M. Waroquier

Modeling Gas Adsorption in Flexible Metal–Organic Frameworks via Hybrid Monte Carlo / Molecular Dynamics Schemes

S.M.J. Rogge, R. Goeminne, R. Demuynck, J.J. Gutiérrez-Sevillano, S. Vandenbrande, L. Vanduyfhuys, M. Waroquier, T. Verstraelen, V. Van Speybroeck
Advanced Theory and Simulations
2 (4), 1800177
2019
A1

Abstract 

Herein, a hybrid Monte Carlo (MC)/molecular dynamics (MD) simulation protocol that properly accounts for the extraordinary structural flexibility of metal–organic frameworks (MOFs) is developed and validated. This is vital to accurately predict gas adsorption isotherms and guest‐induced flexibility of these materials. First, the performance of three recent models to predict adsorption isotherms and flexibility in MOFs is critically investigated. While these methods succeed in providing qualitative insight in the gas adsorption process in MOFs, their accuracy remains limited as the intrinsic flexibility of these materials is very hard to account for. To overcome this challenge, a hybrid MC/MD simulation protocol that is specifically designed to handle the flexibility of the adsorbent, including the shape flexibility, is introduced, thereby unifying the strengths of the previous models. It is demonstrated that the application of this new protocol to the adsorption of neon, argon, xenon, methane, and carbon dioxide in MIL‐53(Al), a prototypical flexible MOF, substantially decreases the inaccuracy of the obtained adsorption isotherms and predicted guest‐induced flexibility. As a result, this method is ideally suited to rationalize the adsorption performance of flexible nanoporous materials at the molecular level, paving the way for the conscious design of MOFs as industrial adsorbents.

Gold Open Access

Ab initio evaluation of Henry coefficients using importance sampling

S. Vandenbrande, M. Waroquier, V. Van Speybroeck, T. Verstraelen
Journal of Chemical Theory and Computation
14 (12), 6359–6369
2018
A1

Abstract 

We present a new algorithm that allows for an efficient evaluation of the Henry coefficient of a guest molecule inside a porous material, which permits to use ab initio energy calculations. The Widom insertion method, which is currently used to compute these Henry coefficients, typically requires millions of energy evaluations. Our new methodology reduces this number by more than 1 order of magnitude, enabling the use of an ab initio potential energy surface. The methodology we propose is reminiscent of the well-known importance sampling technique which is frequently used in Monte Carlo integrations. First, a conventional Widom insertion simulation is performed using a force field. In the second step, the Widom results are used to select a limited number of configurations and only for these configurations the ab initio evaluation of the energy is required. Finally, by appropriately reweighting the latter energies, an accurate estimation of the ab initio Henry coefficient is possible at a moderate computational cost. We apply our methodology to the adsorption of CO2 in Mg-MOF-74, a prototypical case where interactions of a polar guest molecule with unsaturated metal sites dominate the adsorption mechanism. In this case generic force fields such as UFF or Dreiding are inappropriate and the use of ab initio methods is indispensable. In a second case study, we compute Henry coefficients of methane in UiO-66 using different levels of theory. We pay particular attention to the influence of the dispersion corrections and the role of many-body effects. For the final example, we qualitatively investigate adsorption features for a series of functionalized UiO-66 frameworks. Overall the cases we present show that accurate computations of Henry coefficients is extremely challenging, as different levels of theory provide strongly varying results. At the same time ab initio calculations have added value compared to force fields, as they provide a physically more sound description of the adsorption mechanism and in some cases clearly improve correspondence with experiment.

Open Access version available at UGent repository
Gold Open Access

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

R. Demuynck, J. Wieme, S.M.J. Rogge, K. Dedecker, L. Vanduyfhuys, M. Waroquier, V. Van Speybroeck
Journal of Chemical Theory and Computation
14 (11), pp 5511–5526
2018
A1

Abstract 

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

J. Hajek, C. Caratelli, R. Demuynck, K. De Wispelaere, L. Vanduyfhuys, M. Waroquier, V. Van Speybroeck
Chemical Science
9 (10), 2723-2732
2018
A1

Abstract 

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.

Open Access version available at UGent repository
Green Open Access

How chain length and branching influence the alkene cracking reactivity on H-ZSM-5

P. Cnudde, K. De Wispelaere, L. Vanduyfhuys, R. Demuynck, J. Van der Mynsbrugge, M. Waroquier, V. Van Speybroeck
ACS Catalysis
8, 9579 − 9595
2018
A1

Abstract 

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 β-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 β-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 β-scission reactions and to assess the mobility of all species in the pores of the zeolite.

Open Access version available at UGent repository
Gold Open Access

Extension of the QuickFF force field protocol for an improved accuracy of structural, vibrational, mechanical and thermal properties of Metal Organic Frameworks

L. Vanduyfhuys, S. Vandenbrande, J. Wieme, M. Waroquier, T. Verstraelen, V. Van Speybroeck
Journal of Computational Chemistry
39 (16), p. 999-1011
2018
A1

Abstract 

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 transparant 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 is 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.

