OGRe: Optimal Grid Refinement Protocol for Accurate Free Energy Surfaces and Its Application in Proton Hopping in Zeolites and 2D COF Stacking.

While free energy surfaces are the crux of our understanding of many chemical and biological processes, their accuracy is generally unknown. Moreover, many developments to improve their accuracy are often complicated, limiting their general use. Luckily, several tools and guidelines are already in place to identify these shortcomings, but they are typically lacking in flexibility or fail to systematically determine how to improve the accuracy of the free energy calculation. To overcome these limitations, this work introduces OGRe, a Python package for optimal grid refinement in an arbitrary number of dimensions. OGRe is based on three metrics that gauge the confinement, consistency, and overlap of each simulation in a series of umbrella sampling (US) simulations, an enhanced sampling technique ubiquitously adopted to construct free energy surfaces for hindered processes. As these three metrics are fundamentally linked to the accuracy of the weighted histogram analysis method adopted to generate free energy surfaces from US simulations, they facilitate the systematic construction of accurate free energy profiles, where each metric is driven by a specific umbrella parameter. This allows for the derivation of a consistent and optimal collection of umbrellas for each simulation, largely independent of the initial values, thereby dramatically increasing the ease-of-use toward accurate free energy surfaces. As such, OGRe is particularly suited to determine complex free energy surfaces with large activation barriers and shallow minima, which underpin many physical and chemical transformations and hence to further our fundamental understanding of these processes.

Operando Modeling of Zeolite-Catalyzed Reactions Using First-Principles Molecular Dynamics Simulations.

Within this Perspective, we critically reflect on the role of first-principles molecular dynamics (MD) simulations in unraveling the catalytic function within zeolites under operating conditions. First-principles MD simulations refer to methods where the dynamics of the nuclei is followed in time by integrating the Newtonian equations of motion on a potential energy surface that is determined by solving the quantum-mechanical many-body problem for the electrons. Catalytic solids used in industrial applications show an intriguing high degree of complexity, with phenomena taking place at a broad range of length and time scales. Additionally, the state and function of a catalyst critically depend on the operating conditions, such as temperature, moisture, presence of water, etc. Herein we show by means of a series of exemplary cases how first-principles MD simulations are instrumental to unravel the catalyst complexity at the molecular scale. Examples show how the nature of reactive species at higher catalytic temperatures may drastically change compared to species at lower temperatures and how the nature of active sites may dynamically change upon exposure to water. To simulate rare events, first-principles MD simulations need to be used in combination with enhanced sampling techniques to efficiently sample low-probability regions of phase space. Using these techniques, it is shown how competitive pathways at operating conditions can be discovered and how broad transition state regions can be explored. Interestingly, such simulations can also be used to study hindered diffusion under operating conditions. The cases shown clearly illustrate how first-principles MD simulations reveal insights into the catalytic function at operating conditions, which could not be discovered using static or local approaches where only a few points are considered on the potential energy surface (PES). Despite these advantages, some major hurdles still exist to fully integrate first-principles MD methods in a standard computational catalytic workflow or to use the output of MD simulations as input for multiple length/time scale methods that aim to bridge to the reactor scale. First of all, methods are needed that allow us to evaluate the interatomic forces with quantum-mechanical accuracy, albeit at a much lower computational cost compared to currently used density functional theory (DFT) methods. The use of DFT limits the currently attainable length/time scales to hundreds of picoseconds and a few nanometers, which are much smaller than realistic catalyst particle dimensions and time scales encountered in the catalysis process. One solution could be to construct machine learning potentials (MLPs), where a numerical potential is derived from underlying quantum-mechanical data, which could be used in subsequent MD simulations. As such, much longer length and time scales could be reached; however, quite some research is still necessary to construct MLPs for the complex systems encountered in industrially used catalysts. Second, most currently used enhanced sampling techniques in catalysis make use of collective variables (CVs), which are mostly determined based on chemical intuition. To explore complex reactive networks with MD simulations, methods are needed that allow the automatic discovery of CVs or methods that do not rely on a priori definition of CVs. Recently, various data-driven methods have been proposed, which could be explored for complex catalytic systems. Lastly, first-principles MD methods are currently mostly used to investigate local reactive events. We hope that with the rise of data-driven methods and more efficient methods to describe the PES, first-principles MD methods will in the future also be able to describe longer length/time scale processes in catalysis. This might lead to a consistent dynamic description of all steps-diffusion, adsorption, and reaction-as they take place at the catalyst particle level.

