Classical dynamics of chemical reactions in a quantum spirit

A quasi-classical study in a quantum spirit of mode specificity of the H + HOD abstraction reaction

Quantum benchmark calculations of the H + HOD abstraction reaction [B. Zhao et al., Phys. Chem. Chem. Phys., 2018, 20, 17029-17037] provide an opportunity to test approximate methods, such as quasi-classical trajectories (QCTs) with Gaussian binning. However, the large mode-specific enhancements of this reaction lead to special challenges and unphysical QCT cross-section artifacts. We propose and apply a general backward-forward-backward (BFB) trajectory procedure to avoid cross-section artifacts arising from vibrational motion delocalization of the initially prepared reactants. We also develop and apply a general hybrid weighting scheme, in which vibrationally adiabatic products receive unit weights, while vibrationally non-adiabatic products are Gaussian weighted. Motivated by examination of the product vibrational actions, the hybrid weighting is necessary to avoid large cross-section errors. These QCTs with Gaussian weighting extensions are general and are recommended for future polyatomic reaction simulations.

Temperature effects on the branching dynamics in the model ambimodal (6 + 4)/(4 + 2) intramolecular cycloaddition reaction

C14H20 (tetradecapentaene) is a simple model system exhibiting post transition-state behavior, wherein both the (6 + 4) and (4 + 2) cycloaddition products are formed from one ambimocal transition state structure. We studied the bifurcation dynamics starting from the two ambimodal transition state structures, the chair-form and boat-form, using the quasi-classical trajectory, classical molecular dynamics, and ring-polymer molecular dynamics methods on the parameter-optimized semiempirical GFN2-xTB potential energy surface. It was found that the calculated branching fractions differ between the chair-form and boat-form due to the different nature in the IRC pathways. We also investigated the effects of temperature on bifurcation dynamics and found that, at higher temperatures, trajectories stay longer in the intermediate region of the potential energy surface.

Fundamental Invariant Neural Network (FI-NN) Potential Energy Surface for the OH + CH3OH Reaction with Analytical Forces

The hydrogen abstraction reaction of OH + CH3OH plays a great role in combustion and atmospheric and interstellar chemistry and has been extensively studied theoretically and experimentally. Theoretically, the numerical gradients with respect to the Cartesian coordinates of atoms in molecular simulations on our recent potential energy surface (PES) for the title reaction trained using the permutationally invariant polynomial neural network (PIP-NN) approach hinder the extensive calculation because of the unaffordable computation cost. To address this issue, we in this work report a new full-dimensional accurate analytical PES for the title reaction using the fundamental invariant neural network (FI-NN) approach based on 140,192 points of the quality UCCSD(T)-F12a/AVTZ. Besides, the spin-orbit (SO) corrections of OH in the entrance channel were determined at the level of complete active space self-consistent field with the AVTZ basis set. As a compromise between computational cost and efficiency, the Δ-machine learning approach was employed to construct the SO-corrected PES. Based on this new FI-NN PES with analytical forces, thermal rate coefficients and various dynamic properties, including the integral cross sections, the differential cross sections, and the product energy partitioning, were determined by running a total of 5.5 million trajectories. The use of analytical gradients of the FI-NN PES accelerated simulations and about 99% of computation cost was saved, compared to that for the PIP-NN PES with numerical gradients. Such a significant acceleration is achieved mainly by replacing PIPs with FIs.

Role of the Vibrational and Translational Energies in the CN(v)+C2H6(ν1, ν2, ν5 and ν9) Reactions. A Theoretical QCT Study

Quasi-classical trajectory (QCT) calculations were conducted on the newly developed full-dimensional potential energy surface, PES-2023, to analyse two critical aspects: the influence of vibrational versus translational energy in promoting reactivity, and the impact of vibrational excitation within similar vibrational modes. The former relates to Polanyi's rules, while the latter concerns mode selectivity. Initially, the investigation revealed that independent vibrational excitation by a single quantum of ethane's symmetric and asymmetric stretching modes (differing by only 15 cm-1) yielded comparable dynamics, reaction cross-sections, HCN(v) vibrational product distributions, and scattering distributions. This observation dismisses any significant mode selectivity. Moreover, an equivalent amount of energy provided as translational energy (at total energies of 9.6 and 20.0 kcal mol-1) gave rise to slightly lower reactivity compared to the same amount of energy provided as vibrational energy. This effect is more evident at low energies, presenting a counterintuitive scenario in an 'early transition state' reaction. These findings challenge the straightforward application of Polanyi's rules in polyatomic systems. Regarding CN(v) vibrational excitation, our calculations reveal that the reaction cross-section remains practically unaffected by this vibrational excitation, suggesting that the CN stretching mode is a spectator mode. The results were rationalized by considering several factors: the strong coupling between different vibrational modes, and between vibrational modes and the reaction coordinate; and a significant vibrational energy redistribution within the ethane reactant before collision. This redistribution creates an unphysical energy flow, resulting in loss of adiabaticity and vibrational memory before the reactants' collision. These theoretical findings require future confirmation through experimental or theoretical quantum mechanical studies, which are currently unavailable.

