Search

Carbon–carbon bond cleavage reactions, adapted to deconstruct aliphatic hydrocarbon polymers and recover the intrinsic energy and carbon value in plastic waste, have typically been catalysed by metal nanoparticles or air-sensitive organometallics. Metal oxides that serve as supports for these catalysts are typically considered to be inert. Here we show that Earth-abundant, non-reducible zirconia catalyses the hydrogenolysis of polyolefins with activity rivalling that of precious metal nanoparticles. To harness this unusual reactivity, our catalytic architecture localizes ultrasmall amorphous zirconia nanoparticles between two fused platelets of mesoporous silica. Macromolecules translocate from bulk through radial mesopores to the highly active zirconia particles, where the chains undergo selective hydrogenolytic cleavage into a narrow, C18-centred distribution. Calculations indicated that C–H bond heterolysis across a Zr–O bond of a Zr(O)2 adatom model for unsaturated surface sites gives a zirconium hydrocarbyl, which cleaves a C–C bond via β-alkyl elimination.

Chemical and catalytic upcycling processes could help realize a circular plastics economy, but current models for testing mechanistic hypotheses and designing catalysts remain primitive.

Some of the most potent antifreeze proteins (AFPs) are approximately rigid helical structures that bind with one side in contact with the ice surface at specific orientations. These AFPs take random orientations in solution; however, most orientations become sterically inaccessible as the AFP approaches the ice surface. The effect of these inaccessible orientations on the rate of adsorption of AFP to ice has never been explored. Here, we present a diffusion-controlled theory of adsorption kinetics that accounts for these orientational restrictions to predict a rate constant for adsorption (

Magic clusters are metastable faceted nanoparticles that are thought to be important and, sometimes, observable intermediates in the nucleation of certain faceted crystallites. This work develops a broken bond model for spheres with a face-centered-cubic packing that form tetrahedral magic clusters. With just one bond strength parameter, statistical thermodynamics yield a chemical potential driving force, an interfacial free energy, and free energy vs magic cluster size. These properties exactly correspond to those from a previous model by Mule et al. [J. Am. Chem. Soc. 143, 2037 (2021)]. Interestingly, a Tolman length emerges (for both models) when the interfacial area, density, and volume are treated consistently. To describe the kinetic barriers between magic cluster sizes, Mule et al. invoked an energy parameter to penalize the two-dimensional nucleation and growth of new layers in each facet of the tetrahedra. According to the broken bond model, barriers between magic clusters are insignificant without the additional edge energy penalty. We estimate the overall nucleation rate without predicting the rates of formation for intermediate magic clusters by using the Becker–Döring equations. Our results provide a blueprint for constructing free energy models and rate theories for nucleation via magic clusters starting from only atomic-scale interactions and geometric considerations.

Anti-freeze proteins (AFPs) protect organisms at freezing conditions by attaching to the ice surface and arresting its growth. Each adsorbed AFP locally pins the ice surface, resulting in a metastable dimple for which the interfacial forces counteract the driving force for growth. As supercooling increases, these metastable dimples become deeper, until metastability is lost in an engulfment event where the ice irreversibly swallows the AFP. Engulfment resembles nucleation in some respects, and this paper develops a model for the “critical profile” and free energy barrier for the engulfment process. Specifically, we variationally optimize the ice–water interface and estimate the free energy barrier as a function of the supercooling, the AFP footprint size, and the distance to neighboring AFPs on the ice surface. Finally, we use symbolic regression to derive a simple closed-form expression for the free energy barrier as a function of two physically interpretable, dimensionless parameters.

In crystallization, obtaining the proper nucleation and growth parameters is essential to the design of crystallization processes. This paper studies the response of crystal size distribution (CSD)...

Obtaining kinetic constants in rate laws for nucleation and growth is challenging and essential to the design of the crystallization processes. Starting from the coupled species and population bala...

