Theoretical Kinetics Study of the O(3P) + CH4/CD4 Hydrogen Abstraction Reaction: The Role of Anharmonicity, Recrossing Effects, and Quantum Mechanical Tunneling

Kinetic study of the CN + C2H6 hydrogen abstraction reaction based on an analytical potential energy surface

The temperature dependence of the thermal rate constants and kinetic isotope effects (KIE) of the CN + C2H6 gas-phase hydrogen abstraction reaction was theoretically determined within the 25-1000 K temperature range, i.e., from very low- to high-temperature regimes. Based on a recently developed full-dimensional analytical potential energy surface fitted to highly accurate explicitly correlated ab initio calculations, three different kinetic theories were used: canonical variational transition state theory (CVT), quasiclassical trajectory theory (QCT), and ring polymer molecular dynamics (RPMD) method for the computation of rate constants. We found that the thermal rate constants obtained with the three theories show a V-shaped temperature dependence, with a pronounced minimum near 200 K, qualitatively reproducing the experimental measurements. Among the three methods used in this work, the QCT and RPMD methods have the best agreement with the experiment at low and high temperatures, respectively, while the CVT model shows the largest discrepancies. The significant increase in the rate constant at very low temperatures in this very exothermic and practically barrierless reaction could be attributed to the large value of the impact parameter, possibly ruling out the role of the tunneling effect and the intermediate complexes in the entrance channel. The theoretical H/D KIE depicted a "normal" behaviour, i.e., values greater than unity, emulating the experimental measurements and improving previous theoretical results. Finally, the discrepancies between theory and experiments were analysed as a function of several factors, such as limitations of the kinetics theories and the potential energy surface, as well as the uncertainties in the experimental measurements.

Dynamics study of the post-transition-state-bifurcation process of the (HCOOH)H+ → CO + H3O+/HCO+ + H2O dissociation: application of machine-learning techniques

The process of protonated formic acid dissociating from the transition state was studied using ring-polymer molecular dynamics (RPMD), classical MD, and quasi-classical trajectory (QCT) simulations. Temperature had a strong influence on the branching fractions for the HCO⁺ + H₂O and CO + H₃O⁺ dissociation channels. The RPMD and classical MD simulations showed similar behavior, but the QCT dynamics were significantly different owing to the excess energies in the quasi-classical trajectories. Machine-learning analysis identified several key features in the phase information of the vibrational motions at the transition state. We found that the initial configuration and momentum of a hydrogen atom connected to a carbon atom and the shrinking coordinate of the CO bond at the transition state play a role in the dynamics of HCO⁺ + H₂O production.

Fast Predictions of Reaction Barrier Heights: Toward Coupled-Cluster Accuracy

Quantitative estimates of reaction barriers are essential for developing kinetic mechanisms and predicting reaction outcomes. However, the lack of experimental data and the steep scaling of accurate quantum calculations often hinder the ability to obtain reliable kinetic values. Here, we train a directed message passing neural network on nearly 24,000 diverse gas-phase reactions calculated at CCSD(T)-F12a/cc-pVDZ-F12//ωB97X-D3/def2-TZVP. Our model uses 75% fewer parameters than previous studies, an improved reaction representation, and proper data splits to accurately estimate performance on unseen reactions. Using information from only the reactant and product, our model quickly predicts barrier heights with a testing MAE of 2.6 kcal mol^-1 relative to the coupled-cluster data, making it more accurate than a good density functional theory calculation. Furthermore, our results show that future modeling efforts to estimate reaction properties would significantly benefit from fine-tuning calibration using a transfer learning technique. We anticipate this model will accelerate and improve kinetic predictions for small molecule chemistry.

