Diffusion-Limited Kinetics in Reactive Systems.

A proper representation of chemical kinetics is vital to understanding, modeling, and optimizing many important chemical processes. In liquid and surface phases, where diffusion is slow, the rate at which the reactants diffuse together limits the overall rate of many elementary reactions. Commonly, the textbook Smoluchowski theory is utilized to estimate effective rate coefficients in the liquid phase. On surfaces, modelers commonly resort to much more complex and expensive Kinetic Monte Carlo (KMC) simulations. Here, we extend the Smoluchowski model to allow the diffusing species to undergo chemical reactions and derive analytical formulas for the diffusion-limited rate coefficients for 3D, 2D, and 2D/3D interface cases. With these equations, we are able to demonstrate that when species react faster than they diffuse they can react orders of magnitude faster than predicted by Smoluchowski theory, through what we term "the reactive transport effect". We validate the derived steady-state equations against particle Monte Carlo (PMC) simulations, KMC simulations, and non-steady-state solutions. Furthermore, using PMC and KMC simulations, we propose corrections that agree with all limits and the computed data for the 2D and 2D/3D interface steady-state equations, accounting for unique limitations in the associated derived equations. Additionally, we derive equations to handle couplings between diffusion-limited rate coefficients in reaction networks. We believe these equations should make it possible to run much more accurate mean-field simulations of liquids, surfaces, and liquid-surface interfaces accounting for diffusion limitations and the reactive transport effect.

The photoionization of methoxymethanol: Fingerprinting a reactive C2 oxygenate in a complex reactive mixture.

Methoxymethanol (CH3OCH2OH) is a reactive C2 ether-alcohol that is formed by coupling events in both heterogeneous and homogeneous systems. It is found in complex reactive environments-for example those associated with catalytic reactors, combustion systems, and liquid-phase mixtures of oxygenates. Using tunable synchrotron-generated vacuum-ultraviolet photons between 10.0 and 11.5 eV, we report on the photoionization spectroscopy of methoxymethanol. We determine that the lowest-energy photoionization process is the dissociative ionization of methoxymethanol via H-atom loss to produce [C2H5O2]+, a fragment cation with a mass-to-charge ratio (m/z) = 61.029. We measure the appearance energy of this fragment ion to be 10.24 ± 0.05 eV. The parent cation is not detected in the energy range examined. To elucidate the origin of the m/z = 61.029 (C2H5O2) fragment, we used automated electronic structure calculations to identify key stationary points on the cation potential energy surface and compute conformer-specific microcanonical rate coefficients for the important unimolecular processes. The calculated H-atom dissociation pathway results in a [C2H5O2]+ fragment appearance at 10.21 eV, in excellent agreement with experimental results.

Evaluation of Rate Coefficients in the Gas Phase Using Machine-Learned Potentials.

We assess the capability of machine-learned potentials to compute rate coefficients by training a neural network (NN) model and applying it to describe the chemical landscape on the C5H5 potential energy surface, which is relevant to molecular weight growth in combustion and interstellar media. We coupled the resulting NN with an automated kinetics workflow code, KinBot, to perform all necessary calculations to compute the rate coefficients. The NN is benchmarked exhaustively by evaluating its performance at the various stages of the kinetics calculations: from the electronic energy through the computation of zero point energy, barrier heights, entropic contributions, the portion of the PES explored, and finally the overall rate coefficients as formulated by transition state theory.

Sulfur (3P) Reaction with Conjugated Dienes Gives Cyclization to Thiophenes under Single Collision Conditions.

