Louis Vanduyfhuys

Ab initio parametrized force field for the flexible metal-organic framework MIL-53(Al)

A force field is proposed for the flexible metal-organic framework MIL-53(Al), which is calibrated using density functional theory calculations on nonperiodic clusters. The force field has three main contributions: an electrostatic term based on atomic charges derived with a modified Hirshfeld-I method, a van der Waals (vdW) term with parameters taken from the MM3 model, and a valence force field whose parameters were estimated with a new methodology that uses the gradients and Hessian matrix elements retrieved from nonperiodic cluster calculations. The new force field predicts geometries and cell parameters that compare well with the experimental values both for the large and narrow pore phases. The energy profile along the breathing mode of the empty material reveals the existence of two minima, which confirms the intrinsic bistable behavior of the MIL-53. Even without the stimulus of external guest molecules, the material may transform from the large pore (lp) to the narrow pore (np) phase [Liu et al. J. Am. Chem. Soc.2008, 120, 11813]. The relative stability of the two phases critically depends on the vdW parameters, and the MM3 dispersion interaction has the tendency to overstabilize the np phase.

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.

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.

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.

Vibrational fingerprint of the absorption properties of UiO-type MOF materials

The absorption properties of UiO-type metal–organic frameworks are computed using TD-DFT simulations on the organic linkers. A set of nine isoreticular structures, including the UiO-66 and UiO-67 materials and functionalized variants, are examined. The excitation energies from a static geometry optimization are compared with dynamic averages obtained from sampling the ground-state potential energy surface using molecular dynamics. The vibrational modes that impact the excitation energy are identified. This analysis is done using a recently proposed tool based on power spectra of the velocities and the excitation energies. The applied procedure allows including important factors influencing the absorption spectra, such as the periodic framework, linker variation and dynamical effects including harmonic and anharmonic nuclear motions. This methodology allows investigating in detail the vibrational fingerprint of the excitation energy of advanced materials such as MOFs and gives perspectives to tailor materials toward new light-based applications.

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.

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 such as metal organic frameworks can prove a very difficult challenge both for experimentalists as for theoreticians. From theory, the flat potential energy surface of these highly flexible structures often leads to different geometries that are energetically very close to each other. In this work a distinction between various computationally determined structures is made by comparing experimental and theoretically derived X-ray diffractograms which are produced from the materials geometry. The presented approach allows to choose the most appropriate geometry of a MIL-47(V) MOF and even distinguish between different electronic configurations that induce small structural changes. Moreover the techniques presented here are used to verify the applicability of a newly developed force field for this material. The discussed methodology is of significant importance for modelling studies where accurate geometries are crucial, such as mechanical properties and adsorption of guest molecules.