Transition State Theory Research Articles

Fluorination Affects the Force Sensitivity and Nonequilibrium Dynamics of the Mechanochemical Unzipping of Ladderanes.

When multiple reaction steps occur before thermal equilibration, kinetic energy from one reaction step can influence overall product distributions in ways that are not well predicted by transition state theory. An understanding of how the structural features of mechanophores, such as substitutions, affect reactivity, product distribution, and the extent of dynamic effects in the mechanochemical manifolds is necessary for designing chemical reactions and responsive materials. We synthesized two tetrafluorinated [4]-ladderanes with fluorination on different rungs and found that the fluorination pattern influenced the force sensitivity and stereochemical distribution of products in the mechanochemistry of these fluorinated ladderanes. The threshold forces for mechanochemical unzipping of ladderane were decreased by α-fluorination and increased by γ-fluorination; these changes correlated to the different stabilizing or destabilizing effects of fluorination patterns on the first transition state. Using ab initio steered molecular dynamics (AISMD), we compared the product distributions of synthesized and hypothetical ladderanes with different substitution patterns. These calculations suggest that fluorination on the first two bonds of ladderane gives rise to a larger fraction of dynamic trajectories and a larger fraction of E-alkene product through a mechanism resulting from larger momentum because of the greater atomic mass of fluorine. Fluorination on the third and fourth rungs instead gives a larger fraction of E-alkene product primarily due to electronic effects. These combined experimental and computational studies of the mechanochemical unzipping of fluorinated ladderanes provide an example of how relatively simple substituents can affect the extent of nonstatistical dynamics and, thus, mechanochemical outcomes.

Glycosylium Ions in Superacid Mimic the Transition State of Enzyme Reactions.

The hydrolysis of glycosides is a biochemical transformation that occurs in all living organisms, catalyzed by a broad group of enzymes, including glycoside hydrolases. These enzymes cleave the glycosidic bond via a transition state with substantial oxocarbenium ion character, resulting in short-lived oxocarbenium ion-like species. While such transient species have been inferred through theoretical studies and kinetic isotope effect measurements, their direct spectroscopic characterization remains challenging. In this study, we exploit a superacid environment to generate, accumulate, and fully characterize nonprotected 2-deoxy glycosyl cations in the d-glucopyranose, d-galactopyranose, and l-arabinofuranose series using low-temperature NMR spectroscopy, supported by DFT calculations. Additionally, QM/MM MD simulations reveal that the properties of these glycosyl cations in superacid closely resemble those within the active sites of glycosidase enzymes, particularly in terms of conformation and anomeric charge distribution. These findings highlight a parallel between the stabilizing effect of counterions in superacid media and the network of multidentate noncovalent interactions within glycosidase active sites, which stabilize transition states with pronounced oxocarbenium ion character.

Lone Pair-π Interactions in Organic Reactions.

Noncovalent interactions between a lone pair of electrons and π systems can be categorized into two types based on the nature of π systems. Lone pair-π(C═O) interactions with π systems of unsaturated, polarized bonds are primarily attributed to orbital interactions, whereas lone pair-π(Ar) interactions with π systems of aromatic functional groups result from electrostatic attractions (for electron-deficient aryls) or dispersion attractions and Pauli repulsions (for electron-rich/neutral aryls). Unlike well-established noncovalent interactions, lone pair-π interactions have been comparatively underappreciated or less used to influence reaction outcomes. This review emphasizes experimental and computational studies aimed at integrating lone pair-π interactions into the design of catalytic systems and utilizing these interactions to regulate the reactivity and selectivity of chemical transformations. The role of lone pair-π interactions is highlighted in the stabilization or destabilization of transition states and ground-state binding. Examples influenced by lone pair-π interactions with both unsaturated, polarized bonds and aromatic rings as π systems are included. At variance with previous reviews, the present review is not structured according to the physical origin of particular classes of lone pair-π interactions but is divided into chapters according to ways in which lone pair-π interactions affect kinetics and/or selectivity of reactions.

Quantum Chemistry Study on Cl-Initiated Reactions of 2-Chloropropane and 2-Methylpropanoyl Halogen (Cl, Br, F): Mechanism, Kinetics, and Atmospheric Implications.