Roaming in highly excited states: The central atom elimination of triatomic molecule decomposition

Chemical reactions are generally assumed to proceed from reactants to products along the minimum energy path (MEP). However, straying from the MEP-roaming-has been recognized as an unconventional reaction mechanism and found to occur in both the ground and first excited states. Its existence in highly excited states is however not yet established. We report a dissociation channel to produce electronically excited fragments, S(1D)+O2(a1Δg), from SO2 photodissociation in highly excited states. The results revealed two dissociation pathways: One proceeds through the MEP to produce vibrationally colder O2(a1Δg) and the other yields vibrationally hotter O2(a1Δg) by means of a roaming pathway involving an intramolecular O abstraction during reorientation motion. Such roaming dynamics may well be the rule rather than the exception for molecular photodissociation through highly excited states.

Multiple Dissociation Pathways in HNCO Decomposition Governed by Potential Energy Surface Topography

The exquisite features of molecular photochemistry are key to any complete understanding of the chemical processes governed by potential energy surfaces (PESs). It is well established that multiple dissociation pathways relate to nonadiabatic transitions between multiple coupled PESs. However, little detail is known about how the single PES determines reaction outcomes. Here we perform detailed experiments on HNCO photodissociation, acquiring the state-specific correlations of the NH (a1Δ) and CO (X1Σ+) products. The experiments reveal a trimodal CO rotational distribution. Dynamics simulations based on a full-dimensional machine-learning-based PES of HNCO unveil three dissociation pathways exclusively occurring on the S1 excited electronic state. One pathway, following the minimum energy path (MEP) via the transition state, contributes to mild rotational excitation in CO, while the other two pathways deviating substantially from the MEP account for relatively cold and hot CO rotational state populations. These peculiar dynamics are unambiguously governed by the S1 state PES topography, i.e., a narrow acceptance cone in the vicinity of the transition state region. The dynamical picture shown in this work will serve as a textbook example illustrating the importance of the PES topography in molecular photochemistry.

The CN(X 2Σ+) + C2H6 reaction: Dynamics study based on an analytical full-dimensional potential energy surface

The hydrogen abstraction reaction of the cyano radical with molecules of ethane presents some interesting points in the chemistry from ultra-cold to combustion environments especially with regard to HCN(v) product vibrational distribution. In order to understand its dynamics, a new analytical full-dimensional potential energy surface was developed, named PES-2023. It uses a combination of valence bond and mechanic molecular terms as the functional form, fitted to high-level ab initio calculations at the explicitly correlated CCSD(T)-F12/aug-cc-pVTZ level on a reduced and selected number of points describing the reactive process. The new surface showed a continuous and smooth behavior, describing reasonably the topology of the reaction: high exothermicity, low barrier, and presence of intermediate complexes in the entrance and exit channels. Using quasi-classical trajectory calculations (QCT) on the new PES-2023, a dynamics study was performed at room temperature with special emphasis on the HCN(v1,v2,v3) product stretching and bending vibrational excitations, and the results were compared with the experimental evidence, which presented discrepancies in the bending excitation. The available energy was mostly deposited as HCN(v) vibrational energy with the vibrational population inverted in the CH stretching mode and not inverted in the CN stretching and bending modes, thus simulating the experimental evidence. Other dynamics properties at room temperature were also analyzed; cold rotational energy distribution was found, associated with a linear and soft transition state, and backward scattering distribution was found, associated with a rebound mechanism.

