Normal Mode Analysis in Zeolites: Toward an Efficient Calculation of Adsorption Entropies

Anharmonic Correction to Free Energy Barriers from DFT-Based Molecular Dynamics Using Constrained Thermodynamic Integration

For the calculation of anharmonic contributions to free energy barriers, constrained thermodynamic λ-path integration (λ-TI) from a harmonic reference force field to density functional theory is presented as an alternative to the established Blue Moon ensemble method (ξ-TI), in which free energy gradients along the reaction coordinate ξ are integrated. With good agreement in all cases, the λ-TI method is benchmarked against the ξ-TI method for several reactions, including the internal CH₃ group rotation in ethane, a nucleophilic substitution of CH₃Cl, a retro-Diels-Alder reaction, and a proton transfer in zeolite H-SSZ-13. An advantage of λ-TI is that one can use virtually any reference state to compute anharmonic contributions to reaction free energies or free energy barriers. This is particularly relevant for catalysis, where it is now possible to compute anharmonic corrections to the free energy of a transition state relative to any reference, for example, the most stable state of the active site and the reactants in the gas phase. This is in contrast to ξ-TI, where free energy barriers can only be computed relative to an initial state with all reactants coadsorbed. Finally, the Bennett acceptance ratio method combined with λ-TI is demonstrated to reduce the number of required integration grid points with tolerable accuracy, favoring thus λ-TI over ξ-TI in terms of computational efficiency.

Toward Computing Accurate Free Energies in Heterogeneous Catalysis: a Case Study for Adsorbed Isobutene in H-ZSM-5

Herein, we propose a novel computational protocol that enables calculating free energies with improved accuracy by combining the best available techniques for enthalpy and entropy calculation. While the entropy is described by enhanced sampling molecular dynamics techniques, the energy is calculated using ab initio methods. We apply the method to assess the stability of isobutene adsorption intermediates in the zeolite H-SSZ-13, a prototypical problem that is computationally extremely challenging in terms of calculating enthalpy and entropy. We find that at typical operating conditions for zeolite catalysis (400 °C), the physisorbed π-complex, and not the tertiary carbenium ion as often reported, is the most stable intermediate. This method paves the way for sampling-based techniques to calculate the accurate free energies in a broad range of chemistry-related disciplines, thus presenting a big step forward toward predictive modeling.

Anharmonic Correction to Adsorption Free Energy from DFT-Based MD Using Thermodynamic Integration

Adsorption processes are often governed by weak interactions for which the estimation of entropy contributions by means of the harmonic approximation is prone to be inaccurate. Thermodynamic integration (TI) from the harmonic to the fully interacting system (λ-path integration) can be used to compute anharmonic corrections. Here, we combine TI with (curvilinear) internal coordinates in periodic systems to make the formalism available in computational studies. Our implementation of ab initio molecular dynamics in VASP is independent of the reaction path and can be thus applied to study adsorption processes relative to the gas phase and does hence provide a useful tool for computational catalysis. We discuss the application of the approach on three model systems for which exact semianalytical solutions exist and illustrate and quantify the importance of anharmonic vibrations, hindered rotations, and hindered translations (dissociation). Eventually, we apply the method to study the adsorption of small adsorbates in a zeolite (H-SSZ-13).

Entropy driven preference for alkene adsorption at the pore mouth as the origin of pore-mouth catalysis for alkane hydroisomerization in 1D zeolites

This work presents a theoretical basis for a pore-mouth catalysis model developed to explain the positional selectivity of skeletal isomerization on bifunctional metal acid-zeolite catalysts.

Surface chemistry dictates stability and oxidation state of supported single metal catalyst atoms

Single atom catalysts receive considerable attention due to reducing noble metal utilization and potentially eliminating certain side reactions. Yet, the rational design of highly reactive and stable single atom catalysts is hampered by the current lack of fundamental insights at the single atom limit. Here, density functional theory calculations are performed for a prototype reaction, namely CO oxidation, over different single metal atoms supported on alumina. The governing reaction mechanisms and scaling relations are identified using microkinetic modeling and principal component analysis, respectively. A large change in the oxophilicity of the supported single metal atom leads to changes in the rate-determining step and the catalyst resting state. Multi-response surfaces are introduced and built cheaply using a descriptor-based, closed form kinetic model to describe simultaneously the activity, stability, and oxidation state of single metal atom catalysts. A double peaked volcano in activity is observed due to competing rate-determining steps and catalytic cycles. Reaction orders of reactants provide excellent kinetic signatures of the catalyst state. Importantly, the surface chemistry determines the stability, oxidation, and resting state of the catalyst.