Halogenated volatile organic compounds (HVOCs) pose significant bioaccumulative and toxicological risks, necessitating effective strategies for their removal. Here, we show, through a computational study employing density functional theory and coupled cluster methods, the detailed mechanism and kinetic properties of Cl-initiated degradation reactions of 2-chloropropane (2-CP, (CH3)2CHCl) and 2-methylpropanoyl halide ((CH3)2CHCOX, X = Cl, Br, F). The reaction rate constants of all the channels were calculated by the canonical variational transition state theory (CVT) with the correction of the small curvature tunneling effect (SCT) at 200-1000 K. The subsequent transformation pathways of the major radical products of (CH3)2CHCl and (CH3)2CHCOCl in the presence of O2, NO, and HO2 radical were investigated. The results elucidate the reaction pathways and rate constants, which are in excellent agreement with the experimental data at 296 K. We further explore the atmospheric implications of these reactions by assessing the atmospheric lifetime (τ) and ozone depletion potential (ODP). Additionally, we delve into the aquatic toxicity and bioaccumulation potential of the reactants and their transformation products. This study not only advances our knowledge of the atmospheric fate of halogenated hydrocarbons but also underscores the importance of considering the environmental and toxicological impacts in the development of HVOC mitigation strategies.

Semiclassical instanton theory for reaction rates at any temperature: How a rigorous real-time derivation solves the crossover temperature problem.

Instanton theory relates the rate constant for tunneling through a barrier to the periodic classical trajectory on the upturned potential energy surface, whose period is τ = ℏ/(kBT). Unfortunately, the standard theory is only applicable below the "crossover temperature," where the periodic orbit first appears. This paper presents a rigorous semiclassical (ℏ → 0) theory for the rate that is valid at any temperature. The theory is derived by combining Bleistein's method for generating uniform asymptotic expansions with a real-time modification of Richardson's flux-correlation function derivation of instanton theory. The resulting theory smoothly connects the instanton result at low temperature to the parabolic correction to Eyring transition state theory at high-temperature. Although the derivation involves real time, the final theory only involves imaginary-time (thermal) properties, consistent with the standard version of instanton theory. Therefore, it is no more difficult to compute than the standard theory. The theory is illustrated with application to model systems, where it is shown to give excellent numerical results. Finally, the first-principles approach taken here results in a number of advantages over previous attempts to extend the imaginary free-energy formulation of instanton theory. In addition to producing a theory that is a smooth (continuously differentiable) function of temperature, the derivation also naturally incorporates hyperasymptotic (i.e., multi-orbit) terms and provides a framework for further extensions of the theory.

Semiclassical Transition State Theory (SCTST) Rate Coefficients for the Unimolecular Decomposition of the Ethoxy (CH3CH2O) Radical.

The thermal unimolecular decay of ethoxy is important in high-temperature combustion environments where the ethoxy radical is a key reactive intermediate. Two dissociation pathways of ethoxy, including the β-C-C scission to yield CH3 + CH2O and the H-elimination to make H + CH3CHO, were characterized using a high-level coupled-cluster-based composite quantum chemical method (mHEAT-345(QΛ)). The former route is found to be dominant while the latter is insignificant, in agreement with previous experimental and theoretical studies. Thermal rate coefficients are calculated for P = 0.001-658 atm (of air) and T = 300-2500 K using semiclassical transition state theory (SCTST) in combination with a pragmatic two-dimensional E,J-resolved master equation (2DME). The effects of tunneling and anharmonicity on the calculated rate constants are also examined. The tunneling factor is found to be inversely dependent on pressure, contrary to previous observations of pressure-dependent tunneling in entrance channels.

Enhancing Eyringpy: Accurate Rate Constants with Canonical Variational Transition State Theory and the Hindered Rotor Model.

The recrossing effect and hindered rotations can lead to significant inaccuracies in rate constant calculations using transition state theory and the harmonic oscillator approximation. To address these issues, we enhanced Eyringpy, a Python-based computational tool, by integrating the canonical variational transition state theory (CVT) and the hindered rotor model, effectively mitigating the limitations of traditional methods. CVT rate constants are calculated using electronic structure data from nonstationary points along the minimum-energy path. Additionally, we developed an algorithm based on reaction force analysis to autonomously select relevant nonstationary points. Torsions are modeled using one-dimensional hindered rotor approaches proposed by Pitzer-Gwinn and Ayala-Schlegel.

