Quasi-Classical Trajectory Calculation of Rate Constants Using an Ab Initio Trained Machine Learning Model (aML-MD) with Multifidelity Data.

Machine learning (ML) provides a great opportunity for the construction of models with improved accuracy in classical molecular dynamics (MD). However, the accuracy of a ML trained model is limited by the quality and quantity of the training data. Generating large sets of accurate ab initio training data can require significant computational resources. Furthermore, inconsistent or incompatible data with different accuracies obtained using different methods may lead to biased or unreliable ML models that do not accurately represent the underlying physics. Recently, transfer learning showed its potential for avoiding these problems as well as for improving the accuracy, efficiency, and generalization of ML models using multifidelity data. In this work, ab initio trained ML-based MD (aML-MD) models are developed through transfer learning using DFT and multireference data from multiple sources with varying accuracy within the Deep Potential MD framework. The accuracy of the force field is demonstrated by calculating rate constants for the H + HO2 → H2 + 3O2 reaction using quasi-classical trajectories. We show that the aML-MD model with transfer learning can accurately predict the rate constants while reducing the computational cost by more than five times compared to the use of more expensive quantum chemistry training data sets. Hence, the aML-MD model with transfer learning shows great potential in using multifidelity data to reduce the computational cost involved in generating the training set for these potentials.

Isomer-resolved unimolecular dynamics of the hydroperoxyalkyl intermediate (•QOOH) in cyclohexane oxidation.

The oxidation of cycloalkanes is important in the combustion of transportation fuels and in atmospheric secondary organic aerosol formation. A transient carbon-centered radical intermediate (•QOOH) in the oxidation of cyclohexane is identified through its infrared fingerprint and time- and energy-resolved unimolecular dissociation dynamics to hydroxyl (OH) radical and bicyclic ether products. Although the cyclohexyl ring structure leads to three nearly degenerate •QOOH isomers (ß-, γ-, and δ-QOOH), their transition state (TS) barriers to OH products are predicted to differ considerably. Selective characterization of the ß-QOOH isomer is achieved at excitation energies associated with the lowest TS barrier, resulting in rapid unimolecular decay to OH products that are detected. A benchmarking approach is employed for the calculation of high-accuracy stationary point energies, in particular TS barriers, for cyclohexane oxidation (C6H11O2), building on higher-level reference calculations for the smaller ethane oxidation (C2H5O2) system. The isomer-specific characterization of ß-QOOH is validated by comparison of experimental OH product appearance rates with computed statistical microcanonical rates, including significant heavy-atom tunneling, at energies in the vicinity of the TS barrier. Master-equation modeling is utilized to extend the results to thermal unimolecular decay rate constants at temperatures and pressures relevant to cyclohexane combustion.

Radical Stereochemistry: Accounting for Diastereomers in Kinetic Mechanism Development.

Recent work in combustion and atmospheric chemistry has revealed cases in which diastereomers must be distinguished to accurately model a reacting flow. This paper presents an open-source framework for introducing such stereoisomer resolution into a kinetic mechanism. We detail our definitions and algorithms for labeling and enumerating the stereoisomers of a molecule and then generalize our system to describe the transition state (TS) of a reaction. This allows for the stereospecific enumeration of reactants and products while accounting for "fleeting" stereochemistry that is unique to the TS. We also present the AutoMech Chemical Identifier (AMChI), an InChI-like string identifier that accounts for stereocenters omitted by InChI. This identifier is extended to describe the TSs of reactions, providing a universal lookup key for specific reaction channels. The final piece of our methodology is an analytic formula to remove redundancy from a stereoresolved mechanism when its enantiomers exist as a racemic mixture, making it as compact as possible while fully accounting for the differences between diastereomers. In applying our methodology to two subsets of the NUIGMech1.1 mechanism, we find that our approach reduces the extra species added for large-fuel oxidation from 2231 (133%, full expansion) to 694 (41%, nonredundant expansion). We also find that for pyrolysis more than a quarter of the species in the expanded mechanism cannot be properly described by an InChI string, requiring an AMChI string to communicate their identity. Finally, we find that roughly one-quarter of the large-fuel oxidation reactions and one-third of the pyrolysis reactions include fleeting TS stereochemistry, which may have relevant effects on their kinetics.

