On flexible force fields for metal-organic frameworks: Recent developments and future prospects

An automated protocol to construct flexibility parameters for classical forcefields: applications to metal-organic frameworks

In this work, forcefield flexibility parameters were constructed and validated for more than 100 metal-organic frameworks (MOFs). We used atom typing to identify bond types, angle types, and dihedral types associated with bond stretches, angle bends, dihedral torsions, and other flexibility interactions. Our work used Manz's angle-bending and dihedral-torsion model potentials. For a crystal structure containing N atoms in its unit cell, the number of independent flexibility interactions is 3(N atoms - 1). Because the number of bonds, angles, and dihedrals is normally much larger than 3(N atoms - 1), these internal coordinates are redundant. To reduce (but not eliminate) this redundancy, our protocol prunes dihedral types in a way that preserves symmetry equivalency. Next, each dihedral type is classified as non-rotatable, hindered, rotatable, or linear. We introduce a smart selection method that identifies which particular torsion modes are important for each rotatable dihedral type. Then, we computed the force constants for all flexibility interactions together via LASSO regression (i.e., regularized linear least-squares fitting) of the training dataset. LASSO automatically identifies and removes unimportant forcefield interactions. For each MOF, the reference dataset was quantum-mechanically-computed in VASP via DFT with dispersion and included: (i) finite-displacement calculations along every independent atom translation mode, (ii) geometries randomly sampled via ab initio molecular dynamics (AIMD), (iii) the optimized ground-state geometry using experimental lattice parameters, and (iv) rigid torsion scans for each rotatable dihedral type. After training, the flexibility model was validated across geometries that were not part of the training dataset. For each MOF, we computed the goodness of fit (R-squared value) and the root-mean-squared error (RMSE) separately for the training and validation datasets. We compared flexibility models with and without bond-bond cross terms. Even without cross terms, the model yielded R-squared values of 0.910 (avg across all MOFs) ± 0.018 (st. dev.) for atom-in-material forces in the validation datasets. Our SAVESTEPS protocol should find widespread applications to parameterize flexible forcefields for material datasets. We performed molecular dynamics simulations using these flexibility parameters to compute heat capacities and thermal expansion coefficients for two MOFs.

Nanoscale chemical reaction exploration with a quantum magnifying glass

Nanoscopic systems exhibit diverse molecular substructures by which they facilitate specific functions. Theoretical models of them, which aim at describing, understanding, and predicting these capabilities, are difficult to build. Viable quantum-classical hybrid models come with specific challenges regarding atomistic structure construction and quantum region selection. Moreover, if their dynamics are mapped onto a state-to-state mechanism such as a chemical reaction network, its exhaustive exploration will be impossible due to the combinatorial explosion of the reaction space. Here, we introduce a "quantum magnifying glass" that allows one to interactively manipulate nanoscale structures at the quantum level. The quantum magnifying glass seamlessly combines autonomous model parametrization, ultra-fast quantum mechanical calculations, and automated reaction exploration. It represents an approach to investigate complex reaction sequences in a physically consistent manner with unprecedented effortlessness in real time. We demonstrate these features for reactions in bio-macromolecules and metal-organic frameworks, diverse systems that highlight general applicability.

Ferro-piezoelectricity in emerging Janus monolayer BMX2 (M = Ga, In and X = S, Se): ab initio investigations

Nanoscale materials with inter-correlation characteristics are fundamental for developing high performance devices and applications. Hence theoretical research into unprecedented two-dimensional (2D) materials is crucial for improving understanding, especially when piezoelectricity is merged with other unique properties such as ferroelectricity. In this work, an unexplored 2D Janus family BMX₂ (M = Ga, In and X = S, Se) corresponding to group-III ternary chalcogenides has been explored. The structural and mechanical stability, and optical and ferro-piezoelectric properties of BMX₂ monolayers were investigated using first-principles calculations. We found that the lack of imaginary phonon frequencies in the phonon dispersion curves establishes the dynamic stability of the compounds. The monolayers BGaS₂ and BGaSe₂ are indirect semiconductors with bandgaps of 2.13 eV and 1.63 eV, respectively, while BInS₂ is a direct semiconductor with a bandgap of 1.21 eV. BInSe₂ is a novel zero-gap ferroelectric material with quadratic energy dispersion. All monolayers exhibit a high spontaneous polarization. The optical characteristics of the BInSe₂ monolayer show high light absorption ranging from the infrared to the ultraviolet. The BMX₂ structures exhibit in-plane and out-of-plane piezoelectric coefficients of up to 4.35 pm V^-1 and 0.32 pm V^-1. According to our findings, 2D Janus monolayer materials are a promising choice for piezoelectric devices.