Kinetic Study on the H-Abstraction Reactions from 1-Nitropropane by H and OH Radicals.

To improve the comprehension of the combustion kinetics of 1-nitropropane (1-NP), the H-abstraction reactions from 1-NP by H and OH radicals are theoretically explored using the canonical variational transition-state theory combined with the multistructural torsional anharmonicity and small-curvature tunneling corrections (MS-CVT/SCT). The M08-HX/cc-pVTZ method is adopted for geometry optimizations and frequency calculations due to its effective performance in describing the current reaction systems with an average mean unsigned deviation of 0.95 kcal mol-1 against the benchmark by the high-level DLPNO-CCSD(T)/CBS(T-Q) method. The rate constants for the investigated reactions are calculated using the MS-CVT/SCT method at 200-2000 K, and a good agreement is achieved by comparing our calculations with the available literature data. The rate constant calculations show that the multistructural torsional anharmonicity, variational effect, and tunneling effect have different influences on the H-abstraction reactions 1-NP + H/OH, and the reaction channel at the Cβ position is the most important above the room temperature. With our calculations, a literature combustion kinetic model of 1-NP is revised, and the new model demonstrates improved performance across most conditions. Sensitivity analysis demonstrates that the H-abstraction reaction channel, 1-NP + OH = CH3CHCH2NO2 + H2O, alters the combustion kinetics of 1-NP and plays an important role in controlling its ignition process.

Systematic study on the hydrogen abstraction reactions from oxygenated compounds by H and HO2

AbstractTo extend the rule‐based approach for hydrogen abstraction reactions from oxygenated compounds, a systematic investigation was performed to examine the reactivity of gas‐phase hydrogen abstraction reactions from alkyl groups (methyl and ethyl groups) bound to oxygen atoms in five types of oxygenated compounds (alcohols, ethers, formate esters, acetate esters, and carbonate esters) by H atoms and HO2 radicals comprehensively considering rotational conformers. Quantum chemical calculations were conducted at the CBS‐QB3 level for stationary points. Rate constants were determined employing conventional transition state theory (TST). For hydrogen abstraction reactions by H, the rotational conformer distribution partition function was employed to approximate partition functions, owing to the similarity in vibrational energy‐level structures among conformers. In hydrogen abstraction reactions by HO2, the vibrational structures of transition‐state (TS) conformers varied significantly due to the hydrogen bonding, leading to an inappropriate evaluation of rate constants when using the lowest‐energy conformer as a representative. Therefore, the rate constants were calculated by the multi‐structural TST. It was revealed that the differences in functional groups containing O atoms mainly affect the bond dissociation energies of the C–H bonds and the activation energies of hydrogen abstraction reactions only when the C atoms are adjacent to the O atoms. Additionally, it was found that hydrogen bonds formed in the TSs show minor effect on rate parameters for the overall rate constants, apart from the reduction of the pre‐exponential factors for the H‐abstraction reactions from the methylene position of ethyl groups. The comparison with the rate constants from previous studies showed reasonable results, indicating that the rate constants in this study, which thoroughly consider rotational conformers, can be the current best estimates.

Research on the Efficacy of Markov Chains in Analyzing and Predicting Chemical Reaction Rates

Abstract. The Markov chain is a powerful mathematical model used to describe stochastic processes in which the probability of each event depends only on the state attained in the previous event. The chemical reaction rate is a measure of how quickly or slowly a chemical reaction proceeds in multiple stages. This research paper uses the case study of enzymes to investigate the efficacy of the Markov chain in analyzing and predicting chemical reaction rates. By modeling chemical reaction pathways using Markov chains, this study tries to explore how Markov chains help capture and predict a chemical systems dynamic behavior. Scientists have been using multiple methods to predict chemical reaction rates, which involve methods like the Arrhenius equation, transition state theory, molecular dynamics, quantum mechanics, and machine learning. In conclusion, after comparing the advantages and disadvantages of the Markov chain predicting method with those methods above, Markov chains did stand out and provide valuable insights into the understanding of reaction dynamics.