OH Roaming during the Ozonolysis of α-Pinene: A New Route to Highly Oxygenated Molecules?

The formation of low-volatility organic compounds in the ozonolysis of α-pinene, the dominant atmospheric monoterpene, provides an important route to aerosol formation. In this work, we consider a previously unexplored set of pathways for the formation of highly oxygenated molecules in α-pinene ozonolysis. Pioneering, direct experimental observations of Lester and co-workers have demonstrated a significant production of hydroxycarbonyl products in the dissociation of Criegee intermediates. Theoretical analyses indicate that this production arises from OH roaming-induced pathways during the OO fission of the vinylhydroperoxides (VHPs), which in turn come from internal H transfers in the Criegee intermediates. Ab initio kinetics computations are used here to explore the OH roaming-induced channels that arise from the ozonolysis of α-pinene. For computational reasons, the calculations consider a surrogate for α-pinene, where two spectator methyl groups are replaced with H atoms. Multireference electronic structure calculations are used to illustrate a variety of energetically accessible OH roaming pathways for the four VHPs arising from the ozonolysis of this α-pinene surrogate. Ab initio transition-state theory-based master equation calculations indicate that for the dissociation of stabilized VHPs, these OH roaming pathways are kinetically significant with a branching that generally increases from ∼20% at room temperature up to ∼70% at lower temperatures representative of the troposphere. For one of the VHPs, this branching already exceeds 60% at room temperature. For the overall ozonolysis process, these branching ratios would be greatly reduced by a limited branching to the stabilized VHP, although there would also be some modest roaming fraction for the nonthermal VHP dissociation process. The strong exothermicities of the roaming-induced isomerizations/additions and abstractions suggest new routes to fission of the cyclobutane rings. Such ring fissions would facilitate further autoxidation reactions, thereby providing a new route for producing highly oxygenated nonvolatile precursors to aerosol formation.

Quantum and anharmonic effects in non-adiabatic transition state theory.

Quantitative descriptions of non-adiabatic transition rates at intermediate temperatures are challenging due to the simultaneous importance of quantum and anharmonic effects. In this paper, the interplay between quantum effects-for motion across or along the seam of crossing-and anharmonicity in the seam potential is considered within the weak coupling limit. The well-known expression for quantized 1-D motion across the seam (i.e., tunneling) in the linear terms approximation is derived in the thermal domain using the Lagrangian formalism, which is then applied to the case when tunneling is distributed along the seam of crossing (treating motion along the seam classically). For high-frequency quantum modes, a vibrationally adiabatic (VA) approach is developed that introduces to the non-adiabatic rate constant a factor associated with high-frequency wavefunction overlap; this approach treats the high-frequency motion along the seam quantum mechanically. To test these methodologies, the reaction N2O ↔ N2 + O(3P) was chosen. CCSD(T)-F12b/cc-pVTZ-F12 explorations of the 3A'-1A' seam of N2O revealed that seam anharmonicity has a strong effect on the rate constant (a factor of ∼20 at 2000 K). Several quantum effects were found to be significant at intermediate/lower temperatures, including the quantum N-N vibration that was coupled with seam anharmonicity using the VA approach. Finally, a 1-D approximation to non-adiabatic instanton theory is presented to estimate the validity limit of the linear terms model at low temperatures (∼250 K for N2O). We recommend that the assumptions built into many statistical theories for non-adiabatic reactions-harmonic behavior, classical motion, linear terms, and weak coupling-should be verified on a case-by-case basis.

Modeling-Experiment-Theory Analysis of Reactions Initiated from Cl + Methyl Formate.

