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Abstract: The metastability limit can be defined as the average supersaturation at which nucleation first occurs when the supersaturation steadily increases under isothermal conditions. We present a quasi-steady stochastic model for such experiments in terms of the nucleation free energy barrier at some reference supersaturation and in terms of a Damkohler number involving the kinetic prefactor, the observation volume, and the supersaturation schedule as a function of time. Classical nucleation theory provides a model for the dependence of the nucleation free energy barrier on the slowly increasing supersaturation. We derive the average critical supersaturation as a function of two dimensionless parameters and the type of supersaturation schedule. For slow supersaturation rates, the metastable zone width expression for one schedule collapses to earlier expressions from Volmer, Kashchiev, Verdoes, and van Rosmalen, which arose from alternative definitions of the metastability limit. Our findings show that isothermal metastable zone width experiments cannot be performed slowly enough to attain the limit where homogeneous nucleation occurs at the equilibrium boundary of the metastable zone. We also suggest a simple linear regression strategy to extract kinetic parameters for nucleation from isothermal metastability limit experiments. [Copyright &y& Elsevier]

Asparagine deamidation is a decisive event in chemotherapy-induced apoptosis and a major obstacle in the formulation of monoclonal antibodies. Despite the importance of deamidation, little is known about the elementary reactions involved. B3LYP/6-31+G(d,p)/COSMO-RS calculations were used to obtain stable structures and transition states for a network of reactions. Calculated rate constants were incorporated into a kinetic model of the pH dependence and compared to a pseudo-steady-state model. At low pH, the calculations show that deamidation occurs by direct acid-catalyzed hydrolysis to aspartate. At neutral to basic pH, deamidation proceeds by the initial formation of a tetrahedral intermediate. The intermediate can be converted to succinimide by two pathways and three rate-determining steps that shift in relative importance with pH. The calculated pH-dependent rate constant qualitatively agrees with the experimental pH dependence. The rate-determining transition state structures may help to understand chemotherapy-induced apoptosis and improve protein formulations. [ABSTRACT FROM AUTHOR]

For inertial reaction dynamics, a transition state theory rate constant obtained from an inaccurate reaction coordinate can be a posteriori corrected with reactive flux methods. In contrast, reaction coordinate errors in overdamped mean first passage time calculations cannot be a posteriori corrected. This work develops an overdamped version of the transmission coefficient. The calculation requires information from committor analyses and an estimate of the diffusivity along the committor coordinate. We illustrate the calculation for a simple two-dimensional potential that admits exact solutions. [ABSTRACT FROM AUTHOR]

Analyzes the binder-burnout kinetics of polyvinyl butyral from barium titanate platinum multilayer ceramic capacitors with platinum metal electrodes. Combination of thermogravimetric analysis with infrared spectroscopy; Use of heating cycles to evaluate the yield of capacitors.

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. [ABSTRACT FROM AUTHOR]

Amyloid fibrils are thought to grow by a two-step dock-lock mechanism. However, previous simulations of fibril formation (i) overlook the bi-molecular nature of the docking step and obtain rates with first-order units, or (ii) superimpose the docked and locked states when computing the potential of mean force for association and thereby muddle the docking and locking steps. Here, we developed a simple microkinetic model with separate locking and docking steps and with the appropriate concentration dependences for each step. We constructed a simple model comprised of chiral dumbbells that retains qualitative aspects of fibril formation. We used rare events methods to predict separate docking and locking rate constants for the model. The rate constants were embedded in the microkinetic model, with the microkinetic model embedded in a population balance model for "bottom-up" multiscale fibril growth rate predictions. These were compared to "top-down" results using simulation data with the same model and multiscale framework to obtain maximum likelihood estimates of the separate lock and dock rate constants. We used the same procedures to extract separate docking and locking rate constants from experimental fibril growth data. Our multiscale strategy, embedding rate theories, and kinetic models in conservation laws should help to extract docking and locking rate constants from experimental data or long molecular simulations with correct units and without compromising the molecular description. [ABSTRACT FROM AUTHOR]