Theoretical study of the O(3P) + SiH4 reaction: global potential energy surface, kinetics and dynamics study

In order to understand the gas-phase hydrogen abstraction reaction between O(³P) and silane we began by developing the first full-dimensional analytical potential energy surface, named PES-2022. It is basically a valence bond function augmented with molecular mechanic terms describing in an intuitive way stretching and bending nuclei motions, and it is fitted to high level ab initio calculations. The surface presents continuous and smooth behaviour, with analytical first energy derivatives, on which the hydrogen atoms in silane are permutationally symmetric. Based on PES-2022, a kinetics study was performed using the variational transition-state theory with multidimensional tunnelling corrections in the temperature range of 300-1000 K. We observed that experimental and theoretical results show widely spread results, both in absolute value and temperature dependence, possibly because they include the reactivity from both O(³P) and O(¹D) electronic states, which present different mechanisms and multiple channels. When the comparison is performed on the same footing, O(³P) + SiH₄ → HO + SiH₃, the present results agree with Ding and Marshall's experiments and with Zhang et al.'s theoretical rate constants. The kinetic isotope effects (KIEs) reproduced the only experimental value, improving previous theoretical results. Finally, a dynamics study was performed on PES-2022 using quasi-classical trajectory calculations under two different initial conditions, at fixed room temperature and at a fixed collision energy of 8.0 kcal mol^-1. In the first case, the available energy deposited as HO(v) vibration was 47%, with population inversion, P(v = 0)/P(v = 1) = 11/89%, reproducing the experimental evidence. In the second case, the experimental product translational distribution was reasonably simulated, while the angular product distribution presented opposite behaviour, backward versus forward. On analysing this discrepancy, we found that while in the present work the O(³P) + SiH₄ reaction was reported, in the experiment both O(³P) and O(¹D) electronic states are reported. So, the comparison was not performed on the same footing. In sum, agreement of the present results with experiments permits us to be reasonably optimistic about the quality and accuracy of the new PES, and at the same time to highlight the fact that theory/experiment comparisons must be performed on the same footing.

Mechanism and Kinetics of Methane Combustion. Part II: Potential Energy Surface for Hydrogen-Abstraction Reaction of CH4 + O(3P)

Methane combustion plays an important role in various fields such as combustion chemistry and atmospheric chemistry of the stratosphere. Highly accurate study of its initial reaction remains a key challenge. Here, through extensive studies with a state-of-the-art ab initio and neural network method, we present a potential energy surface of the O(³P) + CH₄ → OH + CH₃ reaction on the ground state 1³A and the first excited state 2³A. In this work, the energies of 10 167 points covering all important regions are obtained with state-averaged complete active space self-consistent field calculations and then fitted using the Levenberg-Marquardt algorithm with a root-mean-square error of 0.391 and 0.442 kcal/mol for the 1³A and 2³A states, respectively. This study explores the characteristics of the radical van der Waals (VdW) complex and reveals a detailed mechanism of the methane combustion initial reaction. Within the scope of this mechanism, this surface gives a fairly accurate description of the regions around the saddle point, conical intersection, and vdW wells in the entrance for efficient computational simulations. As a theoretical study on a prototypical polyatomic reaction, it is hopeful that this work will modify our understanding of the primary process in hydrocarbon combustion.

Ring-Polymer Molecular Dynamics Calculations of Thermal Rate Coefficients and Branching Ratios for the Interstellar H3+ + CO → H2 + HCO+/HOC+ Reaction and Its Deuterated Analogue

The reaction between H₃⁺ and CO is important in understanding the H₃⁺ destruction mechanism in the interstellar medium. In this work, thermal rate coefficients for the H₃⁺ + CO and D₃⁺ + CO reactions are calculated using ring-polymer molecular dynamics (RPMD) on a high-level machine-learning potential energy surface. The RPMD results agree well with the classical molecular dynamics results, where nuclear quantum effects are completely ignored, whereas the agreement between the RPMD results and the previous quasi-classical trajectory is good only at low temperatures. The calculated [HCO⁺]/[HOC⁺] product branching ratios decrease as the temperature increases, and the product branching is exclusively determined by the initial collisional orientation, which governs the formation of an ion-dipole complex, H₃⁺···CO or H₃⁺···OC, that dissociates into H₂ + HCO⁺ or H₂ + HOC⁺, respectively, via a direct mechanism. However, the contribution of the indirect mechanism via the rearrangement between H₃⁺···CO and H₃⁺···OC increases as the temperature increases, although its absolute fraction is small.

