Metallicious: Automated Force-Field Parameterization of Covalently Bound Metals for Supramolecular Structures

Metal ions play a central, functional, and structural role in many molecular structures, from small catalysts to metal-organic frameworks (MOFs) and proteins. Computational studies of these systems typically employ classical or quantum mechanical approaches or a combination of both. Among classical models, only the covalent metal model reproduces both geometries and charge transfer effects but requires time-consuming parameterization, especially for supramolecular systems containing repetitive units. To streamline this process, we introduce metallicious, a Python tool designed for efficient force-field parameterization of supramolecular structures. Metallicious has been tested on diverse systems including supramolecular cages, knots, and MOFs. Our benchmarks demonstrate that parameters accurately reproduce the reference properties obtained from quantum calculations and crystal structures. Molecular dynamics simulations of the generated structures consistently yield stable simulations in explicit solvent, in contrast to similar simulations performed with nonbonded and cationic dummy models. Overall, metallicious facilitates the atomistic modeling of supramolecular systems, key for understanding their dynamic properties and host-guest interactions. The tool is freely available on GitHub (https://github.com/duartegroup/metallicious).

Theoretical and computational methodologies for understanding coordination self-assembly complexes

This perspective highlights three theoretical and computational methods to capture the coordination self-assembly processes at the molecular level: quantum chemical modeling, molecular dynamics, and reaction network analysis. These methods cover the different scales from the metal-ligand bond to a more global aspect, and approaches that are best suited to understand the coordination self-assembly from different perspectives are introduced. Theoretical and numerical researches based on these methods are not merely ways of interpreting the experimental studies but complementary to them.

Nucleation of zeolitic imidazolate frameworks: from molecules to nanoparticles

We have studied the clusters involved in the initial stages of nucleation of Zeolitic Imidazolate Frameworks, employing a wide range of computational techniques. In the pre-nucleating solution, the prevalent cluster is the ZnIm₄ cluster (formed by a zinc cation, Zn²⁺, and four imidazolate anions, Im^-), although clusters such as ZnIm₃, Zn₂Im₇, Zn₂Im₇, Zn₃Im₉, Zn₃Im₁₀, or Zn₄Im₁₂ have energies that are not much higher, so they would also be present in solution at appreciable quantities. All these species, except ZnIm₃, have a tetrahedrally coordinated Zn²⁺ cation. Small Zn_xIm_y clusters are less stable than the ZnIm₄ cluster. The first cluster that is found to be more stable than ZnIm₄ is the Zn₄₁Im₈₈ cluster, which is a disordered cluster with glassy structure. Bulk-like clusters do not begin to be more stable than glassy clusters until much larger sizes, since the larger cluster we have studied (Zn₁₄₄Im₂₈₈) is still less stable than the glassy Zn₄₁Im₈₈ cluster, suggesting that Ostwald's rule (the less stable polymorph crystallizes first) could be fulfilled, not for kinetic, but for thermodynamic reasons. Our results suggest that the first clusters formed in the nucleation process would be glassy clusters, which then undergo transformation to any of the various crystal structures possible, depending on the kinetic routes provided by the synthesis conditions. Our study helps elucidate the way in which the various species present in solution interact, leading to nucleation and crystal growth.

Early-Stage Formation of the SIFSIX-3-Zn Metal-Organic Framework: An Automated Computational Study

Metal-organic frameworks (MOFs) have attracted significant attention over the past 2 decades due to their wide applicability as functional materials. However, targeted synthesis of novel MOFs remains problematic as their formation mechanisms are poorly understood, which forces us to rely on serendipity in the synthesis of novel MOFs. Here, we demonstrate a workflow employing the artificial force induced reaction (AFIR) method to investigate the self-assembly process of the node of the SIFSIX-3-Zn MOF, [Zn(pyz)₄(SiF₆)₂]^2- (pyz = pyrazine), in an automated manner. The workflow encompassing AFIR calculations, generation of extensive reaction path networks, propagation simulations of intermediates, and further refinements of identified formation pathways showed that the nodal structure can form through multiple competing pathways involving interconvertible intermediates. This finding provides a plausible rationale for the stochastic multistage processes believed to be key in MOF formation. Furthermore, this work represents the first application of an automated reaction mechanism discovery method to a MOF system using a general workflow that is applicable to study the formation of other MOF motifs as well.

