Quest for Multifunctionality: Current Progress in the Characterization of Heterometallic Metal-Organic Frameworks.

Metal-organic frameworks (MOFs) are a class of porous, crystalline materials that have been systematically developed for a broad range of applications. Incorporation of two or more metals into a single crystalline phase to generate heterometallic MOFs has been shown to lead to synergistic effects, in which the whole is oftentimes greater than the sum of its parts. Because geometric proximity is typically required for metals to function cooperatively, deciphering and controlling metal distributions in heterometallic MOFs is crucial to establish structure-function relationships. However, determination of short- and long-range metal distributions is nontrivial and requires the use of specialized characterization techniques. Advancements in the characterization of metal distributions and interactions at these length scales is key to rapid advancement and rational design of functional heterometallic MOFs. This perspective summarizes the state-of-the-art in the characterization of heterometallic MOFs, with a focus on techniques that allow metal distributions to be better understood. Using complementary analyses, in conjunction with computational methods, is critical as this field moves toward increasingly complex, multifunctional systems.

Machine Learning Predictions of Simulated Self-Diffusion Coefficients for Bulk and Confined Pure Liquids.

Diffusion properties of bulk fluids have been predicted using empirical expressions and machine learning (ML) models, suggesting that predictions of diffusion also should be possible for fluids in confined environments. The ability to quickly and accurately predict diffusion in porous materials would enable new discoveries and spur development in relevant technologies such as separations, catalysis, batteries, and subsurface applications. In this work, we apply artificial neural network (ANN) models to predict the simulated self-diffusion coefficients of real liquids in both bulk and pore environments. The training data sets were generated from molecular dynamics (MD) simulations of Lennard-Jones particles representing a diverse set of 14 molecules ranging from ammonia to dodecane over a range of liquid pressures and temperatures. Planar, cylindrical, and hexagonal pore models consisted of walls composed of carbon atoms. Our simple model for these liquids was primarily used to generate ANN training data, but the simulated self-diffusion coefficients of bulk liquids show excellent agreement with experimental diffusion coefficients. ANN models based on simple descriptors accurately reproduced the MD diffusion data for both bulk and confined liquids, including the trend of increased mobility in large pores relative to the corresponding bulk liquid.

Trends in Siting of Metals in Heterometallic Nd-Yb Metal-Organic Frameworks and Molecular Crystals.

Several studies suggest that metal ordering within metal-organic frameworks (MOFs) is important for understanding how MOFs behave in relevant applications; however, these siting trends can be difficult to determine experimentally. To garner insight into the energetic driving forces that may lead to nonrandom ordering within heterometallic MOFs, we employ density functional theory (DFT) calculations on several bimetallic metal-organic crystals composed of Nd and Yb metal atoms. We also investigate the metal siting trends for a newly synthesized MOF. Our DFT-based energy of mixing results suggest that Nd will likely occupy sites with greater access to electronegative atoms and that local homometallic domains within a mixed-metal Nd-Yb system are favored. We also explore the use of less computationally extensive methods such as classical force fields and cluster expansion models to understand their feasibility for large system sizes. This study highlights the impact of metal ordering on the energetic stability of heterometallic MOFs and crystal structures.

Dramatic Enhancement of Rare-Earth Metal-Organic Framework Stability Via Metal Cluster Fluorination.

Rare-earth polynuclear metal-organic frameworks (RE-MOFs) have demonstrated high durability for caustic acid gas adsorption and separation based on gas adsorption to the metal clusters. The metal clusters in the RE-MOFs traditionally contain RE metals bound by µ3-OH groups connected via organic linkers. Recent studies have suggested that these hydroxyl groups could be replaced by fluorine atoms during synthesis that includes a fluorine-containing modulator. Here, a combined modeling and experimental study was undertaken to elucidate the role of metal cluster fluorination on the thermodynamic stability, structure, and gas adsorption properties of RE-MOFs. Through systematic density-functional theory calculations, fluorinated clusters were found to be thermodynamically more stable than hydroxylated clusters by up to 8-16 kJ/mol per atom for 100% fluorination. The extent of fluorination in the metal clusters was validated through a 19F NMR characterization of 2,5-dihydroxyterepthalic acid (Y-DOBDC) MOF synthesized with a fluorine-containing modulator. 19F magic-angle spinning NMR identified two primary peaks in the isotropic chemical shift (δiso) spectra located at -64.2 and -69.6 ppm, matching calculated 19F NMR δiso peaks at -63.0 and -70.0 ppm for fluorinated systems. Calculations also indicate that fluorination of the Y-DOBDC MOF had negligible effects on the acid gas (SO2, NO2, H2O) binding energies, which decreased by only ∼4 kJ/mol for the 100% fluorinated structure relative to the hydroxylated structure. Additionally, fluorination did not change the relative gas binding strengths (SO2 > H2O > NO2). Therefore, for the first time the presence of fluorine in the metal clusters was found to significantly stabilize RE-MOFs without changing their acid-gas adsorption properties.

Symbolic regression development of empirical equations for diffusion in Lennard-Jones fluids.

