Ab Initio Parametrized Force Field for the Flexible Metal–Organic Framework MIL-53(Al)

An automated protocol to construct flexibility parameters for classical forcefields: applications to metal-organic frameworks

In this work, forcefield flexibility parameters were constructed and validated for more than 100 metal-organic frameworks (MOFs). We used atom typing to identify bond types, angle types, and dihedral types associated with bond stretches, angle bends, dihedral torsions, and other flexibility interactions. Our work used Manz's angle-bending and dihedral-torsion model potentials. For a crystal structure containing N atoms in its unit cell, the number of independent flexibility interactions is 3(N atoms - 1). Because the number of bonds, angles, and dihedrals is normally much larger than 3(N atoms - 1), these internal coordinates are redundant. To reduce (but not eliminate) this redundancy, our protocol prunes dihedral types in a way that preserves symmetry equivalency. Next, each dihedral type is classified as non-rotatable, hindered, rotatable, or linear. We introduce a smart selection method that identifies which particular torsion modes are important for each rotatable dihedral type. Then, we computed the force constants for all flexibility interactions together via LASSO regression (i.e., regularized linear least-squares fitting) of the training dataset. LASSO automatically identifies and removes unimportant forcefield interactions. For each MOF, the reference dataset was quantum-mechanically-computed in VASP via DFT with dispersion and included: (i) finite-displacement calculations along every independent atom translation mode, (ii) geometries randomly sampled via ab initio molecular dynamics (AIMD), (iii) the optimized ground-state geometry using experimental lattice parameters, and (iv) rigid torsion scans for each rotatable dihedral type. After training, the flexibility model was validated across geometries that were not part of the training dataset. For each MOF, we computed the goodness of fit (R-squared value) and the root-mean-squared error (RMSE) separately for the training and validation datasets. We compared flexibility models with and without bond-bond cross terms. Even without cross terms, the model yielded R-squared values of 0.910 (avg across all MOFs) ± 0.018 (st. dev.) for atom-in-material forces in the validation datasets. Our SAVESTEPS protocol should find widespread applications to parameterize flexible forcefields for material datasets. We performed molecular dynamics simulations using these flexibility parameters to compute heat capacities and thermal expansion coefficients for two MOFs.

One Atom Can Make All the Difference: Gas-Induced Phase Transformations in Bisimidazole-Linked Diamondoid Coordination Networks

Coordination networks (CNs) that undergo gas-induced transformation from closed (nonporous) to open (porous) structures are of potential utility in gas storage applications, but their development is hindered by limited control over their switching mechanisms and pressures. In this work, we report two CNs, [Co(bimpy)(bdc)]_n (X-dia-4-Co) and [Co(bimbz)(bdc)]_n (X-dia-5-Co) (H₂bdc = 1,4-benzendicarboxylic acid; bimpy = 2,5-bis(1H-imidazole-1-yl)pyridine; bimbz = 1,4-bis(1H-imidazole-1-yl)benzene), that both undergo transformation from closed to isostructural open phases involving at least a 27% increase in cell volume. Although X-dia-4-Co and X-dia-5-Co only differ from one another by one atom in their N-donor linkers (bimpy = pyridine, and bimbz = benzene), this results in different pore chemistry and switching mechanisms. Specifically, X-dia-4-Co exhibited a gradual phase transformation with a steady increase in the uptake when exposed to CO₂, whereas X-dia-5-Co exhibited a sharp step (type F-IV isotherm) at P/P₀ ≈ 0.008 or P ≈ 3 bar (195 or 298 K, respectively). Single-crystal X-ray diffraction, in situ powder XRD, in situ IR, and modeling (density functional theory calculations, and canonical Monte Carlo simulations) studies provide insights into the nature of the switching mechanisms and enable attribution of pronounced differences in sorption properties to the changed pore chemistry.

Electrical Regulation of CO2 Adsorption in the Metal-Organic Framework MIL-53

Active regulation of pore accessibility in microporous materials by external stimuli has aroused great attention in recent years. Here, we show the first experimental proof that guest adsorption in a dielectric microporous material can be regulated by a moderate external E-field below the gas breakdown voltage. CO₂ adsorption capacity in MIL-53 (Al) was significantly reduced, whereas that of NH₂-MIL-53 (Al) changed insignificantly under a direct current E-field gradient of 286 V/mm. Ab initio DFT calculations revealed that the E-field decreased the charge transfer between the CO₂ molecule and the adsorption site in the MIL-53 framework, which resulted in reduced binding energy and consequently lowered CO₂ adsorption capacity. This effect was only observed in the narrow pore state MIL-53 (Al) but not in its large pore configuration. Our results demonstrate the feasibility of regulating the adsorption of gas molecules in microporous materials using moderate E-fields.

