Sven M. J. Rogge

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.

A Comparison of Barostats for the Mechanical Characterization of Metal–Organic Frameworks

In this paper, three barostat coupling schemes for pressure control, which are commonly used in molecular dynamics simulations, are critically compared to characterize the rigid MOF-5 and flexible MIL-53(Al) metal-organic frameworks. We investigate the performance of the three barostats, the Berendsen, the Martyna-Tuckerman-Tobias-Klein (MTTK), and the Langevin coupling methods, in reproducing the cell parameters and the pressure versus volume behavior in isothermal-isobaric simulations. A thermodynamic integration method is used to construct the free energy profiles as a function of volume at finite temperature. It is observed that the aforementioned static properties are well-reproduced with the three barostats. However, for static properties depending nonlinearly on the pressure, the Berendsen barostat might give deviating results as it suppresses pressure fluctuations more drastically. Finally, dynamic properties, which are directly related to the fluctuations of the cell, such as the time to transition from the large-pore to the closed-pore phase, cannot be well-reproduced by any of the coupling schemes.

Semi-analytical mean-field model for predicting breathing in metal–organic frameworks

A new semi-analytical mean-field model is proposed to rationalise breathing of MIL-53 type materials. The model is applied on two case studies, the guest-induced breathing of MIL-53(Cr) with CO2 and CH4, and the phase transformations for MIL-53(Al) upon xenon adsorption. Experimentally, MIL-53(Cr) breathes upon CO2 adsorption, which was not observed for CH4. This result could be ascribed to the stronger interaction of carbon dioxide with the host matrix. For MIL-53(Al) a phase transition from the large pore phase could be enforced to an intermediate phase with volumes of about 1160–1300 Å3, which corresponds well to the phase observed experimentally upon xenon adsorption. Our thermodynamic model correlates nicely with the adsorption pressure model proposed by Coudert et al. Furthermore the model can predict breathing behaviour of other flexible materials, if the user can determine the free energy of the empty host, the interaction energy between a guest molecule and the host matrix and the pore volume accessible to the guest molecules. This will allow to generate the osmotic potential from which the equilibria can be deduced and the anticipated experimentally observed phase may be predicted.

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.

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

Conspectus 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.

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.

Acidity Constant (pKa ) Calculation of Large Solvated Dye Molecules: Evaluation of Two Advanced Molecular Dynamics Methods.

Abstract pH‐Sensitive dyes are increasingly applied on polymer substrates for the creation of novel sensor materials. Recently, these dye molecules were modified to form a covalent bond with the polymer host. This had a large influence on the pH‐sensitive properties, in particular on the acidity constant (pK a). Obtaining molecular control over the factors that influence the pK a value is mandatory for the future intelligent design of sensor materials. Herein, we show that advanced molecular dynamics (MD) methods have reached the level at which the pK a values of large solvated dye molecules can be predicted with high accuracy. Two MD methods were used in this work: steered or restrained MD and the insertion/deletion scheme. Both were first calibrated on a set of phenol derivatives and afterwards applied to the dye molecule bromothymol blue. Excellent agreement with experimental values was obtained, which opens perspectives for using these methods for designing dye molecules.

Thermodynamic insight into stimuli-responsive behaviour of soft porous crystals

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.Knowledge of the thermodynamic potential is crucial to characterize the macroscopic state of soft porous crystals. Here, the authors present a generalized thermodynamic approach to construct the Helmholtz free energy and identify the conditions under which a material becomes flexible.

Influence of a Confined Methanol Solvent on the Reactivity of Active Sites in UiO-66

Abstract UiO‐66, composed of Zr‐oxide bricks and terephthalate linkers, is currently one of the most studied metal–organic frameworks due to its exceptional stability. Defects can be introduced in the structure, creating undercoordinated Zr atoms which are Lewis acid sites. Here, additional Brønsted sites can be generated by coordinated protic species from the solvent. In this Article, a multilevel modeling approach was applied to unravel the effect of a confined methanol solvent on the active sites in UiO‐66. First, active sites were explored with static periodic density functional theory calculations to investigate adsorption of water and methanol. Solvent was then introduced in the pores with grand canonical Monte Carlo simulations, followed by a series of molecular dynamics simulations at operating conditions. A hydrogen‐bonded network of methanol molecules is formed, allowing the protons to shuttle between solvent methanol, adsorbed water, and the inorganic brick. Upon deprotonation of an active site, the methanol solvent aids the transfer of protons and stabilizes charged configurations via hydrogen bonding, which could be crucial in stabilizing reactive intermediates. The multilevel modeling approach adopted here sheds light on the important role of a confined solvent on the active sites in the UiO‐66 material, introducing dynamic acidity in the system at finite temperatures by which protons may be easily shuttled from various positions at the active sites.