Influence of spin state and electron configuration on the active site and mechanism for catalytic hydrogenation on metal cation catalysts supported on NU-1000: insights from experiments and microkinetic modeling

Spin state is found to determine the mechanism and active site of catalytic hydrogenation on metal cation catalysts.

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.

How Chain Length and Branching Influence the Alkene Cracking Reactivity on H-ZSM-5

Catalytic alkene cracking on H-ZSM-5 involves a complex reaction network with many possible reaction routes and often elusive intermediates. Herein, advanced molecular dynamics simulations at 773 K, a typical cracking temperature, are performed to clarify the nature of the intermediates and to elucidate dominant cracking pathways at operating conditions. A series of C₄–C₈ alkene intermediates are investigated to evaluate the influence of chain length and degree of branching on their stability. Our simulations reveal that linear, secondary carbenium ions are relatively unstable, although their lifetime increases with carbon number. Tertiary carbenium ions, on the other hand, are shown to be very stable, irrespective of the chain length. Highly branched carbenium ions, though, tend to rapidly rearrange into more stable cationic species, either via cracking or isomerization reactions. Dominant cracking pathways were determined by combining these insights on carbenium ion stability with intrinsic free energy barriers for various octene β-scission reactions, determined via umbrella sampling simulations at operating temperature (773 K). Cracking modes A (3° → 3°) and B₂ (3° → 2°) are expected to be dominant at operating conditions, whereas modes B₁ (2° → 3°), C (2° → 2°), D₂ (2° → 1°), and E₂ (3° → 1°) are expected to be less important. All β-scission modes in which a transition state with primary carbocation character is involved have high intrinsic free energy barriers. Reactions starting from secondary carbenium ions will contribute less as these intermediates are short living at the high cracking temperature. Our results show the importance of simulations at operating conditions to properly evaluate the carbenium ion stability for β-scission reactions and to assess the mobility of all species in the pores of the zeolite.

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.

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 .

Computational Design of Functionalized Metal-Organic Framework Nodes for Catalysis

Recent progress in the synthesis and characterization of metal-organic frameworks (MOFs) has opened the door to an increasing number of possible catalytic applications. The great versatility of MOFs creates a large chemical space, whose thorough experimental examination becomes practically impossible. Therefore, computational modeling is a key tool to support, rationalize, and guide experimental efforts. In this outlook we survey the main methodologies employed to model MOFs for catalysis, and we review selected recent studies on the functionalization of their nodes. We pay special attention to catalytic applications involving natural gas conversion.

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.

Metal-organic and covalent organic frameworks as single-site catalysts

Heterogeneous single-site catalysts consist of isolated, well-defined, active sites that are spatially separated in a given solid and, ideally, structurally identical. In this review, the potential of metal-organic frameworks (MOFs) and covalent organic frameworks (COFs) as platforms for the development of heterogeneous single-site catalysts is reviewed thoroughly. In the first part of this article, synthetic strategies and progress in the implementation of such sites in these two classes of materials are discussed. Because these solids are excellent playgrounds to allow a better understanding of catalytic functions, we highlight the most important recent advances in the modelling and spectroscopic characterization of single-site catalysts based on these materials. Finally, we discuss the potential of MOFs as materials in which several single-site catalytic functions can be combined within one framework along with their potential as powerful enzyme-mimicking materials. The review is wrapped up with our personal vision on future research directions.

The Remarkable Amphoteric Nature of Defective UiO-66 in Catalytic Reactions

One of the major requirements in solid acid and base catalyzed reactions is that the reactants, intermediates or activated complexes cooperate with several functions of catalyst support. In this work the remarkable bifunctional behavior of the defective UiO-66(Zr) metal organic framework is shown for acid-base pair catalysis. The active site relies on the presence of coordinatively unsaturated zirconium sites, which may be tuned by removing framework linkers and by removal of water from the inorganic bricks using a dehydration treatment. To elucidate the amphoteric nature of defective UiO-66, the Oppenauer oxidation of primary alcohols has been theoretically investigated using density functional theory (DFT) and the periodic approach. The presence of acid and basic centers within molecular distances is shown to be crucial for determining the catalytic activity of the material. Hydrated and dehydrated bricks have a distinct influence on the acidity and basicity of the active sites. In any case both functions need to cooperate in a concerted way to enable the chemical transformation. Experimental results on UiO-66 materials of different defectivity support the theoretical observations made in this work.

