Modeling the kinetics of bimolecular reactions

Chemography-guided analysis of a reaction path network for ethylene hydrogenation with a model Wilkinson's catalyst

Visualization and analysis of large chemical reaction networks become rather challenging when conventional graph-based approaches are used. As an alternative, we propose to use the chemical cartography ("chemography") approach, describing the data distribution on a 2-dimensional map. Here, the Generative Topographic Mapping (GTM) algorithm - an advanced chemography approach - has been applied to visualize the reaction path network of a simplified Wilkinson's catalyst-catalyzed hydrogenation containing some 105 structures generated with the help of the Artificial Force Induced Reaction (AFIR) method using either Density Functional Theory or Neural Network Potential (NNP) for potential energy surface calculations. Using new atoms permutation invariant 3D descriptors for structure encoding, we've demonstrated that GTM possesses the abilities to cluster structures that share the same 2D representation, to visualize potential energy surface, to provide an insight on the reaction path exploration as a function of time and to compare reaction path networks obtained with different methods of energy assessment.

Hybrid Cluster-Continuum Method for Single-Ion Solvation Free Energy in Acetonitrile Solvent

A new hybrid discrete-continuum approach named the cluster-continuum static approximation (CCSA) has been proposed for acetonitrile solvent. The continuum part uses the conductor-like polarizable continuum model for electrostatic and a surface area-dependent term for nonelectrostatic solvation. The CCSA includes only one explicit acetonitrile solvent molecule and a damping function, which makes the CCSA method reduce to pure continuum solvation in the case of weaker potential of mean force for solute-solvent interaction. The performance of the model was tested for 22 anions and 22 cations, including challenge species that cannot be adequately described by pure continuum solvation. A comparison was done with the widely used solvent model density (SMD) model. For anions, the CCSA reduces to pure continuum solvation and the method has the same performance as the SMD model, with a standard deviation of the mean signed error (SD-MSE) of 2.7 kcal mol-1 for both models. However, the CCSA method for cations considerably outperforms the SMD model, with an SD-MSE of 3.3 kcal mol-1 for the former and 8.4 kcal mol-1 for the latter. The method can be automated, and the present study suggests that continuum solvation models could be parameterized taking into account the explicit solvation as proposed in this work.

Multi-Level Protocol for Mechanistic Reaction Studies Using Semi-Local Fitted Potential Energy Surfaces

In this work, we propose a multi-level protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive potential energy surface (PES), embracing reactants, products and transition state (TS) regions. This approach has been successfully applied to a unimolecular (Bergman cyclization of enediyne) and a bimolecular (SN2 substitution) reaction. In particular, we demonstrate that with only 50 to 150 energy-force evaluations with the accurate reference methods (here complete-active-space self-consistent field, CASSCF, and coupled-cluster singles and doubles, CCSD) it is possible to construct a semi-local PES giving qualitative agreement for stationary-point geometries, intrinsic reaction coordinates and barriers. Furthermore, we find a qualitative agreement in vibrational frequencies and reaction rate coefficients. The key aspect of the method's performance is its multi-level nature, which not only saves computational effort but also allows extracting meaningful information along the reaction path, characterized by zero gradients in all but one direction. Agnostic to the nature of the TS and computationally economic, the protocol can be readily automated and routinely used for mechanistic reaction studies.

Initiation and Carbene Induced Radical Chain Reactions in CH2F2 Pyrolysis

High temperature dissociations of organic molecules typically involve a competition between radical and molecular processes. In this work, we use a modeling, experiment, theory (MET) framework to characterize the high temperature thermal dissociation of CH2F2, a flammable hydrofluorocarbon (HFC) that finds widespread use as a refrigerant. Initiation in CH2F2 proceeds via a molecular elimination channel; CH2F2→CHF+HF. Here we show that the subsequent self-reactions of the singlet carbene, CHF, are fast multichannel processes and a facile source of radicals that initiate rapid chain propagation reactions. These have a marked influence on the decomposition kinetics of CH2F2. The inclusion of these reactions brings the simulations into better agreement with the present and literature experiments. Additionally, flame simulations indicate that inclusion of the CHF+CHF multichannel reaction leads to a noticeable enhancement in predictions of laminar flame speeds, a key parameter that is used to determine the flammability of a refrigerant.

Exhaustive State-to-State Cross Sections and Rate Coefficients for Inelastic N2-N2 Collisions using QCT Combined with Neural Network Models

Using the quasi-classical trajectory method, we systematically studied the state-to-state vibrational relaxation process of N2(v1) + N2(v2) collisions over a wide temperature range (5000-30,000 K). Different temperature dependencies of the single- and multiquantum VV and VT events in various (v1,v2) collisions are captured, with the dominant channel being related to the initial vibrational energy levels (vmax = 50). At a specified relative translational energy, there is a monotonic relationship of the VT cross sections with the vibrational energy level, particularly in high-energy collisions. Additionally, we constructed well-trained neural network models (R-values reaching 0.99) using limited quasi-classical trajectory (QCT) data sets, which can be used to predict the state-to-state cross sections and rate coefficients of the VV processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2 + Δv) and VT processes N2(v1) + N2(v2) → N2(v1 - Δv) + N2(v2) (Δv = ±1, ±2, ±3) for collisions with arbitrary initial vibrational states. This work not only significantly reduces computational resources but also serves as a reference for the study of the state-to-state dynamics of all four-atom collision systems in hypersonic flows.

Reactions dynamics for X + H2 insertion reactions (X = C(1D), N(2D), O(1D), S(1D)) with Cayley propagator ring-polymer molecular dynamics

In this work, rate coefficients of four prototypical insertion reactions, X + H2 → H + XH (X = C(1D), N(2D), O(1D), S(1D)), and associated isotope reactions are calculated based on ring polymer molecular dynamics (RPMD) with Cayley propagator (Cayley-RPMD). The associated kinetic isotope effects are systematically studied too. The Cayley propagator used in this work increases the stability of numerical integration in RPMD calculations and also supports a larger evolution time interval, allowing us to reach both high accuracy and efficiency. So, our results do not only provide chemical kinetic data for the title reactions in an extended temperature range but also consist of experimental results, standard RPMD, and other theoretical methods. The results in this work also reflect that Cayley-RPMD has strong consistency and high reliability in its investigations of chemical dynamics for insertion reactions.