The overconsumption of single-use plastics is creating a global waste catastrophe, with widespread environmental, economic and health-related consequences. Here we show that the benefits of processive enzyme-catalysed conversions of biomacromolecules can be leveraged to affect the selective hydrogenolysis of high-density polyethylene into a narrow distribution of diesel and lubricant-range alkanes using an ordered, mesoporous shell/active site/core catalyst architecture that incorporates catalytic platinum sites at the base of the mesopores. Solid-state nuclear magnetic resonance revealed that long hydrocarbon macromolecules readily move within the pores of this catalyst, with a subsequent escape being inhibited by polymer–surface interactions, a behaviour that resembles the binding and translocation of macromolecules in the catalytic cleft of processive enzymes. Accordingly, the hydrogenolysis of polyethylene with this catalyst proceeds processively to yield a reliable, narrow and tunable stream of alkane products. Achieving plastic deconstruction with high selectivity is crucial for upcycling schemes, but remains challenging. Here, a processive approach for the selective hydrogenolysis of high-density polyethylene into narrow alkane fractions is introduced relying on a Pt/SiO2 catalyst encapsulated in a mesoporous silica shell.

Thiele moduli and effectiveness factors are powerful ways to account for mass transfer limitations on reactions occurring within porous catalyst particles. Effectiveness factors have been developed...

The decoupling approach to solvation free energy calculations requires scaling the interactions between the solute and the solution with all intramolecular interactions preserved. This paper reports a new procedure that makes it possible to these calculations in LAMMPS. The procedure is tested against built-in GROMACS capabilities. The model compounds chosen to test our methodology are ethanol and biphenyl. The LAMMPS and GROMACS results obtained are in good agreement with each other. This work should help perform solvation free energy calculations in LAMMPS and/or other molecular dynamics software having no built-in functions to implement the decoupling approach.

Ab initio calculations have greatly advanced our understanding of homogeneous catalysts and crystalline heterogeneous catalysts. In contrast, amorphous heterogeneous catalysts remain poorly understood. The principal difficulties include (i) the nature of the disorder is quenched and unknown; (ii) each active site has a different local environment and activity; (iii) active sites are rare, often less than ∼20% of potential sites, depending on the catalyst and its preparation method. Few (if any) studies of amorphous heterogeneous catalysts have ever attempted to compute site-averaged kinetics, because the exponential dependence on variable activation energy requires an intractable number of ab initio calculations to converge. We present a new algorithm using machine learning techniques (metric learning kernel regression) and importance sampling to efficiently learn the distribution of activation energies. We demonstrate the algorithm by computing the site-averaged activity for a model amorphous catalyst with quenched disorder.

Thiele moduli and effectiveness factors are powerful ways to factor for diffusion limitations in heterogeneously catalyzed reactions. They have been developed for different rate laws, different geometries, as well as non-isothermal reactions. A recent study [B. Peters, ACS Catal., 2020, 10, 4319–4325] reported new ‘secondary effectiveness factors’ for a series of catalytic reactions A → B → C in a slab geometry. This paper generalizes the secondary effectiveness factors to spherical and cylindrical geometries. We illustrate their use for a batch slurry reactor with catalyst particles of different geometry. For molecular sieves, we show how partition coefficients between the solution and the catalyst particle can enhance the selectivity to the intermediate B. Finally, we introduce generalized expressions for the concentration of B and the ‘secondary’ effectiveness factor for different geometries.

Ab initio computational studies have made tremendous progress in describing the behavior of molecular (homogeneous) catalysts and crystalline versions of heterogeneous catalysts, but not for amorphous heterogeneous catalysts. Even widely used industrial amorphous catalysts like atomically dispersed Cr on silica remain poorly understood and largely intractable to computational investigation. The central problems are that (i) the amorphous support presents an unknown quenched disordered structure, (ii) metal atoms attach to various surface grafting sites with different rates, and (iii) the resulting grafted sites have different activation and catalytic reaction kinetics. This study combines kernel regression and importance sampling techniques to efficiently model grafting of metal ions onto a non-uniform ensemble of support environments. Our analysis uses a simple model of the quenched disordered support environment, grafting chemistry, and catalytic activity of the resulting grafted sites.

A catalytic architecture, comprising a mesoporous silica shell surrounding platinum nanoparticles (NPs) supported on a solid silica sphere (mSiO

This work uses a dual absolute chemical potential route with a centroid reference for the dissolved molecules and an Einstein crystal reference for the solid. We use these calculations to predict the vapour pressure, solubility limit, and chemical potential driving forces for crystallization of napthalene (large and rigid) and succinic acid (floppy and anharmonic). We examine each source of error in the free energy calculations and demonstrate that the chemical potentials can be computed with an overall precision of ca. 0.05 kcal/mol, leading to solubility predictions with precision of ca. 10%. The precise calculations should facilitate studies of nucleation kinetics, growth kinetics, and efforts to develop accurate force fields.

