Quasi‐Harmonic Lattice Dynamics of a Prototypical Metal–Organic Framework

Multiscale Modeling of Physical Properties of Nanoporous Frameworks: Predicting Mechanical, Thermal, and Adsorption Behavior

ConspectusNanoporous frameworks are a large and diverse family of supramolecular materials, whose chemical building units (organic, inorganic, or both) are assembled into a 3D architecture with well-defined connectivity and topology, featuring intrinsic porosity. These materials play a key role in various industrial processes and applications, such as energy production and conversion, fluid separation, gas storage, water harvesting, and many more. The performance and suitability of nanoporous materials for each specific application are directly related to both their physical and chemical properties, and their determination is crucial for process engineering and optimization of performances. In this Account, we focus on some recent developments in the multiscale modeling of physical properties of nanoporous frameworks, highlighting the latest advances in three specific areas: mechanical properties, thermal properties, and adsorption.In the study of the mechanical behavior of nanoporous materials, the past few years have seen a rapid acceleration of research. For example, computational resources have been pooled to create a public large-scale database of elastic constants as part of the Materials Project initiative to accelerate innovation in materials research: those can serve as a basis for data-based discovery of materials with targeted properties, as well as the training of machine learning predictor models.The large-scale prediction of thermal behavior, in comparison, is not yet routinely performed at such a large scale. Tentative databases have been assembled at the DFT level on specific families of materials, such as zeolites, but prediction at larger scale currently requires the use of transferable classical force fields, whose accuracy can be limited.Finally, adsorption is naturally one of the most studied physical properties of nanoporous frameworks, as fluid separation or storage is often the primary target for these materials. We highlight the recent achievements and open challenges for adsorption prediction at a large scale, focusing in particular on the accuracy of computational models and the reliability of comparisons with experimental data available. We detail some recent methodological improvements in the prediction of adsorption-related properties: in particular, we describe the recent research efforts to go beyond the study of thermodynamic quantities (uptake, adsorption enthalpy, and thermodynamic selectivity) and predict transport properties using data-based methods and high-throughput computational schemes. Finally, we stress the importance of data-based methods of addressing all sources of uncertainty.The Account concludes with some perspectives about the latest developments and open questions in data-based approaches and the integration of computational and experimental data together in the materials discovery loop.

Storage and Diffusion of Carbon Dioxide in the Metal Organic Framework MOF-5─A Semi-empirical Molecular Dynamics Study

Metal-organic frameworks (MOFs) have attracted increasing attention due to their high porosity for exceptional gas storage applications. MOF-5 belongs to the family of isoreticular MOFs (IRMOFs) and consists of Zn4O6+ clusters linked by 1,4-benzenedicarboxylate. Due to the large number of atoms in the unit cell, molecular dynamics simulation based on density functional theory has proved to be too demanding, while force field models are often inadequate to model complex host-guest interactions. To overcome this limitation, an alternative semi-empirical approach using a set of approximations and extensive parametrization of interactions called density functional tight binding (DFTB) was applied in this work to study CO2 in the MOF-5 host. Calculations of pristine MOF-5 yield very good agreement with experimental data in terms of X-ray diffraction patterns as well as mechanical properties, such as the negative thermal expansion coefficient and the bulk modulus. In addition, different loadings of CO2 were introduced, and the associated self-diffusion coefficients and activation energies were investigated. The results show very good agreement with those of other experimental and theoretical investigations. This study provides detailed insights into the capability of semi-empirical DFTB-based molecular dynamics simulations of these challenging guest@host systems. Based on the comparison of the guest-guest pair distributions observed inside the MOF host and the corresponding gas-phase reference, a liquid-like structure of CO2 can be deduced upon storage in the host material.