Quantitative kinetics reveal that reactions of HO2 are a significant sink for aldehydes in the atmosphere and may initiate the formation of highly oxygenated molecules via autoxidation

Large aldehydes are widespread in the atmosphere and their oxidation leads to secondary organic aerosols. The current understanding of their chemical transformation processes is limited to hydroxyl radical (OH) oxidation during daytime and nitrate radical (NO3) oxidation during nighttime. Here, we report quantitative kinetics calculations of the reactions of hexanal (C5H11CHO), pentanal (C4H9CHO), and butanal (C3H7CHO) with hydroperoxyl radical (HO2) at atmospheric temperatures and pressures. We find that neither tunneling nor multistructural torsion anharmonicity should be neglected in computing these rate constants; strong anharmonicity at the transition states is also important. We find rate constants for the three reactions in the range 3.2-7.7 × 10-14 cm3 molecule-1 s-1 at 298 K and 1 atm, showing that the HO2 reactions can be competitive with OH and NO3 oxidation under some conditions relevant to the atmosphere. Our findings reveal that HO2-initiated oxidation of large aldehydes may be responsible for the formation of highly oxygenated molecules via autoxidation. We augment the theoretic studies with laboratory flow-tube experiments using an iodide-adduct time-of-flight chemical ionization mass spectrometer to confirm the theoretical predictions of peroxy radicals and the autoxidation pathway. We find that the adduct from HO2 + C5H11CHO undergoes a fast unimolecular 1,7-hydrogen shift with a rate constant of 0.45 s-1. We suggest that the HO2 reactions make significant contributions to the sink of aldehydes.

Kinetics and mechanism of the gas-phase reaction of the hydroxyl radical with meta-aminotoluene compound

CONTEXT

An ab initio investigation into the potential energy landscape of the meta-aminotoluene + •OH reaction has been conducted in this study. The calculated results reveal that the reaction channel leading to the product (NHC6H4CH3 + H2O) prevails under the 300-1700 K temperature range, while the reaction path forming the product (NH2C6H4CH2 + H2O) dominates in the higher-temperature region (T ≥ 1800 K). Within the specified temperature range, the product branching ratio for the former declines from 48 to 30%, while the latter shows an increase, reaching 29%. The overall second-order rate constants of the titled reaction obtained at the pressure 760 Torr (N2) can be illustrated by the modified Arrhenius expression of ktotal = 1.46 × 10-13 T0.58 exp[(-0.759 kcal.mol-1)/RT] cm3 molecule-1 s-1 and ktotal = 1.86 × 10-22 T3.24 exp[(-5.086 kcal.mol-1)/RT] cm3 molecule-1 s-1, covering the temperature range of T = 300-600 K and T > 600 K, respectively. The total rate constant at the ambient conditions in this work, 1.43 × 10-11 cm3 molecule-1 s-1, has been found to be roughly one order of magnitude lower than the available experimental data, ~ 1.2 × 10-10 cm3 molecule-1 s-1, measured by Atkinson et al., Rinke et al., and Witte et al., or the theoretical value, 4.4 × 10-10 cm3 molecule-1 s-1, and calculated by Abdel-Rahman and co-workers for the aniline + •OH reaction.

METHODS

The structures of reactants, transition states, intermediate states, and products of the meta-aminotoluene + •OH reaction are calculated with the aug-cc-pVTZ basis set and the methods DFT/B3LYP and CCSD(T). The rate constants and branching ratios in the 300-2000 K temperature range are calculated with the statistical theoretical TST and RRKM master equation computations including tunneling corrections, with potential energy surface constructed by the CCSD(T)//B3LYP/aug-cc-pVTZ approach.

Theoretical Study of the Temperature- and Pressure-Dependent Rate Constants for Nine Reactions between COn (n = 0-4), Om (m = 1-3), C2O, and C3O2 during the Radiolysis of Carbon Dioxide

We investigate the reaction pathways of nine important CO2-related reactions using the revDSD-PBEP86-D3(BJ)/jun-cc-pV(T+d)Z level and simultaneously employ an accurate composite method (jun-Cheap) based on coupled-cluster (CC) theory. Subsequently, the Rice-Ramsperger-Kassel-Marcus/master equation (RRKM/ME) is solved to calculate the temperature- and pressure-dependent rate constants. This work investigates reactions involving transition states that have been overlooked in previous literature, including the dissociation of singlet-state C3O2, the triple channel formation of C2O + CO to form C3O2, and the formation of O3 + CO. The results show that CO3 is highly prone to dissociation at high temperatures. Finally, the kinetic data show that over a wide temperature range, our calculations are consistent with previous experimental measurements. The majority of the reaction rate constants studied exhibit significant pressure dependence, while the O3 + CO reaction is pressure-independent at low temperatures. These results are instrumental in the development of detailed kinetic models for the CO2 radiolysis reaction network.

Differentiating the Yield of Chemical Reactions Using Parameters in First-Order Kinetic Equations to Identify Elementary Steps That Control the Reactivity from Complicated Reaction Path Networks

The yield of a chemical reaction is obtained by solving its rate equation. This study introduces an approach for differentiating yields by utilizing the parameters of the rate equation, which is expressed as a first-order linear differential equation. The yield derivative for a specific pair of reactants and products is derived by mathematically expressing the rate constant matrix contraction method, which is a simple kinetic analysis method. The parameters of the rate equation are the Gibbs energies of the intermediates and transition states in the reaction path network used to formulate the rate equation. Thus, our approach for differentiating the yield allows a numerical evaluation of the contribution of energy variation to the yield for each intermediate and transition state in the reaction path network. In other words, a comparison of these values automatically extracts the factors affecting the yield from a complicated reaction path network consisting of numerous reaction paths and intermediates. This study verifies the behavior of the proposed approach through numerical experiments on the reaction path networks of a model system and the Rh-catalyzed hydroformylation reaction. Moreover, the possibility of using this approach for designing ligands in organometallic catalysts is discussed.