Cutting-edge molecular modelling to unveil new microscopic insights into the guest-controlled flexibility of metal-organic frameworks

Metal-organic frameworks are a class of porous solids that exhibit intriguing flexibility under stimuli, leading often to reversible giant structural changes upon guest adsorption. DUT-49(Cu) and MIL-53(Cr) are fascinating flexible MOFs owing to their guest-induced breathing and negative gas adsorption behaviors respectively. Molecular simulation is one of the most relevant tools to examine these phenomena at the atomistic scale and gain a unique understanding of the physics behind them. Although molecular dynamics and Monte Carlo simulations are widely used in the field of porous materials, these methods hardly consider the structural deformation of a soft material upon guest adsorption. In this work, a cutting-edge osmotic molecular dynamics approach is developed to consider simultaneously the fluid adsorption process and material flexibility. We demonstrate that this newly developed computational strategy offers a unique opportunity to gain unprecedented molecular insights into the flexibility of this class of materials.

Eleven NanoHUB Simulation Tools Using RASPA Software To Demonstrate Classical Atomistic Simulations of Fluids and Nanoporous Materials

Eleven interactive simulation tools were created on nanoHUB to help users learn how to perform classical atomistic simulations. These tools enable users to perform classical Monte Carlo and molecular dynamics simulations using RASPA software. These tools use comparatively small numbers of production cycles to keep the runtimes short, so that users will not be discouraged by long wait times to see results. Here, we show that these tools produce results of sufficient accuracy and reproducibility for learning purposes. The 11 tools developed were as follows: (1) calculation of the self-diffusion constant of gas molecules in metal-organic frameworks (MOFs), (2) gas adsorption in MOFs using the grand canonical ensemble, (3) Henry's coefficient calculator for gas molecules in MOFs and a zeolite, (4) adsorption of a gas mixture in a MOF, (5) self-diffusion of a gas mixture in a MOF, (6) void fraction calculation for several MOFs and zeolites, (7) surface area calculation for several MOFs and zeolites, (8) calculation of radial distribution function and self-diffusion constant for several pure gases, (9) energy distribution of adsorption sites using a probe molecule in MOFs, (10) molecular dynamics simulation of pure fluids in the NPT ensemble, and (11) gas adsorption in MOFs using the Gibbs ensemble.

Insights into the importance of WPD-loop sequence for activity and structure in protein tyrosine phosphatases

Protein tyrosine phosphatases (PTPs) possess a conserved mobile catalytic loop, the WPD-loop, which brings an aspartic acid into the active site where it acts as an acid/base catalyst. Prior experimental and computational studies, focused on the human enzyme PTP1B and the PTP from Yersinia pestis, YopH, suggested that loop conformational dynamics are important in regulating both catalysis and evolvability. We have generated a chimeric protein in which the WPD-loop of YopH is transposed into PTP1B, and eight chimeras that systematically restored the loop sequence back to native PTP1B. Of these, four chimeras were soluble and were subjected to detailed biochemical and structural characterization, and a computational analysis of their WPD-loop dynamics. The chimeras maintain backbone structural integrity, with somewhat slower rates than either wild-type parent, and show differences in the pH dependency of catalysis, and changes in the effect of Mg²⁺. The chimeric proteins' WPD-loops differ significantly in their relative stability and rigidity. The time required for interconversion, coupled with electrostatic effects revealed by simulations, likely accounts for the activity differences between chimeras, and relative to the native enzymes. Our results further the understanding of connections between enzyme activity and the dynamics of catalytically important groups, particularly the effects of non-catalytic residues on key conformational equilibria.