Performance of GFN1-xTB for periodic optimization of Metal Organic Frameworks

Tight-binding approaches bridge the gap between force field methods and Density Functional Theory (DFT). Density Functional Tight Binding (DFTB) has been employed for a wide range of systems containing up...

Atomistic Mechanisms of Thermal Transformation in a Zr-Metal Organic Framework, MIL-140C

To understand the mechanisms responsible for thermal decomposition of a Zr-MOF (MIL-140C), we perform atomistic-scale molecular dynamics (MD) simulations and discuss the simulation data in comparison with the TEM images obtained for the decomposed Zr-MOF. First, we introduce the ReaxFF parameters suitable for the Zr/C/H/O chemistry and then apply them to investigate the thermal stability and morphological changes in the MIL-140C during heating. Based on the performed simulations we propose an atomic mechanism for the collapse of the MIL-140C and the molecular pathways for carbon monoxide formation, the main product of the MIL-140C thermal degradation. We also determine that the oxidation state of the ZrO_x clusters, evolved due to the thermal degradation, approximates the tetragonal phase of ZrO₂. Both simulations and experiments show a distribution of very small ZrO_x clusters embedded in the disrupted organic sheet that could contribute to the unusual high catalytic activity of the decomposed MIL-140C.

A collection of forcefield precursors for metal-organic frameworks

A host of important performance properties for metal-organic frameworks (MOFs) and other complex materials can be calculated by modeling statistical ensembles. The principle challenge is to develop accurate and computationally efficient interaction models for these simulations. Two major approaches are (i) ab initio molecular dynamics in which the interaction model is provided by an exchange-correlation theory (e.g., DFT + dispersion functional) and (ii) molecular mechanics in which the interaction model is a parameterized classical force field. The first approach requires further development to improve computational speed. The second approach requires further development to automate accurate forcefield parameterization. Because of the extreme chemical diversity across thousands of MOF structures, this problem is still mostly unsolved today. For example, here we show structures in the 2014 CoRE MOF database contain more than 8 thousand different atom types based on first and second neighbors. Our results showed that atom types based on both first and second neighbors adequately capture the chemical environment, but atom types based on only first neighbors do not. For 3056 MOFs, we used density functional theory (DFT) followed by DDEC6 atomic population analysis to extract a host of important forcefield precursors: partial atomic charges; atom-in-material (AIM) C6, C8, and C10 dispersion coefficients; AIM dipole and quadrupole moments; various AIM polarizabilities; quantum Drude oscillator parameters; AIM electron cloud parameters; etc. Electrostatic parameters were validated through comparisons to the DFT-computed electrostatic potential. These forcefield precursors should find widespread applications to developing MOF force fields.

Modelling of framework materials at multiple scales: current practices and open questions

The last decade has seen an explosion of the family of framework materials and their study, from both the experimental and computational points of view. We propose here a short highlight of the current state of methodologies for modelling framework materials at multiple scales, putting together a brief review of new methods and recent endeavours in this area, as well as outlining some of the open challenges in this field. We will detail advances in atomistic simulation methods, the development of material databases and the growing use of machine learning for the prediction of properties. This article is part of the theme issue 'Mineralomimesis: natural and synthetic frameworks in science and technology'.

Protocol for Identifying Accurate Collective Variables in Enhanced Molecular Dynamics Simulations for the Description of Structural Transformations in Flexible Metal-Organic Frameworks