Theoretical insight of reactive oxygen species scavenging mechanism in lignin waste depolymerization products

Apart from natural products and synthesis, phenolic compounds can be produced from the depolymerization of lignin, a major waste in biofuel and paper production. This process yields a plethora of aryl propanoid phenolic derivatives with broad biological activities, especially antioxidant properties. Due to its versatility, our study focuses on investigating the antioxidant mechanisms of several phenolic compounds obtained from renewable and abundant resources, namely, syringol (Hs), 4-allylsyringol (HAs), 4-propenylsyringol (HPns), and 4-propylsyringol (HPs). Employing the density functional theory (DFT) approach in conjunction with the QM-ORSA protocol, we aim to explore the reactivity of these compounds in neutralizing hydroperoxyl radicals in physiological and non-polar media. Kinetic and thermodynamic parameter calculations on the antioxidant activity of these compounds were also included in this study. Additionally, our research utilizes the activation strain model (ASM) for the first time to explain the reactivity of the HT and RAF mechanisms in the peroxyl radical scavenging process. It is predicted that HPs has the best rate constant in both media (1.13 × 108 M-1 s-1 and 1.75 × 108 M-1 s-1, respectively). Through ASM analysis, it is observed that the increase in the interaction energy due to the formation of intermolecular hydrogen bonds during the reaction is an important feature for accelerating the hydrogen transfer process. Furthermore, by examining the physicochemical and toxicity parameters, only Hs is not suitable for further investigation as a therapeutic agent because of potential toxicity and mutagenicity. However, overall, all compounds are considered potent HOO˙ scavengers in lipid-rich environments compared to previously studied antioxidants.

On Accelerating Substrate Optimization Using Computational Gibbs Energy Barriers: A Numerical Consideration Utilizing a Computational Data Set

Substrate optimization is a time- and resource-consuming step in organic synthesis. Recent advances in chemo- and materials-informatics provide systematic and efficient procedures utilizing tools such as Bayesian optimization (BO). This study explores the possibility of reducing the required experiments further by utilizing computational Gibbs energy barriers. To thoroughly validate the impact of using computational Gibbs energy barriers in BO-assisted substrate optimization, this study employs a computational Gibbs energy barrier data set in the literature and performs an extensive numerical investigation virtually regarding the Gibbs energy barriers as virtual experimental results and those with systematic and random noises as virtual computational results. The present numerical investigation shows that even the computational reactivity affected by noises of as much as 20 kJ/mol helps reduce the number of required experiments.

Easy and accurate computation of energy barriers for carbocation solvation: an expeditious tool to face carbocation chemistry

An expeditious procedure for the challenging computation of the free energy barriers (ΔG≠) for the solvation of carbocations is presented. This procedure is based on Marcus Theory (MT) and the popular B3LYP/6-31G(d)//PCM method, and it allows the easy, accurate and inexpensive prediction of these barriers for carbocations of very different stability. This method was validated by the fair mean absolute error (ca. 1.5 kcal mol-1) achieved in the prediction of 19 known experimental barriers covering a range of ca. 50 kcal mol-1. Interestingly, the new procedure also uses an original method for the calculation of the required inner reorganization energy (Λi) and free energy of reaction (ΔG). This procedure should pave the way to face computationally the pivotal issue of carbocation chemistry and could be easily extended to any bimolecular organic reaction.

Theoretical Kinetics studies of isoprene peroxy radical chemistry: The fate of Z-δ-(4-OH, 1-OO)-ISOPOO radical

The OH radical recycling mechanism in isoprene oxidation is one of the most exciting topics in atmospheric chemistry, and the corresponding studies expand our understanding of oxidation mechanisms of volatile organic compounds in the troposphere and provide reliable evidence to improve and develop conventional atmospheric models. In this work, we performed a detailed theoretical kinetics study on the Z-δ-(4-OH, 1-OO)-ISOPOO radical chemistry, which is proposed as the heart of OH recycling in isoprene oxidation. With the full consideration of its accumulation and consumption channels, we studied and discussed the fate of Z-δ-(4-OH, 1-OO)-ISOPOO radical by solving the energy-resolved master equation over a broad range of conditions, including not only room temperatures but also high temperatures of a forest fire or low temperatures and pressures of the upper troposphere. We found non-negligible pressure dependence of its fate at combustion temperatures (up to two orders of magnitude) and demonstrated the significance of both the multi-structural torsional anharmonicity and tunneling for accurately calculating kinetics of the studied system. More interestingly, the tunneling effect on the phenomenological rate constants of the H-shift reaction channel is also found to be pressure-dependent due to the competition with the O2 loss reaction. In addition, our time evolution calculations revealed a two-stage behavior of critical species in this reaction system and estimated the shortest half-lives for the Z-δ-(4-OH, 1-OO)-ISOPOO radical at various temperatures, pressures and altitudes. This detailed kinetics study of Z-δ-(4-OH, 1-OO)-ISOPOO radical chemistry offers a typical example to deeply understand the core mechanism of OH recycling pathways in isoprene oxidation, and provides valuable insights for promoting the development of relevant atmospheric models.

Reactions of a hydrogen atom with haloacetates in aqueous solutions: Computational evidence for proton-coupled electron transfer and competing mechanisms

A computational study of the mechanisms and kinetics of the aqueous reactions of a hydrogen atom with haloacetates is presented. Several mechanisms in the close competition are observed, such as proton-coupled electron transfer (PCET), hydrogen atom transfer (HAT), and halogen abstraction (XA). Computations predict that dechlorination takes place via PCET mechanisms and not via XA, as stated earlier, while XA is the fastest mechanism forIAc - . The reaction rate constants are reasonably well predicted within the theoretically most reliable canonical variational transition state theory with small curvature tunneling corrections and compared with the experimental ones. To reproduce the experimental rate constants of the debromination process it is necessary to include the PCET and XA cumulative values. Small curvature tunneling corrections to the rate constants are the highest for HAT and PCET mechanisms, up to 70 times larger than the Wigner, while variational effects for XA mechanisms are very small.