In situ EPR and Raman spectroscopy in the curing of bis-methacrylate-styrene resins

The curing of bis-methacrylate-styrene resins initiated by the cobalt catalyzed decomposition of cumyl hydroperoxide is monitored at ambient temperatures in situ by EPR and Raman spectroscopy. EPR spectroscopy shows the appearance of organic radicals after ca. 1 h from initiation with an increase in intensity from both polystyrene and methacrylate based radical species over a further ca. 2 h period to reach a maximum spin concentration of ca. 2-3 mM. Alkene conversion to polymer was monitored by Raman spectroscopy in real time in situ with EPR spectroscopy and reveals that the appearance of the radical signals is first observed only as the conversion approaches its maximum extent (70% at room temperature), i.e., the resin reaches a glass-like state. The radicals persist for several months on standing at room temperature. Flash frozen samples (77 K) did not show EPR signals within 1 h of initiation. The nature of the radicals responsible for the EPR spectra observed were explored by DFT methods and isotope labelling experiments (D₈-styrene) and correspond to radicals of both methacrylate and polystyrene. Combined temperature dependent EPR and Raman spectroscopy shows that conversion increases rapidly upon heating of a cured sample, reaching full conversion at 80 °C with initially little effect on the EPR spectrum. Over time (i.e. subsequent to reaching full conversion of alkene) there was a small but clear increase in the EPR signal due to the methacrylate based radicals and minor decrease in the signal due to the polystyrene based radicals. The appearance of the radical signals as the reaction reaches completion and their absence in samples flash frozen before polymerization has halted, indicate that the observed radicals are non-propagating. The formation of the radicals due to stress within the samples is excluded. Hence, the observed radicals are a representative of the steady state concentration of radicals present in the resin over the entire timespan of the polymerization. The data indicate that the lack of EPR signals is most likely due to experimental aspects, in particular spin saturation, rather than low steady state concentrations of propagating radicals during polymerization.

Incorporating Flexibility Effects into Metal-Organic Framework Adsorption Simulations Using Different Models

High-throughput calculations based on molecular simulations to predict the adsorption of molecules inside metal-organic frameworks (MOFs) have become a useful complement to experimental efforts to identify promising adsorbents for chemical separations and storage. For computational convenience, all existing efforts of this kind have relied on simulations in which the MOF is approximated as rigid. In this paper, we use extensive adsorption-relaxation simulations that fully include MOF flexibility effects to explore the validity of the rigid framework approximation. We also examine the accuracy of several approximate methods to incorporate framework flexibility that are more computationally efficient than adsorption-relaxation calculations. We first benchmark various models of MOF flexibility for four MOFs with well-established CO₂ experimental consensus isotherms. We then consider a range of adsorption properties, including Henry's constants, nondilute loadings, and adsorption selectivity, for seven adsorbates in 15 MOFs randomly selected from the CoRE MOF database. Our results indicate that in many MOFs adsorption-relaxation simulations are necessary to make quantitative predictions of adsorption, particularly for adsorption at dilute concentrations, although more standard calculations based on rigid structures can provide useful information. Finally, we investigate whether a correlation exists between the elastic properties of empty MOFs and the importance of including framework flexibility in making accurate predictions of molecular adsorption. Our results did not identify a simple correlation of this type.

Performance-Based Screening of Porous Materials for Carbon Capture

Computational screening methods have changed the way new materials and processes are discovered and designed. For adsorption-based gas separations and carbon capture, recent efforts have been directed toward the development of multiscale and performance-based screening workflows where we can go from the atomistic structure of an adsorbent to its equilibrium and transport properties at different scales, and eventually to its separation performance at the process level. The objective of this work is to review the current status of this new approach, discuss its potential and impact on the field of materials screening, and highlight the challenges that limit its application. We compile and introduce all the elements required for the development, implementation, and operation of multiscale workflows, hence providing a useful practical guide and a comprehensive source of reference to the scientific communities who work in this area. Our review includes information about available materials databases, state-of-the-art molecular simulation and process modeling tools, and a complete catalogue of data and parameters that are required at each stage of the multiscale screening. We thoroughly discuss the challenges associated with data availability, consistency of the models, and reproducibility of the data and, finally, propose new directions for the future of the field.

In silico prediction of annihilators for triplet-triplet annihilation upconversion via auxiliary-field quantum Monte Carlo