DFT-Quality Adsorption Simulations in Metal-Organic Frameworks Enabled by Machine Learning Potentials.

Nanoporous materials such as metal-organic frameworks (MOFs) have been extensively studied for their potential for adsorption and separation applications. In this respect, grand canonical Monte Carlo (GCMC) simulations have become a well-established tool for computational screenings of the adsorption properties of large sets of MOFs. However, their reliance on empirical force field potentials has limited the accuracy with which this tool can be applied to MOFs with challenging chemical environments such as open-metal sites. On the other hand, density-functional theory (DFT) is too computationally demanding to be routinely employed in GCMC simulations due to the excessive number of required function evaluations. Therefore, we propose in this paper a protocol for training machine learning potentials (MLPs) on a limited set of DFT intermolecular interaction energies (and forces) of CO2 in ZIF-8 and the open-metal site containing Mg-MOF-74, and use the MLPs to derive adsorption isotherms from first principles. We make use of the equivariant NequIP model which has demonstrated excellent data efficiency, and as such an error on the interaction energies below 0.2 kJ mol-1 per adsorbate in ZIF-8 was attained. Its use in GCMC simulations results in highly accurate adsorption isotherms and heats of adsorption. For Mg-MOF-74, a large dependence of the obtained results on the used dispersion correction was observed, where PBE-MBD performs the best. Lastly, to test the transferability of the MLP trained on ZIF-8, it was applied to ZIF-3, ZIF-4, and ZIF-6, which resulted in large deviations in the predicted adsorption isotherms and heats of adsorption. Only when explicitly training on data for all ZIFs, accurate adsorption properties were obtained. As the proposed methodology is widely applicable to guest adsorption in nanoporous materials, it opens up the possibility for training general-purpose MLPs to perform highly accurate investigations of guest adsorption.

Mechanistic Characterization of Zeolite-Catalyzed Aromatic Electrophilic Substitution at Realistic Operating Conditions.

Zeolite-catalyzed benzene ethylation is an important industrial reaction, as it is the first step in the production of styrene for polymer manufacturing. Furthermore, it is a prototypical example of aromatic electrophilic substitution, a key reaction in the synthesis of many bulk and fine chemicals. Despite extensive research, the reaction mechanism and the nature of elusive intermediates at realistic operating conditions is not properly understood. More in detail, the existence of the elusive arenium ion (better known as Wheland complex) formed upon electrophilic attack on the aromatic ring is still a matter of debate. Temperature effects and the presence of protic guest molecules such as water are expected to impact the reaction mechanism and lifetime of the reaction intermediates. Herein, we used enhanced sampling ab initio molecular dynamics simulations to investigate the complete mechanism of benzene ethylation with ethene and ethanol in the H-ZSM-5 zeolite. We show that both the stepwise and concerted mechanisms are active at reaction conditions and that the Wheland intermediate spontaneously appears as a shallow minimum in the free energy surface after the electrophilic attack on the benzene ring. Addition of water enhances the protonation kinetics by about 1 order of magnitude at coverages of one water molecule per Brønsted acidic site. In the fully solvated regime, an overstabilization of the BAS as hydronium ion occurs and the rate enhancement disappears. The obtained results give critical atomistic insights in the role of water to selectively tune the kinetics of protonation reactions in zeolites.

Crystals springing into action: metal-organic framework CUK-1 as a pressure-driven molecular spring.

Mercury porosimetry and in situ high pressure single crystal X-ray diffraction revealed the wine-rack CUK-1 MOF as a unique crystalline material capable of a fully reversible mechanical pressure-triggered structural contraction. The near-absence of hysteresis upon cycling exhibited by this robust MOF, akin to an ideal molecular spring, is associated with a constant work energy storage capacity of 40 J g-1. Molecular simulations were further deployed to uncover the free-energy landscape behind this unprecedented pressure-responsive phenomenon in the area of compliant hybrid porous materials. This discovery is of utmost importance from the perspective of instant energy storage and delivery.

Mechanistic Insight into the Framework Methylation of H-ZSM-5 for Varying Methanol Loadings and Si/Al Ratios Using First-Principles Molecular Dynamics Simulations.