CRYSTAL23: A Program for Computational Solid State Physics and Chemistry

The Crystal program for quantum-mechanical simulations of materials has been bridging the realm of molecular quantum chemistry to the realm of solid state physics for many years, since its first public version released back in 1988. This peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals (LCAO) approach and from the corresponding efficiency in the evaluation of the exact Fock exchange series. In particular, this has led to the implementation of a rich variety of hybrid density functional approximations since 1998. Nowadays, it is acknowledged by a broad community of solid state chemists and physicists that the inclusion of a fraction of Fock exchange in the exchange-correlation potential of the density functional theory is key to a better description of many properties of materials (electronic, magnetic, mechanical, spintronic, lattice-dynamical, etc.). Here, the main developments made to the program in the last five years (i.e., since the previous release, Crystal17) are presented and some of their most noteworthy applications reviewed.

Combined Deep Learning and Classical Potential Approach for Modeling Diffusion in UiO-66

Modeling of diffusion of adsorbates through porous materials with atomistic molecular dynamics (MD) can be a challenging task if the flexibility of the adsorbent needs to be included. This is because potentials need to be developed that accurately account for the motion of the adsorbent in response to the presence of adsorbate molecules. In this work, we show that it is possible to use accurate machine learning atomistic potentials for metal-organic frameworks in concert with classical potentials for adsorbates to accurately compute diffusivities though a hybrid potential approach. As a proof-of-concept, we have developed an accurate deep learning potential (DP) for UiO-66, a metal-organic framework, and used this DP to perform hybrid potential simulations, modeling diffusion of neon and xenon through the crystal. The adsorbate-adsorbate interactions were modeled with Lennard-Jones (LJ) potentials, the adsorbent-adsorbent interactions were described by the DP, and the adsorbent-adsorbate interactions used LJ cross-interactions. Thus, our hybrid potential allows for adsorbent-adsorbate interactions with classical potentials but models the response of the adsorbent to the presence of the adsorbate through near-DFT accuracy DPs. This hybrid approach does not require refitting the DP for new adsorbates. We calculated self-diffusion coefficients for Ne in UiO-66 from DFT-MD, our hybrid DP/LJ approach, and from two different classical potentials for UiO-66. Our DP/LJ results are in excellent agreement with DFT-MD. We modeled diffusion of Xe in UiO-66 with DP/LJ and a classical potential. Diffusion of Xe in UiO-66 is about a factor of 30 slower than that of Ne, so it is not computationally feasible to compute Xe diffusion with DFT-MD. Our hybrid DP-classical potential approach can be applied to other MOFs and other adsorbates, making it possible to use an accurate DP generated from DFT simulations of an empty adsorbent in concert with existing classical potentials for adsorbates to model adsorption and diffusion within the porous material, including adsorbate-induced changes to the framework.

A neural network potential for the IRMOF series and its application for thermal and mechanical behaviors

Metal-organic frameworks (MOFs) with their exceptional porous and organized structures have been the subject of numerous applications. Predicting the bulk properties from atomistic simulations requires the most accurate force fields, which is still a major problem due to MOFs' hybrid structures governed by covalent, ionic and dispersion forces. Application of ab initio molecular dynamics to such large periodic systems is thus beyond the current computational power. Therefore, alternative strategies must be developed to reduce computational cost without losing reliability. In this work, we construct a generic neural network potential (NNP) for the isoreticular metal-organic framework (IRMOF) series trained by PBE-D4/def2-TZVP reference data of MOF fragments. We confirmed the success of the resulting NNP on both fragments and bulk MOF structures by prediction of properties such as equilibrium lattice constants, phonon density of states and linker orientation. The RMSE values of energy and force for the fragments are only 0.0017 eV atom^-1 and 0.15 eV Å^-1, respectively. The NNP predicted equilibrium lattice constants of bulk structures, even though not included in training, are off by only 0.2-2.4% from experimental results. Moreover, our fragment based NNP successfully predicts the phenylene ring torsional energy barrier, equilibrium bond distances and vibrational density of states of bulk MOFs. Furthermore, the NNP enables revealing the odd behaviors of selected MOFs such as the dual thermal expansion properties and the effect of mechanical strain on the adsorption of hydrogen and methane molecules. The NNP based molecular dynamics (MD) simulations suggest IRMOF-4 and IRMOF-7 to have positive-to-negative thermal expansion coefficients while the rest to have only negative thermal expansion at the studied temperatures of 200 K to 400 K. The deformation of the bulk structure by reduction of the unit cell volume has been shown to increase the volumetric methane uptake in IRMOF-1 but decrease the volumetric methane uptake in IRMOF-7 due to the steric hindrance. To the best of our knowledge, this study presents the first pre-trained model publicly available giving the opportunity for the researchers in the field to investigate different aspects of IRMOFs by performing large-scale simulation at the first-principles level of accuracy.