Various kinds of flexibility have been observed in metal-organic frameworks, which may originate from the topology of the material or the presence of flexible ligands. The construction of free energy profiles describing the full dynamical behavior along the phase transition path is challenging since it is not trivial to identify collective variables able to identify all metastable states along the reaction path. In this work, a systematic three-step protocol to uniquely identify the dominant order parameters for structural transformations in flexible metal-organic frameworks and subsequently construct accurate free energy profiles is presented. Methodologically, this protocol is rooted in the time-structure based independent component analysis (tICA), a well-established statistical modeling technique embedded in the Markov state model methodology and often employed to study protein folding, that allows for the identification of the slowest order parameters characterizing the structural transformation. To ensure an unbiased and systematic identification of these order parameters, the tICA decomposition is performed based on information from a prior replica exchange (RE) simulation, as this technique enhances the sampling along all degrees of freedom of the system simultaneously. From this simulation, the tICA procedure extracts the order parameters-often structural parameters-that characterize the slowest transformations in the material. Subsequently, these order parameters are adopted in traditional enhanced sampling methods such as umbrella sampling, thermodynamic integration, and variationally enhanced sampling to construct accurate free energy profiles capturing the flexibility in these nanoporous materials. In this work, the applicability of this tICA-RE protocol is demonstrated by determining the slowest order parameters in both MIL-53(Al) and CAU-13, which exhibit a strongly different type of flexibility. The obtained free energy profiles as a function of this extracted order parameter are furthermore compared to the profiles obtained when adopting less-suited collective variables, indicating the importance of systematically selecting the relevant order parameters to construct accurate free energy profiles for flexible metal-organic frameworks, which is in correspondence with experimental findings. The method succeeds in mapping the full free energy surface in terms of appropriate collective variables for MOFs exhibiting linker flexibility. For CAU-13, we show the decreased stability of the closed pore phase by systematically adding adsorbed xylene molecules in the framework.

On flexible force fields for metal-organic frameworks: Recent developments and future prospects

Classical force field simulations can be used to study structural, diffusion, and adsorption properties of metal-organic frameworks (MOFs). To account for the dynamic behavior of the material, parameterization schemes have been developed to derive force constants and the associated reference values by fitting on ab initio energies, vibrational frequencies, and elastic constants. Here, we review recent developments in flexible force field models for MOFs. Existing flexible force field models are generally able to reproduce the majority of experimentally observed structural and dynamic properties of MOFs. The lack of efficient sampling schemes for capturing stimuli-driven phase transitions, however, currently limits the full predictive potential of existing flexible force fields from being realized. This article is categorized under: Structure and Mechanism > Computational Materials ScienceMolecular and Statistical Mechanics > Molecular Mechanics.

Extension of the QuickFF force field protocol for an improved accuracy of structural, vibrational, mechanical and thermal properties of metal-organic frameworks

QuickFF was originally launched in 2015 to derive accurate force fields for isolated and complex molecular systems in a quick and easy way. Apart from the general applicability, the functionality was especially tested for metal-organic frameworks (MOFs), a class of hybrid materials consisting of organic and inorganic building blocks. Herein, we launch a new release of the QuickFF protocol which includes new major features to predict structural, vibrational, mechanical and thermal properties with greater accuracy, without compromising its robustness and transparent workflow. First, the ab initio data necessary for the fitting procedure may now also be derived from periodic models for the molecular system, as opposed to the earlier cluster-based models. This is essential for an accurate description of MOFs with one-dimensional metal-oxide chains. Second, cross terms that couple internal coordinates (ICs) and anharmonic contributions for bond and bend terms are implemented. These features are essential for a proper description of vibrational and thermal properties. Third, the fitting scheme was modified to improve robustness and accuracy. The new features are tested on MIL-53(Al), MOF-5, CAU-13 and NOTT-300. As expected, periodic input data are proven to be essential for a correct description of structural, vibrational and thermodynamic properties of MIL-53(Al). Bulk moduli and thermal expansion coefficients of MOF-5 are very accurately reproduced by static and dynamic simulations using the newly derived force fields which include cross terms and anharmonic corrections. For the flexible materials CAU-13 and NOTT-300, the transition pressure is accurately predicted provided cross terms are taken into account. © 2018 Wiley Periodicals, Inc.

Efficient Construction of Free Energy Profiles of Breathing Metal-Organic Frameworks Using Advanced Molecular Dynamics Simulations

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials.

Flexible Force Field Parameterization through Fitting on the Ab Initio-Derived Elastic Tensor

Constructing functional forms and their corresponding force field parameters for the metal–linker interface of metal–organic frameworks is challenging. We propose fitting these parameters on the elastic tensor, computed from ab initio density functional theory calculations. The advantage of this top-down approach is that it becomes evident if functional forms are missing when components of the elastic tensor are off. As a proof-of-concept, a new flexible force field for MIL-47(V) is derived. Negative thermal expansion is observed and framework flexibility has a negligible effect on adsorption and transport properties for small guest molecules. We believe that this force field parametrization approach can serve as a useful tool for developing accurate flexible force field models that capture the correct mechanical behavior of the full periodic structure.