Conjugated quantitative structure-property relationship models: Prediction of kinetic characteristics linked by the Arrhenius equation

Conjugated QSPR models for reactions integrate fundamental chemical laws expressed by mathematical equations with machine learning algorithms. Herein we present a methodology for building conjugated QSPR models integrated with the Arrhenius equation. Conjugated QSPR models were used to predict kinetic characteristics of cycloaddition reactions related by the Arrhenius equation: rate constantl o g k ${{\rm l}{\rm o}{\rm g}k}$ , pre-exponential factorl o g A ${{\rm l}{\rm o}{\rm g}A}$ , and activation energyE a ${{E}_{{\rm a}}}$ . They were benchmarked against single-task (individual and equation-based models) and multi-task models. In individual models, all characteristics were modeled separately, while in multi-task modelsl o g k ${{\rm l}{\rm o}{\rm g}k}$ ,l o g A ${{\rm l}{\rm o}{\rm g}A}$ andE a ${{E}_{{\rm a}}}$ were treated cooperatively. An equation-based model assessedl o g k ${{\rm l}{\rm o}{\rm g}k}$ using the Arrhenius equation andl o g A ${{\rm l}{\rm o}{\rm g}A}$ andE a ${{E}_{{\rm a}}}$ values predicted by individual models. It has been demonstrated that the conjugated QSPR models can accurately predict the reaction rate constants at extreme temperatures, at which reaction rate constants hardly can be measured experimentally. Also, in the case of small training sets conjugated models are more robust than related single-task approaches.

New prebiotic molecules in the interstellar medium from the reaction between vinyl alcohol and CN radicals: unsupervised reaction mechanism discovery, accurate electronic structure calculations and kinetic simulations

Vinyl alcohol (VyA) and cyanide (CN) radicals are relatively abundant in the interstellar medium (ISM). VyA is the enolic tautomer of acetaldehyde and has two low-lying conformers, characterized by the syn or anti placement of hydroxyl hydrogen with respect to the double bond. In this paper, we present a gas-phase model of the barrierless reactions of both VyA's conformers with CN employing accurate quantum chemical computations in the framework of a master equation approach based on the transition state theory. Our results indicate that both VyA conformers feature a similar reactivity with CN, starting with a barrierless addition to the double bond and followed by different isomerization, dissociation, and/or hydrogen elimination steps. The rate constants computed for temperatures up to 600 K show that several reaction channels are open even under the harsh conditions of the ISM, with the favoured one providing the first feasible formation route of a prebiotic molecule not yet detected in the ISM, namely cyanoacetaldehyde. This finding suggests looking for cyanoacetaldehyde in regions where both VyA and CN have already been detected, like, e.g., Sagittarius B2N or G+0.693-0.027.

Caracal: A Versatile Ring Polymer Molecular Dynamics Simulation Package

A new open-source program package named Caracal covering simulations of molecular systems with ring polymer molecular dynamics (RPMD) is presented. It combines a powerful RPMD implementation including chemical reaction rate calculations and biased periodic and nonperiodic samplings with a collection of easy to set up potential energy surface (PES) methodologies, thus delivering an all-inclusive approach. Most implemented PESs are based on the QMDFF and EVB-QMDFF methods. Where the quantum mechanically derived force field (QMDFF) can be set up for an arbitrary molecular system in a black-box fashion, the empirical valence bond (EVB)-QMDFF connects two QMDFFs and is able to represent the PES of a chemical reaction. With our previously published flavors of this composite method, PESs for almost arbitrary gas phase thermal ground state reactions can be set up. Given an optimized reaction path, the mechanism of the reaction can be classified and RPMD rate constants can be obtained via umbrella sampling and recrossing calculations on an EVB-QMDFF PES. Further, QMDFFs can be polymerized for the description of liquid systems. In this paper, the internal structure as well as the handling philosophy of Caracal are outlined. Further, examples of the different possible kinds of calculations are given.

Modification of ground-state chemical reactivity via light-matter coherence in infrared cavities

Reaction-rate modifications for chemical processes due to strong coupling between reactant molecular vibrations and the cavity vacuum have been reported; however, no currently accepted mechanisms explain these observations. In this work, reaction-rate constants were extracted from evolving cavity transmission spectra, revealing resonant suppression of the intracavity reaction rate for alcoholysis of phenyl isocyanate with cyclohexanol. We observed up to an 80% suppression of the rate by tuning cavity modes to be resonant with the reactant isocyanate (NCO) stretch, the product carbonyl (CO) stretch, and cooperative reactant-solvent modes (CH). These results were interpreted using an open quantum system model that predicted resonant modifications of the vibrational distribution of reactants from canonical statistics as a result of light-matter quantum coherences, suggesting links to explore between chemistry and quantum science.

The atmospheric relevance of primary alcohols and imidogen reactions

Organic alcohols as very volatile compounds play a crucial role in the air quality of the atmosphere. So, the removal processes of such compounds are an important atmospheric challenge. The main goal of this research is to discover the atmospheric relevance of degradation paths of linear alcohols by imidogen with the aid of simulation by quantum mechanical (QM) methods. To this end, we combine broad mechanistic and kinetic results to get more accurate information and to have a deeper insight into the behavior of the designed reactions. Thus, the main and necessary reaction pathways are explored by well-behaved QM methods for complete elucidation of the studying gaseous reactions. Moreover, the potential energy surfaces as  a main factor are computed for easier judging of the most probable pathways in the simulated reactions. Our attempt to find the occurrence of the considered reactions in the atmospheric conditions is completed by precisely evaluating the rate constants of all elementary reactions. All of the computed bimolecular rate constants have a positive dependency on both temperature and pressure. The kinetic results show that H-abstraction from the α carbon is dominant relative to the other sites. Finally, by the results of this study, we conclude that at moderate temperatures and pressures primary alcohols can degrade with imidogen, so they can get atmospheric relevance.