Electronic Structure and Excited States of the Collision Reaction O(3P) + C2H4: A Multiconfigurational Perspective

We present a study of the O(³P) + C₂H₄ scattering reaction, a process that takes place in the interstellar medium and is of relevance in atmospheric chemistry as well. A comprehensive investigation of the electronic properties of the system has been carried out based on multiconfigurational ab initio CASSCF/CASPT2 calculations, using a robust and consistent active space that can deliver accurate potential energy surfaces in the key regions visited by the system. The paper discloses detailed description of the primary reaction pathways and the relevant singlet and triplet excited states at the CASSCF and CASPT2 level, including an accurate description of the critical configurations, such as minima and transition states. The chosen active space and the CASSCF/CASPT2 computational protocol are assessed against coupled-cluster calculations to further check the stability and reliability of the entire multiconfigurational procedure.

A matrix completion algorithm to recover modes orthogonal to the minimum energy path in chemical reactions

Structured statistical methods are promising for recovering or completing information from noisy and incomplete data with high fidelity. In particular, matrix completion exploits underlying structural properties such as rank or sparsity. Our objective is to employ matrix completion to reduce computational effort associated with the calculation of multiple quantum chemical Hessians, which are necessary for identification of temperature-dependent free energy maxima under canonical variational transition state theory (VTST). We demonstrate proof-of-principle of an algebraic variety-based matrix completion method for recovering missing elements in a matrix of transverse Hessian eigenvalues constituting the minimum energy path (MEP) of a reaction. The algorithm, named harmonic variety-based matrix completion (HVMC), utilizes the fact that the points lying on the MEP of a reaction step constitute an algebraic variety in the reaction path Hamiltonian representation. We demonstrate that, with as low as 30% random sampling of matrix elements for the largest system in our test set (46 atoms), the complete matrix of eigenvalues can be recovered. We further establish algorithm performance for VTST rate calculations by quantifying errors in zero-point energies and vibrational free energies. Motivated by this success, we outline next steps toward developing a practical HVMC algorithm, which utilizes a gradient-based sampling protocol for low-cost VTST rate computations.

VTST and RPMD kinetics study of the nine-body X + C2H6 (X ≡ H, Cl, F) reactions based on analytical potential energy surfaces

Thermal rate constants of nine-atom hydrogen abstraction reactions, X + C2H6 → HX + C2H5 (X ≡ H, Cl, F) with qualitatively different reaction paths, have been investigated using two kinetics approaches - variational transition state theory with multidimensional tunnelling (VTST/MT) and ring polymer molecular dynamics (RPMD) - and full dimensional analytical potential energy surfaces. For the H + C2H6 reaction, which proceeds through a noticeable barrier height of 11.62 kcal mol-1, kinetics approaches showed excellent agreement between them (with differences less than 30%) and with the experiment (with differences less than 60%) in the wide temperature range of 200-2000 K. For X = Cl and F, however, the situation is very different. The barrier height is either low or very low, 2.44 and 0.23 kcal mol-1, respectively, and the presence of van der Waals complexes in the entrance channel leads to a very flat topography and, consequently, imposes theoretical challenges. For the Cl(2P) reaction, VTST/MT underestimates the experimental rate constants (with differences less than 86%), and RPMD demonstrates better agreement (with differences less than 47%), although the temperature dependence is opposite to the experiment at low temperatures. Finally, for the F(2P) reaction, available experimental information shows discrepancies, both in the absolute values of the rate constants and also in the temperature dependence. Unfortunately, kinetics theories did not resolve this discrepancy. Different possible causes of these theory/experiment discrepancies were analyzed.