Enhancing the catalytic activity of hydronium ions through constrained environments

The dehydration of alcohols is involved in many organic conversions but has to overcome high free-energy barriers in water. Here we demonstrate that hydronium ions confined in the nanopores of zeolite HBEA catalyse aqueous phase dehydration of cyclohexanol at a rate significantly higher than hydronium ions in water. This rate enhancement is not related to a shift in mechanism; for both cases, the dehydration of cyclohexanol occurs via an E1 mechanism with the cleavage of C_β–H bond being rate determining. The higher activity of hydronium ions in zeolites is caused by the enhanced association between the hydronium ion and the alcohol, as well as a higher intrinsic rate constant in the constrained environments compared with water. The higher rate constant is caused by a greater entropy of activation rather than a lower enthalpy of activation. These insights should allow us to understand and predict similar processes in confined spaces.

Alcohol dehydration can be challenging in aqueous phase. Here the authors show that hydronium ions confined with zeolite pores catalyse alcohol dehydration at a significantly increased rate relative to aqueous phase hydronium ions, driven by an increased association between the ion and alcohol and a greater entropy of activation.

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.

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.

First principle chemical kinetics in zeolites: the methanol-to-olefin process as a case study

To optimally design next generation catalysts a thorough understanding of the chemical phenomena at the molecular scale is a prerequisite. Apart from qualitative knowledge on the reaction mechanism, it is also essential to be able to predict accurate rate constants. Molecular modeling has become a ubiquitous tool within the field of heterogeneous catalysis. Herein, we review current computational procedures to determine chemical kinetics from first principles, thus by using no experimental input and by modeling the catalyst and reacting species at the molecular level. Therefore, we use the methanol-to-olefin (MTO) process as a case study to illustrate the various theoretical concepts. This process is a showcase example where rational design of the catalyst was for a long time performed on the basis of trial and error, due to insufficient knowledge of the mechanism. For theoreticians the MTO process is particularly challenging as the catalyst has an inherent supramolecular nature, for which not only the Brønsted acidic site is important but also organic species, trapped in the zeolite pores, must be essentially present during active catalyst operation. All these aspects give rise to specific challenges for theoretical modeling. It is shown that present computational techniques have matured to a level where accurate enthalpy barriers and rate constants can be predicted for reactions occurring at a single active site. The comparison with experimental data such as apparent kinetic data for well-defined elementary reactions has become feasible as current computational techniques also allow predicting adsorption enthalpies with reasonable accuracy. Real catalysts are truly heterogeneous in a space- and time-like manner. Future theory developments should focus on extending our view towards phenomena occurring at longer length and time scales and integrating information from various scales towards a unified understanding of the catalyst. Within this respect molecular dynamics methods complemented with additional techniques to simulate rare events are now gradually making their entrance within zeolite catalysis. Recent applications have already given a flavor of the benefit of such techniques to simulate chemical reactions in complex molecular environments.

Experimental and Theoretical Methods in Kinetic Studies of Heterogeneously Catalyzed Reactions

This review aims to illustrate the potential of kinetic analysis in general and microkinetic modeling in particular for rational catalyst design. Both ab initio calculations and experiments providing intrinsic kinetic data allow us to assess the effects of catalytic properties and reaction conditions on the activity and selectivity of the targeted reactions. Three complementary approaches for kinetic analysis of complex reaction networks are illustrated, using select examples of acid zeolite–catalyzed reactions from the authors' recent work. Challenges for future research aimed at defining targets for synthesis strategies that enable us to tune zeolite properties are identified.

Effect of Anharmonicity on Adsorption Thermodynamics

The effect of anharmonic corrections to the vibrational energies of extended systems is explored. Particular attention is paid to the thermodynamics of adsorption of small molecules on catalytically relevant systems typically affected by anharmonicity. The implemented scheme obtains one-dimensional anharmonic model potentials by distorting the equilibrium structure along the normal modes using both rectilinear (Cartesian) or curvilinear (internal) representations. Only in the latter case, the modes are decoupled also at higher order of the potential and the thermodynamic functions change in the expected directions. The method is applied to calculate ab initio enthalpies, entropies, and Gibbs free energies for the adsorption of methane in acidic chabazite (H-CHA) and on MgO(001) surface. The values obtained for the adsorption of methane in H-CHA (273.15 K, 0.1 MPa, θ = 0.5) are ΔH = -19.3, -TΔS = 11.9, and ΔG = -7.5 kJ/mol. For methane on the MgO(001) (47 K, 1.3 × 10(-14) MPa, θ = 1) ΔH = -14.4, -TΔS = 16.6, and ΔG = 2.1 kJ/mol are obtained. The calculated desorption temperature is 44 K, and the desorption prefactor is 4.26 × 10(12) s(-1). All calculated results agree within chemical accuracy limits with experimental data.