We combine crossed-beam velocity map imaging with high-level ab initio/transition state theory modeling of the reaction of S(3P) with 1,3-butadiene and isoprene under single collision conditions. For the butadiene reaction, we detect both H and H2 loss from the initial adduct, and from reaction with isoprene, we see both H loss and methyl loss. Theoretical calculations confirm these arise following intersystem crossing to the singlet surface forming long-lived intermediates. For the butadiene reaction, these lose H2 to form thiophene as the dominant channel, H to form the detected 2H-thiophenyl radical, or ethene, giving thioketene. For isoprene, additional reaction products are suggested by theory, including the observed H and methyl loss radicals, but also methyl thiophene, thioformaldehyde, and thioketene. The results for S(3P) + 1,3-butadiene, showing direct cyclization to the aromatic product and yielding few bimolecular product channels, are in striking contrast to those for the analogous O(3P) reaction.

Pynta─An Automated Workflow for Calculation of Surface and Gas-Surface Kinetics.

Many important industrial processes rely on heterogeneous catalytic systems. However, given all possible catalysts and conditions of interest, it is impractical to optimize most systems experimentally. Automatically generated microkinetic models can be used to efficiently consider many catalysts and conditions. However, these microkinetic models require accurate estimation of many thermochemical and kinetic parameters. Manually calculating these parameters is tedious and error prone, involving many interconnected computations. We present Pynta, a workflow software for automating the calculation of surface and gas-surface reactions. Pynta takes the reactants, products, and atom maps for the reactions of interest, generates sets of initial guesses for all species and saddle points, runs all optimizations, frequency, and IRC calculations, and computes the associated thermochemistry and rate coefficients. It is able to consider all unique adsorption configurations for both adsorbates and saddle points, allowing it to handle high index surfaces and bidentate species. Pynta implements a new saddle point guess generation method called harmonically forced saddle point searching (HFSP). HFSP defines harmonic potentials based on the optimized adsorbate geometries and which bonds are breaking and forming that allow initial placements to be optimized using the GFN1-xTB semiempirical method to create reliable saddle point guesses. This method is reaction class agnostic and fast, allowing Pynta to consider all possible adsorbate site placements efficiently. We demonstrate Pynta on 11 diverse reactions involving monodenate, bidentate, and gas-phase species, many distinct reaction classes, and both a low and a high index facet of Cu. Our results suggest that it is very important to consider reactions between adsorbates adsorbed in all unique configurations for interadsorbate group transfers and reactions on high index surfaces.

Multifidelity Neural Network Formulations for Prediction of Reactive Molecular Potential Energy Surfaces.

This paper focuses on the development of multifidelity modeling approaches using neural network surrogates, where training data arising from multiple model forms and resolutions are integrated to predict high-fidelity response quantities of interest at lower cost. We focus on the context of quantum chemistry and the integration of information from multiple levels of theory. Important foundations include the use of symmetry function-based atomic energy vector constructions as feature vectors for representing structures across families of molecules and single-fidelity neural network training capabilities that learn the relationships needed to map feature vectors to potential energy predictions. These foundations are embedded within several multifidelity topologies that decompose the high-fidelity mapping into model-based components, including sequential formulations that admit a general nonlinear mapping across fidelities and discrepancy-based formulations that presume an additive decomposition. Methodologies are first explored and demonstrated on a pair of simple analytical test problems and then deployed for potential energy prediction for C5H5 using B2PLYP-D3/6-311++G(d,p) for high-fidelity simulation data and Hartree-Fock 6-31G for low-fidelity data. For the common case of limited access to high-fidelity data, our computational results demonstrate that multifidelity neural network potential energy surface constructions achieve roughly an order of magnitude improvement, either in terms of test error reduction for equivalent total simulation cost or reduction in total cost for equivalent error.

The Identity and Chemistry of C7H7 Radicals Observed during Soot Formation.