One-dimensional (1D) nucleation is important in crystal growth, amyloid fibril formation, and supramolecular polymerization. The nucleation rate can be readily calculated, but there is no consensus on the critical length. In this work, we employ a splitting probability to derive an analytical expression for the critical length, which corresponds to a 50% survival probability. For a 1D nucleus on a crystal step, this critical length depends on the supersaturation (driving force) and is nearly independent of the kink (surface) energy. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The article discusses the research by Delley and colleagues which explores the proton transfer mechanism to explain the initiation mechanism of the Phillips polymerization catalyst. Topics discussed include kinds of transition state theory, such as density functional theory (DFT) and standard microkinetic modeling techniques, ethylene ligand which facilitates diene displacement, and ethylene polymerization.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This work reexamines seeded simulation results for NaCl nucleation from a supersaturated aqueous solution at 298.15 K and 1 bar pressure. We present a linear regression approach for analyzing seeded simulation data that provides both nucleation rates and uncertainty estimates. Our results show that rates obtained from seeded simulations rely critically on a precise driving force for the model system. The driving force vs. solute concentration curve need not exactly reproduce that of the real system, but it should accurately describe the thermodynamic properties of the model system. We also show that rate estimates depend strongly on the nucleus size metric. We show that the rate estimates systematically increase as more stringent local order parameters are used to count members of a cluster and provide tentative suggestions for appropriate clustering criteria. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Nucleation and crystal growth are important in material synthesis, climate modeling, biomineralization, and pharmaceutical formulation. Despite tremendous efforts, the mechanisms and kinetics of nucleation remain elusive to both theory and experiment. Here we investigate sodium chloride (NaCl) nucleation from supersaturated brines using seeded atomistic simulations, polymorph-specific order parameters, and elements of classical nucleation theory. We find that NaCl nucleates via the common rock salt structure. Ion desolvation--not diffusion--is identified as the limiting resistance to attachment. Two different analyses give approximately consistent attachment kinetics: diffusion along the nucleus size coordinate and reaction-diffusion analysis of approach-to-coexistence simulation data from Aragones et al. (J. Chem. Phys. 2012, 136, 244508). Our simulations were performed at realistic supersaturations to enable the first direct comparison to experimental nucleation rates for this system. The computed and measured rates converge to a common upper limit at extremely high supersaturation. However, our rate predictions are between 15 and 30 orders of magnitude too fast. We comment on possible origins of the large discrepancy. [ABSTRACT FROM AUTHOR]

The Pictet-Spengler reaction, which yields either a β-carboline or a tetrahydroquinoline product from an aromatic amine and an aldehyde, is widely utilized in plant alkaloid biosynthesis. Here we deconvolute the role that the biosynthetic enzyme strictosidine synthase plays in catalyzing the stereoselective synthesis of a β-carboline product. Notably, the rate-controlling step of the enzyme mechanism, as identified by the appearance of a primary kinetic isotope effect (KIE), is the rearomatization of a positively charged intermediate. The KIE of a nonenzymatic Pictet-Spengler reaction indicates that rearomatization is also rate-controlling in solution, suggesting that the enzyme does not significantly change the mechanism of the reaction. Additionally, the pH dependence of the solution and enzymatic reactions provides evidence for a sequence of acid-base catalysis steps that catalyze the Pictet-Spengler reaction. An additional acid-catalyzed step, most likely protonation of a carbinolamine intermediate, is also significantly rate controlling. We propose that this step is efficiently catalyzed by the enzyme. Structural analysis of a bisubstrate inhibitor bound to the enzyme suggests that the active site is exquisitely tuned to correctly orient the iminium intermediate for productive cyclization to form the diastereoselective product. Furthermore, ab initio calculations suggest the structures of possible productive transition states involved in the mechanism. Importantly, these calculations suggest that a spiroindolenine intermediate, often invoked in the Pictet-Spengler mechanism, does not occur. A detailed mechanism for enzymatic catalysis of the β-carboline product is proposed from these data. [ABSTRACT FROM AUTHOR]

This study presents a population balance model for the kinetics of nucleation and growth in covalent organic framework (COF) synthesis. The model incorporates second-order nucleation and first-order growth rates, consistent with proposals in the literature. Despite having non-linear terms, an implicit analytic solution is derived and then converted to explicit solutions for the monomer concentration and size distribution of COF flakes as a function of time. For experimental definitions of the induction time and the initial growth rate based on yield (y) vs time (t) curves, the model predicts power-law relationships: tind=0.409kN-1/3kG-2/3cA0-1 and dy/dtmax=0.965kN1/3kG2/3cA0, respectively. We discuss the implications for the interpretation of Arrhenius plots. We also discuss key discrepancies with experiments, including the predicted attainment of 100% yield instead of 30%-40% as observed and the value of the yield at the inflection point in the yield vs time curve. We suggest extensions to the model, including nucleation and growth kinetics with equilibrium solubility limitations and two-dimensional nucleation for the formation of multilayer COF particles., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Many polymer upcycling efforts aim to convert plastic waste into high-value liquid hydrocarbons. However, the subsequent cleavage of middle distillates to light gases can be problematic. The reactor often contains a vapor phase (light gases and middle distillates) and a liquid phase (molten polymers and waxes with a suspended or dissolved catalyst). Because the catalyst resides in the liquid phase, middle distillates that partition into the vapor phase are protected against further cleavage into light gases. In this paper, we consider a simple reactive separation strategy, in which a gas outflow removes the volatile products as they form. We combine vapor-liquid equilibrium models and population balance equations (PBEs) to describe polymer upcycling in a two-phase semibatch reactor. The results suggest that the temperature, headspace volume, and flow rate of the reactor can be used to tune selectivity toward the middle distillates, in addition to the molecular mechanism of catalysis. We anticipate that two-phase reactor models will be important in many polymer upcycling processes and that reactive separation strategies will provide ways to boost the yield of the desired products in these cases.