The adsorption of large rod-like molecules or crystallites on a flat crystal face, similar to Buffon’s needle, requires the rods to “land,” with their binding sites in precise orientational alignment with matching sites on the surface. An example is provided by long, helical antifreeze proteins (AFPs), which bind at specific facets and orientations on the ice surface. The alignment constraint for adsorption, in combination with the loss in orientational freedom as the molecule diffuses toward the surface, results in an entropic barrier that hinders the adsorption. Prior kinetic models do not factor in the complete geometry of the molecule, nor explicitly enforce orientational constraints for adsorption. Here, we develop a diffusion-controlled adsorption theory for AFP molecules binding at specific orientations to flat ice surfaces. We formulate the diffusion equation with relevant boundary conditions and present analytical solutions to the attachment rate constant. The resulting rate constant is a function of the length and aspect ratio of the AFP, the distance threshold associated with binding, and solvent conditions such as temperature and viscosity. These results and methods of calculation may also be useful for predicting the kinetics of crystal growth through oriented attachment.

In the theory of solidification, the kinetic coefficient multiplies the local supercooling to give the solid–liquid interface velocity. The same coefficient should drive interface migration at the coexistence temperature in proportion to a curvature force. This work computes the ice–water kinetic coefficient from molecular simulations starting from a sinusoidal ice–water interface at the coexistence temperature. We apply this method to the basal and prismatic ice planes and compare results to previous estimates from equilibrium correlation functions and simulations at controlled supercooling.

In an infrequent metadynamics (iMetaD) simulation, a well-tempered metadynamics bias accumulates in the reactant basin, accelerating escapes to the product state. Like the earlier hyperdynamics strategy, iMetaD enables estimates of the unbiased escape rates. However, iMetaD applies the bias to visited locations in a collective variable (CV) space, not to the more specific visited locations in a full configuration space as done in hyperdynamics. This difference makes rate estimates from iMetaD sensitive to the choice of CVs, to parameters that control the bias deposition rate, and to the preparation of the initial state within the reactant basin. This paper uses an extremely simple discrete state model to illustrate complications that can arise in systems that exhibit fluxional transitions between sub-basins of the reactant state. Specifically, we show how the reactant-to-product escape time and relaxation times within the reactant basin(s) impose bounds on the admissible parameter choices for an iMetaD calculation. Predictions from the discrete state model are validated by iMetaD simulations on a corresponding two-dimensional potential energy surface.

We study the prototypical S

We study the prototypical SN2 reaction Cl$^-$ + CH$_3$Cl $\to$ CH$_3$Cl + Cl$^-$ in water using quantum mechanics / molecular mechanics (QM/MM) computer simulations with transition path sampling and inertial likelihood maximization. We have identified a new solvent coordinate to complement the original atom-exchange coordinate used in the classic analysis by Chandrasekhar, Smith, and Jorgensen [Ref1]. The new solvent coordinate quantifies instantaneous solvent induced polarization relative to the equilibrium average charge density at each point along the reaction pathway. On the basis of likelihood scores and committor distributions, the new solvent coordinate improves upon the description of solvent dynamical effects relative to previously proposed solvent coordinates. However, it does not increase the transmission coefficient or the accuracy of a transition state theory rate calculation., 11 pages, 10 figures

A new future for polyethylene Most current plastic recycling involves chopping up the waste and repurposing it in materials with less stringent engineering requirements than the original application. Chemical decomposition at the molecular level could, in principle, lead to higher-value products. However, the carbon-carbon bonds in polyethylene, the most common plastic, tend to resist such approaches without exposure to high-pressure hydrogen. F. Zhang et al. now report that a platinum/alumina catalyst can transform waste polyethylene directly into long-chain alkylbenzenes, a feedstock for detergent manufacture, with no need for external hydrogen (see the Perspective by Weckhuysen). Science , this issue p. 437 ; see also p. 400

Of all plastics, the most abundantly produced is polyethylene, most of which is destined for landfills, shipping ports, and natural environments. The limited degradability and recyclability of this synthetic polymer motivates the development of chemical recycling methods. One possible approach consists of selective depolymerization to propylene with tandem olefin metathesis and double bond isomerization catalysts. In this paper, we transform thousands of coupled rate equations, pseudo-steady-state approximations, and local density approximations into one simple and analytically solvable Fokker-Planck type equation. The Fokker-Planck equation gives concise expressions for the rate of propylene production and polymer molecular weight evolution as functions of catalyst concentrations, rate constants, and ethylene concentrations.

