plus0Environment 200 400 600 ACS Paragon Minimization step Minimization step

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E-E0 (kcal·mol−1 )

50 40 30 20 10 0 10 2000

0

UFF4MOF

UFF



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

30 25 20 15 10 5 0 5 2000

BTW-FF

2000

40 35 30 25 20 15 10 5 0 5 2000

0

2000

DWES 25 20 15 10 5 0 5 0 2000 ACS1000 0 1000 Paragon Plus Environment V-V0 (Å 3 ) V-V0 (Å 3 )

DREIDING 50 40 30 20 10 0 10 2000 0 2000 3 V-V0 (Å ) HKUST-1 IRMOF-1 IRMOF-10 UIO-66



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

40 35 30 25 20 15 10 5 0 5 1000

Letters UFF The Journal of Physical Chemistry DREIDING 300

50 40 30 20 10 0 10 1000

0

250 200 150 100 50 0 50 1000 2000

0

UFF4MOF

2000 V-V0 ( )

HKUST-1 IRMOF-1 IRMOF-10 UIO-66 0 V-V0 (Å 3 )

1000


Å3

Page 30 of 33

4000


Page 31 of 33


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

120 100 80 60 40 20 0 20 2000

2000

0

UFF4MOF

2000 V-V0 ( )

HKUST-1 IRMOF-1 IRMOF-10 UIO-66


120 100 80 60 40 20 0 20 2000

0

100 80 60 40 20 0 20 4000 2000

0

2000ACS Paragon 4000 Plus Environment V-V0 (Å 3 )

Å3

4000



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

300 250 200 150 100 50 0 50 2000


50 40 30 20 10 0 10 1000

0

2000

100 80 60 40 20 0 20 4000 2000

0

UFF4MOF

2000 V-V0 ( )

HKUST-1 IRMOF-1 IRMOF-10 UIO-66 0 V-V0 (Å 3 )

1000


Å3

Page 32 of 33

4000

Page 33 of 33

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

P


𝑑𝑃 𝐾 = −𝑉 = 𝐵𝑢𝑙𝑘 𝑀𝑜𝑑𝑢𝑙𝑖 𝑑𝑉

𝑲𝑭𝑭 = 𝑲𝑫𝑭𝑻 ± 𝟓% V

FF =


UFF Dreiding BTW-FF UFF4MOF Dubbledam

Force-Field Prediction of Materials Properties in Metal-Organic

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