Rochus Schmid

One of the most compelling features of certain MOFs is their ability to undergo stimuli-induced phase transformations with large changes in the accessible pore volume, leading to phenomena like “gate opening”. Theoretical simulations are an indispensable tool in order to understand such processes on a molecular level. However, adsorption phenomena are usually investigated within the approximation of periodic boundary conditions (PBC) and using Grand Canonical methods. This ignores the interface to the gas reservoir and any transport effects, which prevents the investigation of transformation kinetics. Previously, we developed methods to simulate explicit MOF nanocrystallites beyond PBC with the aim to understand size effects. In this work, the results of the natural next step, namely an in silico adsorption experiment for DUT-8 (Cu) nanocrystallites (about 10 nm edge length) in a reservoir of carbon dioxide are presented: Unbiased molecular dynamics simulations reveal a surprisingly rapid gate opening within a few nanoseconds. The first-order phase transition is initiated by a characteristic pore opening at an edge of the crystallite. The anisotropy of the pillared-layer MOF, with its channels along the crystallographic c-axis, leads to a rapid transport along these channels when the pore opening of the MOF proceeds. The simulations allow for an unprecedented view on the molecular mechanism, including the structural transformation of the MOF and the connected transport of the guest molecules into the MOF pores. Already this first attempt of a realistic adsorption simulation beyond PBC revealed the widening of a single channel at the obtuse angle edge of the NC as the secret “Open Sesame!” to open the gate. This confirms that for an in–depth view into the kinetics of adsorption induced phase transformations, an explicit interface between MOF and gas reservoir is pivotal and serves as a basis for further investigations with even larger systems and more realistic surface terminations to be performed in the future.

One of the most compelling features of certain MOFs is their ability to undergo stimuli-induced phase transformations with large changes in the accessible pore volume, leading to phenomena like “gate opening”. Theoretical simulations are an indispensable tool in order to understand such processes on a molecular level. However, adsorption phenomena are usually investigated within the approximation of periodic boundary conditions (PBC) and using Grand Canonical methods. This ignores the interface to the gas reservoir and any transport effects, which prevents the investigation of transformation kinetics. Previously, we developed methods to simulate explicit MOF nanocrystallites beyond PBC with the aim to understand size effects. In this work, the results of the natural next step, namely an in silico adsorption experiment for DUT-8 (Cu) nanocrystallites (about 10 nm edge length) in a reservoir of carbon dioxide are presented: Unbiased molecular dynamics simulations reveal a surprisingly rapid gate opening within a few nanoseconds. The first-order phase transition is initiated by a characteristic pore opening at an edge of the crystallite. The anisotropy of the pillared-layer MOF, with its channels along the crystallographic c-axis, leads to a rapid transport along these channels when the pore opening of the MOF proceeds. The simulations allow for an unprecedented view on the molecular mechanism, including the structural transformation of the MOF and the connected transport of the guest molecules into the MOF pores. Already this first attempt of a realistic adsorption simulation beyond PBC revealed the widening of a single channel at the obtuse angle edge of the NC as the secret “Open Sesame!” to open the gate. This confirms that for an in–depth view into the kinetics of adsorption induced phase transformations, an explicit interface between MOF and gas reservoir is pivotal and serves as a basis for further investigations with even larger systems and more realistic surface terminations to be performed in the future.

A rigorous yet flexible methodology was developed to generate realistic molecular char models that take experimental data on char geometry and elemental composition into account parametrically. Following this methodology, three upper-nanoscale models of an activated hydrochar derived from cellulose, with the composition C17708H5036O5962 were constructed, with densities from 0.90 to 1.15 gcm–3, porosities ranging from 20% to 36%, and maximum pore sizes between 20 and 30 Å. These models were employed to investigate the mobility of the light gases O2, N2, and CO2, which are typically present in oxy-fuel atmospheres confined within char nanopores and for which literature data are sparse and rather inconclusive. To achieve this, nonreactive molecular dynamics simulations were performed for several nanoseconds, using a modified formulation of the generic Universal Force Field. The studied combinations of char systems and gas molecules were investigated systematically with respect to gas molecule load and char pore size regime, encoded by the char density, porosity, and maximum pore diameter, to resolve the dependence of the diffusion dynamics of the confined gases on these parameters. Their interplay was quantified by computing self-diffusion coefficients for the confined gas species at 298.15 K, revealing absolute values in the 10–8 m2s–1 range for O2 and N2 and in the 10–9 m2s–1 range for CO2. The obtained values are comparable to the effective diffusion constants measured in previous experimental studies on related porous media, indicating that the models are sufficiently realistic within the chosen size regime. Furthermore, a linear decay of the gas diffusivities with the char density, linear growth with the char porosity, and superlinear growth with the maximum pore diameter were observed. Regression models fitted to the diffusion data may be incorporated into general diffusion equations, taking the pore size regime into account and supplementing future experimental studies on gas diffusion in char. The employed computational workflow can be used to characterize char and therein confined gases under experimentally inaccessible conditions.

