Rigid Body Approximation for the Anharmonic Description of Molecule-Surface Vibrations

We present an anharmonic approach for molecule-surface vibrations that employs rigid body coordinates, based on the Rodrigues rotation formula, to describe curvilinear displacements (rotations and translations) of the molecule along normal modes. These displacements are used to calculate energy data points from which one-dimensional polynomial potentials are fitted using cubic splines. In these potentials, for each of the six rigid body modes separately, one-dimensional Schrödinger equations are solved with harmonic oscillator or Fourier functions (for pure rotations) as basis sets. The anharmonic vibrational energies obtained are used to calculate partition functions and from them enthalpies, entropies, and Gibbs free energies of adsorption. Our numerical implementation has been successfully tested for Morse and cosine potentials with known analytical solutions. The methods have been applied to adsorption of CH₄ on the hydroxyl group of the proton form of the chabazite zeolite (H-CHA), as well as to adsorption of CH₄ and CO on the Mg²⁺ ions of the metal-organic framework (MOF) Mg₂(dobdc). To obtain the best estimates for thermodynamic functions, we include the coupling between molecule-surface vibrations and intrasystem vibrations at the harmonic level. The calculated Gibbs free energies show that the coupling is small for CH₄/H-CHA and CO/MOF (between -0.7 and +0.1 kJ/mol) but substantial for CH₄/MOF (-3.4 kJ/mol). The predicted anharmonic effect on the Gibbs free energy of adsorption for CH₄/H-CHA, CH₄/MOF, and CO/MOF is -4.7, 0.3 ± 0.7, and -2.4 ± 0.6 kJ/mol, respectively, which results in +4.2, +0.9 ± 0.7, and -0.4 ± 0.6 kJ/mol, respectively, for the deviation from experiment. This is well within chemical accuracy limits (±4.2 kJ/mol) for the adsorption of CH₄ and CO in the MOF. The larger deviation for CH₄/H-CHA, at the edge of the chemical accuracy range, is most likely due to contributions from soft zeolite modes which are neglected in our approach.

The apparent surface free energy of rare earth oxides is governed by hydrocarbon adsorption

The surface free energy of rare earth oxides (REOs) has been debated during the last decade, with some reporting REOs to be intrinsically hydrophilic and others reporting hydrophobic. Here, we investigate the wettability and surface chemistry of pristine and smooth REO surfaces, conclusively showing that hydrophobicity stems from wettability transition due to volatile organic compound adsorption. We show that, for indoor ambient atmospheres and well-controlled saturated hydrocarbon atmospheres, the apparent advancing and receding contact angles of water increase with exposure time. We examined the surfaces comprehensively with multiple surface analysis techniques to confirm hydrocarbon adsorption and correlate it to wettability transition mechanisms. We demonstrate that both physisorption and chemisorption occur on the surface, with chemisorbed hydrocarbons promoting further physisorption due to their high affinity with similar hydrocarbon molecules. This study offers a better understanding of the intrinsic wettability of REOs and provides design guidelines for REO-based durable hydrophobic coatings.

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REOs are intrinsically hydrophilic but become hydrophobic as they adsorb hydrocarbons

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Our results demonstrate that both physisorption and chemisorption occur on the surface

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The adsorption of hydrocarbons was confirmed by multiple surface chemistry analysis

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Our work offers a better fundamental understanding of the intrinsic wettability of REO

Complex Reaction Network Thermodynamic and Kinetic Autoconstruction Based on Ab Initio Statistical Mechanics: A Case Study of O2 Activation on Ag4 Clusters

An approach based on ab initio statistical mechanics is demonstrated for autoconstructing complex reaction networks. Ab initio molecular dynamics combined with Markov state models are employed to study relevant transitions and corresponding thermodynamic and kinetic properties of a reaction. To explore the capability and flexibility of this approach, we present a study of oxygen activation on Ag4 as a model reaction. Specifically, with the same sampled trajectories, it is possible to study the structural effects and the reaction rate of the cited reaction. The results show that this approach is suitable for automatized construction of reaction networks, especially for non-well-studied reactions, which can benefit from this ab initio molecular dynamics based approach to construct comprehensive reaction networks with Markov state models without prior knowledge about the potential energy landscape.