Methyl formate (MF; CH3OCHO) is the smallest representative of esters, which are common components of biodiesel. The present study characterizes the thermal dissociation kinetics of the radicals formed by H atom abstraction from MF─CH3OCO and CH2OCHO─through a combination of modeling, experiment, and theory. For the experimental effort, excimer laser photolysis of Cl2 was used as a source of Cl atoms to initiate reactions with MF in the gas phase. Time-resolved species profiles of MF, Cl2, HCl, CO2, CH3, CH3Cl, CH2O, and CH2ClOCHO were measured and quantified using photoionization mass spectrometry at temperatures of 400-750 K and 10 Torr. The experimental data were simulated using a kinetic model, which was informed by ab initio-based theoretical kinetics calculations and included chlorine chemistry and secondary reactions of radical decomposition products. We calculated the rate coefficients for the H-abstraction reactions Cl + MF → HCl + CH3OCO (R1a) and Cl + MF → HCl + CH2OCHO (R1b): k1a,theory = 6.71 × 10-15·T1.14·exp(-606/T) cm3/molecule·s; k1b,theory = 4.67 × 10-18·T2.21·exp(-245/T) cm3/molecule·s over T = 200-2000 K. Electronic structure calculations indicate that the barriers to CH3OCO and CH2OCHO dissociation are 13.7 and 31.6 kcal/mol and lead to CH3 + CO2 (R3) and CH2O + HCO (R5), respectively. The master equation-based theoretical rate coefficients are k3,theory (P = ∞) = 2.94 × 109·T1.21·exp(-6209/T) s-1 and k5,theory (P = ∞) = 8.45 × 108·T1.39·exp(-15132/T) s-1 over T = 300-1500 K. The calculated branching fractions into R1a and R1b and the rate coefficient for R5 were validated by modeling of the experimental species time profiles and found to be in excellent agreement with theory. Additionally, we found that the bimolecular reactions CH2OCHO + Cl, CH2OCHO + Cl2, and CH3 + Cl2 were critical to accurately model the experimental data and constrain the kinetics of MF-radicals. Inclusion of the kinetic parameters determined in this study showed a significant impact on combustion simulations of larger methyl esters, which are considered as biodiesel surrogates.

Bimolecular Reaction of Methyl-Ethyl-Substituted Criegee Intermediate with SO2.

Methyl-ethyl-substituted Criegee intermediate (MECI) is a four-carbon carbonyl oxide that is formed in the ozonolysis of some asymmetric alkenes. MECI is structurally similar to the isoprene-derived methyl vinyl ketone oxide (MVK-oxide) but lacks resonance stabilization, making it a promising candidate to help us unravel the effects of size, structure, and resonance stabilization that influence the reactivity of atmospherically important, highly functionalized Criegee intermediates. We present experimental and theoretical results from the first bimolecular study of MECI in its reaction with SO2, a reaction that shows significant sensitivity to the Criegee intermediate structure. Using multiplexed photoionization mass spectrometry, we obtain a rate coefficient of (1.3 ± 0.3) × 10-10 cm3 s-1 (95% confidence limits, 298 K, 10 Torr) and demonstrate the formation of SO3 under our experimental conditions. Through high-level theory, we explore the effect of Criegee intermediate structure on the minimum energy pathways for their reactions with SO2 and obtain modified Arrhenius fits to our predictions for the reaction of both syn and anti conformers of MECI with SO2 (ksyn = 4.42 × 1011 T-7.80exp(-1401/T) cm3 s-1 and kanti = 1.26 × 1011 T-7.55exp(-1397/T) cm3 s-1). Our experimental and theoretical rate coefficients (which are in reasonable agreement at 298 K) show that the reaction of MECI with SO2 is significantly faster than MVK-oxide + SO2, demonstrating the substantial effect of resonance stabilization on Criegee intermediate reactivity.

Theoretical Kinetics Predictions for Reactions on the NH2O Potential Energy Surface.