Solid solutions, structurally ordered but compositionally disordered mixtures, can form for salts, metals, and even organic compounds. The NaCl-KCl system forms a solid solution at all compositions between 657{\deg}C and 505{\deg}C. Below a critical temperature of 505{\deg}C, the system exhibits a miscibility gap with coexisting Na-rich and K-rich rocksalt phases. We calculate the phase diagram in this region using the semi-grand canonical Widom method, which averages over virtual particle transmutations. We verify our results by comparison with free energies calculated from thermodynamic integration and extrapolate the location of the critical point. The calculations reproduce the experimental phase diagram remarkably well and illustrate how solid-solid equilibria and chemical potentials, including those at metastable conditions, can be computed for materials that form solid solutions., Comment: 10 pages, 9 figures

The prediction of crystal growth rates from solution is a longstanding challenge and paramount opportunity for pharmaceuticals, materials science, biomineralization, and beyond. This work overcomes the key obstacle by calculating solute attachment rates to the crystal surface via atomistic simulations and rare-event methods. These rates are combined with the multiscale spiral growth model to produce the first parameter-free in silico crystal growth rate predictions. Our results are in excellent agreement with experimental measurements for sodium chloride grown from aqueous solution.

The slow nucleation of clathrate hydrates is a central challenge for their use in the storage and transportation of natural gas. Molecules that strongly adsorb to the clathrate-water interface decrease the crystal-water surface tension, lowering the barrier for clathrate nucleation. Surfactants are widely used to promote the nucleation and growth of clathrate hydrates. It has been proposed that these amphiphilic molecules bind to the clathrate surface via hydrogen bonding. However, recent studies reveal that PVCap, an amphiphilic polymer, binds to clathrates through hydrophobic moieties. Here we use molecular dynamic simulations and theory to investigate the mode and strength of binding of surfactants to the clathrate-water interface and their effect on the nucleation rate. We find that the surfactants bind to the clathrate-water interface exclusively through their hydrophobic tails. The binding is strong, driven by the entropy of dehydration of the alkyl chain, as it penetrates empty cavities at the hydrate surface. The hydrophobic attraction of alkyl groups to the clathrate surface also results in strong adsorption of alkanes. We identify two regimes for the binding of surfactants as a function of their density at the hydrate surface, which we interpret to correspond to the two steps of the Langmuir adsorption isotherm observed in experiments. Our results indicate that hydrophobic attraction to the clathrate-water interface is key for the design of soluble additives that promote the nucleation of hydrates. We use the calculated adsorption coefficients to estimate the concentration of sodium dodecyl sulfate (SDS) required to reach nucleation rates for methane hydrate consistent with those measured in experiments. To our knowledge, this study is the first to quantify the effect of surfactant concentration in the nucleation rate of clathrate hydrates.

Using density functional theory, we examine a possible homolysis initiation mechanism for the Phillips catalyst, starting from CrII sites exposed to ethylene. Spin-crossing in an abundant quintet bis(ethylene) CrII site leads to cycloaddition to form a chromacyclopentane site. One Cr–C bond then homolyzes to generate a tethered n-butyl radical: [Cr(CH2)3CH2•]. If the radical attaches to a nearby inorganic Cr site, it yields two alkylCrIII sites capable of Cossee–Arlman polymerization. The overall computed barrier for this initiation process is 132 kJ/mol, which is comparable to the 120 kJ/mol value that we estimated from reported initiation times in industrial reactors. Poisson statistics suggest that this mechanism could activate ∼35% of Cr sites on a commercial catalyst with a loading of 0.4 Cr/nm2. Pairwise Cr grafting, amplification by complementary initiation reactions, or the creation of dangling bonds that form as the silica support fractures, might explain the apparent increase in per-site activit...