The energy of the lowest-lying triplet state (T1) relative to the ground and first-excited singlet states (S0, S1) plays a critical role in optical multiexcitonic processes of organic chromophores. Focusing on triplet–triplet annihilation (TTA) upconversion, the S0 to T1 energy gap, known as the triplet energy, is difficult to measure experimentally for most molecules of interest. Ab initio predictions can provide a useful alternative, however low-scaling electronic structure methods such as the Kohn–Sham and time-dependent variants of Density Functional Theory (DFT) rely heavily on the fraction of exact exchange chosen for a given functional, and tend to be unreliable when strong electronic correlation is present. Here, we use auxiliary-field quantum Monte Carlo (AFQMC), a scalable electronic structure method capable of accurately describing even strongly correlated molecules, to predict the triplet energies for a series of candidate annihilators for TTA upconversion, including 9,10 substituted anthracenes and substituted benzothiadiazole (BTD) and benzoselenodiazole (BSeD) compounds. We compare our results to predictions from a number of commonly used DFT functionals, as well as DLPNO-CCSD(T₀), a localized approximation to coupled cluster with singles, doubles, and perturbative triples. Together with S1 estimates from absorption/emission spectra, which are well-reproduced by TD-DFT calculations employing the range-corrected hybrid functional CAM-B3LYP, we provide predictions regarding the thermodynamic feasibility of upconversion by requiring (a) the measured T1 of the sensitizer exceeds that of the calculated T1 of the candidate annihilator, and (b) twice the T1 of the annihilator exceeds its S1 energetic value. We demonstrate a successful example of in silico discovery of a novel annihilator, phenyl-substituted BTD, and present experimental validation via low temperature phosphorescence and the presence of upconverted blue light emission when coupled to a platinum octaethylporphyrin (PtOEP) sensitizer. The BTD framework thus represents a new class of annihilators for TTA upconversion. Its chemical functionalization, guided by the computational tools utilized herein, provides a promising route towards high energy (violet to near-UV) emission.

Electronic structure theories such as AFQMC can accurately predict the low-lying excited state energetics of organic chromophores involved in triplet–triplet annihilation upconversion. A novel class of benzothiadiazole annihilators is discovered.

Standard Practices of Reticular Chemistry

Reticular chemistry is a growing field of science with a multitude of practitioners with diverse frames of thinking, making the need for standard practices and quality indicators ever more compelling.

Metal-Organic Framework Nanoparticles Induce Pyroptosis in Cells Controlled by the Extracellular pH

Ion homeostasis is essential for cellular survival, and elevated concentrations of specific ions are used to start distinct forms of programmed cell death. However, investigating the influence of certain ions on cells in a controlled way has been hampered due to the tight regulation of ion import by cells. Here, it is shown that lipid-coated iron-based metal-organic framework nanoparticles are able to deliver and release high amounts of iron ions into cells. While high concentrations of iron often trigger ferroptosis, here, the released iron induces pyroptosis, a form of cell death involving the immune system. The iron release occurs only in slightly acidic extracellular environments restricting cell death to cells in acidic microenvironments and allowing for external control. The release mechanism is based on endocytosis facilitated by the lipid-coating followed by degradation of the nanoparticle in the lysosome via cysteine-mediated reduction, which is enhanced in slightly acidic extracellular environment. Thus, a new functionality of hybrid nanoparticles is demonstrated, which uses their nanoarchitecture to facilitate controlled ion delivery into cells. Based on the selectivity for acidic microenvironments, the described nanoparticles may also be used for immunotherapy: the nanoparticles may directly affect the primary tumor and the induced pyroptosis activates the immune system.

Highly modulated supported triazolium-based ionic liquids: direct control of the electronic environment on Cu nanoparticles

A series of new triazolium-based supported ionic liquids (SILPs), decorated with Cu NPs, were successfully prepared and applied to the N-arylation of aryl halides with anilines. The triazoles moieties were functionalised using copper-catalysed azide-alkyne cycloaddition. SILP surface characterisation showed a strong correlation between the triazolium cation volume and textural properties. STEM images showed well-dispersed Cu NPs on SILPs with a mean diameter varying from 3.6 to 4.6 nm depending on the triazolium cation used. Besides, XPS results suggest that the Cu(0)/Cu(i) ratio can be modulated by the electronic density of triazolium substituents. XPS and computational analysis gave mechanistic insights into the Cu NP stabilisation pathways, where the presence of electron-rich groups attached to a triazolium ring plays a critical role in leading to a cation adsorption pathway (E _ads = 72 kcal mol^-1). In contrast, less electron-rich groups favour the anion adsorption pathway (E _ads = 63 kcal mol^-1). The Cu@SILP composite with electron-rich groups showed the highest activity for the C-N Ullmann coupling reaction, which suggests that electron-rich groups might act as an electron-like reservoir to facilitate oxidative addition for N-arylation. This strategy firmly suggests the strong dependence of the nature of triazolium-based SILPs on the Cu NP surface active sites, which may provide a new environment to confine and stabilise MNPs for catalytic applications.