Recent modeling studies of ammonia oxidation, which are motivated by the prospective role of ammonia as a zero-carbon fuel, have indicated significant discrepancies among the existing literature mechanisms. In this study, high-level theoretical kinetics predictions have been obtained for reactions on the NH2O potential energy surface, including the NH2 + O, HNO + H, and NH + OH reactions. These reactions have previously been highlighted as important reactions in NH3 oxidation with high sensitivity and high uncertainty. The potential energy surface is explored with coupled cluster calculations, including large basis sets and high-level corrections to yield high-accuracy (∼0.2 kcal/mol 2σ uncertainty) estimates of the stationary point energies. Variational transition state theory is used to predict the microcanonical rate constants, which are then incorporated in master equation treatments of the temperature- and pressure-dependent kinetics. For radical-radical channels, the microcanonical rates are obtained from variable reaction coordinate transition state theory implementing directly evaluated multireference electronic energies. The analysis yields predictions for the total rate constants as well as the branching ratios. We find that the NO + H2 channel contributes 10% of the total NH2 + O flux at combustion temperatures, although this channel is not included in modern NH3 oxidation mechanisms. Modeling is used to illustrate the ramifications of these rate predictions on the kinetics of NH3 oxidation and NOx formation. The present results for NH2 + O are important for predicting the chain branching and formation of NO in the oxidation of NH3 and thermal DeNOx.

OH Roaming and Beyond in the Unimolecular Decay of the Methyl-Ethyl-Substituted Criegee Intermediate: Observations and Predictions.

Alkene ozonolysis generates short-lived Criegee intermediates that are a significant source of hydroxyl (OH) radicals. This study demonstrates that roaming of the separating OH radicals can yield alternate hydroxycarbonyl products, thereby reducing the OH yield. Specifically, hydroxybutanone has been detected as a stable product arising from roaming in the unimolecular decay of the methyl-ethyl-substituted Criegee intermediate (MECI) under thermal flow cell conditions. The dynamical features of this novel multistage dissociation plus a roaming unimolecular decay process have also been examined with ab initio kinetics calculations. Experimentally, hydroxybutanone isomers are distinguished from the isomeric MECI by their higher ionization threshold and distinctive photoionization spectra. Moreover, the exponential rise of the hydroxybutanone kinetic time profile matches that for the unimolecular decay of MECI. A weaker methyl vinyl ketone (MVK) photoionization signal is also attributed to OH roaming. Complementary multireference electronic structure calculations have been utilized to map the unimolecular decay pathways for MECI, starting with 1,4 H atom transfer from a methyl or methylene group to the terminal oxygen, followed by roaming of the separating OH and butanonyl radicals in the long-range region of the potential. Roaming via reorientation and the addition of OH to the vinyl group of butanonyl is shown to yield hydroxybutanone, and subsequent C-O elongation and H-transfer can lead to MVK. A comprehensive theoretical kinetic analysis has been conducted to evaluate rate constants and branching yields (ca. 10-11%) for thermal unimolecular decay of MECI to conventional and roaming products under laboratory and atmospheric conditions, consistent with the estimated experimental yield (ca. 7%).

Radical-Radical Reactions in Molecular Weight Growth: The Phenyl + Propargyl Reaction.