We used aerosol mass spectrometry coupled with tunable synchrotron photoionization to measure radical and closed-shell species associated with particle formation in premixed flames and during pyrolysis of butane, ethylene, and methane. We analyzed photoionization (PI) spectra for the C7H7 radical to identify the isomers present during particle formation. For the combustion and pyrolysis of all three fuels, the PI spectra can be fit reasonably well with contributions from four radical isomers: benzyl, tropyl, vinylcyclopentadienyl, and o-tolyl. Although there are significant experimental uncertainties in the isomeric speciation of C7H7, the results clearly demonstrate that the isomeric composition of C7H7 strongly depends on the combustion or pyrolysis conditions and the fuel or precursors. Fits to the PI spectra using reference curves for these isomers suggest that all of these isomers may contribute to m/z 91 in butane and methane flames, but only benzyl and vinylcyclopentadienyl contribute to the C7H7 isomer signal in the ethylene flame. Only tropyl and benzyl appear to play a role during pyrolytic particle formation from ethylene, and only tropyl, vinylcyclopentadienyl, and o-tolyl appear to participate during particle formation from butane pyrolysis. There also seems to be a contribution from an isomer with an ionization energy below 7.5 eV for the flames but not for the pyrolysis conditions. Kinetic models with updated and new reactions and rate coefficients for the C7H7 reaction network predict benzyl, tropyl, vinylcyclopentadienyl, and o-tolyl to be the primary C7H7 isomers and predict negligible contributions from other C7H7 isomers. These updated models provide better agreement with the measurements than the original versions of the models but, nonetheless, underpredict the relative concentrations of tropyl, vinylcyclopentadienyl, and o-tolyl in both flames and pyrolysis and overpredict benzyl in pyrolysis. Our results suggest that there are additional important formation pathways for the vinylcyclopentadienyl, tropyl, and o-tolyl radicals and/or loss pathways for the benzyl radical that are currently unaccounted for in the present models.

Unimolecular Reactions of 2,4-Dimethyloxetanyl Radicals.

Alkyl-substituted oxetanes are cyclic ethers formed via unimolecular reactions of QOOH radicals produced via a six-membered transition state in the preceding isomerization step of organic peroxy radicals, ROO. Owing to radical isomer-specific formation pathways, cyclic ethers are unambiguous proxies for inferring QOOH reaction rates. Therefore, accounting for subsequent oxidation of cyclic ethers is important in order to accurately determine rates for QOOH → products. Cyclic ethers can react via unimolecular reaction (ring-opening) or via bimolecular reaction with O2 to form cyclic ether-peroxy adducts. The computations herein provide reaction mechanisms and theoretical rate coefficients for the former type in order to determine competing pathways for the cyclic ether radicals. Rate coefficients of unimolecular reactions of 2,4-dimethyloxetanyl radicals were computed using master equation modeling from 0.01 to 100 atm and from 300 to 1000 K. Coupled-cluster methods were utilized for stationary-point energy calculations, and uncertainties in the computed rate coefficients were accounted for using variation in barrier heights and in well depths. The potential energy surfaces reveal accessible channels to several species via crossover reactions, such as 2-methyltetrahydrofuran-5-yl and pentanonyl isomers. For the range of temperature over which 2,4-dimethyloxetane forms during n-pentane oxidation, the following are the major channels: 2,4-dimethyloxetan-1-yl → acetaldehyde + allyl, 2,4-dimethyloxetan-2-yl → propene + acetyl, and 2,4-dimethyloxetan-3-yl → 3-butenal + methyl, or, 1-penten-3-yl-4-ol. Well-skipping reactions were significant in a number of channels and also exhibited a markedly different pressure dependence. The calculations show that rate coefficients for ring-opening are approximately an order of magnitude lower for the tertiary 2,4-dimethyloxetanyl radicals than for the primary and secondary 2,4-dimethyloxetanyl radicals. Unlike for reactions of the corresponding ROO radicals, however, unimolecular rate coefficients are independent of the stereochemistry. Moreover, rate coefficients of cyclic ether radical ring-opening are of the same order of magnitude as O2 addition, underscoring the point that a competing network of reactions is necessary to include for accurate chemical kinetics modeling of species profiles for cyclic ethers.