The methanol-to-hydrocarbon process is known to proceed autocatalytically in H-ZSM-5 after an induction period where framework methoxy species are formed. In this work, we provide mechanistic insight into the framework methylation within H-ZSM-5 at high methanol loadings and varying acid site densities by means of first-principles molecular dynamics simulations. The molecular dynamics simulations show that stable methanol clusters form in the zeolite pores, and these clusters commonly deprotonate the active site; however, the cluster size is dependent on the temperature and acid site density. Enhanced sampling molecular dynamics simulations give evidence that the barrier for methanol conversion is significantly affected by the neighborhood of an additional acid site, suggesting that cooperative effects influence methanol clustering and reactivity. The insights obtained are important steps in optimizing the catalyst and engineering the induction period of the methanol-to-hydrocarbon process.

Thermal Engineering of Metal-Organic Frameworks for Adsorption Applications: A Molecular Simulation Perspective.

Thermal engineering of metal-organic frameworks for adsorption-based applications is very topical in view of their industrial potential, in particular, since heat management and thermal stability have been identified as important obstacles. Hence, a fundamental understanding of the structural and chemical features underpinning their intrinsic thermal properties is highly sought-after. Herein, we investigate the nanoscale behavior of a diverse set of frameworks using molecular simulation techniques and critically compare properties such as thermal conductivity, heat capacity, and thermal expansion with other classes of materials. Furthermore, we propose a hypothetical thermodynamic cycle to estimate the temperature rise associated with adsorption for the most important greenhouse and energy-related gases (CO2 and CH4). This macroscopic response on the heat of adsorption connects the intrinsic thermal properties with the adsorption properties and allows us to evaluate their importance.

How Chain Length and Branching Influence the Alkene Cracking Reactivity on H-ZSM-5.

Catalytic alkene cracking on H-ZSM-5 involves a complex reaction network with many possible reaction routes and often elusive intermediates. Herein, advanced molecular dynamics simulations at 773 K, a typical cracking temperature, are performed to clarify the nature of the intermediates and to elucidate dominant cracking pathways at operating conditions. A series of C4-C8 alkene intermediates are investigated to evaluate the influence of chain length and degree of branching on their stability. Our simulations reveal that linear, secondary carbenium ions are relatively unstable, although their lifetime increases with carbon number. Tertiary carbenium ions, on the other hand, are shown to be very stable, irrespective of the chain length. Highly branched carbenium ions, though, tend to rapidly rearrange into more stable cationic species, either via cracking or isomerization reactions. Dominant cracking pathways were determined by combining these insights on carbenium ion stability with intrinsic free energy barriers for various octene ß-scission reactions, determined via umbrella sampling simulations at operating temperature (773 K). Cracking modes A (3° → 3°) and B2 (3° → 2°) are expected to be dominant at operating conditions, whereas modes B1 (2° → 3°), C (2° → 2°), D2 (2° → 1°), and E2 (3° → 1°) are expected to be less important. All ß-scission modes in which a transition state with primary carbocation character is involved have high intrinsic free energy barriers. Reactions starting from secondary carbenium ions will contribute less as these intermediates are short living at the high cracking temperature. Our results show the importance of simulations at operating conditions to properly evaluate the carbenium ion stability for ß-scission reactions and to assess the mobility of all species in the pores of the zeolite.

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 the intrinsic dynamic nature of the rigid UiO-66 metal-organic framework.

UiO-66 is a showcase example of an extremely stable metal-organic framework, which maintains its structural integrity during activation processes such as linker exchange and dehydration. The framework can even accommodate a substantial number of defects without compromising its stability. These observations point to an intrinsic dynamic flexibility of the framework, related to changes in the coordination number of the zirconium atoms. Herein we follow the dynamics of the framework in situ, by means of enhanced sampling molecular dynamics simulations such as umbrella sampling, during an activation process, where the coordination number of the bridging hydroxyl groups capped in the inorganic Zr6(µ3-O)4(µ3-OH)4 brick is reduced from three to one. Such a reduction in the coordination number occurs during the dehydration process and in other processes where defects are formed. We observe a remarkable fast response of the system upon structural changes of the hydroxyl group. Internal deformation modes are detected, which point to linker decoordination and recoordination. Detached linkers may be stabilized by hydrogen bonds with hydroxyl groups of the inorganic brick, which gives evidence for an intrinsic dynamic acidity even in the absence of protic guest molecules. Our observations yield a major step forward in the understanding on the molecular level of activation processes realized experimentally but that is hard to track on a purely experimental basis.

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.

Elucidating the Vibrational Fingerprint of the Flexible Metal-Organic Framework MIL-53(Al) Using a Combined Experimental/Computational Approach.

