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.

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.

Quantum Chemical Free Energies: Structure Optimization and Vibrational Frequencies in Normal Modes

A computational protocol is presented that uses normal mode coordinates for structure optimization and for obtaining harmonic frequencies by numerical differentiation. It reduces numerical accuracy problems encountered when density functional theory with plane wave basis sets is applied to systems with flat potential energy surfaces. The approach is applied to calculate Gibbs free energies for adsorption of methane, ethane, and propane on the Brønsted acidic sites of zeolite H-CHA. The values obtained (273.15 K, 0.1 MPa,), -0.25, -5.95, and -16.76 kJ/mol, respectively, follow the trend of the experimental values, which is not the case for results obtained with the standard approach (Cartesian optimization, frequencies from Cartesian distortions). Anharmonicity effects have been approximately taken into account by solving one-dimensional Schrödinger equations along each normal mode. This leads to a systematic increase of the Gibbs free energy of adsorption of 4.5, 5.0, and 3.1 kJ/mol for methane, ethane, and propane, respectively, making adsorption at a given pressure and temperature less likely. This is due to an increase of low vibrational frequencies associated with hindered translations and rotations of the adsorbed molecules and the floppy modes of the zeolite framework.

The roles of entropy and enthalpy in stabilizing ion-pairs at transition states in zeolite acid catalysis

Acidic zeolites are indispensable catalysts in the petrochemical industry because they select reactants and their chemical pathways based on size and shape. Voids of molecular dimensions confine reactive intermediates and transition states that mediate chemical reactions, stabilizing them by van der Waals interactions. This behavior is reminiscent of the solvation effects prevalent within enzyme pockets and has analogous consequences for catalytic specificity. Voids provide the "right fit" for certain transition states, reflected in their lower free energies, thus extending the catalytic diversity of zeolites well beyond simple size discrimination. This catalytic diversity is even more remarkable because acid strength is essentially unaffected by confinement among known crystalline aluminosilicates. In this Account, we discuss factors that determine the "right fit" for a specific chemical reaction, exploring predictive criteria that extend the prevailing discourse based on size and shape. We link the structures of reactants, transition states, and confining voids to chemical reactivity and selectivity. Confinement mediates enthalpy-entropy compromises that determine the Gibbs free energies of transition states and relevant reactants; these activation free energies determine turnover rates via transition state theory. At low temperatures (400-500 K), dimethyl ether carbonylation occurs with high specificity within small eight-membered ring (8-MR) voids in FER and MOR zeolite structures, but at undetectable rates within larger voids (MFI, BEA, FAU, and SiO(2)-Al(2)O(3)). More effective van der Waals stabilization within 8-MR voids leads to lower ion-pair enthalpies but also lower entropies; taken together, carbonylation activation free energies are lower within 8-MR voids. The "right fit" is a "tight fit" at low temperatures, a consequence of how temperature appears in the defining equation for Gibbs free energy. In contrast, entropy effects dominate in high-temperature alkane activation (700-800 K), for which the "right fit" becomes a "loose fit". Alkane activation turnovers are still faster on 8-MR MOR protons because these transition states are confined only partially within shallow 8-MR pockets; they retain higher entropies than ion-pairs fully confined within 12-MR channels at the expense of enthalpic stability. Selectivities for n-alkane dehydrogenation (relative to cracking) and isoalkane cracking (relative to dehydrogenation) are higher on 8-MR than 12-MR sites because partial confinement preferentially stabilizes looser ion-pair structures; these structures occur later along reaction coordinates and are higher in energy, consistent with Marcus theory for charge-transfer reactions. Enthalpy differences between cracking and dehydrogenation ion-pairs for a given reactant are independent of zeolite structure (FAU, FER, MFI, or MOR) and predominantly reflect the different gas-phase proton affinities of alkane C-C and C-H bonds, as expected from Born-Haber thermochemical cycles. These thermochemical relations, together with statistical mechanics-based treatments, predict that rotational entropy differences between intact reactants and ion-pair transition states cause intrinsic cracking rates to increase with n-alkane size. Through these illustrative examples, we highlight the effects of reactant and catalyst structures on ion-pair transition state enthalpies and entropies. Our discussion underscores the role of temperature in mediating enthalpic and entropic contributions to free energies and, in turn, to rates and selectivities in zeolite acid catalysis.