The method of Gaussian weighted trajectories. V. On the 1GB procedure for polyatomic processes

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.

A new ground electronic state potential energy surface of HeLiH+: Analytical representation and investigation of the dynamics of He + LiH+ (v = 0, j = 0) → LiHe+ + H reaction

An improved global potential energy surface (PES) for the electronic ground state of the HeLiH+ system is reported. The data points are calculated at the full configuration-interaction level of theory and extrapolated to the complete basis set limit. The fitting procedure implements a combination of neural network and Aguado-Paniagua functional forms to fit the ab initio data points. The fitted surface reproduces the ab initio data points accurately in short as well as long ranges and has an overall root mean square error of 1.76 × 10-3 eV (14.21 cm-1) in energy space <10 and 9.28 × 10-4 eV (7.48 cm-1) upto 2 eV. The optimized global minimum is also accurately reproduced using the fitted surface. To establish the accuracy of the new PES, dynamics investigation of the He + LiH+(v = 0, j = 0) → LiHe+ + H reaction is performed using the Coriolis coupled quantum mechanical and quasi-classical trajectory methods. The results, such as integral cross sections and rate constants, show the effect of the opening of the collision-induced dissociation (CID) channel at low collision energy and are significantly different from the earlier study of Tacconi et al. [Phys. Chem. Chem. Phys. 14, 637-645 (2012)]. These discrepancies appear to be a result of the treatment of the CID channel in the dynamics calculations, which is excluded from the reactive channel in the current work.

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.

First-principles mode-specific reaction dynamics

Controlling the outcome of chemical reactions by exciting specific vibrational and/or rotational modes of the reactants is one of the major goals of modern reaction dynamics studies. In the present Perspective, we focus on first-principles vibrational and rotational mode-specific dynamics computations on reactions of neutral and anionic systems beyond six atoms such as X + C2H6 [X = F, Cl, OH], HX + C2H5 [X = Br, I], OH- + CH3I, and F- + CH3CH2Cl. The dynamics simulations utilize high-level ab initio analytical potential energy surfaces and the quasi-classical trajectory method. Besides initial state specificity and the validity of the Polanyi rules, mode-specific vibrational-state assignment for polyatomic product species using normal-mode analysis and Gaussian binning is also discussed and compared with experiment.

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.

Combined Quantum Mechanical and Quasi-Classical State-to-State Dynamical Study on the Isotopic Effect in H/D + LiH+/LiD+ → H2/HD/D2 + Li+ Reactions

Coriolis-coupled quantum mechanical (QM-CC) and quasi-classical trajectory (QCT) calculations are carried out to investigate the dynamics of the H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ reactions on the ground electronic state potential energy surface reported by Martinazzo et al. (Martinazzo et al., J. Chem. Phys. 2003, 119, 11241). The QM-CC and QCT results at the initial state-selected and state-to-state levels are used to investigate the validity and accuracy of the QCT method for these exoergic barrierless reactions. Furthermore, the QCT method is used to understand the isotopic effects on reaction observables like total and state-to-state integral cross section, differential cross section, product energy disposal, and rate constants of H(D) + LiH+(v = 0, j = 0) → H2(HD) (v', j') + Li+ and H(D) + LiD+(v = 0, j = 0) → HD(D2) (v', j') + Li+ reactions. Attempts are also made to understand the impact of the isotopic substitution on the reaction mechanism. It is observed that QM-CC and QCT results closely follow each other at the initial state-selected and state-to-state levels. Noticeable kinematic effects of reagents on the reactivity and mechanism of the reactions are also observed.

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.

Quantum and semiclassical studies of nonadiabatic electronic transitions between N(4S) and N(2D) by collisions with N2

The dynamics and kinetics of spin-forbidden transitions between N(2D) and N(4S) via collisions with N2 molecules are investigated using a quantum wave packet (WP) method and the semi-classical coherent switches with decay of mixing (CSDM) method. These electronic transition processes are competing with exchange reaction channels on both the doublet and quartet potential energy surfaces. The WP and CSDM quenching rate coefficients are found in reasonable agreement with each other, and both reproduce the previous theoretical results. For the excitation process, the agreement between the two approaches is dependent on the treatment of the zero-point energy (ZPE) in the product, because the high endoergicity of this process leads to severe violation of the vibrational ZPE. The Gaussian-binning (GB) method is found to improve the agreement with the quantum result. The excitation rate coefficients are found to be two orders of magnitude smaller than that of the adiabatic exchange reaction, underscoring the inefficient intersystem crossing due to the weak spin-orbit coupling between the two spin manifolds of the N3 system.