Antifreeze proteins (AFPs) bind to the ice-water surface and prevent ice growth at temperatures below 0 °C through a Gibbs-Thomson effect. Each adsorbed AFP creates a metastable depression on the surface that locally resists ice growth, until ice engulfs the AFP. We recently predicted the susceptibility to engulfment as a function of AFP size, distance between AFPs, and supercooling [ J. Chem. Phys. 2023, 158, 094501]. For an ensemble of AFPs adsorbed on the ice surface, the most isolated AFPs are the most susceptible, and when an isolated AFP gets engulfed, its former neighbors become more isolated and more susceptible to engulfment. Thus, an initial engulfment event can trigger an avalanche of subsequent engulfment events, leading to a sudden surge of unrestrained ice growth. This work develops a model to predict the supercooling at which the first engulfment event will occur for an ensemble of randomly distributed AFP pinning sites on an ice surface. Specifically, we formulate an inhomogeneous survival probability that accounts for the AFP coverage, the distribution of AFP neighbor distances, the resulting ensemble of engulfment rates, the ice surface area, and the cooling rate. We use the model to predict thermal hysteresis trends and compare with experimental data.

Single-atom centers on amorphous supports include catalysts for polymerization, partial oxidation, metathesis, hydrogenolysis, and more. The disordered environment makes each site different, and the kinetics exponentially magnifies these differences to make ab initio site-averaged kinetics calculations extremely difficult. This work extends the importance learning algorithm for efficient and precise site-averaged kinetics estimates to ab initio calculations and multistep reaction mechanisms. Specifically, we calculate site-averaged proton transfer relaxation rates on an ensemble of cluster models representing Brønsted acid sites on silica-alumina. We include direct and water-assisted proton transfer pathways and simultaneously estimate the water adsorption and activation enthalpies for forward and backward proton transfers. We use density functional theory (DFT) to obtain a site-averaged rate, somewhat like a turnover frequency, for the proton transfer relaxation rate. Finally, we show that importance learning can provide orders-of-magnitude acceleration over standard sampling methods for site-averaged rate calculations in cases where the rate is dominated by a few highly active sites.

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.

C-H/Et-Al exchange in zirconium-catalyzed reactions of saturated hydrocarbons and AlEt 3 affords versatile organoaluminum compounds and ethane. The grafting of commercially available Zr(O t Bu) 4 on silica/alumina gives monopodal ≡SiO-Zr(O t Bu) 3 surface pre-catalyst sites that are activated in situ by ligand exchange with AlEt 3 . The catalytic C-H alumination of dodecane at 150 °C followed by quenching in air affords n -dodecanol as the major product, revealing selectivity for methyl group activation. Shorter hydrocarbon or alcohol products were not detected under these conditions. Catalytic reactions of cyclooctane and AlEt 3 , however, afford ring-opened products, indicating that C-C bond cleavage occurs readily in methyl group-free reactants. This selectivity for methyl group alumination enables the C-H alumination of polyethylenes, polypropylene, polystyrene, and poly-α-olefin oils without significant chain deconstruction. In addition, the smallest hydrocarbon, methane, undergoes selective mono-alumination under solvent-free catalytic conditions, providing a direct route to Al-Me species.

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.

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.

Solid-fluid phase equilibria are difficult to predict in simulations because bound degrees of freedom in the crystal phase must be converted to free translations and rotations in the fluid phase. Here, we avoid the solid-to-fluid transformation step by starting with chemical potentials for two reference systems, one for the fluid phase and one for the solid phase. For the solid, we start from the Einstein crystal and transform to the fully interacting molecular crystal. For the fluid phase, we introduce a new reference system, the "centroid," and then transform to gas phase molecules. We illustrate the new calculations by predicting the sublimation vapor pressure of succinic acid in the temperature range of 300 K-350 K.

Polymorph free-energy differences are critical to several applications. A recently proposed diabat interpolation framework estimated free-energy differences between polymorphs by quadratic interpolation of diabats. This work extends the Zwanzig-Bennett relation to the NPT ensemble so that the diabats directly give Gibbs free-energy differences. We also demonstrate how the approach can be used in cases where the diabats are not parabolic. We illustrate the diabat method for Gibbs free-energy difference of zirconium (BCC and HCP phases) and compare it with the conventional lattice switch Monte Carlo approach.