Thermal Treatment Effect on CO and NO Adsorption on Fe(II) and Fe(III) Species in Fe3O-Based MIL-Type Metal-Organic Frameworks: A Density Functional Theory Study

The properties of metal–organic frameworks (MOFs) based on triiron oxo-centered (Fe₃O) metal nodes are often related to the efficiency of the removal of the solvent molecules and the counteranion chemisorbed on the Fe₃O unit by postsynthetic thermal treatment. Temperature, time, and the reaction environment play a significant role in modifying key features of the materials, that is, the number of open metal sites and the reduction of Fe(III) centers to Fe(II). IR spectroscopy allows the inspection of these postsynthetic modifications by using carbon monoxide (CO) and nitric oxide (NO) as probe molecules. However, the reference data sets are based on spectra recorded for iron zeolites and oxides, whose structures are different from the Fe₃O one. We used density functional theory to study how the adsorption enthalpy and the vibrational bands of CO and NO are modified upon dehydration and reduction of Fe₃O metal nodes. We obtained a set of theoretical spectra that can model the modification observed in previously reported experimental spectra. Several CO and NO bands were previously assigned to heterogeneous Fe(II) and Fe(III) sites, suggesting a large defectivity of the materials. On the basis of the calculations, we propose an alternative assignment of these bands by considering only crystallographic iron sites. These findings affect the common description of Fe₃O-based MOFs as highly defective materials. We expect these results to be of interest to the large community of scientists working on Fe(II)- and Fe(III)-based MOFs and related materials.

Thermal treatment of triiron oxo-centered (Fe₃O)-based metal−organic frameworks is a common postsynthetic method to determine the material performances in many applications: we used density functional theory methods to study how the efficacy of the treatment modifies the energetics and the vibrational bands of nitric oxide (NO) and carbon monoxide. The obtained data set is meant to be part of the characterization toolboxes aimed at the assessment of thermal treatment protocols.

Electronic Structure Modeling of Metal-Organic Frameworks

Owing to their molecular building blocks, yet highly crystalline nature, metal-organic frameworks (MOFs) sit at the interface between molecule and material. Their diverse structures and compositions enable them to be useful materials as catalysts in heterogeneous reactions, electrical conductors in energy storage and transfer applications, chromophores in photoenabled chemical transformations, and beyond. In all cases, density functional theory (DFT) and higher-level methods for electronic structure determination provide valuable quantitative information about the electronic properties that underpin the functions of these frameworks. However, there are only two general modeling approaches in conventional electronic structure software packages: those that treat materials as extended, periodic solids, and those that treat materials as discrete molecules. Each approach has features and benefits; both have been widely employed to understand the emergent chemistry that arises from the formation of the metal-organic interface. This Review canvases these approaches to date, with emphasis placed on the application of electronic structure theory to explore reactivity and electron transfer using periodic, molecular, and embedded models. This includes (i) computational chemistry considerations such as how functional, k-grid, and other model variables are selected to enable insights into MOF properties, (ii) extended solid models that treat MOFs as materials rather than molecules, (iii) the mechanics of cluster extraction and subsequent chemistry enabled by these molecular models, (iv) catalytic studies using both solids and clusters thereof, and (v) embedded, mixed-method approaches, which simulate a fraction of the material using one level of theory and the remainder of the material using another dissimilar theoretical implementation.

A Supramolecular View on the Cooperative Role of Brønsted and Lewis Acid Sites in Zeolites for Methanol Conversion

A systematic molecular level and spectroscopic investigation is presented to show the cooperative role of Brønsted acid and Lewis acid sites in zeolites for the conversion of methanol. Extra-framework alkaline-earth metal containing species and aluminum species decrease the number of Brønsted acid sites, as protonated metal clusters are formed. A combined experimental and theoretical effort shows that postsynthetically modified ZSM-5 zeolites, by incorporation of extra-framework alkaline-earth metals or by demetalation with dealuminating agents, contain both mononuclear [MOH]⁺ and double protonated binuclear metal clusters [M(μ-OH)₂M]²⁺ (M = Mg, Ca, Sr, Ba, and HOAl). The metal in the extra-framework clusters has a Lewis acid character, which is confirmed experimentally and theoretically by IR spectra of adsorbed pyridine. The strength of the Lewis acid sites (Mg > Ca > Sr > Ba) was characterized by a blue shift of characteristic IR peaks, thus offering a tool to sample Lewis acidity experimentally. The incorporation of extra-framework Lewis acid sites has a substantial influence on the reactivity of propene and benzene methylations. Alkaline-earth Lewis acid sites yield increased benzene methylation barriers and destabilization of typical aromatic intermediates, whereas propene methylation routes are less affected. The effect on the catalytic function is especially induced by the double protonated binuclear species. Overall, the extra-framework metal clusters have a dual effect on the catalytic function. By reducing the number of Brønsted acid sites and suppressing typical catalytic reactions in which aromatics are involved, an optimal propene selectivity and increased lifetime for methanol conversion over zeolites is obtained. The combined experimental and theoretical approach gives a unique insight into the nature of the supramolecular zeolite catalyst for methanol conversion which can be meticulously tuned by subtle interplay of Brønsted and Lewis acid sites.