Manipulating hydrogen bond dissociation rates and mechanisms in water dimer through vibrational strong coupling

The vibrational strong coupling (VSC) between molecular vibrations and cavity photon modes has recently emerged as a promising tool for influencing chemical reactivities. Despite numerous experimental and theoretical efforts, the underlying mechanism of VSC effects remains elusive. In this study, we combine state-of-art quantum cavity vibrational self-consistent field/configuration interaction theory (cav-VSCF/VCI), quasi-classical trajectory method, along with the quantum-chemical CCSD(T)-level machine learning potential, to simulate the hydrogen bond dissociation dynamics of water dimer under VSC. We observe that manipulating the light-matter coupling strength and cavity frequencies can either inhibit or accelerate the dissociation rate. Furthermore, we discover that the cavity surprisingly modifies the vibrational dissociation channels, with a pathway involving both water fragments in their ground vibrational states becoming the major channel, which is a minor one when the water dimer is outside the cavity. We elucidate the mechanisms behind these effects by investigating the critical role of the optical cavity in modifying the intramolecular and intermolecular coupling patterns. While our work focuses on single water dimer system, it provides direct and statistically significant evidence of VSC effects on molecular reaction dynamics.

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.

Vibrational mode-specific dynamics of the F- + CH3CH2Cl multi-channel reaction

We investigate the mode-specific dynamics of the ground-state, C-Cl stretching (v₁₀), CH₂ wagging (v₇), sym-CH₂ stretching (v₁), and sym-CH₃ stretching (v₃) excited F^- + CH₃CH₂Cl(v_k = 0, 1) [k = 10, 7, 1, 3] → Cl^- + CH₃CH₂F (S_N2), HF + CH₃CHCl^-, FH⋯Cl^- + C₂H₄, and Cl^- + HF + C₂H₄ (E2) reactions using a full-dimensional high-level analytical global potential energy surface and the quasi-classical trajectory method. Excitation of the C-Cl stretching, CH₂ stretching, and CH₂/CH₃ stretching modes enhances the S_N2, proton abstraction, and FH⋯Cl^- and E2 channels, respectively. Anti-E2 dominates over syn-E2 (kinetic anti-E2 preference) and the thermodynamically-favored S_N2 (wider reactive anti-E2 attack angle range). The direct (a) S_N2, (b) proton abstraction, (c) FH⋯Cl^- + C₂H₄, (d) syn-E2, and (e) anti-E2 channels proceed with (a) back-side/backward, (b) isotropic/forward, (c) side-on/forward, (d) front-side/forward, and (e) back-side/forward attack/scattering, respectively. The HF products are vibrationally cold, especially for proton abstraction, and their rotational excitation increases for proton abstraction, anti-E2, and syn-E2, in order. Product internal-energy and mode-specific vibrational distributions show that CH₃CH₂F is internally hot with significant C-F stretching and CH₂ wagging excitations, whereas C₂H₄ is colder. One-dimensional Gaussian binning technique is proved to solve the normal mode analysis failure caused by methyl internal rotation.

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.

Global potential energy surface and product pair-correlated distributions for the F(2P) + SiH4 reaction - comparison with experiments