Computer simulation of the early stages of self-assembly and thermal decomposition of ZIF-8

We employ all-atom well-tempered metadynamics simulations to study the mechanistic details of both the early stages of nucleation and crystal decomposition for the benchmark metal–organic framework (MOF) ZIF-8. To do so, we developed and validated a force field that reliably models the modes of coordination bonds via a Morse potential functional form and employs cationic and anionic dummy atoms to capture coordination symmetry. We also explored a set of physically relevant collective variables and carefully selected an appropriate subset for our problem at hand. After a rapid increase of the Zn–N connectivity, we observe the evaporation of small clusters in favor of a few large clusters, which leads to the formation of an amorphous highly connected aggregate. [Formula: see text] and [Formula: see text] complexes are observed with lifetimes in the order of a few picoseconds, while larger structures, such as four-, five-, and six-membered rings, have substantially longer lifetimes of a few nanoseconds. The free ligands act as “templating agents” for the formation of sodalite cages. ZIF-8 crystal decomposition results in the formation of a vitreous phase. Our findings contribute to a fundamental understanding of MOF’s synthesis that paves the way to controlling synthesis products. Furthermore, our developed force field and methodology can be applied to model solution processes that require coordination bond reactivity for other ZIFs besides ZIF-8.

Understanding Metal-Organic Framework Nucleation from a Solution with Evolving Graphs

A mechanistic understanding of metal-organic framework (MOF) synthesis and scale-up remains underexplored due to the complex nature of the interactions of their building blocks. In this work, we investigate the collective assembly of building units at the early stages of MOF nucleation, using MIL-101(Cr) as a prototypical example. Using large-scale molecular dynamics simulations, we observe that the choice of solvent (water and N,N-dimethylformamide), the introduction of ions (Na⁺ and F^-) and the relative populations of MIL-101(Cr) half-secondary building unit (half-SBU) isomers have a strong influence on the cluster formation process. Additionally, the shape, size, nucleation and growth rates, crystallinity, and short and long-range order largely vary depending on the synthesis conditions. We evaluate these properties as they naturally emerge when interpreting the self-assembly of MOF nuclei as the time evolution of an undirected graph. Solution-induced conformational complexity and ionic concentration have a dramatic effect on the morphology of clusters emerging during assembly. While pure solvents lead to the rapid formation of a small number of large clusters, the presence of ions in aqueous solutions results in smaller clusters and slower nucleation. This diversity is captured by the key features of the graph representation. Principle component analysis on graph properties reveals that only a small number of molecular descriptors is needed to deconvolute MOF self-assembly. Descriptors such as the average coordination number between half-SBUs and fractal dimension are of particulalr interest as they can be can be followed experimentally by techniques like by time-resolved spectroscopy. Ultimately, graph theory emerges as an approach that can be used to understand complex processes revealing molecular descriptors accessible by both simulation and experiment.

Computational Modeling of Supramolecular Metallo-organic Cages-Challenges and Opportunities

Self-assembled metallo-organic cages have emerged as promising biomimetic platforms that can encapsulate whole substrates akin to an enzyme active site. Extensive experimental work has enabled access to a variety of structures, with a few notable examples showing catalytic behavior. However, computational investigations of metallo-organic cages are scarce, not least due to the challenges associated with their modeling and the lack of accurate and efficient protocols to evaluate these systems. In this review, we discuss key molecular principles governing the design of functional metallo-organic cages, from the assembly of building blocks through binding and catalysis. For each of these processes, computational protocols will be reviewed, considering their inherent strengths and weaknesses. We will demonstrate that while each approach may have its own specific pitfalls, they can be a powerful tool for rationalizing experimental observables and to guide synthetic efforts. To illustrate this point, we present several examples where modeling has helped to elucidate fundamental principles behind molecular recognition and reactivity. We highlight the importance of combining computational and experimental efforts to speed up supramolecular catalyst design while reducing time and resources.