Theoretical Insights into the Dynamics of Gas-Phase Bimolecular Reactions with Submerged Barriers

Much attention has been paid to the dynamics of both activated gas-phase bimolecular reactions, which feature monotonically increasing integral cross sections and Arrhenius kinetics, and their barrierless capture counterparts, which manifest monotonically decreasing integral cross sections and negative temperature dependence of the rate coefficients. In this Perspective, we focus on the dynamics of gas-phase bimolecular reactions with submerged barriers, which often involve radicals or ions and are prevalent in combustion, atmospheric chemistry, astrochemistry, and plasma chemistry. The temperature dependence of the rate coefficients for such reactions is often non-Arrhenius and complex, and the corresponding dynamics may also be quite different from those with significant barriers or those completely dominated by capture. Recent experimental and theoretical studies of such reactions, particularly at relatively low temperatures or collision energies, have revealed interesting dynamical behaviors, which are discussed here. The new knowledge enriches our understanding of the dynamics of these unusual reactions.

Theoretical studies on the kinetics and dynamics of the BeH+ + H2O reaction: comparison with the experiment

The reaction of BeH+ with background gaseous H2O may play a role in qubit loss for quantum information processing with Be+ as trapped ions, and yet its reaction mechanism has not been well understood until now. In this work, a globally accurate, full-dimensional ground-state potential energy surface (PES) for the BeH+ + H2O reaction was constructed by fitting a total of 170 438 ab initio energy points at the level of RCCSD(T)-F12/aug-cc-pVTZ using the fundamental invariant-neural network method. The total root-mean-square error of the final PES was 0.178 kcal mol-1. For comparison, quasi-classical trajectory calculations were carried out on the PES at an experimental temperature of 150 K. The obtained thermal rate constant and product branching ratio of the BeD+ + H2O reaction agreed quite well with experimental results. In addition, the vibrational state distributions and energy disposals of the products were calculated and rationalized using the sudden vector projection model.

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.

Hyperthermal Dynamics and Kinetics of the C(3P) + N2(X1Σg+) → CN(X2Σ+) + N(4S) Reaction

The hyperthermal dynamics and kinetics of the title reaction, which plays an important role in hypersonic chemistry for atmospheric entry vehicles, are investigated using quasi-classical trajectory methods on a recently developed ground electronic state potential energy surface. The dynamics calculations indicated that the reaction follows a complex-forming mechanism, despite its large endoergicity. The calculated differential cross section is forward-backward symmetric, consistent with a long-lived reaction intermediate supported by the NCN potential well. The lifetime of the reaction complex is sufficiently long that the vibrational distribution of the CN product can be predicted by the phase space theory. The calculated vibrational state specific and thermal rate coefficients follow the Arrhenius behavior, and the agreement with existing low-temperature experimental thermal rate coefficients is satisfactory. Extrapolations to high temperatures relevant to hypersonic conditions are provided.

Nonadiabatic Reactive Quenching of OH(A2Σ+) by H2: Origin of High Vibrational Excitation in the H2O Product

The nonadiabatic dynamics of the reactive quenching channel of the OH(A²Σ⁺) + H₂/D₂ collisions is investigated with a semiclassical surface hopping method, using a recently developed four-state diabatic potential energy matrix (DPEM). In agreement with experimental observations, the H₂O/HOD products are found to have significant vibrational excitation. Using a Gaussian binning method, the H₂O vibrational state distribution is determined. The preferential energy disposal into the product vibrational modes is rationalized by an extended Sudden Vector Projection model, in which the h and g vectors associated with the conical intersection are found to have large projections with the product normal modes. However, our calculations did not find significant insertion trajectories, suggesting the need for further improvement of the DPEM.

Capturing quantum effects with quasi-classical trajectories in the D + H+3 → H2D+ + H reaction