Crystal growth rates depend on the density of kink sites along step edges, ρ. The supersaturation-dependence of the kink density, ρ(S), is often ignored despite available nonequilibrium models for centrosymmetric crystals. The aim of this work is to derive ρ(S) from a rather simple one-dimensional nucleation framework in a manner that accounts for multiheight kinks. These become more prevalent at higher S and/or lower kink energies where the step front roughens (i.e., higher ρ). We arrive at a density of kinetic kinks that contribute to the step velocity and make comparisons with other models and simulations. Our model almost entirely eliminates systematic errors in predicted step velocities and crystal growth rates.

Desolvation barriers are present for solute-solvent exchange events, such as ligand binding to an enzyme active site, during protein folding, and at battery electrodes. For solution-grown crystals, desolvation at kink sites can be the rate-limiting step for growth. However, desolvation and the associated kinetic barriers are poorly understood. In this work, we use rare-event simulation techniques to investigate attachment/detachment events at kink sites of a NaCl crystal in water. We elucidate the desolvation mechanism and present an optimized reaction coordinate, which involves one solute collective variable and one solvent collective variable. The attachment/detachment pathways for Na+ and Cl- are qualitatively similar, with quantitative differences that we attribute to different ion sizes and solvent coordination. The attachment barriers primarily result from kink site desolvation, while detachment barriers largely result from breaking ion-crystal bonds. We compute ion detachment rates from kink sites and compare with results from an independent study. We anticipate that the reaction coordinate and desolvation mechanism identified in this work may be applicable to other alkali halides.

Recent theories and simulations suggest that molecular additives can bind to the surfaces of nuclei, lower the surface energy, and accelerate nucleation. Experiments have shown that oligomeric and polymeric additives can also modify nucleation rates of proteins, ice, and minerals; however, general design principles for oligomeric or polymeric promoters do not yet exist. Here we investigate oligomeric additives for which each segment of the oligomer can bind to surfaces of nuclei. We use semigrand canonical Monte Carlo simulations in a Potts lattice gas model to study the effects of oligomer chain length, volume fraction, and binding strength. We find that increasing each of those parameters lowers the nucleation barrier. At extremely low oligomer concentrations, the nucleation kinetics can be modeled as though each oligomer is a heterogeneous nucleation site in solution.

On the occasion of Alexis T. Bell’s fiftieth year at Berkeley, we are honored to discuss a few aspects of his extensive contributions to catalysis, reaction engineering, and understanding of molecular-scale structure in catalytic processes. The illustrations provided here help reveal some of his traits most valued by our community: a drive to employ the best methods of instrumentational and computational analysis available; the instinct to search for the essence of the most important problems at hand, and the skill to write about them with exceptional clarity; and the formation and nurturing of collaborative teams to focus on the most essential questions.

Amorphous materials are widely used as components of solid catalysts and have been the subject of much applied research. In some instances, their catalytic performance is demonstrably superior to that of their crystalline counterparts, due in part to their greater flexibility. Amorphous or disordered phases can also be generated from crystalline phases under reaction conditions, and thus, ex situ observations of long-range order may provide an incomplete or misleading picture. Until recently, theorists and experimentalists have mostly neglected these important materials in fundamental studies, preferring instead to study “well-defined” (often crystalline) catalysts that are potentially more tractable and amenable to computational modeling of their structure–activity relationships. The amorphous materials were assumed to be simply nonuniform versions of compositionally similar materials with long-range order, having the same key features at short and medium length scales. In this Perspective, shortcomings ...

Almost all molecules are non-centrosymmetric, which produces interaction anisotropy within a crystal lattice. This anisotropy generates multiple types of kink sites on each crystal step and repeating patterns of rows with different growth units from the perspective of the lattice interaction environment, even for pure molecular crystals. As a result, unstable edge rows may be generated that dissolve under conditions of crystal growth. A method to account for edge surface structures, considering such effects, is required to accurately model the step velocity, which is vital for a mechanistic description of crystal growth. We classify both thermodynamic and kinetic contributions to step row instability and develop expressions for kink densities and step velocities that capture these important non-centrosymmetric phenomena. To demonstrate the utility of our framework, we consider in depth the case of an alternating-row A–B step. Our mechanistic predictions compare favorably to kinetic Monte Carlo simulations...