Comprehensive Kinetics on the C7H7 Potential Energy Surface under Combustion Conditions.

The automated kinetics workflow code, KinBot, was used to explore and characterize the regions of the C7H7 potential energy surface that are relevant to combustion environments and especially soot inception. We first explored the lowest-energy region, which includes the benzyl, fulvenallene + H, and cyclopentadienyl + acetylene entry points. We then expanded the model to include two higher-energy entry points, vinylpropargyl + acetylene and vinylacetylene + propargyl. The automated search was able to uncover the pathways from the literature. In addition, three important new routes were discovered: a lower-energy pathway connecting benzyl with vinylcyclopentadienyl, a decomposition mechanism from benzyl that results in side-chain hydrogen atom loss to produce fulvenallene + H, and shorter and lower energy routes to the dimethylene-cyclopentenyl intermediates. We systematically reduced the extended model to a chemically relevant domain composed of 63 wells, 10 bimolecular products, 87 barriers, and 1 barrierless channel and constructed a master equation using the CCSD(T)-F12a/cc-pVTZ//ωB97X-D/6-311++G(d,p) level of theory to provide rate coefficients for chemical modeling. Our calculated rate coefficients show excellent agreement with measured ones. We also simulated concentration profiles and calculated branching fractions from the important entry points to provide an interpretation of this important chemical landscape.

Automated Reaction Kinetics of Gas-Phase Organic Species over Multiwell Potential Energy Surfaces.

Automation of rate-coefficient calculations for gas-phase organic species became possible in recent years and has transformed how we explore these complicated systems computationally. Kinetics workflow tools bring rigor and speed and eliminate a large fraction of manual labor and related error sources. In this paper we give an overview of this quickly evolving field and illustrate, through five detailed examples, the capabilities of our own automated tool, KinBot. We bring examples from combustion and atmospheric chemistry of C-, H-, O-, and N-atom-containing species that are relevant to molecular weight growth and autoxidation processes. The examples shed light on the capabilities of automation and also highlight particular challenges associated with the various chemical systems that need to be addressed in future work.

Sella, an Open-Source Automation-Friendly Molecular Saddle Point Optimizer.

We present a new algorithm for the optimization of molecular structures to saddle points on the potential energy surface using a redundant internal coordinate system. This algorithm automates the procedure of defining the internal coordinate system, including the handling of linear bending angles, for example, through the addition of dummy atoms. Additionally, the algorithm supports constrained optimization using the null-space sequential quadratic programming formalism. Our algorithm determines the direction of the reaction coordinate through iterative diagonalization of the Hessian matrix and does not require evaluation of the full Hessian matrix. Geometry optimization steps are chosen using the restricted step partitioned rational function optimization method, and displacements are realized using a high-performance geodesic stepping algorithm. This results in a robust and efficient optimization algorithm suitable for use in automated frameworks. We have implemented our algorithm in Sella, an open-source software package designed to optimize atomic systems to saddle point structures. We also introduce a new benchmark test comprising 500 molecular structures that approximate saddle point geometries and show that our saddle point optimization algorithm outperforms the algorithms implemented in several leading electronic structure theory packages.

Unimolecular isomerisation of 1,5-hexadiyne observed by threshold photoelectron photoion coincidence spectroscopy.