In this paper we study the gas-phase hydrogen abstraction reaction between fluorine atoms and silane in a three-step process: potential energy surface, kinetics and dynamics. Firstly, we developed for the first time an analytical full-dimensional surface, named PES-2021, using high-level explicitly-correlated ab initio data as the input. PES-2021 represents a continuous and smooth potential with analytical gradients and includes intuitive concepts (stretching and bending nuclear motions). Based on the PES-2021 quasi-classical trajectory (QCT) calculations were performed to analyse the kinetics and dynamics. Secondly, in the kinetics study at room temperature we observed a very fast reaction with a rate constant of 3.90 × 10^-10 cm³ molecule^-1 s^-1, reproducing the scarce experimental evidence. Finally, the third step is the dynamics study, which was performed under two different conditions, a temperature of 77 K and a collision energy of 2.5 kcal mol^-1, for direct comparison with experiments. In the first case, we found the largest fraction, 44%, deposited as HF(v) vibration, where the most populated states were HF(v = 2, 3), both results reproducing the experimental evidence. The largest discrepancy with the experiment was found in the HF(j) rotational distribution, where hotter distributions were found, this discrepancy being associated with limitations of the QCT method. The second case, E = 2.5 kcal mol^-1, was a state-to-state correlated study and, therefore, more difficult. The theory overestimates (again) and consequently underestimates, respectively, the rotational and vibrational fractions of the HF(v,j) product as compared with experiments. While experimentally the SiH₃ product appears excited only in the umbrella mode, ν₂ = 0-5, correlated with the HF(v) co-product vibrational excited in v = 3 and 4, theoretically a wider vibrational distribution is found in both products, and these distributions have, obviously, an influence on the product correlated speed distributions. However, the product correlated angular distribution is well reproduced. In general, these results allowed us to test the capacity of PES-2021 + QCT tools to simulate the experimental evidence, revealing that agreement is better when average properties are compared, making the comparison worse when state-to-state properties are compared. Different causes of the theory/experiment discrepancies were analysed, and it was found that they are due, mainly, to limitations of the QCT method.

Theoretical study of the Cl(2P) + SiH4 reaction: global potential energy surface and product pair-correlated distributions. Comparison with experiment

For the theoretical study of the title reaction, an analytical full-dimensional potential energy surface named PES-2021 was developed for the first time, by fitting high-level explicitly-correlated ab initio data. This reaction presented high exothermicity, (298 K) = -11.6 kcal mol^-1, reproducing the experimental evidence; it is a barrierless reaction and no intermediate complexes were found. PES-2021 is a continuous and smooth potential energy surface, it includes intuitive concepts in its development and fitting, such as stretching and bending nuclear motions, and it presents analytical first energy derivatives. Based on PES-2021, kinetics and dynamics studies were carried out using quasi-classical trajectory calculations. In the kinetics study, over the temperature range 300-450 K, we observed that rate constants were practically independent of temperature, with an almost zero activation energy, as compared to 0.0 and -0.48 kcal mol^-1 experimentally reported. In this kinetics study the role of the spin-orbit effect on reactivity was analysed. In the dynamics study, different product pair-correlated dynamics properties were compared with the only experimental evidence: product energy partition, product vibrational distribution, product angular distribution and product speed distribution. We observed two mechanisms of reaction, a stripping mechanism associated with large impact parameters and forward scattering, and an indirect mechanism associated with sideways-backward scattering related with "nearly-trapped" trajectories due to the product rotation. In general, theoretical results reasonably simulate the experimental measurements when they consider some rotational and vibrational constraints as well as binning techniques to mimic a quantum-mechanical behaviour. Although the agreement is not quantitative, the present results shed light on the mechanism of this difficult polyatomic reactive system.

Detailed quasiclassical dynamics of the F- + CH3Br reaction on an ab initio analytical potential energy surface

Dynamics and mechanisms of the F^- + CH₃Br(v = 0) → Br^- + CH₃F (S_N2 via Walden inversion, front-side attack, and double inversion), F^- + inverted-CH₃Br (induced inversion), HF + CH₂Br^- (proton abstraction), and FH⋯Br^- + ¹CH₂ reactions are investigated using a high-level global ab initio potential energy surface, the quasiclassical trajectory method, as well as non-standard configuration- and mode-specific analysis techniques. A vector-projection method is used to identify inversion and retention trajectories; then, a transition-state-attack-angle-based approach unambiguously separates the front-side attack and the double-inversion retention pathways. The Walden-inversion S_N2 channel becomes direct rebound dominated with increasing collision energy as indicated by backward scattering, initial back-side attack preference, and the redshifting of product internal energy peaks in accord with CF stretching populations. In the minor retention and induced-inversion pathways, almost the entire available energy transfers into product rotation-vibration, and retention mainly proceeds with indirect, slow double inversion following induced inversion with about 50% probability. Proton abstraction is dominated by direct stripping (evidenced by forward scattering) with CH₃-side initial attack preference, providing mainly vibrationally ground state products with significant zero-point energy violation.