Quasi-HKUST Prepared via Postsynthetic Defect Engineering for Highly Improved Catalytic Conversion of 4-Nitrophenol

HKUST-1 [Cu₃(BTC)₂(H₂O)₃]_n·nH₂OMeOH was submitted to thermolysis under controlled conditions at temperatures between 100 and 300 °C. This treatment resulted in partial ligand decarboxylation, generating coordinatively unsaturated Cu²⁺ sites with extra porosity on the way to the transformation of the initial HKUST-1 framework to CuO. The obtained materials retaining in part the HKUST-1 original crystal structure (quasi-MOFs) were used to promote 4-nitrophenol conversion to 4-aminophenol. Because of the partial linker decomposition, the quasi-MOF treated at 240 °C contains coordinatively unsaturated Cu²⁺ ions distributed throughout the Q-HKUST lattice together with micro- and mesopores. These defects explain the excellent catalytic performance of QH-240 with an apparent rate constant of 1.02 × 10^-2 s^-1 in excess of NaBH₄ and an activity factor and half-life time of 51 s^-1g^-1 and 68 s, respectively, which is much better than that of the HKUST parent. Also, the induction period decreases from the order of minutes to seconds in the presence of the HKUST and QH-240 catalysts, respectively. Kinetic studies fit with the Langmuir-Hinshelwood theory in which both 4-nitrophenol and BH₄^- should be adsorbed onto the catalyst surface. The values of the true rate constant (k), the adsorption constants of 4-nitrophenol and BH₄^- (K_4-NP and K_BH4^-), as well as the activation energy are in agreement with a rate-determining step involving the reduction of 4-nitrophenol by the surface-bound hydrogen species.

Detailed total scattering analysis of disorder in ZIF-8

This work investigates the X-ray scattering signatures of disorder in the zeolitic imidazolate framework ZIF-8. Two layer disorder models are examined in reciprocal space and compared with conventional Rietveld analysis. Stacking faults along the [001] direction of the cubic lattice are in poor agreement with experimental powder diffraction data, consistent with previously reported density functional theory studies showing that these defects are energetically unfavorable compared with amorphization. Meanwhile, fluctuation of layer position along the [110] direction of the cubic lattice shows a significant agreement with experimental data. This result is interpreted analogously to an anisotropic strain mechanism, suggesting links between elastic anisotropy and crystallographic imperfections found in metal–organic framework materials. In direct space, it is demonstrated that models accounting for the static position disorder amongst the linker and metal sublattices are required to fit the experimental pair distribution function data.

Too Many Materials and Too Many Applications: An Experimental Problem Waiting for a Computational Solution

Finding the best material for a specific application is the ultimate goal of materials discovery. However, there is also the reverse problem: when experimental groups discover a new material, they would like to know all the possible applications this material would be promising for. Computational modeling can aim to fulfill this expectation, thanks to the sustained growth of computing power and the collective engagement of the scientific community in developing more efficient and accurate workflows for predicting materials' performances. We discuss the impact that reproducibility and automation of the modeling protocols have on the field of gas adsorption in nanoporous crystals. We envision a platform that combines these tools and enables effective matching between promising materials and industrial applications.