We present quasi-classical trajectory (QCT) cross sections, rate constants, and product state distributions for the D + H+3 → H₂D⁺ + H reaction. Using the same H+4 potential surface, the rate constants obtained from several QCT-based methods correcting for zero-point effects by Gaussian binning the product H₂D⁺ are compared to ring polymer molecular dynamics (RPMD) rate constants [Bulut et al., J. Phys. Chem. A, 2019, 123, 8766] which include quantum effects and to recent experimentally derived rate constants [Bowen et al., J. Chem. Phys., 2021, 154, 084307]. QCT with standard binning predicts rate constants that increase slowly as the temperature decreases from 1500 to 100 K. In contrast, the RPMD rate constants decrease rapidly with decreasing temperature. By 100 K, the QCT standard binning rate constant is more than 3 orders of magnitude larger than the RPMD rate constant. We show that QCT with Gaussian binning and proper normalization captures the zero-point effects and reproduces the RPMD rate constants over a large temperature range. Furthermore, the simple technique of counting only reactive trajectories with vibrational energy above the product zero-point energy matches the RPMD results well down to ∼300 K. The present Gaussian binned rate constants are in fair agreement with new experimentally derived rate constants from 100 to 1500 K. However, because the Gaussian binned rate constants do not include tunneling, important at lower temperatures, and the RPMD and experimentally derived rate constants have significant differences, the roles of the competing effects of zero-point energy, internal excitation of the H+3, and quantum tunneling are not simple and require further study for a consistent picture of the dynamics. Since rate constants for complex forming reactions, such as the title reaction, are difficult to converge with RPMD, alternative QCT-based methods, which include quantum effects and in addition provide product state distributions as described here, are highly desirable.

Dissection of the Multichannel Reaction O(3P) + C2H2: Differential Cross-Sections and Product Energy Distributions

The O(³P) + C₂H₂ reaction plays an important role in hydrocarbon combustion. It has two primary competing channels: H + HCCO (ketenyl) and CO + CH₂ (triplet methylene). To further understand the microscopic dynamic mechanism of this reaction, we report here a detailed quasi-classical trajectory study of the O(³P) + C₂H₂ reaction on the recently developed full-dimensional potential energy surface (PES). The entrance barrier TS1 is the rate-limiting barrier in the reaction. The translation of reactants can greatly promote reactivity, due to strong coupling with the reaction coordinate at TS1. The O(³P) + C₂H₂ reaction progress through a complex-forming mechanism, in which the intermediate HCCHO lives at least through the duration of a rotational period. The energy redistribution takes place during the creation of the long-lived high vibrationally (and rotationally) excited HCCHO in the reaction. The product energy partitioning of the two channels and CO vibrational distributions agree with experimental data, and the vibrational state distributions of all modes of products present a Boltzmann-like distribution.

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.

Vibrational energy pooling via collisions between asymmetric stretching excited CO2: a quasi-classical trajectory study on an accurate full-dimensional potential energy surface

In low temperature plasmas, energy transfer between asymmetric stretching excited CO₂ molecules can be highly efficient, which leads to further excitation (and de-excitation) of the CO₂ molecules: CO₂(v_as) + CO₂(v_as) → CO₂(v_as + 1) + CO₂(v_as - 1). Through such a vibrational ladder climbing mechanism, CO₂ can be activated and eventually dissociates. To gain mechanistic insight of such processes, a full-dimensional accurate potential energy surface (PES) for the CO₂ + CO₂ system is developed using the permutational invariant polynomial-neural network method based on CCSD(T)-F12a/AVTZ energies at about 39 000 geometries. This PES is used in quasi-classical trajectory (QCT) studies of the vibrational energy transfer between CO₂ molecules excited in the asymmetric stretching mode. A machine learning algorithm is used to determine state-specific rate coefficients for the vibrational transfer processes from a limited data set. In addition to the CO₂(v_as + 1) + CO₂(v_as - 1) channel, the QCT simulations revealed significant contributions from the CO₂(v_as + 2,3) + CO₂(v_as - 2,3) channels, particularly at low collision energies/temperatures. These multi-vibrational-quantum processes are attributed to enhanced energy flow in the collisional complex formed by enhanced dipole-dipole interaction between asymmetric stretching excited CO₂ molecules.

Reactive, Inelastic, and Dissociation Processes in Collisions of Atomic Nitrogen with Molecular Oxygen

Collisions of atomic nitrogen with molecular oxygen have been treated with the quasiclassical trajectory method (QCT) in order to obtain a complete database of vibrationally detailed cross sections and rate coefficients for reactive, inelastic, and dissociation processes. For reaction rate coefficients, the agreement with experimental and theoretical data in the literature is excellent on the whole available interval 300-5000 K, with reliable extension to 20,000 K. For the inelastic case and for dissociation, no comparisons are available; therefore, a study of QCT reliability is proposed. In the inelastic case, it is found that "purely inelastic" and "quasireactive" collisions show not only different mechanisms but also different QCT levels of reliability at low energy. For dissociation, similar considerations bring to the conclusion that for the present collisional system, the QCT method is appropriate on the whole energy range studied. Rate coefficients for all the processes studied are provided in the electronic form.