Estimation of frequency factors for the calculation of kinetic isotope effects from classical and path integral free energy simulations

We use the modified Bigeleisen-Mayer equation to compute kinetic isotope effect values for non-enzymatic phosphoryl transfer reactions from classical and path integral molecular dynamics umbrella sampling. The modified form of the Bigeleisen-Mayer equation consists of a ratio of imaginary mode vibrational frequencies and a contribution arising from the isotopic substitution's effect on the activation free energy, which can be computed from path integral simulation. In the present study, we describe a practical method for estimating the frequency ratio correction directly from umbrella sampling in a manner that does not require normal mode analysis of many geometry optimized structures. Instead, the method relates the frequency ratio to the change in the mass weighted coordinate representation of the minimum free energy path at the transition state induced by isotopic substitution. The method is applied to the calculation of 16/18O and 32/34S primary kinetic isotope effect values for six non-enzymatic phosphoryl transfer reactions. We demonstrate that the results are consistent with the analysis of geometry optimized transition state ensembles using the traditional Bigeleisen-Mayer equation. The method thus presents a new practical tool to enable facile calculation of kinetic isotope effect values for complex chemical reactions in the condensed phase.

Comparison of Implicit and Explicit Solvent Approaches in Ab Initio Evaluation of Thermochemistry in Solution: Application in Studying Boron Isotope Fractionation in Water

Evaluation of thermochemistry in solution plays a key role in numerous fields. For this task, the solvent effects are commonly included in theoretical computations based on either implicit or explicit solvent approaches. In the present study, we evaluate and compare the performance of some of the most widely applied methods based on these two approaches. For studying the solvent effect on thermochemistry with an explicit solvent, we demonstrate that partial normal mode analysis with frozen geometry of solvent molecules for multiple solute-solvent configurations can yield quite accurate and reliable results for a drastically reduced computational cost. As a case study, we consider the evaluation of the equilibrium constant for the boron isotope exchange between boric acid and borate (k_3-4) in pure and saline water which is of high geochemical importance. Employing three different rigorous and high-precision theoretical approaches, we provide a reliable estimation of k_3-4 which is a value within 1.028 to 1.030 for both pure and saline water which is in excellent agreement with experimental data.

Computational Studies on the Reactivity of Polycyclic Aromatic Hydrocarbons

Polycyclic aromatic hydrocarbons (PAHs) are widely present in the environment as toxic pollutants. In this study, quantum chemistry methods are used to study reactions of PAHs in both particle and gas phases. Seven theoretical methods are exploited to predict the reactive sites of 15 PAHs in the particle phase. Among these methods, the performance of the condensed Fukui function (CFF) is optimum. The gas-phase reactions of eight PAHs are also investigated. Except for fluorene, CFF predicts correctly the gas-phase mono-nitro products for seven systems. The products of fluorene predicted by CFF are 1-nitrofluorene and 3-nitrofluorene, which is however inconsistent with the experimental results. Transition state theory is then used to investigate the reaction mechanism of fluorene. Calculated rate constants for 3-nitrofluorene and 2-nitrofluorene formation are much bigger than that for 1-nitrofluorene formation, which is in agreement with the experimental results.

Molecular Understanding and Practical In Silico Catalyst Design in Computational Organocatalysis and Phase Transfer Catalysis-Challenges and Opportunities

Through the lens of organocatalysis and phase transfer catalysis, we will examine the key components to calculate or predict catalysis-performance metrics, such as turnover frequency and measurement of stereoselectivity, via computational chemistry. The state-of-the-art tools available to calculate potential energy and, consequently, free energy, together with their caveats, will be discussed via examples from the literature. Through various examples from organocatalysis and phase transfer catalysis, we will highlight the challenges related to the mechanism, transition state theory, and solvation involved in translating calculated barriers to the turnover frequency or a metric of stereoselectivity. Examples in the literature that validated their theoretical models will be showcased. Lastly, the relevance and opportunity afforded by machine learning will be discussed.

An efficient algorithm for capturing quantum effects in classical reactive scattering: application to D + H+3 → H2D+ + H

Motivated by a recent semiclassical analysis of chemical reaction thresholds [Bonnet et al., J. Chem. Phys., 2022, 157, 094114], we present an efficient algorithm for including zero-point energy (ZPE) effects in classical reactive scattering. The algorithm is an extension of the quasi-classical trajectory (QCT) Gaussian binning method. We apply it to the astrophysically important D + H+3 reaction, where there are significant quantum effects and where application of other methods is problematic [Braunstein et al., Phys. Chem. Chem. Phys., 2022, 24, 5489]. The rate constants computed with the new, general algorithm closely match recent Ring Polymer Molecular Dynamics (RPMD) [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] and experimentally derived [Bowen et al., J. Chem. Phys., 2021, 154, 084307] ones spanning ∼4 orders of magnitude from 70 to 1500 K.

Why Should the Reaction Order of a Bimolecular Reaction be 2.33 Instead of 2?

Predicting the reaction kinetics, that is, how fast a reaction can happen in a solution, is essential information for many processes, such as industrial chemical manufacturing, refining, synthesis and separation of petroleum products, environmental processes in air and water, biological reactions in cells, biosensing, and drug delivery. Collision theory was originally developed to explain the reaction kinetics of gas reactions with no dilution. For a reaction in a diluted inert gas solution or a diluted liquid solution, diffusion often dominates the collision process. Thus, it is necessary to include diffusion in such a calculation. Traditionally, the classical Smoluchowski rate is used as a starting point to predict the collision frequency of two molecules in a diluted solution. In this report, a different collision model is derived from the adsorption of molecules on a flat surface. A surprising result is obtained, showing that the reaction order for bimolecular reactions should be 2 and 1/3 instead of 2, following a fractal reaction kinetics.