The unimolecular isomerisation of the prompt propargyl + propargyl "head-to-head" adduct, 1,5-hexadiyne, to fulvene and benzene by the 3,4-dimethylenecyclobut-1-ene (DMCB) intermediate (all C6H6) was studied in the high-pressure limit by threshold photoelectron (TPE) spectroscopy. TPE spectra (TPES) were recorded with photoelectron photoion coincidence spectroscopy using synchrotron vacuum ultraviolet radiation. Reference TPES, obtained using pure compounds or judiciously extracted from the pyrolysis data, served as basis functions for pyrolysis quantification. From these spectra, we measured a revised fulvene ionisation energy of 8.401 ± 0.005 eV. Temperature-dependent pyrolysis spectra were decomposed using these basis functions. The basis function coefficients were converted to product yields relying on assumed integral threshold photoionisation cross sections obtained by three, partially mutually exclusive sets of assumptions. Thus, the product yields of DMCB, fulvene, and benzene have been established, as well as their uncertainty. The derived mole fractions are consistent with modeling based on the C6H6 potential and RRKM master equation model of Miller and Klippenstein [J. Phys. Chem. A, 2003, 107, 7783]. Although our results are fully consistent with the parallel isomerisation pathways to benzene and fulvene found by Miller and Klippenstein, we observe the onset of fulvene at a lower temperature than that of the onset of benzene, in agreement with the master equation model but in contrast to the previous experiments of Stein et al. [Proc. Combust. Inst., 1990, 23, 85]. This work promotes the use of photoion mass-selected threshold photoelectron spectroscopy as a rapid, sensitive, isomer-selective, and quantitative detection tool among the panoply of established analytical techniques.

Formation of Organic Acids and Carbonyl Compounds in n-Butane Oxidation via γ-Ketohydroperoxide Decomposition.

A crucial chain-branching step in autoignition is the decomposition of ketohydroperoxides (KHP) to form an oxy radical and OH. Other pathways compete with chain-branching, such as "Korcek" dissociation of γ-KHP to a carbonyl and an acid. Here we characterize the formation of a γ-KHP and its decomposition to formic acid+acetone products from observations of n-butane oxidation in two complementary experiments. In jet-stirred reactor measurements, KHP is observed above 590 K. The KHP concentration decreases with increasing temperature, whereas formic acid and acetone products increase. Observation of characteristic isotopologs acetone-d3 and formic acid-d0 in the oxidation of CH3 CD2 CD2 CH3 is consistent with a Korcek mechanism. In laser-initiated oxidation experiments of n-butane, formic acid and acetone are produced on the timescale of KHP removal. Modelling the time-resolved production of formic acid provides an estimated upper limit of 2 s-1 for the rate coefficient of KHP decomposition to formic acid+acetone.

Stereoisomer-dependent unimolecular kinetics of 2,4-dimethyloxetanyl peroxy radicals.

2,4,dimethyloxetane is an important cyclic ether intermediate that is produced from hydroperoxyalkyl (QOOH) radicals in the low-temperature combustion of n-pentane. However, the reaction mechanisms and rates of consumption pathways remain unclear. In the present work, the pressure- and temperature-dependent kinetics of seven cyclic ether peroxy radicals, which stem from 2,4,dimethyloxetane via H-abstraction and O2 addition, were determined. The automated kinetic workflow code, KinBot, was used to model the complexity of the chemistry in a stereochemically resolved manner and solve the resulting master equations from 300-1000 K and from 0.01-100 atm. The main conclusions from the calculations include (i) diastereomeric cyclic ether peroxy radicals show significantly different reactivities, (ii) the stereochemistry of the peroxy radical determines which QOOH isomerization steps are possible, (iii) conventional QOOH decomposition pathways, such as cyclic ether formation and HO2 elimination, compete with ring-opening reactions, which primarily produce OH radicals, the outcome of which is sensitive to stereochemistry. Ring-opening reactions lead to unique products, such as unsaturated, acyclic peroxy radicals, that form direct connections with species present in other chemical kinetics mechanisms through "cross-over" reactions that may complicate the interpretation of experimental results from combustion of n-pentane and, by extension, other alkanes. For example, one cross-over reaction involving 1-hydroperoxy-4-pentanone-2-yl produces 2-(hydroperoxymethyl)-3-butanone-1-yl, which is an iso-pentane-derived ketohydroperoxide (KHP). At atmospheric pressure, the rate of chemical reactions of all seven peroxy radicals compete with that of collisional stabilization, resulting in well-skipping reactions. However, at 100 atm, only one out of seven peroxy radicals undergoes significant well-skipping reactions. The rates produced from the master equation calculations provide the first foundation for the development of detailed sub-mechanisms for cyclic ether intermediates. In addition, analysis of the complex reaction mechanisms of 2,4-dimethyloxetane-derived peroxy radicals provides insights into the effects of stereoisomers on reaction pathways and product yields.