An accurate potential energy surface and ring polymer molecular dynamics study of the Cl + CH4→ HCl + CH3reaction

Thermal rate coefficients for the Cl + CH₄/CD₄reactions were studied on a new full-dimensional accurate potential energy surface with the spin–orbit corrections considered in the entrance channel.

New Stress Test for Ring Polymer Molecular Dynamics: Rate Coefficients of the O(3P) + HCl Reaction and Comparison with Quantum Mechanical and Quasiclassical Trajectory Results

In the past decade, ring polymer molecular dynamics (RPMD) has emerged as a very efficient method to determine thermal rate coefficients for a great variety of chemical reactions. This work presents the application of this methodology to study the O(³P) + HCl reaction, which constitutes a stringent test for any dynamical calculation due to rich resonant structure and other dynamical features. The rate coefficients, calculated on the ³A' and ³A″ potential energy surfaces (PESs) by Ramachandran and Peterson [ J. Chem. Phys. 2003 , 119 , 9590 ], using RPMD and quasiclassical trajectories (QCT) are compared with the existing experimental and the quantum mechanical (QM) results by Xie et al. [ J. Chem. Phys. 2005 122 , 014301 ]. The agreement is very good at T > 600 K, although RPMD underestimates rate coefficients by a factor between 4 and 2 in the 200-500 K interval. The origin of these discrepancies lies in the large contribution from tunneling on the ³A″ PES, which is enhanced by resonances due to quasibound states in the van der Waals wells. Although tunneling is fairly well accounted for by RPMD even below the crossover temperature, the effect of resonances, a long-time effect, is not included in the methodology. At the highest temperatures studied in this work, 2000-3300 K, the RPMD rate coefficients are somewhat larger than the QM ones, but this is shown to be due to limitations in the QM calculations and the RPMD are believed to be more reliable.

The hydrogen abstraction reaction H + C2H6 → H2(v,j) + C2H5. Part II. Theoretical kinetics and dynamics study

Two important issues motivated the present study: the role of the tunnelling contribution at low temperatures and the role of the alkyl fragment in the dynamics.

The low temperature D+ + H2→ HD + H+ reaction rate coefficient: a ring polymer molecular dynamics and quasi-classical trajectory study

The reaction between D⁺ and H₂ plays an important role in astrochemistry at low temperatures and also serves as a prototype for a simple ion-molecule reaction. Its ground X[combining tilde]¹A' state has a very small thermodynamic barrier (up to 1.8 × 10^-2 eV) and the reaction proceeds through the formation of an intermediate complex lying within the potential well with a depth of at least 0.2 eV, thus representing a challenge for dynamical studies. In the present work, we analyze the title reaction within the temperature range of 20-100 K by means of ring polymer molecular dynamics (RPMD) and quasi-classical trajectory (QCT) methods over the full-dimensional global potential energy surface developed by Aguado et al. [A. Aguado, O. Roncero, C. Tablero, C. Sanz and M. Paniagua, J. Chem. Phys., 2000, 112, 1240]. The computed thermal RPMD and QCT rate coefficients are found to be almost independent of temperature and fall within the range of 1.34-2.01 × 10^-9 cm³ s^-1. They are also in very good agreement with previous time-independent quantum mechanical and statistical quantum method calculations. Furthermore, we observe that the choice of asymptotic separation distance between the reactants can markedly alter the rate coefficient in the low temperature regime (20-50 K). Therefore it is of utmost importance to correctly assign the value of this parameter for dynamical studies, particularly at very low temperatures of astrochemical importance. We finally conclude that the experimental rate measurements for the title reaction are highly desirable in future.