Mechanistic studies on the oxidation reaction of n-pentane

The oxidation reaction mechanism of n-pentane is investigated using density functional theory and transition state theory as a case study to elucidate the combustion characteristics of liquids with low boiling points. This study divides the oxidation reaction of n-pentane into four steps. First, n-pentane decomposes to form n-pentyl radicals C5H11 and H, CH3 and C4H9, and C2H5 and C3H7 radicals. Second, n-pentane primarily undergoes H-abstraction reactions with H, CH3, C2H5, and C3H7 radicals to form the C5H11 radicals. Subsequently, C5H11 radicals react with O2 in an addition reaction to form n-pentyl peroxy radicals ROO. Finally, ROO radical undergoes internal H-atom transfer to form hydroperoxy pentyl radicals QOOH, which then undergoes cyclization and bond scission to produce cyclic ethers, alkenes, aldehydes, OH radicals, and HO2 radicals. Results indicate that n-pentane readily decomposes into C2H5 and C3H7 radicals, with a bond dissociation energy of 367.1 KJ/mol. The H-abstraction reactions involving H and CH3 radicals have the fastest rates, which require the lowest energy barriers of 21.6 and 41.9 KJ/mol, respectively. The reaction between C5H11 and O2 is a barrierless addition reaction. The oxidation of n-pentane, which leads to the formation of 2-methyloxirane and OH radicals, exhibits the fastest reaction rate.

Correlative Activation Free Energy (CAFE) Model: Application to Viscous Processes in Inorganic Oxide Glass-Formers

We explore the concept of correlative activation free energy (CAFE) for the analysis and interpretation of viscosity data of a collection of 847 inorganic oxide glass formers that exhibit various degrees of non-Arrhenius behavior. The CAFE model formalism is strictly based on transition state theory and accounts for the variation in the activation barrier for the viscous dissipation due to the structural evolution the system undergoes upon traversing the glass transition regime. Thus, fitting parameters are meaningful in a statistical thermodynamic context. Compared to the VFT and MYEGA equations, fits using the CAFE model are more robust when extrapolating to infinite temperature because the latter encodes non-enthalpic contributions to the rate coefficient more realistically. The CAFE model-based analysis reveals a strong connection between melt fragility and the degree of change in the potential energy landscape with temperature. Accordingly, while the average ground-state potential energy of the glass forming liquid gradually increases with temperature, the energy of the activated state remains relatively invariant. Our analysis also allows one to estimate the number of atoms involved in the viscous relaxation process, which ranges from approximately 10 to 50 atoms for the oxide glass formers studied. We observe that thermally activated dynamic phenomena exhibited by glassy networks, such as the mixed alkali effect, persist into the supercooled liquid state.

Reduced Cost Computation and Exploitation of Accurate Radial Interaction Potentials for Barrier-Less Processes.

Barrier-less steps are typical of radical and ionic reactions in the gas-phase, which often take place in extreme environments such as the combustion reactors operating at very high temperatures or the interstellar medium, characterized by ultralow temperatures and pressures. The difficulty of experimental studies in conditions mimicking these environments suggests that computational approaches can provide a valuable support. In this connection, the most advanced treatments of these processes in the framework of transition state theory are able to deliver accurate kinetic parameters provided that the underlying potential energy surface is sufficiently accurate. Since this requires a balanced treatment of static and dynamic correlation (which play different roles in different regions), very sophisticated and expensive quantum chemical approaches are required. One effective solution of this problem is offered by the computation of accurate one-dimensional radial potentials, which are then used to correct the results of a Monte Carlo sampling performed by cheaper quantum chemical approaches. In this paper, we will show that, for a large panel of different barrier-less reaction steps, the radial potential is ruled by the R-4 term and that addition of a further R-6 contribution provides quantitative agreement with the reference points. The consequences of this outcome are not trivial, since the reference potential can be fitted by a very limited number of points possibly with a nonlinear spacing. In the case of reaction steps ruled by long-range transition states, generalized expressions are also given for computing reaction rates in the framework of the phase-space theory. All these improvements pave the way toward the computation of reaction rates for barrier-less reactions involving large molecules.