Quantitative Kinetics of HO2 Reactions with Aldehydes in the Atmosphere: High-Order Dynamic Correlation, Anharmonicity, and Falloff Effects Are All Important

Kinetics provides the fundamental parameters for elucidating sources and sinks of key atmospheric species and for atmospheric modeling more generally. Obtaining quantitative kinetics in the laboratory for the full range of atmospheric temperatures and pressures is quite difficult. Here, we use computational chemistry to obtain quantitative rate constants for the reactions of HO₂ with HCHO, CH₃CHO, and CF₃CHO. First, we calculate the high-pressure-limit rate constants by using a dual-level strategy that combines conventional transition state theory using a high level of electronic structure wave function theory with canonical variational transition state theory including small-curvature tunneling using density functional theory. The wave-function level is beyond-CCSD(T) for HCHO and CCSD(T)-F12a (Level-A) for XCHO (X = CH₃, CF₃), and the density functional (Level-B) is specifically validated for these reactions. Then, we calculate the pressure-dependent rate constants by using system-specific quantum RRK theory (SS-QRRK) and also by an energy-grained master equation. The two treatments of the pressure dependence agree well. We find that the Level-A//Level-B method gives good agreement with CCSDTQ(P)/CBS. We also find that anharmonicity is an important factor that increases the rate constants of all three reactions. We find that the HO₂ + HCHO reaction has a significant dependence on pressure, but the HO₂ + CF₃CHO reaction is almost independent of pressure. Our findings show that the HO₂ + HCHO reaction makes important contribution to the sink for HCHO, and the HO₂ + CF₃CHO reaction is the dominant sink for CF₃CHO in the atmosphere.

Chemical reaction thresholds according to classical-limit quantum dynamics

Classical-limit quantum dynamics is used to explain the origin of the quantum thresholds of chemical reactions from their classical dynamics when these are vibrationally nonadiabatic across the interaction region. This study is performed within the framework of an elementary model of chemical reaction that mimics the passage from the free rotation of the reagents to the bending vibration at the transition state to the free rotation of the products.

Acid Enriched with Methanol: Formation of a Prebiotic Cluster in the Interstellar Medium

Organic molecules are a potential source of prebiotic chemistry in the interstellar medium (ISM). Methanol (MetOH) is a very important source of more complex molecules. H 3 O + (aq) and Cl - (aq) are fundamental to living organisms and can be generated in the ISM from the dissociation of HCl with just four water molecules, yielding the (H 3 O) + (H 2 O) 3 Cl - ion-pair. Here, a detailed mechanism, based on density functional theory (DFT) and ab-initio (2 nd order Mfller-Plesset perturbation theory, MP2) calculations, is suggested for the substitution reactions of these water molecules by MetOH. The time required for formation of an appreciable amount of the product ((H 3 O) + (MetOH) 3 Cl - ) can be only few years. Such reaction can take place in Sagittarius B2, where HCl, H 2 O and MetOH have already been identified and it can be an important source for the formation of more complex prebiotic structures.

Ion Chemistry of Carbon Dioxide in Nonthermal Reaction with Molecular Hydrogen

The exothermic hydrogen transfer from H₂ to CO₂^·+ leading to H and HCO₂⁺ is investigated in a combined experimental and theoretical work. The experimental mass/charge ratios of the ionic product (HCO₂⁺) and the ionic reactant (CO₂^·+) are recorded as a function of the photoionization energy of the synchrotron radiation. Theoretical density functional calculations and variational transition state theory are employed and adapted to analyze the energetic and the kinetics of the reaction, which turns out to be barrierless and with nonthermal rate coefficients controlled by nonstatistical processes. This study aims to understand the mechanisms and energetics that drive the reactivity of the elementary reaction of CO₂^·+ with H₂ in different processes.

Full-dimensional potential energy surface for the H + CH3OH reaction. Theoretical kinetics and dynamics study

The dynamics and kinetics of the abstraction reactions of hydrogen atoms with methanol have been studied using quasi-classical trajectory calculations and variational transition state theory with tunnelling corrections, based on a new analytical potential energy surface (PES). The new PES is a valence-bond/molecular mechanics (VB/MM) expression that provides us with the potential energy for any set of Cartesian coordinates. Two reaction channels are considered: hydrogen abstraction from the methyl group (R1) and hydrogen abstraction from the alcohol group (R2), R1 being much more likely to occur in the wide temperature range under study (250-1000 K), as expected from the lower barrier height. Our dynamic calculations at a collision energy of 20 kcal mol^-1 show that the H₂ co-product is produced mainly in its vibrational ground-state and little rotation excitation is found. As for our kinetic results, they agree with those from previous theoretical studies as well as with those from kinetic experimental results (rate constants and kinetic isotopic effects), lending confidence to the analytical PES presented here. Thus, we expect this PES to be a simple yet powerful tool to understand such an important reaction in combustion chemistry at very high temperatures and interstellar chemistry at very low temperatures.

Gliding on Ice in Search of Accurate and Cost-Effective Computational Methods for Astrochemistry on Grains: The Puzzling Case of the HCN Isomerization

The isomerization of hydrogen cyanide to hydrogen isocyanide on icy grain surfaces is investigated by an accurate composite method (jun-Cheap) rooted in the coupled cluster ansatz and by density functional approaches. After benchmarking density functional predictions of both geometries and reaction energies against jun-Cheap results for the relatively small model system HCN···(H2O)2, the best performing DFT methods are selected. A large cluster containing 20 water molecules is then employed within a QM/QM' approach to include a realistic environment mimicking the surface of icy grains. Our results indicate that four water molecules are directly involved in a proton relay mechanism, which strongly reduces the activation energy with respect to the direct hydrogen transfer occurring in the isolated molecule. Further extension of the size of the cluster up to 192 water molecules in the framework of a three-layer QM/QM'/MM model has a negligible effect on the energy barrier ruling the isomerization. Computation of reaction rates by the transition state theory indicates that on icy surfaces, the isomerization of HNC to HCN could occur quite easily even at low temperatures thanks to the reduced activation energy that can be effectively overcome by tunneling.

