Zeolite Adsorption Free Energies from ab Initio Potentials of Mean Force

The Entropy of van der Waals Fluid

Thermodynamic state functions are fundamental quantities in many fields. In this work, the van der Waals (vdW) equation of state and calculation formulas of state functions are derived with statistical thermodynamic method in three-dimensional (3D) and two-dimensional (2D) spaces. The heat capacity at constant volume (CV,m ) or area (CA,m ) is exactly the same as that of ideal gas, but the heat capacity at constant pressure (Cp,m ) and other state functions are different from those of ideal gas. The vdW equation of state is a cubic equation, which leads to the fact that the entropy and free energy changes of vdW fluid can be expressed as explicit expressions of volume rather than pressure. Therefore, the adsorbate entropy at constant area can still be theoretically proven to have a linear relationship with the gas-phase entropy at constant volume. However, the linear correlation between it and gas-phase entropy at constant pressure is no longer strictly true in theory. In addition, since the vdW equation of state is applicable to both gas and liquid, the linear correlation between adsorbate entropy and liquid-phase entropy can also be found. At last, the reference state for real gas or fluid at a constant molar volume is suggested.

Free and internal energies for the adsorption of short alkanes into the zeolite SSZ-13 from ab initio molecular dynamics simulations

Electronic structure calculations have become a valuable tool in understanding chemical reactions of hydrocarbons in zeolite pores. However, commonly applied approaches to calculate free energies based on static electronic structure calculations significantly overestimate the entropic penalty for molecular adsorption into zeolite pores. Here, we use ab initio molecular dynamics (AIMD) simulations to model the adsorption of methane, ethane, and propane to purely siliceous and protonated SSZ-13. In our analyses we focus on the internal and Helmholtz free energies of adsorption of each molecule and compare our results to various approaches for the calculation of free energies based on static calculations. We find that only an approach that retains two thirds of the translational entropy of the adsorbate upon adsorption compares favorably with AIMD simulations. However, comparison to experimental measurements of Gibbs free energies of adsorption reported in the literature implies that we might not have captured the full complexity of alkane adsorption in our model. We expect that results in this work will help to develop a better understanding of alkane adsorption in zeolites, and that the provided data will serve as a benchmark for free energy calculations of alkane adsorption in zeolites in the future.

Structural dynamics of Ru clusters during nitrogen dissociation in ammonia synthesis

The dynamic evolution of catalyst structures greatly influences the reactivity, especially sub-nanometer clusters, exhibiting complex configurational fluctuation. In the present work, we study the structural dynamics of a Ru₁₉ cluster during the dissociation of N₂ and calculate the reaction free energies using ab initio molecular dynamics (AIMD). Our AIMD calculation predicts a peak-shaped reaction entropy curve due to the adsorption-induced phase transition of the Ru₁₉ cluster. The low melting points of sub-nanometer clusters make it possible to activate N₂ at low temperatures. This work demonstrates that the dynamic changes of cluster structures have a non-negligible effect on reaction free energy and offer an opportunity for achieving ammonia synthesis under mild conditions.

Accelerating Metadynamics-Based Free-Energy Calculations with Adaptive Machine Learning Potentials

There is an increasing demand for free-energy calculations using ab initio molecular dynamics these days. Metadynamics (MetaD) is frequently utilized to reconstruct the free-energy surface, but it is often computationally intractable for the first-principles calculations. Machine learning potentials (MLPs) have become popular alternatives. However, the training could be a long and arduous process before using them in practical applications. To accelerate MetaD use with MLPs for the free-energy calculation in an easy manner, we propose the adaptive machine learning potential-accelerated metadynamics (AMLP-MetaD). In this method, the MLP in the form of a Gaussian approximation potential (GAP) can adapt itself based on its uncertainty estimation, which decides whether to accept the model prediction or recalculate it with a reference method (usually density functional theory) for further training during the MetaD simulation. We demonstrate that the free-energy landscape similar to the ab initio one can be obtained using AMLP-MetaD with a 10-time speedup. Moreover, the quality of the free-energy results can be deeply improved using Δ-MLP, which is the GAP-corrected density functional tight binding in our case. We exemplify this novel method with two model systems, CO adsorption on the Pt₁₃ cluster and the Pt(111) surface, which are of vital importance in heterogeneous catalysis. The successful application in these two tests highlights that our proposed method can be used in both cluster and periodic systems and for up to two collective variables.

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).

Computational Methods in Heterogeneous Catalysis

The unprecedented ability of computations to probe atomic-level details of catalytic systems holds immense promise for the fundamentals-based bottom-up design of novel heterogeneous catalysts, which are at the heart of the chemical and energy sectors of industry. Here, we critically analyze recent advances in computational heterogeneous catalysis. First, we will survey the progress in electronic structure methods and atomistic catalyst models employed, which have enabled the catalysis community to build increasingly intricate, realistic, and accurate models of the active sites of supported transition-metal catalysts. We then review developments in microkinetic modeling, specifically mean-field microkinetic models and kinetic Monte Carlo simulations, which bridge the gap between nanoscale computational insights and macroscale experimental kinetics data with increasing fidelity. We finally review the advancements in theoretical methods for accelerating catalyst design and discovery. Throughout the review, we provide ample examples of applications, discuss remaining challenges, and provide our outlook for the near future.