Towards operando computational modeling in heterogeneous catalysis

An increased synergy between experimental and theoretical investigations in heterogeneous catalysis has become apparent during the last decade. Experimental work has extended from ultra-high vacuum and low temperature towards operando conditions. These developments have motivated the computational community to move from standard descriptive computational models, based on inspection of the potential energy surface at 0 K and low reactant concentrations (0 K/UHV model), to more realistic conditions. The transition from 0 K/UHV to operando models has been backed by significant developments in computer hardware and software over the past few decades. New methodological developments, designed to overcome part of the gap between 0 K/UHV and operando conditions, include (i) global optimization techniques, (ii) ab initio constrained thermodynamics, (iii) biased molecular dynamics, (iv) microkinetic models of reaction networks and (v) machine learning approaches. The importance of the transition is highlighted by discussing how the molecular level picture of catalytic sites and the associated reaction mechanisms changes when the chemical environment, pressure and temperature effects are correctly accounted for in molecular simulations. It is the purpose of this review to discuss each method on an equal footing, and to draw connections between methods, particularly where they may be applied in combination.

A Universal Descriptor for the Entropy of Adsorbed Molecules in Confined Spaces

Confinement of hydrocarbons in nanoscale pockets and pores provides tunable capability for controlling molecules in catalysts, sorbents, and membranes for reaction and separation applications. While computation of the enthalpic interactions of hydrocarbons in confined spaces has improved, understanding and predicting the entropy of confined molecules remains a challenge. Here we show, using a set of nine aluminosilicate zeolite frameworks with broad variation in pore and cavity structure, that the entropy of adsorption can be predicted as a linear combination of rotational and translational entropy. The extent of entropy lost upon adsorption is predicted using only a single material descriptor, the occupiable volume (V _occ). Predictive capability of confined molecular entropy permits an understanding of the relation with adsorption enthalpy, the ability to computationally screen microporous materials, and an understanding of the role of confinement on the kinetics of molecules in confined spaces.

First-principles theoretical assessment of catalysis by confinement: NO-O2 reactions within voids of molecular dimensions in siliceous crystalline frameworks

This work provides theoretical underpinnings for the ability of voids of molecular dimensions to enhance chemical reactions by mere confinement.

Density functional theory methods that include dispersive forces are used to show how voids of molecular dimensions enhance reaction rates by the mere confinement of transition states analogous to those involved in homogeneous routes and without requiring specific binding sites or structural defects within confining voids. These van der Waals interactions account for the observed large rate enhancements for NO oxidation in the presence of purely siliceous crystalline frameworks. The minimum free energy paths for NO oxidation within chabazite (CHA) and silicalite (SIL) frameworks involve intermediates similar in stoichiometry, geometry, and kinetic relevance to those involved in the homogeneous route. The termolecular transition state for the kinetically-relevant cis-NOO₂NO isomerization to trans-NOO₂NO is strongly stabilized by confinement within CHA (by 36.3 kJ mol^–1 in enthalpy) and SIL (by 39.2 kJ mol^–1); such enthalpic stabilization is compensated, in part, by concomitant entropy losses brought forth by confinement (CHA: 44.9; SIL: 45.3, J mol^–1 K^–1 at 298 K). These enthalpy and entropy changes upon confinement agree well with those measured and combine to significantly decrease activation free energies and are consistent with the rate enhancements that become larger as temperature decreases because of the more negative apparent activation energies in confined systems compared with homogeneous routes. Calculated free energies of confinement are in quantitative agreement with measured rate enhancements and with their temperature sensitivity. Such quantitative agreements reflect preeminent effects of geometry in determining the van der Waals contributions from contacts between the transition states (TS) and the confining walls and the weak effects of the level of theory on TS geometries. NO oxidation reactions are chosen here to illustrate these remarkable effects of confinement because detailed kinetic analysis of rate data are available, but also because of their critical role in the treatment of combustion effluents and in the synthesis of nitric acid and nitrates. Similar effects are evident from rate enhancements by confinement observed for Diels–Alder and alkyne oligomerization reactions. These reactions also occur in gaseous media at near ambient temperatures, for which enthalpic stabilization upon confinement of their homogeneous transition states becomes the preeminent component of activation free energies.

Equilibrium study of dried orange peel for its efficiency in removal of cupric ions from water

Excess of copper ion (>2 mg/L) in water is toxic to human beings and the ecosystem. Various water treatment technologies for copper remediation have been investigated in the past. Along with industrial effluents, Bordeaux mixture is also a noteworthy copper contamination source in the agricultural ecosystem. In our study, the biosorbent efficiency of dried orange peel was investigated through an environment-friendly process for the removal of cupric ions. Effects of pH, adsorbate concentration, adsorbent dosage, and temperature for the removal of Cu (II) were studied. Slightly acidic environment (pH = 6) was found to be optimum for removal of copper. The equilibrium data were well fitted with the Langmuir and Freundlich isotherms. The surface morphology of the adsorbent was studied using scanning electron microscope. Crystalline nonhomogenous surface was observed after copper adsorption. Desorption study indicated that 0.1N H₂SO₄ is the best eluent for the removal of adsorbed copper from the powdered dried orange peel.