Metal-organic and covalent organic frameworks as single-site catalysts

Heterogeneous single-site catalysts consist of isolated, well-defined, active sites that are spatially separated in a given solid and, ideally, structurally identical. In this review, the potential of metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) as platforms for the development of heterogeneous single-site catalysts is reviewed thoroughly. In the first part of this article, synthetic strategies and progress in the implementation of such sites in these two classes of materials are discussed. Because these solids are excellent playgrounds to allow a better understanding of catalytic functions, we highlight the most important recent advances in the modelling and spectroscopic characterization of single-site catalysts based on these materials. Finally, we discuss the potential of MOFs as materials in which several single-site catalytic functions can be combined within one framework along with their potential as powerful enzyme-mimicking materials. The review is wrapped up with our personal vision on future research directions.

CO2 Capture and Separations Using MOFs: Computational and Experimental Studies

This Review focuses on research oriented toward elucidation of the various aspects that determine adsorption of CO₂ in metal-organic frameworks and its separation from gas mixtures found in industrial processes. It includes theoretical, experimental, and combined approaches able to characterize the materials, investigate the adsorption/desorption/reaction properties of the adsorbates inside such environments, screen and design new materials, and analyze additional factors such as material regenerability, stability, effects of impurities, and cost among several factors that influence the effectiveness of the separations. CO₂ adsorption, separations, and membranes are reviewed followed by an analysis of the effects of stability, impurities, and process operation conditions on practical applications.

Force-Field Prediction of Materials Properties in Metal-Organic Frameworks

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, HKUST-1, 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 that they are not parametrized 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, noticeable deviations can be observed when looking at properties sensitive to framework vibrational modes. This observation is more pronounced upon the introduction of framework charges.

Dioxygen binding to Fe-MOF-74: microscopic insights from periodic QM/MM calculations

Accurate MOF-FF parameter sets were determined for the ferrous and ferric forms of an iron-based metal–organic framework (MOF) called Fe-MOF-74. For this purpose, density functional theory (DFT) calculations were applied to truncated cluster models of Fe-MOF-74, and the DFT-calculated geometries and energy derivatives were used for the force-field parameterization. The resultant parameter sets performed remarkably well in reproducing the experimentally determined structure of the MOF. We also performed periodic quantum mechanics (QM) / molecular mechanics (MM) calculations employing a subtractive scheme called ONIOM, with the optimized MOF-FF parameters used for the MM calculations, in an attempt to evaluate the binding energies between O2 and several Fe-MOF-74 variants. The calculated binding energy for Fe-MOF-74 agreed very well with the experimental value, and QM/MM geometry optimization calculations confirmed that the O2-bound complex has a side-on geometry. Our calculations also predicted that, when the two neighboring iron ions around the O2-binding site are replaced with other metal ions (Mg2+, Ni2+, Zn2+, Co2+, or Mn2+), there are noticeable variations in the binding energy, indicating that these substituted metal ions affect the O2 binding indirectly.

Structures of Metal-Organic Frameworks with Rod Secondary Building Units

Rod MOFs are metal-organic frameworks in which the metal-containing secondary building units consist of infinite rods of linked metal-centered polyhedra. For such materials, we identify the points of extension, often atoms, which define the interface between the organic and inorganic components of the structure. The pattern of points of extension defines a shape such as a helix, ladder, helical ribbon, or cylinder tiling. The linkage of these shapes into a three-dimensional framework in turn defines a net characteristic of the original structure. Some scores of rod MOF structures are illustrated and deconstructed into their underlying nets in this way. Crystallographic data for all nets in their maximum symmetry embeddings are provided.

Thermodynamic Insight in the High-Pressure Behavior of UiO-66: Effect of Linker Defects and Linker Expansion

In this Article, we present a molecular-level understanding of the experimentally observed loss of crystallinity in UiO-66-type metal-organic frameworks, including the pristine UiO-66 to -68 as well as defect-containing UiO-66 materials, under the influence of external pressure. This goal is achieved by constructing pressure-versus-volume profiles at finite temperatures using a thermodynamic approach relying on ab initio derived force fields. On the atomic level, the phenomenon is reflected in a sudden drop in the number of symmetry operators for the crystallographic unit cell because of the disordered displacement of the organic linkers with respect to the inorganic bricks. For the defect-containing samples, a reduced mechanical stability is observed, however, critically depending on the distribution of these defects throughout the material, hence demonstrating the importance of judiciously characterizing defects in these materials.