Symbolic regression (SR) with a multi-gene genetic program has been used to elucidate new empirical equations describing diffusion in Lennard-Jones (LJ) fluids. Examples include equations to predict self-diffusion in pure LJ fluids and equations describing the finite-size correction for self-diffusion in binary LJ fluids. The performance of the SR-obtained equations was compared to that of both the existing empirical equations in the literature and to the results from artificial neural net (ANN) models recently reported. It is found that the SR equations have improved predictive performance in comparison to the existing empirical equations, even though employing a smaller number of adjustable parameters, but show an overall reduced performance in comparison to more extensive ANNs.

Machine Learning-Based Upscaling of Finite-Size Molecular Dynamics Diffusion Simulations for Binary Fluids.

Molecular diffusion coefficients calculated using molecular dynamics (MD) simulations suffer from finite-size (i.e., finite box size and finite particle number) effects. Results from finite-sized MD simulations can be upscaled to infinite simulation size by applying a correction factor. For self-diffusion of single-component fluids, this correction has been well-studied by many researchers including Yeh and Hummer (YH); for binary fluid mixtures, a modified YH correction was recently proposed for correcting MD-predicted Maxwell-Stephan (MS) diffusion rates. Here we use both empirical and machine learning methods to identify improvements to the finite-size correction factors for both self-diffusion and MS diffusion of binary Lennard-Jones (LJ) fluid mixtures. Using artificial neural networks (ANNs), the error in the corrected LJ fluid diffusion is reduced by an order of magnitude versus existing YH corrections, and the ANN models perform well for mixtures with large dissimilarities in size and interaction energies where the YH correction proves insufficient.

Machine learning prediction of self-diffusion in Lennard-Jones fluids.

Different machine learning (ML) methods were explored for the prediction of self-diffusion in Lennard-Jones (LJ) fluids. Using a database of diffusion constants obtained from the molecular dynamics simulation literature, multiple Random Forest (RF) and Artificial Neural Net (ANN) regression models were developed and characterized. The role and improved performance of feature engineering coupled to the RF model development was also addressed. The performance of these different ML models was evaluated by comparing the prediction error to an existing empirical relationship used to describe LJ fluid diffusion. It was found that the ANN regression models provided superior prediction of diffusion in comparison to the existing empirical relationships.

Impact of intrinsic framework flexibility for selective adsorption of sarin in non-aqueous solvents using metal-organic frameworks.

Molecular modeling of mixture adsorption in nanoporous materials can provide insight into the molecular-level details that underlie adsorptive separations. Modeling of adsorption often employs a rigid framework approximation for computational convenience. All real materials, however, have intrinsic flexibility due to thermal vibrations of their atoms. In this article, we examine quantitative predictions of the adsorption selectivity for a dilute concentration of a chemical warfare agent, sarin, from bulk mixtures with aqueous and non-aqueous (methanol, isopropyl alcohol) solvents using metal-organic frameworks (MOFs). These predictions were made in MOFs approximated as rigid and also in MOFs allowed to have intrinsic flexibility. Including framework flexibility appears to have important consequences for quantitative predictions of adsorption selectivity, particularly for sarin/water mixtures. Our observations suggest the intrinsic flexibility of MOFs can have a nontrivial impact on adsorption modeling of molecular mixtures, especially for mixtures containing polar species and molecules of different sizes.

Insights into the solvent-assisted degradation of organophosphorus compounds by a Zr-based metal-organic framework.

The degradation of a chemical warfare agent simulant using a catalytically active Zr-based metal-organic framework (MOF) as a function of different solvent systems was investigated. Complementary molecular modelling studies indicate that the differences in the degradation rates are related to the increasing size in the nucleophile, which hinders the rotation of the product molecule during degradation. Methanol was identified as an appropriate solvent for non-aqueous degradation applications and demonstrated to support the MOF-based destruction of both sarin and soman.

Spectroscopically Resolved Binding Sites for the Adsorption of Sarin Gas in a Metal-Organic Framework: Insights beyond Lewis Acidity.

Here we report molecular level details regarding the adsorption of sarin (GB) gas in a prototypical zirconium-based metal-organic framework (MOF, UiO-66). By combining predictive modeling and experimental spectroscopic techniques, we unambiguously identify several unique bindings sites within the MOF, using the P═O stretch frequency of GB as a probe. Remarkable agreement between predicted and experimental IR spectrum is demonstrated. As previously hypothesized, the undercoordinated Lewis acid metal site is the most favorable binding site. Yet multiple sites participate in the adsorption process; specifically, the Zr-chelated hydroxyl groups form hydrogen bonds with the GB molecule, and GB weakly interacts with fully coordinated metals. Importantly, this work highlights that subtle orientational effects of bound GB are observable via shifts in characteristic vibrational modes; this finding has large implications for degradation rates and opens a new route for future materials design.

Distinguishing between bulk and edge hydroxyl vibrational properties of 2 : 1 phyllosilicates via deuteration.

Observation of vibrational properties of phyllosilicate edges via a combined molecular modeling and experimental approach was performed. Deuterium exchange was utilized to isolate edge vibrational modes from their internal counterparts. The appearance of a specific peak within the broader D2O band indicates the presence of deuteration on the edge surface, and this peak is confirmed with the simulated spectra. These results are the first to unambiguously identify spectroscopic features of phyllosilicate edge sites.