Large Pressure Effects Caused by Internal Rotation in the s-cis-syn-Acrolein Stabilized Criegee Intermediate at Tropospheric Temperature and Pressure

Criegee intermediates are important atmospheric oxidants, and quantitative kinetics for stabilized Criegee intermediates are key parameters for atmospheric modeling but are still limited. Here we report barriers and rate constants for unimolecular reactions of s-cis-syn-acrolein oxide (scsAO), in which the vinyl group makes it a prototype for Criegee intermediates produced in the ozonolysis of isoprene. We find that the MN15-L and M06-2X density functionals have CCSD(T)/CBS accuracy for the unimolecular cyclization and stereoisomerization of scsAO. We calculated high-pressure-limit rate constants by the dual-level strategy that combines (a) high-level wave function-based conventional transition-state theory (which includes coupled-cluster calculations with quasiperturbative inclusion of quadruple excitations because of the strongly multiconfigurational character of the electronic wave function) and (b) canonical variational transition-state theory with small-curvature tunneling based on a validated density functional. We calculated pressure-dependent rate constants both by system-specific quantum Rice-Ramsperger-Kassel theory and by solving the master equation. We report rate constants for unimolecular reactions of scsAO over the full range of atmospheric temperature and pressure. We found that the unimolecular reaction rates of this larger-than-previously studied Criegee intermediate depend significantly on pressure. Particularly, we found that falloff effects decrease the effective unimolecular cyclization rate constant of scsAO by about a factor of 3, but the unimolecular reaction is still the dominant atmospheric sink for scsAO at low altitudes. The large falloff caused by the inclusion of the stereoisomerization channel in the master equation calculations has broad implications for mechanistic analysis of reactions with competitive internal rotations that can produce stable rotamers.

CARNOT: a Fragment-Based Direct Molecular Dynamics and Virtual-Reality Simulation Package for Reactive Systems

Traditionally, the study of reaction mechanisms of complex reaction systems such as combustion has been performed on an individual basis by optimizations of transition structure and minimum energy path or by reaction dynamics trajectory calculations for one elementary reaction at a time. It is effective, but time-consuming, whereas important and unexpected processes could have been missed. In this article, we present a direct molecular dynamics (DMD) approach and a virtual-reality simulation program, CARNOT, in which plausible chemical reactions are simulated simultaneously at finite temperature and pressure conditions. A key concept of the present ab initio molecular dynamics method is to partition a large, chemically reactive system into molecular fragments that can be adjusted on the fly of a DMD simulation. The theory represents an extension of the explicit polarization method to reactive events, called ReX-Pol. We propose a highest-and-lowest adapted-spin approximation to define the local spins of individual fragments, rather than treating the entire system by a delocalized wave function. Consequently, the present ab initio DMD can be applied to reactive systems consisting of an arbitrarily varying number of closed and open-shell fragments such as free radicals, zwitterions, and separate ions found in combustion and other reactions. A graph-data structure algorithm was incorporated in CARNOT for the analysis of reaction networks, suitable for reaction mechanism reduction. Employing the PW91 density functional theory and the 6-31+G(d) basis set, the capabilities of the CARNOT program were illustrated by a combustion reaction, consisting of 28 650 atoms, and by reaction network analysis that revealed a range of mechanistic and dynamical events. The method may be useful for applications to other types of complex reactions.

Kinetic Analysis of a Reaction Path Network Including Ambimodal Transition States: A Case Study of an Intramolecular Diels-Alder Reaction

This study proposes a methodology for the kinetic analysis of a reaction path network including ambimodal transition states (TSs), through which an ensemble of trajectories bifurcates to multiple minima in a phenomenon called dynamical bifurcation. The proposed methodology consists of three techniques: an automated reaction path search to construct a reaction path network including ambimodal TSs, an ab initio molecular dynamics simulation to evaluate the branching ratio, and the definition of rate constants incorporating this ratio. Applying the procedure to a Diels-Alder reaction, it was found that the inclusion of dynamical bifurcations is necessary to explain the experimental reaction yield of a byproduct. In addition, it was verified that the products take 10¹³ s to reach thermal equilibrium and that the experimental selectivity is determined by the dynamical bifurcations.

Master Equation Study of Hydrogen Abstraction from HCHO by OH Via a Chemically Activated Intermediate

The abstraction reaction of hydrogen from formaldehyde by OH radical plays an important role in formaldehyde oxidation. The reaction involves a bimolecular association to form a chemically activated hydrogen-bonded reaction...

Predicting a Kind of Unusual Multiple-States Dimerization-Modes Transformation in Protein PD-L1 System by Computational Investigation and a Generalized Rate Theory

The new cancer immunotherapy has been carried out with an almost messianic zeal, but its molecular basis remains unclear due to the complexity of programmed death ligand 1 (PD-L1) dimerization. In this study, a new and integral multiple dimerization-modes transformation process of PD-L1s (with a new PD-L1 dimerization mode and a new transformation path discovered) and the corresponding mechanism are predicted using theoretical and computational methods. The results of the state analysis show that 5 stable binding states exist in system. A generalized inter-state transformation rate (GITR) theory is also proposed in such multiple-states self-assembly system to explore the kinetic characteristics of inter-state transformation. A “drug insertion” path was identified as the dominant path of the PD-L1 dimerization-modes transformation. Above results can provide supports for both the relative drug design and other multiple-states self-assembly system from the theoretical chemistry perspective.