In this work, mid-infrared (mid-IR), far-IR, and Raman spectra are presented for the distinct (meta)stable phases of the flexible metal-organic framework MIL-53(Al). Static density functional theory (DFT) simulations are performed, allowing for the identification of all IR-active modes, which is unprecedented in the low-frequency region. A unique vibrational fingerprint is revealed, resulting from aluminum-oxide backbone stretching modes, which can be used to clearly distinguish the IR spectra of the closed- and large-pore phases. Furthermore, molecular dynamics simulations based on a DFT description of the potential energy surface enable determination of the theoretical Raman spectrum of the closed- and large-pore phases for the first time. An excellent correspondence between theory and experiment is observed. Both the low-frequency IR and Raman spectra show major differences in vibrational modes between the closed- and large-pore phases, indicating changes in lattice dynamics between the two structures. In addition, several collective modes related to the breathing mechanism in MIL-53(Al) are identified. In particular, we rationalize the importance of the trampoline-like motion of the linker for the phase transition.

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.

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.

Minimal Basis Iterative Stockholder: Atoms in Molecules for Force-Field Development.

Atomic partial charges appear in the Coulomb term of many force-field models and can be derived from electronic structure calculations with a myriad of atoms-in-molecules (AIM) methods. More advanced models have also been proposed, using the distributed nature of the electron cloud and atomic multipoles. In this work, an electrostatic force field is defined through a concise approximation of the electron density, for which the Coulomb interaction is trivially evaluated. This approximate "pro-density" is expanded in a minimal basis of atom-centered s-type Slater density functions, whose parameters are optimized by minimizing the Kullback-Leibler divergence of the pro-density from a reference electron density, e.g., obtained from an electronic structure calculation. The proposed method, Minimal Basis Iterative Stockholder (MBIS), is a variant of the Hirshfeld AIM method, but it can also be used as a density-fitting technique. An iterative algorithm to refine the pro-density is easily implemented with a linear-scaling computational cost, enabling applications to supramolecular systems. The benefits of the MBIS method are demonstrated with systematic applications to molecular databases and extended models of condensed phases. A comparison to 14 other AIM methods shows its effectiveness when modeling electrostatic interactions. MBIS is also suitable for rescaling atomic polarizabilities in the Tkatchenko-Scheffler scheme for dispersion interactions.

A Breathing Zirconium Metal-Organic Framework with Reversible Loss of Crystallinity by Correlated Nanodomain Formation.

The isoreticular analogue of the metal-organic framework UiO-66(Zr), synthesized with the flexible trans-1,4-cyclohexanedicarboxylic acid as linker, shows a peculiar breathing behavior by reversibly losing long-range crystalline order upon evacuation. The underlying flexibility is attributed to a concerted conformational contraction of up to two thirds of the linkers, which breaks the local lattice symmetry. X-ray scattering data are described well by a nanodomain model in which differently oriented tetragonal-type distortions propagate over about 7-10 unit cells.

Mechanical energy storage performance of an aluminum fumarate metal-organic framework.

The aluminum fumarate MOF A520 or MIL-53-FA is revealed to be a promising material for mechanical energy-related applications with performances in terms of work and heat energies which surpass those of any porous solids reported so far. Complementary experimental and computational tools are deployed to finely characterize and understand the pressure-induced structural transition at the origin of these unprecedented levels of performance.

QuickFF: A program for a quick and easy derivation of force fields for metal-organic frameworks from ab initio input.

QuickFF is a software package to derive accurate force fields for isolated and complex molecular systems in a quick and easy manner. Apart from its general applicability, the program has been designed to generate force fields for metal-organic frameworks in an automated fashion. The force field parameters for the covalent interaction are derived from ab initio data. The mathematical expression of the covalent energy is kept simple to ensure robustness and to avoid fitting deficiencies as much as possible. The user needs to produce an equilibrium structure and a Hessian matrix for one or more building units. Afterward, a force field is generated for the system using a three-step method implemented in QuickFF. The first two steps of the methodology are designed to minimize correlations among the force field parameters. In the last step, the parameters are refined by imposing the force field parameters to reproduce the ab initio Hessian matrix in Cartesian coordinate space as accurate as possible. The method is applied on a set of 1000 organic molecules to show the easiness of the software protocol. To illustrate its application to metal-organic frameworks (MOFs), QuickFF is used to determine force fields for MIL-53(Al) and MOF-5. For both materials, accurate force fields were already generated in literature but they requested a lot of manual interventions. QuickFF is a tool that can easily be used by anyone with a basic knowledge of performing ab initio calculations. As a result, accurate force fields are generated with minimal effort. © 2015 Wiley Periodicals, Inc.

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.

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.