Unlocking the computational design of metal-organic cages

Metal-organic cages are macrocyclic structures that can possess an intrinsic void that can hold molecules for encapsulation, adsorption, sensing, and catalysis applications. As metal-organic cages may be comprised from nearly any combination of organic and metal-containing components, cages can form with diverse shapes and sizes, allowing for tuning toward targeted properties. Therefore, their near-infinite design space is almost impossible to explore through experimentation alone and computational design can play a crucial role in exploring new systems. Although high-throughput computational design and screening workflows have long been known as powerful tools in drug and materials discovery, their application in exploring metal-organic cages is more recent. We show examples of structure prediction and host-guest/catalytic property evaluation of metal-organic cages. These examples are facilitated by advances in methods that handle metal-containing systems with improved accuracy and are the beginning of the development of automated cage design workflows. We finally outline a scope for how high-throughput computational methods can assist and drive experimental decisions as the field pushes toward functional and complex metal-organic cages. In particular, we highlight the importance of considering realistic, flexible systems.

Modeling the Layer-by-Layer Growth of HKUST-1 Metal-Organic Framework Thin Films

Metal organic frameworks have emerged as an important new class of materials with many applications, such as sensing, gas separation, drug delivery. In many cases, their performance is limited by structural defects, including vacancies and domain boundaries. In the case of MOF thin films, surface roughness can also have a pronounced influence on MOF-based device properties. Presently, there is little systematic knowledge about optimal growth conditions with regard to optimal morphologies for specific applications. In this work, we simulate the layer-by-layer (LbL) growth of the HKUST-1 MOF as a function of temperature and reactant concentration using a coarse-grained model that permits detailed insights into the growth mechanism. This model helps to understand the morphological features of HKUST-1 grown under different conditions and can be used to predict and optimize the temperature for the purpose of controlling the crystal quality and yield. It was found that reactant concentration affects the mass deposition rate, while its effect on the crystallinity of the generated HKUST-1 film is less pronounced. In addition, the effect of temperature on the surface roughness of the film can be divided into three regimes. Temperatures in the range from 10 to 129 °C allow better control of surface roughness and film thickness, while film growth in the range of 129 to 182 °C is characterized by a lower mass deposition rate per cycle and rougher surfaces. Finally, for T larger than 182 °C, the film grows slower, but in a smooth fashion. Furthermore, the potential effect of temperature on the crystallinity of LbL-grown HKUST-1 was quantified. To obtain high crystallinity, the operating temperature should preferably not exceed 57 °C, with an optimum around 28 °C, which agrees with experimental observations.

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.

Early stages of phase selection in MOF formation observed in molecular Monte Carlo simulations

Metal–organic frameworks (MOF) comprising metal nodes bridged by organic linkers show great promise because of their guest-specific gas sorption, separation, drug-delivery, and catalytic properties. The selection of metal node, organic linker, and synthesis conditions in principle offers engineered control over both structure and function. For MOFs to realise their potential and to become more than just promising materials, a degree of predictability in the synthesis and a better understanding of the self-assembly or initial growth processes is of paramount importance. Using cobalt succinate, a MOF that exhibits a variety of phases depending on synthesis temperature and ligand to metal ratio, as proof of concept, we present a molecular Monte Carlo approach that allows us to simulate the early stage of MOF assembly. We introduce a new Contact Cluster Monte Carlo (CCMC) algorithm which uses a system of overlapping “virtual sites” to represent the coordination environment of the cobalt and both metal–metal and metal–ligand associations. Our simulations capture the experimentally observed synthesis phase distinction in cobalt succinate at 348 K. To the best of our knowledge this is the first case in which the formation of different MOF phases as a function of composition is captured by unbiased molecular simulations. The CCMC algorithm is equally applicable to any system in which short-range attractive interactions are a dominant feature, including hydrogen-bonding networks, metal–ligand coordination networks, or the assembly of particles with “sticky” patches, such as colloidal systems or the formation of protein complexes.