Open Access version available at UGent repository
Gold Open Access

Thermodynamic insight into stimuli-responsive behavior of soft porous crystals

L. Vanduyfhuys, S.M.J. Rogge, J. Wieme, S. Vandenbrande, G. Maurin, M. Waroquier, V. Van Speybroeck
Nature Communications
9, 1, 204
2018
A1

Abstract 

Knowledge of the thermodynamic potential in terms of the independent variables allows to characterize the macroscopic state of the system. However, in practice, it is difficult to access this potential experimentally due to irreversible transitions that occur between equilibrium states. A showcase example of sudden transitions between (meta)stable equilibrium states is observed for soft porous crystals possessing a network with long-range structural order, which can transform between various states upon external stimuli such as pressure, temperature and guest adsorption. Such phase transformations are typically characterized by large volume changes and may be followed experimentally by monitoring the volume change in terms of certain external triggers. Herein, we present a generalized thermodynamic approach to construct the underlying Helmholtz free energy as a function of the state variables that governs the observed behaviour based on microscopic simulations. This concept allows a unique identification of the conditions under which a material becomes flexible.

Open Access version available at UGent repository
Gold Open Access

The Importance of Cell Shape Sampling To Accurately Predict Flexibility in Metal-Organic Frameworks

S.M.J. Rogge, S. Caroes, R. Demuynck, M. Waroquier, V. Van Speybroeck, A. Ghysels
Journal of Chemical Theory and Computation
14 (3), 1186-1197
2018
A1

Abstract 

In this work, the influence of cell shape sampling on the predicted stability of the different metastable phases in flexible metal–organic frameworks at finite temperatures is investigated. The influence on the free energy by neglecting cell shape sampling is quantified for the prototypical MIL-53(Al) and the topical DUT-49(Cu). This goal is achieved by constructing free energy profiles in ensembles either in which the phase space associated with the cell shape is sampled explicitly or in which the cell shape is kept fixed. When neglecting cell shape sampling, thermodynamic integration of the hydrostatic pressure yields unreliable free energy profiles that depend on the choice of the fixed cell shape. In this work, we extend the thermodynamic integration procedure via the introduction of a generalized pressure, derived from the Lagrangian strain tensor and the second Piola–Kirchhoff tensor. Using this generalized procedure, the dependence on the unit cell shape can be eliminated, and the inaccuracy in free energy stemming from the lack of cell shape sampling can be uniquely quantified. Finally, it is shown that the inaccuracy in free energy when fixing the cell shape at room temperature stems mainly from entropic contributions for both MIL-53(Al) and DUT-49(Cu).

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

R. Demuynck, S.M.J. Rogge, L. Vanduyfhuys, J. Wieme, M. Waroquier, V. Van Speybroeck
Journal of Chemical Theory and Computation (JCTC)
13 (12), 5861-5873
2017
A1

Abstract 

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.

Open Access version available at UGent repository
Gold Open Access

Reliably Modeling the Mechanical Stability of Rigid and Flexible Metal-Organic Frameworks

S.M.J. Rogge, M. Waroquier, V. Van Speybroeck
Accounts of Chemical Research
51 (1), 138-148
2018
A1

Abstract 

Over the past two decades, metal–organic frameworks (MOFs) have matured from interesting academic peculiarities toward a continuously expanding class of hybrid, nanoporous materials tuned for targeted technological applications such as gas storage and heterogeneous catalysis. These oft-times crystalline materials, composed of inorganic moieties interconnected by organic ligands, can be endowed with desired structural and chemical features by judiciously functionalizing or substituting these building blocks. As a result of this reticular synthesis, MOF research is situated at the intriguing intersection between chemistry and physics, and the building block approach could pave the way toward the construction of an almost infinite number of possible crystalline structures, provided that they exhibit stability under the desired operational conditions. However, this enormous potential is largely untapped to date, as MOFs have not yet found a major breakthrough in technological applications. One of the remaining challenges for this scale-up is the densification of MOF powders, which is generally achieved by subjecting the material to a pressurization step. However, application of an external pressure may substantially alter the chemical and physical properties of the material. A reliable theoretical guidance that can presynthetically identify the most stable materials could help overcome this technological challenge.

In this Account, we describe the recent research the progress on computational characterization of the mechanical stability of MOFs. So far, three complementary approaches have been proposed, focusing on different aspects of mechanical stability: (i) the Born stability criteria, (ii) the anisotropy in mechanical moduli such as the Young and shear moduli, and (iii) the pressure-versus-volume equations of state. As these three methods are grounded in distinct computational approaches, it is expected that their accuracy and efficiency will vary. To date, however, it is unclear which set of properties are suited and reliable for a given application, as a comprehensive comparison for a broad variety of MOFs is absent, impeding the widespread use of these theoretical frameworks.

Herein, we fill this gap by critically assessing the performance of the three computational models on a broad set of MOFs that are representative for current applications. These materials encompass the mechanically rigid UiO-66(Zr) and MOF-5(Zn) as well as the flexible MIL-47(V) and MIL-53(Al), which undergo pressure-induced phase transitions. It is observed that the Born stability criteria and pressure-versus-volume equations of state give complementary insight into the macroscopic and microscopic origins of instability, respectively. However, interpretation of the Born stability criteria becomes increasingly difficult when less symmetric materials are considered. Moreover, pressure fluctuations during the simulations hamper their accuracy for flexible materials. In contrast, the pressure-versus-volume equations of state are determined in a thermodynamic ensemble specifically targeted to mitigate the effects of these instantaneous fluctuations, yielding more accurate results. The critical Account presented here paves the way toward a solid computational framework for an extensive presynthetic screening of MOFs to select those that are mechanically stable and can be postsynthetically densified before their use in targeted applications.

Open Access version available at UGent repository
Gold Open Access

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