A Transition State Theory-Based Continuum Plasticity Model Accounting for the Local Stress Fluctuation

Based on the transition state theory, a continuum plasticity theory is developed for metallic materials. Moreover, the nature of local stress fluctuation within a material point is considered by incorporating the probability distribution of the stresses. The model is applied to investigate the mechanical behaviors of 316 L stainless steel under various loading cases. The simulated results closely match the results obtained by the polycrystal plasticity model and experiments. The mechanical behaviors associated with strain rate sensitivity, temperature dependence, stress relaxation, and strain creep are correctly captured by the model. Furthermore, the proposed model successfully characterizes the Bauschinger effect, which is challenging to capture with a conventional continuum model without additional assumptions. The proposed model could be further employed in the design, manufacturing, and service of engineering components.

Impact of Temperature on Reaction Rate in Catalytic Reactions

Purpose: The aim of the study was to assess the impact of temperature on reaction rate in catalytic reactions. Methodology: This study adopted a desk methodology. A desk study research design is commonly known as secondary data collection. This is basically collecting data from existing resources preferably because of its low cost advantage as compared to a field research. Our current study looked into already published studies and reports as the data was easily accessed through online journals and libraries. Findings: The study indicated that as higher temperatures generally increase the rate at which reactions occur. This is due to the fact that elevated temperatures provide the reactant molecules with more kinetic energy, enabling them to collide more frequently and with greater force, which is necessary to overcome the activation energy barrier. In catalytic reactions, temperature not only accelerates the intrinsic rate of the reaction but can also affect the activity and selectivity of the catalyst. However, too high a temperature can lead to catalyst deactivation through processes such as sintering or coke formation, where the catalyst surface is altered or blocked. Thus, an optimal temperature range is crucial to balance enhanced reaction rates while maintaining catalyst integrity and performance. Implications to Theory, Practice and Policy: Arrhenius equation, transition state theory and collision theory may be used to anchor future studies on the impact of temperature on reaction rate in catalytic reactions. In practical applications, industries should implement advanced temperature control systems to maintain optimal reaction conditions during catalytic processes. Policymakers have a critical role in shaping the landscape of catalytic reactions by developing regulatory guidelines focused on temperature management.

Analysis of differential scanning calorimetry data for aged plutonium.

Differential scanning calorimetry data for samples of a 52 year old plutonium alloy with 3.3 at. % Ga that were heated beyond the melting point is analyzed using transition state theory to find activation energies for the δ to ɛ and ɛ to liquid phase transitions. A Bayesian statistical method involving a Gaussian process model is used to find mean values and confidence intervals for the activation energies. The activation energy for the δ to ɛ phase transition increases by 3.3 ± 3.8% per decade, relative to the case when all age related plutonium lattice point defects have been removed through annealing. The corresponding increase in activation energy for the ɛ to liquid transition is shown to be 7.1 ± 1.8% per decade. It is postulated that the change in activation energy with age for both phase transitions is caused, in part, by the accumulation of the same type of lattice point defects associated with the observed increase in elastic bulk modulus over time.

The characteristics and mechanism of NaHCO3 compound fly ash in suppressing gas explosions in pipeline networks

Gas has been widely concerned due to its importance in the industrial and energy fields. In order to improve the inhibition effect of gas explosion, under the self-constructed pipe network system, the inhibition of gas explosion by composite inhibitor of fly ash and NaHCO3 with different ratios was investigated, and the microscopic inhibition mechanism of the two kinds of powders on the explosion of gas was investigated based on the method of density functional theory and transition state theory from the perspective of molecular dynamics. The results show that: the composite powder explosion suppression is better than a single powder, explosion suppression effect with the increase in the proportion of the mass of NaHCO3 significantly improve the 5 groups of conditions NaHCO3 loading of 40% (by mass) is the best, this time, the explosion of the peak overpressure, the peak flame propagation velocity, the peak flame temperature compared to the maximum reduction in the percentage of the measures taken for the maximum of 74.42%, 81.93%, 68.71%. In addition, NaHCO3, fly ash effectively inhibit the key primitive reaction of gas explosion. When the temperature reaches a certain point, the two and O*, O2, OH* and H* reaction rate higher than the rate of CH4 oxidation chain reaction, the dominant reaction, the maximum difference in rate constants of 70.95, 58.81, 60.06, 44.94. The study of the transition from the macro-scale to the molecular level of the study, in-depth understanding of the mechanism of explosion suppression, to reduce the risk of explosion from the ground up, and enriches the Gas explosion prevention and control of the theoretical system, for the operators to provide a strong technical guarantee for safe production.