Mechanical Vibrational Relaxation of NO Scattering from Metal and Insulator Surfaces: When and Why They Are Different

NO scattering from metallic and insulating surfaces represents contrasting benchmark systems for understanding energy transfer at gas-surface interface. Strikingly different behaviors of highly vibrationally excited NO scattered from Au(111) and LiF(001) were observed and attributed to disparate electronic structures between metals and insulators. Here, we reveal an alternative mechanical origin of this discrepancy by comparative molecular dynamics simulations with globally accurate adiabatic neural network potentials of both systems. We find that highly vibrating NO can reach for the high-dissociation barrier on Au(111), by which vibrational energy can largely transfer to translation or rotation and further dissipate into substrate phonons. This mechanical energy transfer channel is forbidden in the purely repulsive NO/LiF(001) system or for low-vibrating NO on Au(111), where molecular vibration is barely coupled to other degrees of freedom. Our results emphasize that the initial state and potential energy landscape concurrently influence the mechanical energy transfer dynamics of gas-surface scattering.

Computational approaches to dissociative chemisorption on metals: towards chemical accuracy

We review the state-of-the-art in the theory of dissociative chemisorption (DC) of small gas phase molecules on metal surfaces, which is important to modeling heterogeneous catalysis for practical reasons, and for achieving an understanding of the wealth of experimental information that exists for this topic, for fundamental reasons. We first give a quick overview of the experimental state of the field. Turning to the theory, we address the challenge that barrier heights (E_b, which are not observables) for DC on metals cannot yet be calculated with chemical accuracy, although embedded correlated wave function theory and diffusion Monte-Carlo are moving in this direction. For benchmarking, at present chemically accurate E_b can only be derived from dynamics calculations based on a semi-empirically derived density functional (DF), by computing a sticking curve and demonstrating that it is shifted from the curve measured in a supersonic beam experiment by no more than 1 kcal mol^-1. The approach capable of delivering this accuracy is called the specific reaction parameter (SRP) approach to density functional theory (DFT). SRP-DFT relies on DFT and on dynamics calculations, which are most efficiently performed if a potential energy surface (PES) is available. We therefore present a brief review of the DFs that now exist, also considering their performance on databases for E_b for gas phase reactions and DC on metals, and for adsorption to metals. We also consider expressions for SRP-DFs and briefly discuss other electronic structure methods that have addressed the interaction of molecules with metal surfaces. An overview is presented of dynamical models, which make a distinction as to whether or not, and which dissipative channels are modeled, the dissipative channels being surface phonons and electronically non-adiabatic channels such as electron-hole pair excitation. We also discuss the dynamical methods that have been used, such as the quasi-classical trajectory method and quantum dynamical methods like the time-dependent wave packet method and the reaction path Hamiltonian method. Limits on the accuracy of these methods are discussed for DC of diatomic and polyatomic molecules on metal surfaces, paying particular attention to reduced dimensionality approximations that still have to be invoked in wave packet calculations on polyatomic molecules like CH₄. We also address the accuracy of fitting methods, such as recent machine learning methods (like neural network methods) and the corrugation reducing procedure. In discussing the calculation of observables we emphasize the importance of modeling the properties of the supersonic beams in simulating the sticking probability curves measured in the associated experiments. We show that chemically accurate barrier heights have now been extracted for DC in 11 molecule-metal surface systems, some of which form the most accurate core of the only existing database of E_b for DC reactions on metal surfaces (SBH10). The SRP-DFs (or candidate SRP-DFs) that have been derived show transferability in many cases, i.e., they have been shown also to yield chemically accurate E_b for chemically related systems. This can in principle be exploited in simulating rates of catalyzed reactions on nano-particles containing facets and edges, as SRP-DFs may be transferable among systems in which a molecule dissociates on low index and stepped surfaces of the same metal. In many instances SRP-DFs have allowed important conclusions regarding the mechanisms underlying observed experimental trends. An important recent observation is that SRP-DFT based on semi-local exchange DFs has so far only been successful for systems for which the difference of the metal work function and the molecule's electron affinity exceeds 7 eV. A main challenge to SRP-DFT is to extend its applicability to the other systems, which involve a range of important DC reactions of e.g. O₂, H₂O, NH₃, CO₂, and CH₃OH. Recent calculations employing a PES based on a screened hybrid exchange functional suggest that the road to success may be based on using exchange functionals of this category.