Clusters produced in simulations of MOF assembly at metal : ligand ratios of (a) 5 : 1 and (b) 1 : 1 with identical interaction 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.

Location controlled symmetry reduction: paradigm of an open metalloporphyrin framework based on the tetracarboxy porphyrin linker

The change in position of coordinating groups on symmetrical tetracarboxy porphyrin leads to novel class of reduced symmetry linker, which lay down pathway to obtain versatile coordination architectures to trap geometrically variant guest molecules.

Molecular simulations of self-assembly processes in metal-organic frameworks: Model dependence

Molecular simulation is a powerful tool for investigating microscopic behavior in various chemical systems, where the use of suitable models is critical to successfully reproduce the structural and dynamic properties of the real systems of interest. In this context, molecular dynamics simulation studies of self-assembly processes in metal-organic frameworks (MOFs), a well-known class of porous materials with interesting chemical and physical properties, are relatively challenging, where a reasonably accurate representation of metal-ligand interactions is anticipated to play an important role. In the current study, we both investigate the performance of some existing models and introduce and test new models to help explore the self-assembly in an archetypal Zn-carboxylate MOF system. To this end, the behavior of six different Zn-ion models, three solvent models, and two ligand models was examined and validated against key experimental structural parameters. To explore longer time scale ordering events during MOF self-assembly via explicit solvent simulations, it is necessary to identify a suitable combination of simplified model components representing metal ions, organic ligands, and solvent molecules. It was observed that an extended cationic dummy atom (ECDA) Zn-ion model combined with an all-atom carboxylate ligand model and a simple dipolar solvent model can reproduce characteristic experimental structures for the archetypal MOF system. The successful use of these models in extensive sets of molecular simulations, which provide key insights into the self-assembly mechanism of this archetypal MOF system occurring during the early stages of this process, has been very recently reported.

Modeling Coordination-Directed Self-Assembly of M2L4 Nanocapsule Featuring Competitive Guest Encapsulation

Exploring the mechanism of self-assembly and guest encapsulation of nanocapsules is highly imperative for the design of sophisticated molecular containers and multistimuli-responsive functional materials. Here we present a molecular dynamics simulation protocol with implicit solvent and simulated annealing techniques to investigate the self-assembly and competitive guest (C₆₀ and C₇₀ fullerenes) encapsulation of a M₂L₄ nanocapsule that is self-assembled by the coordination of mercury cations and bent bidentate ligands. Stepwise formation of the nanocapsule and competitive fullerene encapsulation during dynamic structural changes in the self-assembly were detected successfully. Such processes were driven by coordination bonding and π-π stacking and obey the minimum total potential energy principle. Potential of mean force calculations for guest binding to the M₂L₄ nanocapsule explained the mechanism underlying the competitive encapsulations of C₆₀ and C₇₀. This work helps design new functional nanomaterials capable of guest encapsulation and release.

Probing Molecular Mechanisms of Self-Assembly in Metal-Organic Frameworks

Metal-organic framework materials (MOFs) are a class of nanoporous materials, important to many applications (e.g., gas storage, separation), and their synthesis has received considerable attention. Yet, very little is known about the mechanisms of self-assembly of MOFs. Here, we provide molecular-level insights into the previously unexplored behavior of the self-assembly process, through molecular dynamics simulations, for an archetypal Zn-carboxylate MOF system exhibiting complex vertex topologies (e.g., paddle-wheel clusters). A key finding of this study is the characterization of a stochastic and multistage ordering process intrinsic to self-assembly of the Zn-carboxylate MOF system. A variety of transient intermediate structures consisting of various types of Zn-ion clusters and carboxylate-ligand coordination, and featuring a range of geometric arrangements, are observed during structural evolution. The general features deduced here for the mechanism of the self-assembly of this archetypal MOF system expose the complexities of the various molecular-level events that can occur during the early stages of this process spanning time scales of nano- to microseconds. More generally, we provide fundamental insights that elucidate key aspects of the early stages of the self-assembly mechanism for an important class of nanoporous materials, and of experimental studies exploring nucleation and growth processes in such materials.