Understanding Brønsted-Acid Catalyzed Monomolecular Reactions of Alkanes in Zeolite Pores by Combining Insights from Experiment and Theory

Acidic zeolites are effective catalysts for the cracking of large hydrocarbon molecules into lower molecular weight products required for transportation fuels. However, the ways in which the zeolite structure affects the catalytic activity at Brønsted protons are not fully understood. One way to characterize the influence of the zeolite structure on the catalysis is to study alkane cracking and dehydrogenation at very low conversion, conditions for which the kinetics are well defined. To understand the effects of zeolite structure on the measured rate coefficient (k_app ), it is necessary to identify the equilibrium constant for adsorption into the reactant state (K_ads-H+ ) and the intrinsic rate coefficient of the reaction (k_int ) at reaction temperatures, since k_app is proportional to the product of K_ads-H+ and k_int . We show that K_ads-H+ cannot be calculated from experimental adsorption data collected near ambient temperature, but can, however, be estimated accurately from configurational-bias Monte Carlo (CBMC) simulations. Using monomolecular cracking and dehydrogenation of C₃ -C₆ alkanes as an example, we review recent efforts aimed at elucidating the influence of the acid site location and the zeolite framework structure on the observed values of k_app and its components, K_ads-H+ and k_int .

Hydride Transfer versus Deprotonation Kinetics in the Isobutane-Propene Alkylation Reaction: A Computational Study

The alkylation of isobutane with light alkenes plays an essential role in modern petrochemical processes for the production of high-octane gasoline. In this study we have employed periodic DFT calculations combined with microkinetic simulations to investigate the complex reaction mechanism of isobutane-propene alkylation catalyzed by zeolitic solid acids. Particular emphasis was given to addressing the selectivity of the alkylate formation versus alkene formation, which requires a high rate of hydride transfer in comparison to the competitive oligomerization and deprotonation reactions resulting in catalyst deactivation. Our calculations reveal that hydride transfer from isobutane to a carbenium ion occurs via a concerted C-C bond formation between a tert-butyl fragment and an additional olefin, or via deprotonation of the tert-butyl fragment to generate isobutene. A combination of high isobutane concentration and low propene concentration at the reaction center favor the selective alkylation. The key reaction step that has to be suppressed to increase the catalyst lifetime is the deprotonation of carbenium intermediates that are part of the hydride transfer reaction cycle.

Mechanistic insights into the formation of butene isomers from 1-butanol in H-ZSM-5: DFT based microkinetic modelling

First principles microkinetic modelling provides in-depth mechanistic insights into the competing reaction pathways for zeolite-catalyzed conversion of 1-butanol to butene isomers.

Ethene hydrogenation vs. dimerization over a faujasite-supported [Rh(C2H4)2] complex. A computational study of mechanism

A DFT study allows one to understand the selectivity for ethene hydrogenation over dimerization by the well-characterized faujasite-supported [Rh(C₂H₄)₂]⁺ complex.

Effect of zeolite confinement on the conversion of 1-butanol to butene isomers: mechanistic insights from DFT based microkinetic modelling

First principles microkinetic modelling shows that, unlike in H-ZSM-5 and H-ZSM-22, trans-2-butene formation in H-FER occurs via direct dehydration of 1-butanol.

Advances in theory and their application within the field of zeolite chemistry

Zeolites are versatile and fascinating materials which are vital for a wide range of industries, due to their unique structural and chemical properties, which are the basis of applications in gas separation, ion exchange and catalysis. Given their economic impact, there is a powerful incentive for smart design of new materials with enhanced functionalities to obtain the best material for a given application. Over the last decades, theoretical modeling has matured to a level that model guided design has become within reach. Major hurdles have been overcome to reach this point and almost all contemporary methods in computational materials chemistry are actively used in the field of modeling zeolite chemistry and applications. Integration of complementary modeling approaches is necessary to obtain reliable predictions and rationalizations from theory. A close synergy between experimentalists and theoreticians has led to a deep understanding of the complexity of the system at hand, but also allowed the identification of shortcomings in current theoretical approaches. Inspired by the importance of zeolite characterization which can now be performed at the single atom and single molecule level from experiment, computational spectroscopy has grown in importance in the last decade. In this review most of the currently available modeling tools are introduced and illustrated on the most challenging problems in zeolite science. Directions for future model developments will be given.