Critical Role of Surface Defects in the Controllable Deposition of Li2S on Graphene: From Molecule to Crystallite

Uncontrollable electrochemical deposition of Li₂S has negative impacts on the electrochemical performance of lithium-sulfur batteries, but the relationship between the deposition and the surface defects is rarely reported. Herein, ab initio molecular dynamics (AIMD) and density functional theory (DFT) approaches are used to study the Li₂S deposition behaviors on pristine and defected graphene substrates, including pyridinic N (PDN) doped and single vacancy (SV), as well as the interfacial characteristics, in that such defects could improve the polarity of the graphene material, which plays a vital role in the cathode. The result shows that due to the constraint of molecular vibration, Li₂S molecules tend to form stable adsorption with PDN atoms and SV defects, followed by the nucleation of Li₂S clusters on these sites. Moreover, the clusters are more likely to grow near these sites following a spherical pattern, while a lamellar pattern is favorable on pristine graphene substrates. It is also discovered that PDN atoms and SV defects provide atomic-level pathways for the electronic transfer within the Li₂S-electrode interface, further improving the electrochemical performance of the Li-S battery. It is found for the first time that surface defects also have strong impacts on the deposition pattern of Li₂S and provide electronic pathways simultaneously. Our work demonstrated the interior relationship between the surface defects in carbon substrates and the stability of Li₂S precipitates, which is of high significance to understand the electrochemical kinetics and design Li-S battery with long cycle life.

Solvation and Mobilization of Copper Active Sites in Zeolites by Ammonia: Consequences for the Catalytic Reduction of Nitrogen Oxides

ConspectusCopper-exchanged chabazite (Cu-CHA) zeolites are catalysts used in diesel emissions control for the abatement of nitrogen oxides (NO_x) via selective catalytic reduction (SCR) reactions with ammonia as the reductant. The discovery of these materials in the early 2010s enabled a step-change improvement in diesel emissions aftertreatment technology. Key advantages of Cu-CHA zeolites over prior materials include their effectiveness at the lower temperatures characteristic of diesel exhaust, their durability under high-temperature hydrothermal conditions, and their resistance to poisoning from residual hydrocarbons present in exhaust. Fundamental catalysis research has since uncovered mechanistic and kinetic features that underpin the ability of Cu-CHA to selectively reduce NO_x under strongly oxidizing conditions and to achieve improved NO_x conversion relative to other zeolite frameworks, particularly at low exhaust temperatures and with ammonia instead of other reductants.One critical mechanistic feature is the NH₃ solvation of exchanged Cu ions at low temperatures (<523 K) to create cationic Cu-amine coordination complexes that are ionically tethered to anionic Al framework sites. This ionic tethering confers regulated mobility that facilitates interconversion between mononuclear and binuclear Cu complexes, which is necessary to propagate SCR through a Cu²⁺/Cu⁺ redox cycle during catalytic turnover. This dynamic catalytic mechanism, wherein single and dual metal sites interconvert to mediate different half-reactions of the redox cycle, combines features canonically associated with homogeneous and heterogeneous reaction mechanisms.In this Account, we describe how a unified experimental and theoretical interrogation of Cu-CHA catalysts in operando provided quantitative evidence of regulated Cu ion mobility and its role in the SCR mechanism. This approach relied on new synthetic methods to prepare model Cu-CHA zeolites with varied active-site structures and spatial densities in order to verify that the kinetic and mechanistic models describe the catalytic behavior of a family of materials of diverse composition, and on new computational approaches to capture the active-site structure and dynamics under conditions representative of catalysis. Ex situ interrogation revealed that the Cu structure depends on the conditions for the zeolite synthesis, which influence the framework Al substitution patterns, and that statistical and electronic structure models can enumerate Cu site populations for a known Al distribution. This recognition unifies seemingly disparate spectroscopic observations and inferences regarding Cu ion structure and responses to different external conditions. SCR rates depend strongly on the Cu spatial density and zeolite composition in kinetic regimes where Cu⁺ oxidation with O₂ becomes rate-limiting, as occurs at lower temperatures and under fuel-rich conditions. Transient experiments, ab initio molecular dynamics simulations, and statistical models relate these sensitivities to the mobility constraints imposed by the CHA framework on NH₃-solvated Cu ions, which regulate the pore volume accessible to these ions and their ability to pair and complete the catalytic cycle. This highlights the key characteristics of the CHA framework that enable superior performance under low-temperature SCR reaction conditions.This work illustrates the power of precise control over a catalytic material, simultaneous kinetic and spectroscopic interrogation over a wide range of reaction conditions, and computational strategies tailored to capture those reaction conditions to reveal in microscopic detail the mechanistic features of a complex and widely practiced catalysis. In doing so, it highlights the key role of ion mobility in catalysis and thus potentially a more general phenomenon of reactant solvation and active site mobilization in reactions catalyzed by exchanged metal ions in zeolites.