Insights into the Formation of Hydroxyl Radicals with Nonthermal Vibrational Excitation in the Meinel Airglow

To understand night time airglow in the Meinel bands and heat conversion from the highly excited OH radicals in the upper atmosphere via the important atmospheric reaction H + O₃ → OH + O₂, we report here a quasi-classical trajectory study of the reaction dynamics on a recently developed full-dimensional potential energy surface (PES). Our results indicate that the reaction energy of this highly exoergic reaction is almost exclusively channeled into the vibration of the OH product, underscoring an extreme departure from the statistical limit. The calculated OH vibrational distribution is highly inverted and peaks near the highest accessible vibrational state, in excellent agreement with experimental observations, validating the accuracy of the PES. More importantly, the dynamical origin of the nonthermal excitation of the OH vibrational mode is identified by its large projection onto the reaction coordinate at a small potential barrier in the entrance channel, which controls the energy flow into various degrees of freedom in the products.

Semiclassical initial value representation: From Møller to Miller

The initial value representation (IVR) was proposed five decades ago by Miller [J. Chem. Phys. 53, 3578 (1970)] in order to improve the feasibility and accuracy of semiclassical (SC) scattering calculations. Møller operators, which play a fundamental role in quantum scattering theory, do not appear in his formulation based on action-angle coordinates. These operators were introduced much later by Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)] in SC-IVR calculations performed in Cartesian coordinates within the Tannor and Weeks [J. Chem. Phys. 98, 3884 (1993)] formulation of quantum scattering theory. Remarkably, Møller operators were found to boost the numerical efficiency of SC-IVR calculations. The purpose of this work is to show within a simple model of light-induced rotational transitions that, in fact, Møller operators were already underlying Miller's pioneering formulation. In line with the results of Garashchuk and Light [J. Chem. Phys. 114, 1060 (2001)], removing the action of these operators in Miller's theory strongly decreases its numerical efficiency.

Advances and New Challenges to Bimolecular Reaction Dynamics Theory

Dynamics of bimolecular reactions in the gas phase are of foundational importance in combustion, atmospheric chemistry, interstellar chemistry, and plasma chemistry. These collision-induced chemical transformations are a sensitive probe of the underlying potential energy surface(s). Despite tremendous progress in past decades, our understanding is still not complete. In this Perspective, we survey the recent advances in theoretical characterization of bimolecular reaction dynamics, stimulated by new experimental observations, and identify key new challenges.

Time-independent quantum theory on vibrational inelastic scattering between atoms and open-shell diatomic molecules: Applications to NO + Ar and NO + H scattering

A full-dimensional rigorous quantum mechanical treatment of non-reactive inelastic scattering of an open-shell diatom [e.g., NO(²Π)] with a structureless and spinless atom is presented within the time-independent close-coupling framework. The inclusion of the diatomic vibrational degree of freedom allows the investigation of transitions between different vibrational manifolds, in addition to those between different rotational, spin-orbit, and Λ-doublet states. This method is applied to the scattering of vibrationally excited NO(²Π) with Ar and H (with its spin ignored). The former has negligible vibrational inelasticity, thanks to the weak interaction between the two collisional partners. This conclusion justifies the commonly used two-dimensional approximation in treating NO scattering with rare gas atoms. The latter, on the other hand, is shown to undergo significant vibrational relaxation, even in the ultra-cold regime, owing to a chemically bonded (HNO) complex on the lowest-lying singlet potential energy surfaces.

Final-State-Resolved Dynamics of the H3+ + CO → H2 +HCO+/HOC+ Reaction: A Quasi-Classical Trajectory Study

The ion-molecule reaction H₃⁺ + CO → H₂ + HCO⁺/HOC⁺, which initiates the formation of crucial organic molecules, plays a key role in interstellar and circumstellar environments. In this work, the quasi-classical trajectory method is employed to study the reaction dynamics on a recently developed full-dimensional global potential energy surface (PES). The calculated product internal energy distributions and relative internal excited fractions agree reasonably well with the experimental measurements. For the two reaction channels, most of the available energy flows into the vibrational modes of HCO⁺ or HOC⁺ at low collision energies, followed by the translational mode and the rotational modes of HCO⁺ or HOC⁺. As the collision energy increases, the proportion of the product translational energy increases while the proportion of the product vibrational energy decreases. Furthermore, the CH and CO stretching modes and their combination bands are effectively excited for the product HCO⁺ while the bending mode is remarkably excited for the product HOC⁺.