Free energies of crystals computed using a center of mass constraint require a finite-size correction, as shown in previous work by Polson et al. [J. Chem. Phys. 112, 5339-5342 (2000)]. Their reference system is an Einstein crystal with equal spring constants. In this paper, we extend the work of Polson et al. [J. Chem. Phys. 112, 5339-5342 (2000)] to the case of differing spring constants. The generalization is convenient for constraining the center of mass in crystals with atoms of differing masses, and it helps to optimize the free energy calculations. To test the theory, we compare the free energies of LiI and NaCl crystals from calculations with differing spring constants to those computed using equal spring constants. Using these center of mass finite size corrections, we compute the true free energies of these crystals for different system sizes to eliminate the intrinsic finite-size effects. These calculations help demonstrate the size of these finite-size corrections relative to other contributions to the absolute free energy of the crystals.

For disordered catalysts such as atomically dispersed "single-atom" metals on amorphous silica, the active sites inherit different properties from their quenched-disordered local environments. The observed kinetics are site-averages, typically dominated by a small fraction of highly active sites. Standard sampling methods require expensive ab initio calculations at an intractable number of sites to converge on the site-averaged kinetics. We present a new method that efficiently estimates the site-averaged turnover frequency (TOF). The new estimator uses the same importance learning algorithm [Vandervelden et al., React. Chem. Eng. 5, 77 (2020)] that we previously used to compute the site-averaged activation energy. We demonstrate the method by computing the site-averaged TOF for a simple disordered lattice model of an amorphous catalyst. The results show that with the importance learning algorithm, the site-averaged TOF and activation energy can now be obtained concurrently with orders of magnitude reduction in required ab initio calculations.

Lattice-switch Monte Carlo and the related diabat methods have emerged as efficient and accurate ways to compute free energy differences between polymorphs. In this work, we introduce a one-to-one mapping from the reference positions and displacements in one molecular crystal to the positions and displacements in another. Two features of the mapping facilitate lattice-switch Monte Carlo and related diabat methods for computing polymorph free energy differences. First, the mapping is unitary so that its Jacobian does not complicate the free energy calculations. Second, the mapping is easily implemented for molecular crystals of arbitrary complexity. We demonstrate the mapping by computing free energy differences between polymorphs of benzene and carbamazepine. Free energy calculations for thermodynamic cycles, each involving three independently computed polymorph free energy differences, all return to the starting free energy with a high degree of precision. The calculations thus provide a force field independent validation of the method and allow us to estimate the precision of the individual free energy differences.

In ethylene polymerization by the Phillips catalyst, inorganic Cr(II) sites are believed to be activated by reaction with ethylene to form (alkyl)CrIII sites, in a process that takes about 1 h at ca. 373 K. The detailed mechanism of this spontaneous self-initiation has long remained unknown. It must account both for the formation of the first Cr–C bond and for the one-electron oxidation of Cr(II) to Cr(III). In this study, we used density functional theory to investigate a two-step initiation mechanism by which ethylene oxidative addition leads first to various (organo)CrIV sites, and subsequent Cr–C bond homolysis gives (organo)CrIII sites capable of polymerizing ethylene. Pathways involving spin crossing, C–H oxidative addition, H atom transfer, and Cr–C bond homolytic cleavage were explored using a chromasiloxane cluster model. In particular, we used classical variational transition theory to compute free energy barriers and estimate rates for bond homolysis. A viable route to a four-coordinate bis(alk...

Reaction coordinates are integral to several classic rate theories that can (a) predict kinetic trends across conditions and homologous reactions, (b) extract activation parameters with a clear physical interpretation from experimental rates, and (c) enable efficient calculations of free energy barriers and rates. New trajectory-based rare events methods can provide rates directly from dynamical trajectories without a reaction coordinate. Trajectory-based frameworks can also generate ideal (but abstract) reaction coordinates such as committors and eigenfunctions of the master equation. However, rates and mechanistic insights obtained from trajectory-based methods and abstract coordinates are not readily generalized across simulation conditions or reaction families. We discuss methods for identifying physically meaningful reaction coordinates, including committor analysis, variational transition state theory, Kramers–Langer–Berezhkovskii–Szabo theory, and statistical inference methods that can use path sampling data to screen, mix, and optimize thousands of trial coordinates. Special focus is given to likelihood maximization and inertial likelihood maximization approaches.