Computational Investigation of Correlations in Adsorbate Entropy for Pure-Silica Zeolite Adsorbents

Vast numbers of unstudied hypothetical porous frameworks continue to spark interest in optimizing adsorption and catalytic processes. Evaluating the use of such materials depends on the accessibility of thermodynamic metrics such as the free energy, which, in turn, depend on the satisfactory estimation or calculation of the adsorption entropy, which often remains elusive. Previous works using simulations and experimental data have demonstrated relationships between the entropy and system descriptors, allowing for sensible predictions based on more-easily obtained physical parameters. However, the resultant conclusions were either based on experimental data for industrially relevant alkanes or lacked a significant sample size. In this paper, we evaluate correlations between gas-phase and adsorbed-phase entropies for a larger and more chemically diverse set of adsorbate molecules by using force fields and statistical mechanical expressions to calculate those entropies. In total, we perform calculations for 37 molecules across 10 chemical categories available in the TraPPE force field set, as adsorbed in five siliceous zeolites. Our results show that linear correlations between the gas- and adsorbed-phase entropies persist for the larger and diverse set of adsorbate molecules studied here, proving a broader applicability and justifying the use of simple correlations for many adsorbates and, presumably, adsorbent materials.

Unraveling the mysterious failure of Cu/SAPO-34 selective catalytic reduction catalysts

Commercial Cu/SAPO-34 selective catalytic reduction (SCR) catalysts have experienced unexpected and quite perplexing failure. Understanding the causes at an atomic level is vital for the synthesis of more robust Cu/SAPO-34 catalysts. Here we show, via application of model catalysts with homogeneously dispersed isolated Cu ions, that Cu transformations resulting from low-temperature hydrothermal aging and ambient temperature storage can be semi-quantitatively probed with 2-dimensional pulsed electron paramagnetic resonance. Coupled with kinetics, additional material characterizations and DFT simulations, we propose the following catalyst deactivation steps: (1) detachment of Cu(II) ions from cationic positions in the form of Cu(OH)₂; (2) irreversible hydrolysis of the SAPO-34 framework forming terminal Al species; and (3) interaction between Cu(OH)₂ and terminal Al species forming SCR inactive, Cu-aluminate like species. Especially significant is that these reactions are greatly facilitated by condensed water molecules under wet ambient conditions, causing low temperature failure of the commercial Cu/SAPO-34 catalysts.

Understanding the failure of commercial Cu/SAPO-34 selective catalytic reduction (SCR) catalysts at an atomic level is vital for the synthesis of more robust catalysts. Here the authors unravel the mysterious failure of Cu/SAPO-34 SCR catalysts via application of model catalysts and 2-dimensional pulsed electron paramagnetic resonance

Consequences of exchange-site heterogeneity and dynamics on the UV-visible spectrum of Cu-exchanged SSZ-13

The speciation and structure of Cu ions and complexes in chabazite (SSZ-13) zeolites, which are relevant catalysts for nitrogen oxide reduction and partial methane oxidation, depend on material composition and reaction environment. Ultraviolet-visible (UV-Vis) spectra of Cu-SSZ-13 zeolites synthesized to contain specific Cu site motifs, together with ab initio molecular dynamics and time-dependent density functional theory calculations, were used to test the ability to relate specific spectroscopic signatures to specific site motifs. Geometrically distinct arrangements of two framework Al atoms in six-membered rings are found to exchange Cu2+ ions that become spectroscopically indistinguishable after accounting for the finite-temperature fluctuations of the Cu coordination environment. Nominally homogeneous single Al exchange sites are found to exchange a heterogeneous mixture of [CuOH]+ monomers, O- and OH-bridged Cu dimers, and larger polynuclear complexes. The UV-Vis spectra of the latter are sensitive to framework Al proximity, to precise ligand environment, and to finite-temperature structural fluctuations, precluding the precise assignment of spectroscopic features to specific Cu structures. In all Cu-SSZ-13 samples, these dimers and larger complexes are reduced by CO to Cu+ sites at 523 K, leaving behind isolated [CuOH]+ sites with a characteristic spectroscopic identity. The various mononuclear and polynuclear Cu2+ species are distinguishable by their different responses to reducing environments, with implications for their relevance to catalytic redox reactions.

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.

Cu-CHA – a model system for applied selective redox catalysis

We review the structural chemistry and reactivity of copper-exchanged molecular sieves with chabazite (CHA) topology, as an industrially applied catalyst in ammonia mediated reduction of harmful nitrogen oxides (NH₃-SCR) and as a general model system for red-ox active materials (also the recent results in the direct conversion of methane to methanol are considered).