The mechanism for hydrocarbon ring growth in sooting environments is still the subject of considerable debate. The reaction of phenyl radical (C6H5) with propargyl radical (H2CCCH) provides an important prototype for radical-radical ring-growth pathways. We studied this reaction experimentally over the temperature range of 300-1000 K and pressure range of 4-10 Torr using time-resolved multiplexed photoionization mass spectrometry. We detect both the C9H8 and C9H7 + H product channels and report experimental isomer-resolved product branching fractions for the C9H8 product. We compare these experiments to theoretical kinetics predictions from a recently published study augmented by new calculations. These ab initio transition state theory-based master equation calculations employ high-quality potential energy surfaces, conventional transition state theory for the tight transition states, and direct CASPT2-based variable reaction coordinate transition state theory (VRC-TST) for the barrierless channels. At 300 K only the direct adducts from radical-radical addition are observed, with good agreement between experimental and theoretical branching fractions, supporting the VRC-TST calculations of the barrierless entrance channel. As the temperature is increased to 1000 K we observe two additional isomers, including indene, a two-ring polycyclic aromatic hydrocarbon, and a small amount of bimolecular products C9H7 + H. Our calculated branching fractions for the phenyl + propargyl reaction predict significantly less indene than observed experimentally. We present further calculations and experimental evidence that the most likely cause of this discrepancy is the contribution of H atom reactions, both H + indenyl (C9H7) recombination to indene and H-assisted isomerization that converts less stable C9H8 isomers into indene. Especially at low pressures typical of laboratory investigations, H-atom-assisted isomerization needs to be considered. Regardless, the experimental observation of indene demonstrates that the title reaction leads, either directly or indirectly, to the formation of the second ring in polycyclic aromatic hydrocarbons.

High-Accuracy Heats of Formation for Alkane Oxidation: From Small to Large via the Automated CBH-ANL Method.

It is generally challenging to obtain high-accuracy predictions for the heat of formation for species with more than a handful of heavy atoms, such as those of importance in standard combustion mechanisms. To this end, we construct the CBH-ANL approach and illustrate that, for a set of 194 alkane oxidation species, it can be used to produce ΔHf(0 K) values with 2σ uncertainties of 0.2-0.5 kcal mol-1. This set includes the alkanes, hydroperoxides, and alkyl, peroxy, and hydroperoxyalkyl radicals for 17 representative hydrocarbon fuels containing up to 10 heavy atoms with various degrees of branching in the alkane backbone. The CBH-ANL approach, automated in the QTC and AutoMech software suites, builds balanced chemical equations for the calculation of ΔHf(0 K), in which the reference species may be up to five heavy atoms. The high-level ANL0 and ANL1 reference ΔHf(0 K) values are further refined for even the largest of these reference species with a novel laddering approach. We perform a comprehensive quantification of the uncertainties for both the individual reference species (the largest of which is 0.15 kcal mol-1) and the propagation of those uncertainties when used in the calculation of ΔHf(0 K) for the 194 target species. We examine the sensitivity of the predicted ΔHf(0 K) values to (i) electronic energies from various methods, including ωB97X-D/cc-pVTZ, B2PLYP-D3/cc-pVTZ, CCSD(T)-F12b/cc-pVDZ-F12//B2PLYP-D3/cc-pVTZ, and CCSD(T)-F12b/cc-pVTZ-F12//B2PLYP-D3/cc-pVTZ; (ii) the zero-point vibrational energies (ZPVEs), where we consider harmonic ZPVEs as well as two scaling-based estimates of the anharmonic ZPVEs, all implemented for both ωB97X-D/cc-pVTZ and B2PLYP-D3/cc-pVTZ calculations; (iii) the particular CBH-ANL scheme employed; and (iv) the procedure for choosing the reference conformer for the analyses. The discussion concludes with a summary of the estimated overall uncertainty in the predictions and a validation of the predictions for the alkane subset.

Bimolecular Peroxy Radical (RO2) Reactions and Their Relevance in Radical Initiated Oxidation of Hydrocarbons.