The importance of O3 excited potential energy surfaces in O2-O high-temperature kinetics

The mechanism of vibrational relaxation and dissociation in the O₂-O system at elevated temperatures is investigated by means of molecular dynamics. The most recent O₃ potential energy surfaces (PESs), obtained from the first principles quantum mechanical calculations [Varga et al., J. Chem. Phys. 147, 154312 (2017)], are used to derive a complete set of state-specific rate coefficients of vibrational energy transfer and dissociation. Unlike most of the previous efforts that utilize only the lowest and supposedly most reactive 1¹A' O₃ PES [A. Varandas and A. Pais, Mol. Phys. 65, 843 (1988)], this paper demonstrates the necessity to account for a complete ensemble of all excited O₃ PESs that correlate with O₂(X) and O(³P) when high-temperature kinetics is of interest. At the same time, it is found that the Varandas 1¹A' O₃ PES adequately describes vibrational energy transfer and dissociating dynamics when compared to the most recent 1¹A' O₃ PES by Varga et al. [J. Chem Phys. 147, 154312 (2017)]. The differences between this new dataset and previous rate coefficients are quantified by the master equation model.

When classical trajectories get to quantum accuracy: II. The scattering of rotationally excited H2 on Pd(111)

The classical trajectory method in a quantum spirit assigns statistical weights to classical paths on the basis of two semiclassical corrections: Gaussian binning and the adiabaticity correction.

A global ab initio potential energy surface and dynamics of the proton-transfer reaction: OH− + D2 → HOD + D−

The reaction mechanisms of OH⁻ + D₂ → HOD + D⁻ were first revealed by theory, based on an accurate full-dimensional PES.

When Classical Trajectories Get to Quantum Accuracy: The Scattering of H2 on Pd(111)

When elementary reactive processes occur at such low energies that only a few states of reactants and/or products are available, quantum effects strongly manifest and the standard description of the dynamics within the classical framework fails. We show here, for H₂ scattering on Pd(111), that by pseudoquantizing in the spirit of Bohr the relevant final actions of the system, along with adequately treating the diffraction-mediated trapping of the incoming wave, classical simulations achieve an unprecedented agreement with state-of-the-art quantum dynamics calculations.

Experimental and Theoretical Study of the O(1D) + HD Reaction

This work addresses the kinetics and dynamics of the gas-phase reaction between O(¹D) and HD molecules down to low temperature. Here, measurements were performed by using a supersonic flow (Laval nozzle) reactor coupled with pulsed laser photolysis for O(¹D) production and pulsed-laser-induced fluorescence for O(¹D) detection to obtain rate constants over the 50-300 K range. Additionally, temperature-dependent branching ratios (OD + H/OH + D) were obtained experimentally by comparison of the H/D atom atom yields with those of a reference reaction. In parallel, theoretical rate constants and branching ratios were calculated by using three different techniques; mean potential phase space theory (MPPST), the statistical quantum mechanical method (SQM), and ring polymer molecular dynamics (RPMD). Although the agreement between experimental and theoretical rate constants is reasonably good, with differences not exceeding 30% over the entire temperature range, the theoretical branching ratios derived by the MPPST and SQM methods are as much as 50% larger than the experimental ones. These results are presented in the context of earlier work, while the possible origins of the discrepancies between experiment and theory are discussed.

Theoretical Study of Barrierless Chemical Reactions Involving Nearly Elastic Rebound: The Case of S(1D) + X2, X = H, D