A combined theoretical and experimental investigation of the kinetics and dynamics of the O(1D) + D2 reaction at low temperature

The O(¹D) + H₂ reaction is a prototype for simple atom-diatom insertion type mechanisms considered to involve deep potential wells. While exact quantum mechanical methods can be applied to describe the dynamics, such calculations are challenging given the numerous bound quantum states involved. Consequently, efforts have been made to develop alternative theoretical strategies to portray accurately the reactive process. Here we report an experimental and theoretical investigation of the O(¹D) + D₂ reaction over the 50-296 K range. The calculations employ three conceptually different approaches - mean potential phase space theory, the statistical quantum mechanical method and ring polymer molecular dynamics. The calculated rate constants are in excellent agreement over the entire temperature range, exhibiting only weak temperature dependence. The agreement between experiment and theory is also very good, with discrepancies smaller than 26%. Taken together, the present and previous theoretical results validate the hypothesis that long-lived complex formation dominates the reaction dynamics at low temperature.

Kinetics study of the CN + CH4 hydrogen abstraction reaction based on a new ab initio analytical full-dimensional potential energy surface

We have developed an analytical full-dimensional potential energy surface, named PES-2017, for the gas-phase hydrogen abstraction reaction between the cyano radical and methane.

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Recent advances in quantum scattering calculations on polyatomic bimolecular reactions

This review surveys quantum scattering calculations on chemical reactions of polyatomic molecules in the gas phase published in the last ten years.

A ring polymer molecular dynamics study of the OH + H2(D2) reaction

Using ring polymer molecular dynamics we have calculated the rate coefficients for the OH + H₂ reaction.

Thermal Rate Constants for the O(3P) + CH4 → OH + CH3 Reaction: The Effects of Quantum Tunneling and Potential Energy Barrier Shape

The rate constants and kinetic isotope effects for the O(³P) + CH₄ reaction have been investigated with the quantum instanton method in full dimensionality. The calculated rate constants are in good agreement with the experimental values above 400 K, below which the measured values are scattered. Compared to other theoretical approaches, the quantum instanton method predicts the largest quantum tunneling effect, so it gives the largest rate constants at low temperatures. The calculated kinetic isotope effects are always much larger than 1 and increase with decreasing temperature, due to the zero-point energy and quantum tunneling. Our calculations on different potential energy surfaces demonstrate that the potential energy barrier shape dominates the magnitude of quantum tunneling and has a great effect on the kinetic isotope effect.

Ring-Polymer Molecular Dynamics for the Prediction of Low-Temperature Rates: An Investigation of the C((1)D) + H2 Reaction

Quantum mechanical calculations are important tools for predicting the rates of elementary reactions, particularly for those involving hydrogen and at low temperatures where quantum effects become increasingly important. These approaches are computationally expensive, however, particularly when applied to complex polyatomic systems or processes characterized by deep potential wells. While several approximate techniques exist, many of these have issues with reliability. The ring-polymer molecular dynamics method was recently proposed as an accurate and efficient alternative. Here, we test this technique at low temperatures (300-50 K) by analyzing the behavior of the barrierless C((1)D) + H2 reaction over the two lowest singlet potential energy surfaces. To validate the theory, rate coefficients were measured using a supersonic flow reactor down to 50 K. The experimental and theoretical rates are in excellent agreement, supporting the future application of this method for determining the kinetics and dynamics of a wide range of low-temperature reactions.

Stress Test for Quantum Dynamics Approximations: Deep Tunneling in the Muonium Exchange Reaction D + HMu → DMu + H

Quantum effects play a crucial role in chemical reactions involving light atoms at low temperatures, especially when a light particle is exchanged between two heavier partners. Different theoretical methodologies have been developed in the last decades attempting to describe zero-point energy and tunneling effects without abandoning a classical or semiclassical framework. In this work, we have chosen the D + HMu → DMu + H reaction as a stress test system for three well-established methods: two representative versions of transition state theory (TST), canonical variational theory and semiclassical instanton, and ring polymer molecular dynamics (RPMD). These calculations will be compared with accurate quantum mechanical results. Despite its apparent simplicity, the exchange of the extremely light muonium atom (0.114 u) becomes a most challenging reaction for conventional methods. The main result of this work is that RPMD provides an overall better performance than TST-based methods for such a demanding reaction. RPMD might well turn out to be a useful tool beyond TST applicability.