Efficient solid fuel combustion models use semi-global mechanisms with effective parameters, traditionally derived from a small set of reference fuels and conditions. This limits their transferability. Atomistic simulations can compute thermodynamic properties such as reaction enthalpies and adsorption energies. This enables the determination of rate coefficients for elementary reaction steps and diffusion constants across a broad range of temperatures and pressures, including those inaccessible to experiments. Unlike empirical data tied to specific fuels, kinetic parameters from simulations depend on molecular composition and structure. This allows for seamless kinetic models applicable to different solid fuels. Computational results on diffusion and adsorption also complement experiments, aiding the development of improved sorption models. To achieve this, various computational chemistry tools are employed. Char models are built using reactive and non-reactive molecular dynamics. Small molecule diffusivity is isolated via non-reactive simulations, while reactive dynamics combined with molecular graph analysis are used to identify possible reaction pathways. Accurate electronic structure methods are used to compute rate coefficients.

Owing to their dynamic phase behaviour and unique gas sorption properties, flexible metal-organic frameworks (MOFs) have emerged as a promising class of materials for applications in gas-related technologies and beyond. Resolving the crystal structures of the distinct phases is essential for understanding their transformation mechanisms and rational tuning framework responsiveness. Here, we revisit the prototypical flexible MOFs ZIF-7 (Zn(bim)₂, bim^– = benzimidazolate) and ZIF-9 (Co(bim)₂) and resolve the long-standing ambiguity surrounding their guest-free narrow-pore (np) phases. Using microcrystal three-dimensional electron diffraction combined with powder X-ray diffraction (PXRD) and density functional theory calculations, we determine the crystal structures of both np phases. The results rectify previous structural models and incomplete structural descriptions of the np phase of ZIF-7 and, for the first time, establish the structure of the np phase of ZIF-9. In contrast to the high-symmetry, guest-accommodating large-pore (lp) phases adopt distorted, densely packed frameworks with strongly deformed sodalite cages, reduced void fractions, and enhanced framework densities. Variable-temperature PXRD and differential scanning calorimetry further reveal metal-dependent anisotropic thermal expansion of the np phases and entropy-driven np-lp transitions.

An electrostatic model, based on the well‐established charge equilibration method is presented, that allows for a fast prediction of partial atomic charges within non‐reactive force fields for metal–organic frameworks with typical elemental compositions. The required molecular information is inferred in a topological fashion, with generic topological bond lengths, based on experimental covalent radii of the contained elements. The model is parameterized on the basis of atom types, that encode the local atomic coordination environment up the nearest bonded neighbors. Consequently, the model is geometry‐independent, requiring only a graph representation of the molecular bonds, which is easily retrieved due to the explicit bond definitions in non‐reactive force fields. Therefore, by sacrificing the dependence of the atomic charges on changes in the system's geometry, the proposed model avoids the computation of distance matrices, increasing the overall performance. By parameterizing the model on three different atomic encoding levels of increasing parametric resolution, the model's accuracy is systematically increased. To this end, a global optimization scheme is employed, in which the model parameters of atomic width, electronegativity and hardness, are trained to reproduce a set of reference charges. These, were obtained from the QMOF database, which hosts electronic structure properties computed for over 20 000 MOFs and related materials. Curated subsets of the QMOF database were generated depending on the employed atom encoding scheme with a balanced atom type incidence. These subsets were used for the training and testing of the new model, containing atomic reference charges of around 10 000 MOFs for selected metallic species and with comparable relative atom type distributions between the sets. The model is able to predict charges with an accuracy below 0.02 e for the most detailed atom typing scheme for a wide chemical space without the need to to correct for charge neutrality.