The freezing of water affects the processes that determine Earth's climate. Therefore, accurate weather and climate forecasts hinge on good predictions of ice nucleation rates. Such rate predictions are based on extrapolations using classical nucleation theory, which assumes that the structure of nanometre-sized ice crystallites corresponds to that of hexagonal ice, the thermodynamically stable form of bulk ice. However, simulations with various water models find that ice nucleated and grown under atmospheric temperatures is at all sizes stacking-disordered, consisting of random sequences of cubic and hexagonal ice layers. This implies that stacking-disordered ice crystallites either are more stable than hexagonal ice crystallites or form because of non-equilibrium dynamical effects. Both scenarios challenge central tenets of classical nucleation theory. Here we use rare-event sampling and free energy calculations with the mW water model to show that the entropy of mixing cubic and hexagonal layers makes stacking-disordered ice the stable phase for crystallites up to a size of at least 100,000 molecules. We find that stacking-disordered critical crystallites at 230 kelvin are about 14 kilojoules per mole of crystallite more stable than hexagonal crystallites, making their ice nucleation rates more than three orders of magnitude higher than predicted by classical nucleation theory. This effect on nucleation rates is temperature dependent, being the most pronounced at the warmest conditions, and should affect the modelling of cloud formation and ice particle numbers, which are very sensitive to the temperature dependence of ice nucleation rates. We conclude that classical nucleation theory needs to be corrected to include the dependence of the crystallization driving force on the size of the ice crystallite when interpreting and extrapolating ice nucleation rates from experimental laboratory conditions to the temperatures that occur in clouds.

According to Classical Nucleation Theory (CNT), the transition from liquid to crystal occurs in a single activated step with a transition state controlled by the size of the crystal embryo. This picture has been challenged in the last two decades by several reports of two-step crystallization processes in which the liquid first produces pre-ordered or dense domains, within which the crystal nucleates in a second step. Pre-ordering preceding crystal nucleation has been recently reported in simulations of ice crystallization, raising the question of whether the mechanism of ice nucleation involves two steps. In this paper, we investigate the heterogeneous nucleation of ice on carbon surfaces. We use molecular simulations with efficient coarse-grained models combined with rare event sampling methods and free energy calculations to elucidate the role of pre-ordering of liquid water at the carbon surface in the reaction coordinate for heterogeneous nucleation. We find that ice nucleation proceeds through a classical mechanism, with a single barrier between liquid and crystal. The reaction coordinate that determines the crossing of the nucleation barrier is the size of the crystal nucleus, as predicted by CNT. Wetting of the critical ice nuclei within pre-ordered domains decreases the nucleation barrier, increasing the nucleation rates. The preferential pathway for crystallization involves the early creation of pre-ordered domains that are the birthplace of the ice crystallites but do not represent a minimum in the free energy pathway from liquid to ice. We conclude that a preferential pathway through an intermediate-order precursor does not necessarily result in a two-step mechanism.

The copper hydride clusters [Cu14 H12 (phen)6(PPh3)4][X]2 (X=Cl or OTf; OTf=trifluoromethanesulfonate, phen=1,10-phenanthroline) are obtained in good yields by the reaction of [(Ph3P)CuH]6 with phen, in the presence of a halide or pseudohalide source. The complex [Cu14H12 (phen)6(PPh3)4][Cl]2 reacts with CO2 in CH2Cl2 , in the presence of excess Ph3 P, to form the formate complex [(Ph3P)2Cu(κ(2)-O2CH)], along with [(phen)(Ph3 P)CuCl]., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The reaction mechanism for nitrous oxide decomposition has been studied on hydrated and dehydrated mononuclear iron sites in Fe-ZSM-5 using density functional theory. In total, 46 different surface species with different spin states (spin multiplicity M(S) = 4 or 6) and 63 elementary reactions were considered. Heats of adsorption, activation barriers, reaction rates, and minimum energy pathways were determined. The approximate minimum energy pathways and transition states were calculated using the "growing string method" and a modified "dimer method". Spin surface crossing (e.g., O(2) desorption) was considered. The minimum potential energy structure on the seam of two potential energy surfaces was determined with a multiplier penalty function algorithm by Powell and approximate rates of spin surface crossings were calculated. It was found that nitrous oxide decomposition is first order with respect to nitrous oxide concentration and zero order with respect to oxygen concentration. Water impurities in the gas stream have a strong inhibiting effect. In the concentration range of 1-100 ppb, the presence of water vapor influences the surface composition and the apparent rate coefficient. This is especially relevant in the temperature range of 600-700 K where most experimental kinetic studies are performed. Apparent activation barriers determined over this temperature range vary from 28.4 (1 ppb H(2)O) to 54.8 kcal/mol (100 ppb H(2)O). These results give an explanation why different research groups and different catalyst pretreatments often result in very different activation barriers and preexponential factors. Altogether perfect agreement with experimental results could be achieved.