Atomistic Insight Into the Host-Guest Interaction of a Photoresponsive Metal-Organic Framework

Photoresponsive functional materials have gained increasing attention due to their externally tunable properties. Molecular switches embedded in these materials enable the control of phenomena at the atomic level by light. Metal-organic frameworks (MOFs) provide a versatile platform to immobilize these photoresponsive units within defined molecular environments to optimize the intended functionality. For the application of these photoresponsive MOFs (pho-MOFs), it is crucial to understand the influence of the switching state on the host-guest interaction. Therefore, we present a detailed insight into the impact of molecular switching on the intermolecular interactions. By performing atomistic simulations, we revealed that due to different interactions of the guest molecules with the two isomeric states of an azobenzene-functionalized MOF, both the adsorption sites and the orientation of the molecules within the pores are modulated. By shedding light on the host-guest interaction, our study highlights the unique potential of pho-MOFs to tailor molecular interaction by light.

The force of MOFs: the potential of switchable metal–organic frameworks as solvent stimulated actuators

The force exerted by flexible metal–organic framework through expansion was experimentally evaluated for MIL-53(Al).

Ab Initio Flexible Force Field for Metal-Organic Frameworks Using Dummy Model Coordination Bonds

We present force fields developed from periodic density functional theory (DFT) calculations that can be used in classical molecular simulations to model M-MOF-74 (M = Co, Fe, Mg, Mn, Ni, Zn) and its extended linker analogs. Our force fields are based on cationic dummy models (CDMs). These dummy models simplify the methodology required to tune the parameters and improve the accuracy of the force fields. We used our force fields to compare mechanical properties across the M-MOF-74 series and determine that increasing the size of the linker decreases the framework rigidity. In addition, we applied our force fields to an extended linker analog of Mg-MOF-74 and characterized the free energy of a previously reported deformation pattern in which the one-dimensional hexagonal channels of the framework become irregular. The free energy profiles confirm that the deformation is adsorbate induced and impossible to access solely by a pressure stimulus. On the basis of our results, we conclude that the force fields presented here and others that may be developed using our methodology are transferable across metal-organic framework series that share a metal center topology. Finally, we believe that these force fields have the potential to be adapted for the study of complex problems in MOF chemistry, including defects and crystal growth, that have thus far been beyond the scope of classical molecular simulations.

From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5

The development of first-principles-quality reactive atomistic potentials for organic-inorganic hybrid materials is still a substantial challenge because of the very different physics of the atomic interactions-from covalent via ionic bonding to dispersion-that have to be described in an accurate and balanced way. In this work we used a prototypical metal-organic framework, MOF-5, as a benchmark case to investigate the applicability of high-dimensional neural network potentials (HDNNPs) to this class of materials. In HDNNPs, which belong to the class of machine learning potentials, the energy is constructed as a sum of environment-dependent atomic energy contributions. We demonstrate that by the use of this approach it is possible to obtain a high-quality potential for the periodic MOF-5 crystal using density functional theory (DFT) reference calculations of small molecular fragments only. The resulting HDNNP, which has a root-mean-square error (RMSE) of 1.6 meV/atom for the energies of molecular fragments not included in the training set, is able to provide the equilibrium lattice constant of the bulk MOF-5 structure with an error of about 0.1% relative to DFT, and also, the negative thermal expansion behavior is accurately predicted. The total energy RMSE of periodic structures that are completely absent in the training set is about 6.5 meV/atom, with errors on the order of 2 meV/atom for energy differences. We show that in contrast to energy differences, achieving a high accuracy for total energies requires careful variation of the stoichiometries of the training structures to avoid energy offsets, as atomic energies are not physical observables. The forces, which have RMSEs of about 94 meV/ a₀ for the molecular fragments and 130 meV/ a₀ for bulk structures not included in the training set, are insensitive to such offsets. Therefore, forces, which are the relevant properties for molecular dynamics simulations, provide a realistic estimate of the accuracy of atomistic potentials.

The role of molecular modelling and simulation in the discovery and deployment of metal-organic frameworks for gas storage and separation

Metal-organic frameworks (MOFs) are highly tuneable, extended-network, crystalline, nanoporous materials with applications in gas storage, separations, and sensing. We review how molecular models and simulations of gas adsorption in MOFs have informed the discovery of performant MOFs for methane, hydrogen, and oxygen storage, xenon, carbon dioxide, and chemical warfare agent capture, and xylene enrichment. Particularly, we highlight how large, open databases of MOF crystal structures, post-processed to enable molecular simulations, are a platform for computational materials discovery. We discuss how to orient research efforts to routinise the computational discovery of MOFs for adsorption-based engineering applications.