Low-dimensional projection of reactivity classes in chemical reaction dynamics using supervised dimensionality reduction.

Transition state theory (TST) provides a framework to estimate the rate of chemical reactions. Despite its great success with many reaction systems, the underlying assumptions such as local equilibrium and nonrecrossing do not necessarily hold in all cases. Although dynamical systems theory can provide the mathematical foundation of reaction tubes existing in phase space that enables us to predict the fate of reactions free from the assumptions of TST, numerical demonstrations for large systems have been yet one of the challenges. Here, we propose a dimensionality reduction algorithm to demonstrate structures in phase space (called reactive islands) that predict reactivity in systems with many degrees of freedom. The core of this method is the application of supervised principal component analysis, where a coordinate transformation is performed to preserve the dynamical information on reactivity (i.e., to which potential basin the system moves from a region of interest) as much as possible. The reactive island structures are expected to be reflected in the transformed, low-dimensional phase space. As an illustrative example, the algorithm is scrutinized using a modified Hénon-Heiles Hamiltonian system extended to many degrees of freedom, which has three channels leading to three different products from one stable potential basin. It is shown that our algorithm can predict the reactivity in the transformed, low-dimensional coordinate system better than a naïve coordinate system and that the reactivity distribution in the transformed low-dimensional space is considered to reflect the underlying reactive islands.

Electrostatically Dominated Pre-Organization inCyclodextrin Metal-Organic Frameworks.

Electrostatic interactions between oppositely charged entities play a key role in pre-organizing substrates and stabilizing transition states of reactions in enzymes. The use of electrostatic interactions to pre-organize ions in nanoconfined pores, however, has not been investigated to its full potential. Herein, we describe how carboxylate anions can be pre-organized at the behest of their electrostatic interactions with K+ cations in nanoconfined tunnels present in γ-cyclodextrin metal-organic frameworks, i.e., CD-MOFs. Several carboxylate anions, which are all much smaller than the cavities of the tunnels, were visualized by X-ray crystallography when nanoconfined in CD-MOFs, despite the large voids present in the tunnels. These anions were found to be aligned within a planar array defined by four K+ cations, positioned around the periphery of the tunnels. The strong electrostatic interactions between the carboxylate anions and the K+ cations dictate the orientation of the anions and override the influence of other possible noncovalent bonding interactions between them and the tunnels. Consequently, the aligned pairs of γ-cyclodextrin rings constituting the tunnels become distorted, resulting in their lower symmetry and fewer disordered carboxylate anions in the solid-state. Our findings offer a transformative strategy for controlling the packing and orientation of ions in nanoconfined environments.

Contrasting Historical and Physical Perspectives in Asymmetric Catalysis: ▵▵G≠ versus Enantiomeric Excess.

With the rise of machine learning (ML), the modeling of chemical systems has reached a new era and has the potential to revolutionize how we understand and predict chemical reactions. Here, we probe the historic dependence on utilizing enantiomeric excess (ee) as a target variable and discuss the benefits of using relative Gibbs free activation energies (ΔΔG≠), grounded firmly in transition-state theory, emphasizing practical benefits for chemists. This perspective is intended to discuss best practices that enhance modeling efforts especially for chemists with an experimental background in asymmetric catalysis that wish to explore modelling of their data. We outline the enhanced modeling performance using ΔΔG≠, escaping physical limitations, addressing temperature effects, managing non-linear error propagation, adjusting for data distributions and how to deal with unphysical predictions,in order to streamline modeling for the practical chemist and provide simple guidelines to strong statistical tools. For this endeavor, we gathered ten datasets from the literature covering very different reaction types. We evaluated the datasets using fingerprint-, descriptor-, and graph neural network-based models. Our results highlight the distinction in performance among varying model complexities with respect to the target representation, emphasizing practical benefits for chemists.