For some values of the total angular momentum consistent with reaction, the title processes involve nonreactive trajectories proceeding through a single rebound mechanism during which the internal motion of the reagent diatom is nearly unperturbed. When such paths are in a significant amount, the classical reaction probability is found to be markedly lower than the quantum mechanical one. This finding was recently attributed to an unusual quantum effect called diffraction-mediated trapping, and a semiclassical correction was proposed in order to take into account this effect in the classical trajectory method. In the present work, we apply the resulting approach to the calculation of opacity functions as well as total and state-resolved integral cross sections (ICSs) and compare the values obtained with exact quantum ones, most of which are new. As the title reactions proceed through a deep insertion well, mean potential statistical calculations are also presented. Seven values of the collision energy, ranging from 30 to 1127 K, are considered. Two remarkable facts stand out: (i) The corrected classical treatment strongly improves the accuracy of the opacity function as compared to the usual classical treatment. When the entrance transition state is tight, however, those trajectories crossing it with a bending vibrational energy below the zero point energy must be discarded. (ii) The quantum opacity function, particularly its cutoff, is finely reproduced by the statistical approach. Consequently, the total ICS is also very well described by the two previous approximate methods. These, however, do not predict state-resolved ICSs with the same accuracy, proving thereby that (i) one or several genuine quantum effects involved in the dynamics are missed by the corrected classical treatment and (ii) the dynamics are not fully statistical.

An accurate full-dimensional permutationally invariant potential energy surface for the interaction between H2O and CO

The first full-dimensional accurate potential energy surface was developed for the CO + H₂O system based onca.102 000 points calculated at the CCSD(T)-F12a/AVTZ level using a permutation invariant polynomial-neural network (PIP-NN) method.

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.

New Method To Extract Final-State Information of Polyatomic Reactions Based on Normal Mode Analysis

State-to-state reaction dynamics provides a comprehensive insight into reaction mechanisms of chemical reactions at the atomic level. A new scheme to extract final-state information based on normal mode analysis is proposed in this work. Different from the traditional scheme extracting the coordinates and momenta from the last step of each trajectory, they are taken in the new scheme from a specific step of each reactive trajectory within the last vibrational period of the product molecule by demanding the corresponding geometry of the step to have the minimum potential energy. Test calculations on the collisions between the atom H and the molecules H₂O, H₂S, and NH₃ show that the new scheme works much better than the traditional one. In addition, the new scheme is applied to calculate the vibrational state distribution of the product NH₂ in the reaction H + NH₃ → H₂ + NH₂.

Semiclassical initial value theory of rotationally inelastic scattering: Some remarks on the phase index in the interaction picture

This paper deals with the treatment of quantum interferences in the semiclassical initial value theory of rotationally inelastic scattering in the interaction picture. Like many semiclassical methods, the previous approach involves a phase index related to sign changes of a Jacobian whose square root is involved in the calculations. It is shown that replacing the original phase index by a new one extends the range of applicability of the theory. The resulting predictions are in close agreement with exact quantum scattering results for a model of atom-rigid diatom collision involving strong interferences. The developments are performed within the framework of the planar rotor model, but are readily applicable to three-dimensional collisions.

Tracking the energy flow in the hydrogen exchange reaction OH + H2O → H2O + OH

The prototypical hydrogen exchange reaction OH + H2O → H2O + OH has attracted considerable interest due to its importance in a wide range of chemically active environments. In this work, an accurate global potential energy surface (PES) for the ground electronic state was developed based on ∼44 000 ab initio points at the level of UCCSD(T)-F12a/aug-cc-pVTZ. The PES was fitted using the fundamental invariant-neural network method with a root mean squared error of 4.37 meV. The mode specific dynamics was then studied by the quasi-classical trajectory method on the PES. Furthermore, the normal mode analysis approach was employed to calculate the final vibrational state distribution of the product H2O, in which a new scheme to acquire the Cartesian coordinates and momenta of each atom in the product molecule from the trajectories was proposed. It was found that, on one hand, excitation of either the symmetric stretching mode or the asymmetric stretching mode of the reactant H2O promotes the reaction more than the translational energy, which can be rationalized by the sudden vector projection model. On the other hand, the relatively higher efficacy of exciting the symmetric stretching mode than that of the asymmetric stretching mode is caused by the prevalence of the indirect mechanism at low collision energies and the stripping mechanism at high collision energies. In addition, the initial collision energy turns ineffectively into the vibrational energy of the products H2O and OH while a fraction of the energy transforms into the rotational energy of the product H2O. Fundamental excitation of the stretching modes of H2O results in the product H2O having the highest population in the fundamental state of the asymmetric stretching mode, followed by the ground state and the fundamental state of the symmetric stretching mode.

An accurate full-dimensional potential energy surface and quasiclassical trajectory dynamics of the H + H2O2 two-channel reaction

Quasiclassical trajectory calculations reveal interesting dynamics features based on an accurate FI-NN PES for the H + H₂O₂ two-channel reaction.