Exploring the Flexibility of MIL-47(V)-Type Materials Using Force Field Molecular Dynamics Simulations

The flexibility of three MIL-47(V)-type materials (MIL-47, COMOC-2, and COMOC-3) has been explored by constructing the pressure versus volume and free energy versus volume profiles at various temperatures ranging from 100 to 400 K. This is done with first-principles-based force fields using the recently proposed QuickFF parametrization protocol. Specific terms were added for the materials at hand to describe the asymmetry of the one-dimensional vanadium-oxide chain and to account for the flexibility of the organic linkers. The force fields are used in a series of molecular dynamics simulations at fixed volumes but varying unit cell shapes. The three materials show a distinct pressure-volume behavior, which underlines the ability to tune the mechanical properties by varying the linkers toward different applications such as nanosprings, dampers, and shock absorbers.

Coarse graining of force fields for metal–organic frameworks

We have adapted our genetic algorithm based optimization approach, originally developed to generate force field parameters from quantum mechanic reference data, to derive a first coarse grained force field for a MOF, taking the atomistic MOF-FF as a reference.

Metal-organic frameworks as potential shock absorbers: the case of the highly flexible MIL-53(Al)

The mechanical energy absorption ability of the highly flexible MIL-53(Al) MOF material was explored using a combination of experiments and molecular simulations. A pressure-induced transition between the large pore and the closed pore forms of this solid was revealed to be irreversible and associated with a relatively large energy absorption capacity. Both features make MIL-53(Al) the first potential MOF candidate for further use as a shock absorber.

Fine-tuning the theoretically predicted structure of MIL-47(V) with the aid of powder X-ray diffraction

The structural characterization of complex crystalline materials can be simplified by closely comparing theoretical and experimental diffraction patterns.

Mixed matrix membranes containing MIL-53(Al) for potential application in organic solvent nanofiltration

PMIA MMMs with various amounts of MIL-53(Al) were developed through non-solvent induced phase separation and the MMMs permeance was increased dramatically while keeping high rejections in organic solvent nanofiltration.

Transferable Force Field for Metal-Organic Frameworks from First-Principles: BTW-FF

We present an ab-initio derived force field to describe the structural and mechanical properties of metal-organic frameworks (or coordination polymers). The aim is a transferable interatomic potential that can be applied to MOFs regardless of metal or ligand identity. The initial parametrization set includes MOF-5, IRMOF-10, IRMOF-14, UiO-66, UiO-67, and HKUST-1. The force field describes the periodic crystal and considers effective atomic charges based on topological analysis of the Bloch states of the extended materials. Transferable potentials were developed for the four organic ligands comprising the test set and for the associated Cu, Zn, and Zr metal nodes. The predicted materials properties, including bulk moduli and vibrational frequencies, are in agreement with explicit density functional theory calculations. The modal heat capacity and lattice thermal expansion are also predicted.

Structural Dynamics in a "Breathing" Metal-Organic Framework Studied by Electron Paramagnetic Resonance of Nitroxide Spin Probes

Reversible structural rearrangements ("breathing") of metal-organic frameworks (MOFs) are interesting and complex phenomena with many potential applications. They are often triggered by small amounts of adsorbed guest molecules; therefore, the guest-host interactions in breathing MOFs are intensively investigated. Due to the sensitivity limitations, most analytical methods require relatively high concentrations of guests in these studies. However, because guest molecules are not "innocent", breathing behavior may become suppressed and unperturbed structural states inaccessible. We propose here the use of guest nitroxide molecules in tiny concentrations (such as 1 molecule per 1000 unit cells), which serve as spin probes for electron paramagnetic resonance (EPR), for effective study of breathing phenomena in MOFs. Using a perspective MIL-53(Al) framework as an example, we demonstrate the great advantage of this general approach, which avoids perturbation of the framework structure and allows in-depth investigation of guest-host interactions in the breathing mode.

Analysis of the basis set superposition error in molecular dynamics of hydrogen-bonded liquids: application to methanol

An efficient protocol is presented to compensate for the basis set superposition error (BSSE) in DFT molecular dynamics (MD) simulations using localized Gaussian basis sets. We propose a classical correction term that can be added a posteriori to account for BSSE. It is tested to what extension this term will improve radial distribution functions (RDFs). The proposed term is pairwise between certain atoms in different molecules and was calibrated by fitting reference BSSE data points computed with the counterpoise method. It is verified that the proposed exponential decaying functional form of the model is valid. This work focuses on hydrogen-bonded liquids, i.e., methanol, and more specific on the intermolecular hydrogen bond, but in principle the method is generally applicable on any type of interaction where BSSE is significant. We evaluated the relative importance of the Grimme-dispersion versus BSSE and found that they are of the same order of magnitude, but with an opposite sign. Upon introduction of the correction, the relevant RDFs, obtained from MD, have amplitudes equal to experiment.