The kinetics of peroxy radical (RO2) reactions have been of long-standing interest in atmospheric and combustion chemistry. Nevertheless, the lack of kinetic studies at higher temperatures for their reactions with other radicals such as OH has precluded the inclusion of this class of reactions in detailed kinetics models developed for combustion applications. In this work, guided by the limited room-temperature experimental studies on selected alkyl-peroxy radicals and literature theoretical kinetics on the prototypical CH3O2 + OH system, we have performed parametric studies on the effect of uncertainties in the rate coefficients and branching ratios to potential product channels for RO2 + OH reactions at higher temperatures. Literature kinetics models were used to simulate autoignition delays, laminar flame speeds, and speciation profiles in flow and stirred reactors for a variety of common combustion-relevant fuels. Inclusion of RO2 + OH reactions was found to retard autoignition in fuel-lean (φ = 0.5) mixtures of ethane and dimethyl ether in air. The observed effects were noticeably more pronounced in ozone-enriched combustion of ethane and dimethyl ether. The simulations also examined the influence of ozone doping levels, pressures, and equivalence ratios for both ethane and dimethyl ether oxidation. Sensitivity and flux analyses revealed that the RO2 + OH reaction is a significant sink of RO2 radicals at the early stage of autoignition, affecting fuel oxidation through RO2 ↔ QOOH, RO2 ↔ alkene + HO2, or RO2 + HO2 ↔ ROOH + O2. Additionally, the kinetic stability of the trioxide formed from RO2 + OH reactions was investigated using master equation analyses. Last, we discuss other bimolecular reactions that are missing in literature kinetics models but are relevant to hydrocarbon oxidation initiated by external radical sources (plasma-enhanced, ozone-enriched combustion, etc.). The present simulations provide a strong motivation for better characterizing the bimolecular kinetics of peroxy radicals.

Spiers Memorial Lecture: Theory of unimolecular reactions.

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our ability to model and predict the kinetics of such reactions has grown in leaps and bounds through the synergy of ever more sophisticated experimental studies with increasingly high level theoretical analyses. This review begins with a brief historical overview of the progress from the Lindemann mechanism to the master equation, which now provides the cornerstone for most theoretical analyses. The current status of ab initio transition state theory based implementations of the master equation is then reviewed, beginning with a discussion of the energy resolved chemical conversion rates, followed by a review of the pressure dependence of the thermal kinetics. The latter discussion focusses on the collisional energy and angular momentum transfer rates as well as the complexities of non-thermal effects and of multiple-well multiple-channel reactions. The synergy with recent state-of-the-art experiments is used to motivate these discussions. Attempts to automate the calculations are also briefly reviewed. Throughout the discussion, we provide our perspective on current understanding and continuing challenges and opportunities. One key challenge relates to the coupling of sequences of reactions, which frequently leads to deviations from the classic presumption of thermal reactants.

Energy-resolved and time-dependent unimolecular dissociation of hydroperoxyalkyl radicals (˙QOOH).

Hydroperoxyalkyl radicals (˙QOOH) are transient intermediates in the atmospheric oxidation of volatile organic compounds and combustion of hydrocarbon fuels in low temperature (<1000 K) environments. The carbon-centered ˙QOOH radicals are a critical juncture in the oxidation mechanism, but have generally eluded direct experimental observation of their structure, stability, and dissociation dynamics. Recently, this laboratory demonstrated that a prototypical ˙QOOH radical [˙CH2(CH3)2COOH] can be synthesized by an alternative route, stabilized in a pulsed supersonic expansion, and characterized by its infrared (IR) spectroscopic signature and unimolecular dissociation rate to OH radical and cyclic ether products. The present study focuses on a partially deuterated ˙QOOD analog ˙CH2(CH3)2COOD, generated in the laboratory by H-atom abstraction from partially deuterated tert-butyl hydroperoxide, (CH3)3COOD. IR spectral features associated with jet-cooled and isolated ˙QOOD radicals are observed in the vicinity of the transition state (TS) barrier leading to OD radical and cyclic ether products. The overtone OD stretch (2νOD) of ˙QOOD is identified by IR action spectroscopy with UV laser-induced fluorescence detection of OD products. Direct time-domain measurement of the unimolecular dissociation rate for ˙QOOD (2νOD) extends prior rate measurements for ˙QOOH. Partial deuteration results in a small increase in the TS barrier predicted by high level electronic structure calculations due to changes in zero-point energies; the imaginary frequency is unchanged. Comparison of the unimolecular decay rates obtained experimentally with those predicted theoretically for both ˙QOOH and ˙QOOD confirm that unimolecular decay is enhanced by heavy-atom tunneling involving simultaneous O-O bond elongation and C-C-O angle contraction along the reaction pathway.