An electrostatic model, based on the well-established charge equilibration method is presented, that allows for a fast prediction of partial atomic charges within non-reactive force fields for metal-organic frameworks with typical elemental compositions. The required molecular information is inferred in a topological fashion, with generic topological bond lengths, based on experimental covalent radii of the contained elements. The model is parameterized on the basis of atom types, that encode the local atomic coordination environment up the nearest bonded neighbors. Consequently, the model is geometry-independent, requiring only a graph representation of the molecular bonds, which is easily retrieved due to the explicit bond definitions in non-reactive force fields. Therefore, by sacrificing the dependence of the atomic charges on changes in the system's geometry, the proposed model avoids the computation of distance matrices, increasing the overall performance. By parameterizing the model on three different atomic encoding levels of increasing parametric resolution, the model's accuracy is systematically increased. To this end, a global optimization scheme is employed, in which the model parameters of atomic width, electronegativity and hardness, are trained to reproduce a set of reference charges. These, were obtained from the QMOF database, which hosts electronic structure properties computed for over 20000 MOFs and related materials. Curated subsets of the QMOF database were generated depending on the employed atom encoding scheme with a balanced atom type incidence. These subsets were used for the training and testing of the new model, containing atomic reference charges of around 10000 MOFs for selected metallic species and with comparable relative atom type distributions between the sets. The model is able to predict charges with an accuracy below 0.02 e for the most detailed atom typing scheme for a wide chemical space without the need to to correct for charge neutrality.

Host-guest complexation has captivated the curiosity of researchers across disciplines, sparking both experimental and computational studies. Yet, the most common guest, the solvent, is often neglected. In this work we propose a collective variable (CV) to control the occupation of any given supramolecular structure in molecular dynamics simulations. The accessible volume of the structures is approximated by a tetrahedral tessellation and is thereby able to adapt in shape and size during the simulation for flexible systems. With a symmetric and smooth function, we can determine a continuous loading by switching the solvent molecules from outside to inside. By applying a harmonic bias, the number of solvent molecules within the cavity can be systematically controlled, and e.g. by umbrella sampling the free energy profile for increased solvent loading can be computed. The approach is applied and validated for a purely organic porous liquid system and a palladium-based metal-organic cage compound. The influence of the smoothing parameter is tested and the results are compared to available experimental data as well as prior simulation results. The method is shown to be versatile and efficient in quantifying the loading of flexible and deforming molecular cages while monitoring the subsequent reactions of their hosts, with relevance for catalytic processes or separation using such tunable systems.

The oxy-fuel combustion of biochar connected with carbon capture, storage, and utilization technologies is an environmentally beneficial alternative for the replacement of fossil fuels. Biochar itself consists of porously stacked layers of hydrocarbons containing several heteroatoms, such as oxygen, nitrogen, and sulfur. At present, only limited information on the combustion mechanisms for oxygen and nitrogen functionalities is available in the literature; specific information on the combustion mechanisms of sulfur-containing groups (SFGs) is lacking. In this study, we present electronic structure calculations to uncover the mechanisms of the initial oxidation reactions of SFGs. Furthermore, it is examined if the reaction mechanisms remain similar or change with increasing system size. For this purpose, we apply an automatized workflow combining reactive molecular dynamics simulations with static electronic structure calculations at different levels of theory. The results show that terminal groups such as thiols, sulfonic acids, thioketones, and S,S-dioxides follow similar reaction pathways. These SFGs are all gradually oxidized before they eventually are eliminated as SO_x(H_y) species from the carbon framework. Embedded thiophenes follow somewhat different reaction pathways that lead to the elimination of HOS· radicals or carbonyl sulfide (COS), depending on the system size. For the found oxidation channels, we report reaction and activation energies and rate constants that can be used to improve comprehensive kinetic models for the combustion of sulfur-containing biochar as a biomass-based renewable energy source.