A theoretical investigation of the hydrolysis of uranium hexafluoride: the initiation mechanism and vibrational spectroscopy.

Depleted uranium hexafluoride (UF6), a stockpiled byproduct of the nuclear fuel cycle, reacts readily with atmospheric humidity, but the mechanism is poorly understood. We compare several potential initiation steps at a consistent level of theory, generating underlying structures and vibrational modes using hybrid density functional theory (DFT) and computing relative energies of stationary points with double-hybrid (DH) DFT. A benchmark comparison is performed to assess the quality of DH-DFT data using reference energy differences obtained using a complete-basis-limit coupled-cluster (CC) composite method. The associated large-basis CC computations were enabled by a new general-purpose pseudopotential capability implemented as part of this work. Dispersion-corrected parameter-free DH-DFT methods, namely PBE0-DH-D3(BJ) and PBE-QIDH-D3(BJ), provided mean unsigned errors within chemical accuracy (1 kcal mol-1) for a set of barrier heights corresponding to the most energetically favorable initiation steps. The hydrolysis mechanism is found to proceed via intermolecular hydrogen transfer within van der Waals complexes involving UF6, UF5OH, and UOF4, in agreement with previous studies, followed by the formation of a previously unappreciated dihydroxide intermediate, UF4(OH)2. The dihydroxide is predicted to form under both kinetic and thermodynamic control, and, unlike the alternate pathway leading to the UO2F2 monomer, its reaction energy is exothermic, in agreement with observation. Finally, harmonic and anharmonic vibrational simulations are performed to reinterpret literature infrared spectroscopy in light of this newly identified species.

A New Pathway for Intersystem Crossing: Unexpected Products in the O(3P) + Cyclopentene Reaction.

We investigated the reaction of O(3P) with cyclopentene at 4 Torr and 298 K using time-resolved multiplexed photoionization mass spectrometry, where O(3P) radicals were generated by 351 nm photolysis of NO2 and reacted with excess cyclopentene in He under pseudo-first-order conditions. The resulting products were sampled, ionized, and detected by tunable synchrotron vacuum ultraviolet radiation and an orthogonal acceleration time-of-flight mass spectrometer. This technique enabled measurement of both mass spectra and photoionization spectra as functions of time following the initiation of the reaction. We observe propylketene (41%), acrolein + ethene (37%), 1-butene + CO (19%), and cyclopentene oxide (3%), of which the propylketene pathway was previously unidentified experimentally and theoretically. The automatically explored reactive potential energy landscape at the CCSD(T)-F12a/cc-pVTZ//ωB97X-D/6-311++G(d,p) level and the related master equation calculations predict that cyclopentene oxide is formed on the singlet potential energy surface, whereas propylketene is first formed on the triplet surface. These calculations provide evidence that significant intersystem crossing can happen in this reaction not only around the geometry of the initial triplet adduct but also around that of triplet propylketene. The formation of 1-butene + CO is initiated on the triplet surface, with bond cleavage and hydrogen transfer occurring during intersystem crossing to the singlet surface. At present, we are unable to explain the mechanistic origins of the acrolein + ethene channel, and we thus refrain from assigning singlet or triplet reactivity to this channel. Overall, at least 60% of the products result from triplet reactivity. We propose that the reactivity of cyclic alkenes with O(3P) is influenced by their greater effective degree of unsaturation compared with acyclic alkenes. This work also suggests that searches for minimum-energy crossing points that connect triplet surfaces to singlet surfaces should extend beyond the initial adducts.