Molecular Simulations of Hydrogen Bond Cluster Size and Reorientation Dynamics in Liquid and Glassy Azole Systems.

We simulated the dynamics of azole groups (pyrazole, imidazole, 1,2,3-triazole, 1,2,4-triazole, and tetrazole) as neat liquids and tethered via linkers to aliphatic backbones to determine how tethering and varying functional groups affect hydrogen bond networks and reorientation dynamics, both factors which are thought to influence proton conduction. We used the DL_Poly_2 molecular dynamics code with the GAFF force field to simulate tethered systems over the temperature range 200-900 K and the corresponding neat liquids under liquid state temperatures at standard pressure. We computed hydrogen bond cluster sizes; orientational order parameters; orientational correlation functions associated with functional groups, linkers, and backbones; time scales; and activation energies associated with orientational randomization. All tethered systems exhibit a liquid to glassy-solid transition upon cooling from 600 to 500 K, as evidenced by orientational order parameters and correlation functions. Tethering the azoles was generally found to produce hydrogen bond cluster sizes similar to those in untethered liquids and hydrogen bond lifetimes longer than those in liquids. The simulated rates of functional group reorientation decreased dramatically upon tethering. The activation energies associated with orientational randomization agree well with NMR data for tethered imidazole systems at lower temperatures and for tethered 1,2,3-triazole systems at both low- and high-temperature ranges. Overall, our simulations corroborate the notion that tethering functional groups dramatically slows the process of reorientation. We found a linear correlation between gas-phase hydrogen bond energies and tethered functional group reorientation barriers for all azoles except for imidazole, which acts as an outlier because of both atomic charges and molecular structure.

Solute location in a nanoconfined liquid depends on charge distribution.

Nanostructured materials that can confine liquids have attracted increasing attention for their diverse properties and potential applications. Yet, significant gaps remain in our fundamental understanding of such nanoconfined liquids. Using replica exchange molecular dynamics simulations of a nanoscale, hydroxyl-terminated silica pore system, we determine how the locations explored by a coumarin 153 (C153) solute in ethanol depend on its charge distribution, which can be changed through a charge transfer electronic excitation. The solute position change is driven by the internal energy, which favors C153 at the pore surface compared to the pore interior, but less so for the more polar, excited-state molecule. This is attributed to more favorable non-specific solvation of the large dipole moment excited-state C153 by ethanol at the expense of hydrogen-bonding with the pore. It is shown that a change in molecule location resulting from shifts in the charge distribution is a general result, though how the solute position changes will depend upon the specific system. This has important implications for interpreting measurements and designing applications of mesoporous materials.

Thermodynamic Driving Forces for Dye Molecule Position and Orientation in Nanoconfined Solvents.

The results of replica exchange molecular dynamics simulations of a coumarin 153 (C153) dye molecule dissolved in ethanol confined within a 2.4 nm hydrophilic amorphous silica pore are presented. The C153 dye position and orientation distributions provide insight into time-dependent fluorescence measurements in nanoconfined solvents as well as general features of chemistry in mesoporous materials. In addition to the distributions themselves, the free energy, internal energy, and entropic contributions have been calculated to explore the factors determining the distributions. The most likely location of C153 is found to be near the pore surface, but two possible hydrogen-bonding structures lead to differing orientations. Internal energy and entropy are found to be competing forces within the pore, with entropy playing a significant role with unexpected consequences. These results represent a crucial step in determining how the nanoconfining framework can affect measurements of solvation dynamics.

Simulating Hydrogen-Bond Structure and Dynamics in Glassy Solids Composed of Imidazole Oligomers.

We simulated structural and dynamical properties of imidazoles tethered to aliphatic backbones to determine how chain length influences the competition between extended hydrogen-bond networks and imidazole reorientation dynamics. We performed molecular dynamics simulations on hypothetical solids using the GAFF Amber force field over the temperature range 300-800 K, for chain lengths varying from monomers to pentamers. We investigated the effect of heterogeneity by simulating monodisperse and polydisperse solids with the same average chain length. We computed hydrogen-bond cluster sizes and percolation ratios; orientational order parameters associated with imidazole rings, tethering linkers, and backbones; and orientational correlation functions for imidazole rings. We found the surprising result that chain-length heterogeneity negligibly affects system density at standard pressure, the fraction of percolating hydrogen-bonded clusters, and the order parameters for backbone, linker, and imidazole ring. Decreasing oligomer chain length from pentamers to shorter chains decreases the tendency to form percolating hydrogen-bond networks while dramatically decreasing imidazole ring reorientation times from a broad range of 100-700 ps for pentamers down to 20 ps for monomers, hence quantifying the competition between hydrogen-bond cluster size and reorientation rate. The computed orientational order parameters suggest the following hierarchy of structural excitations: imidazole ring reorientation in the range 400-500 K, linker motion around 500-600 K, and backbone relaxation at 600-700 K in this model. The question remains for this class of systems which of these motions is crucial for facile proton transport.