Trends in the thermal stability of two-dimensional covalent organic frameworks

Two-dimensional covalent organic frameworks (2D COFs) are synthetically diverse, layered macromolecules. Their covalent lattices are thought to confer high thermal stability, which is typically evaluated with thermogravimetric analysis (TGA). However, TGA measures the temperature at which volatile degradation products are formed and is insensitive to changes of the periodic structure of the COF. Here, we study the thermal stability of ten 2D COFs using a combination of variable-temperature X-ray diffraction, TGA, diffuse reflectance infrared spectroscopy, and density functional theory calculations. We find that 2D COFs undergo a general two-step thermal degradation process. At the first degradation temperature, 2D COFs lose their crystallinity without chemical degradation. Then, at higher temperatures, they chemically degrade into volatile byproducts. Several trends emerge from this exploration of 2D COF stability. Boronate ester-linked COFs are generally more thermally stable than comparable imine-linked COFs. Smaller crystalline lattices are more robust to thermal degradation than chemically similar larger lattices. Finally, pore-functionalized COFs degrade at significantly lower temperatures than their unfunctionalized analogues. These trends offer design criteria for thermally resilient 2D COF materials. These findings will inform and encourage a broader exploration of mechanical deformation in 2D networks, providing a necessary step towards their practical use.

Thermoelasticity of Flexible Organic Crystals from Quasi-harmonic Lattice Dynamics: The Case of Copper(II) Acetylacetonate

A computationally affordable approach, based on quasi-harmonic lattice dynamics, is presented for the quantum-mechanical calculation of thermoelastic moduli of flexible, stimuli-responsive, organic crystals. The methodology relies on the simultaneous description of structural changes induced by thermal expansion and strain. The complete thermoelastic response of the mechanically flexible metal-organic copper(II) acetylacetonate crystal is determined and discussed in the temperature range 0-300 K. The elastic moduli do not just shrink with temperature but they do so anisotropically. The present results clearly indicate the need for an explicit account of thermal effects in the simulation of mechanical properties of elastically flexible organic materials. Indeed, predictions from standard static calculations on this flexible metal-organic crystal are off by up to 100%.

Destruction of Metal-Organic Frameworks: Positive and Negative Aspects of Stability and Lability

Metal-organic frameworks (MOFs), constructed from organic linkers and inorganic building blocks, are well-known for their high crystallinity, high surface areas, and high component tunability. The stability of MOFs is a key prerequisite for their potential practical applications in areas including storage, separation, catalysis, and biomedicine since it is essential to guarantee the framework integrity during utilization. However, MOFs are prone to destruction under external stimuli, considerably hampering their commercialization. In this Review, we provide an overview of the situations where MOFs undergo destruction due to external stimuli such as chemical, thermal, photolytic, radiolytic, electronic, and mechanical factors and offer guidelines to avoid unwanted degradation happened to the framework. Furthermore, we discuss possible destruction mechanisms and their varying derived products. In particular, we highlight cases that utilize MOF instability to fabricate varying materials including hierarchically porous MOFs, monolayer MOF nanosheets, amorphous MOF liquids and glasses, polymers, metal nanoparticles, metal carbide nanoparticles, and carbon materials. Finally, we provide a perspective on the utilization of MOF destruction to develop advanced materials with a superior hierarchy for various applications.

Understanding the Balance of Entropy and Enthalpy in Hydrogen-Halide Noncovalent Bonding

Hydrogen bonds are of great scientific interest, determining the free energy landscape and hence chemical and physical properties of many materials systems, for example, the hybrid organic-inorganic perovskites. Although these interactions are critical, understanding them is difficult in complex, multicomponent systems; hydrogen halides are ideal as simple binary model compounds for understanding the role of hydrogen bonding in physical properties like phase transitions. Here we investigate the orthorhombic low-temperature phase and the cubic high-temperature phase in HX (X = F, Cl, Br, or I) systems to understand how different hydrogen-halide bonds influence free energy profiles. We show that hydrogen fluoride has a qualitatively different behavior due to strong hydrogen bonding and hence a very different vibrational entropy. Heavier halides are in contrast rather similar in their physical properties; however, dispersion interactions play a more crucial role in these. These results have implications for the rational design of materials with hydrogen-halide bonds and tuning material properties in systems like mixed anion CH₃NH₃PbX₃ perovskites.