Ionization of 2- and 4(5)-Nitroimidazoles Radiosensitizers: A "Kinetic Competition" Between NO2 and NO Losses

Nitroimidazoles are a class of chemicals with a remarkable broad spectrum of applications from the production of explosives to the use as radiosensitizers in radiotherapy. The understanding of thedynamics of their fragmentation induced by ionizing sources is of fundamental interest. The goal of this work is to theoretically investigate the kinetic competition between the two most important decomposition channels of 2, 4 and 5‐Nitroimidazole cations: the NO and NO₂ losses. The calculated rate constants of the two processes are in very good agreement with the experimental Photoelectron‐Photoion Coincidence (PEPICO) branching ratio. This study solves the intriguing and theoretically unexplained experimental observation that 2‐Nitroimidazole, at variance with the other two regio‐isomers is a source for only NO at low energies (<12.76 eV). This is a key point for biomedical application of the nitroimidazoles, because NO is the vasodilator that favors the reoxigenation of hypoxic tumor tissues.

Reaction of the N Atom with Electronically Excited O2 Revisited: A Theoretical Study

The kinetics of the reaction of N with electronically excited O₂ (singlet a¹Δ_g and b¹Σ_g⁺ states), potentially relevant for NO_x formation in nonthermal air plasma, is theoretically studied using the multireference second-order perturbation theory. The corresponding thermodynamically and kinetically favored reaction pathways together with possible intersystem crossings are identified. It has been revealed that the energy barrier for the N + O₂(a¹Δ_g) → NO + O reaction is approximately twice the barrier height for the counterpart process with O₂(X³Σ_g^-). The molecular oxygen in the b¹Σ_g⁺ state, in turn, proved to be even less reactive to atomic nitrogen than O₂(a¹Δ_g). Appropriate thermal rate constants for specified reaction channels are calculated by the variational transition-state theory incorporating corrections for the tunneling effect, nonadiabatic transitions, and anharmonicity of vibrations for transition states and reactants. The corresponding three-parameter Arrhenius expressions for the broad temperature range (T = 300-4000 K) are reported. At last, post-transition-state molecular dynamics simulations indicate that the N + O₂(a¹Δ_g) reaction produces vibrationally much colder NO molecules than the N + O₂(X³Σ_g^-) process.

Formation of Substituted Alkyls as Precursors of Peroxy Radicals with a Rapid H-Shift in the Atmosphere

Long straight-chain alkyl peroxy (ROO) radicals substituted with C═C and oxo functional groups are expected to undergo a rapid hydrogen shift (H-shift), which is a critical step in the atmospheric autoxidation mechanism. The existence of a weak tertiary C-H bond plays a key role in the rapid H-shift. Here, the reaction kinetics between OH and two typical long straight-chain functionalized volatile organic compounds, 3-methyl-1-hexene (3-MH) and 2-methylpentanal (2-MP), was theoretically investigated to reveal the fate of the weak C-H bond. The results indicate that the most favored reaction pathways are direct consumption (H-abstraction of 2-MP) and indirect destruction (addition of OH to 3-MH) of the "weak" tertiary C-H bond. The yields of abstraction pathways producing precursors of ROO radicals that undergo rapid H-shifts are computed to be less than 10% for both 3-MH + OH and 2-MP + OH reactions.

Initiation reactions in the high temperature decomposition of styrene

The thermal decomposition of styrene was investigated in a combined experimental, theory and modeling study with particular emphasis placed on the initial dissociation reactions. Two sets of shock tube/time-of-flight mass spectrometry (TOF-MS) experiments were performed to identify reaction products and their order of appearance. One set of experiments was conducted with a miniature high repetition rate shock tube at the Advanced Light Source at Lawrence Berkeley National Laboratory using synchrotron vacuum ultraviolet photoionization. The other set of experiments was performed in a diaphragmless shock tube (DFST) using electron impact ionization. The datasets span 1660–2260 K and 0.5–12 atm. The results show a marked transition from aromatic products at low temperatures to polyacetylenes, up to C₈H₂, at high temperatures. The TOF-MS experiments were complemented by DFST/LS (laser schlieren densitometry) experiments covering 1800–2250 K and 60–240 Torr. These were particularly sensitive to the initial dissociation reactions. These reactions were investigated theoretically and revealed the dissociation of styrene to be a complex multichannel process with strong pressure and temperature dependencies that were evaluated with multi-well master equation simulations. Simulations of the LS data with a mechanism developed in this work are in excellent agreement with the experimental data. From these simulations, rate coefficients for the dissociation of styrene were obtained that are in good agreement with the theoretical predictions. The simulation results also provide fair predictions of the temperature and pressure dependencies of the products observed in the TOF-MS studies. Prior experimental studies of styrene pyrolysis concluded that the main products were benzene and acetylene. In contrast, this study finds that the majority of styrene dissociates to create five styryl radical isomers. Of these, α-styryl accounts for about 50% with the other isomers consuming approximately 20%. It was also found that C–C bond scission to phenyl and vinyl radicals consumes up to 25% of styrene. Finally the dissociation of styrene to benzene and vinylidene accounts for roughly 5% of styrene consumption. Comments are made on the apparent differences between the results of this work and prior literature.

A combined theoretical and experimental study showing styrene primarily decomposes to styryl radicals + H.

Connecting Gas-Phase Computational Chemistry to Condensed Phase Kinetic Modeling: The State-of-the-Art

In recent decades, quantum chemical calculations (QCC) have increased in accuracy, not only providing the ranking of chemical reactivities and energy barriers (e.g., for optimal selectivities) but also delivering more reliable equilibrium and (intrinsic/chemical) rate coefficients. This increased reliability of kinetic parameters is relevant to support the predictive character of kinetic modeling studies that are addressing actual concentration changes during chemical processes, taking into account competitive reactions and mixing heterogeneities. In the present contribution, guidelines are formulated on how to bridge the fields of computational chemistry and chemical kinetics. It is explained how condensed phase systems can be described based on conventional gas phase computational chemistry calculations. Case studies are included on polymerization kinetics, considering free and controlled radical polymerization, ionic polymerization, and polymer degradation. It is also illustrated how QCC can be directly linked to material properties.