Kinetic and Dynamic Studies of the F(2P) + ND3 → DF + ND2 Reaction

The fast F reaction with NH₃ poses a big challenge to experimental studies because of secondary chemical and collisional reactions. The quasi-classical trajectory method is utilized to investigate the mode specificity, product energy disposal, and temperature dependence of the thermal rate coefficient of F + ND₃ → DF + ND₂ on a recently developed potential energy surface. The effect of isotopic substitution is explored by comparing the F + ND₃ reaction with the F + NH₃ reaction. The computed results permit a better understanding of the F + ammonia reaction. The DF vibrational state has a Λ-type distribution, in accordance with the experimental measurement by the fast flow reactor technique. The product ND₂ is dominantly populated in the ground state, and a considerable amount of ND₂ is produced in the fundamental states of the bending mode. The similar vibrational state distributions of HF and NH₂ in the F + NH₃ reaction indicate a weak isotopic substitution effect on the product energy disposal. Exciting the umbrella mode of ND₃ suppresses the reaction at low energies below 5 kcal mol^-1, in sharp contrast to the observation in the F + NH₃ reaction. These dynamical behaviors can be partially explained by the sudden vector projection model. In addition, the thermal rate coefficient of F + ND₃ shows no temperature dependence in the range between 150 and 2000 K. There exists an inverse kinetic isotope effect at temperatures from 150 to 1500 K.

First-Principles Reaction Dynamics beyond Six-Atom Systems

Moving beyond the six-atomic benchmark systems, we discuss the new age and future of first-principles reaction dynamics, which investigates complex, multichannel chemical reactions. We describe the methodology starting from the benchmark ab initio characterization of the stationary points, followed by full-dimensional potential energy surface (PES) developments and reaction dynamics computations. We highlight our composite ab initio approach providing benchmark stationary-point properties with subchemical accuracy, the Robosurfer program system enabling automatic PES development, and applications for the Cl + C2H6, F + C2H6, and OH- + CH3I post-six-atom reactions focusing on ab initio issues and their solutions as well as showing the excellent agreement between theory and experiment.

Effects of bending excitation on the reaction dynamics of fluorine atoms with ammonia

Vibrational excitation has been established as an efficient way to control the chemical reaction outcome. Stretching vibration of polyatomic molecules is believed to be efficient to promote abstraction reactions since energy is placed directly into the breaking bond. In this work, we report on a counterexample showing that exciting the low-frequency umbrella bending mode of ammonia enhances its reaction with fluorine atoms much more than exciting the high-frequency symmetric or asymmetric stretching mode over a wide range of collision energy, validated using both quasiclassical trajectory simulations and full-dimensional quantum dynamics calculations under the centrifugal-sudden approximation. This interesting mode-specific reaction dynamic originates from the increased chance of capturing the fluorine atom by ammonia due to the enlarged attractive interaction between them and the enhancement of the direct stripping reaction mediated by two submerged barriers.

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.

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⁺.

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.

Dynamics of H + HeH+(v = 0, j = 0) → H2+ + He: Insight on the Possible Complex-Forming Behavior of the Reaction

The H + HeH⁺→ He + H₂⁺ reaction has been studied by means of a combination of theoretical approaches: a statistical quantum method (SQM), ring polymer molecular dynamics (RPMD), and the quasiclassical trajectory (QCT) method. Cross sections and rate constants have been calculated in an attempt to investigate the dynamics of the process. The comparison with previous calculations and experimental results reveals that despite the fact that statistical predictions seem to reproduce some of the overall observed features, the analysis at a more detailed state-to-state level shows noticeable deviations from a complex-forming dynamics. We find some differences in cross sections and rate constants obtained in the QCT calculation with a Gaussian binning procedure with respect to previous works in which the standard histogram binning was employed.

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.

Theoretical study of the F(2P) + NH3→ HF + NH2 reaction on an accurate potential energy surface: dynamics and kinetics

The highly exothermic hydrogen abstraction reaction of the F atom with NH₃ is investigated using the quasi-classical trajectory method on a newly developed potential energy surface (PES) for the ground electronic state. The full-dimensional PES is constructed by fitting 41 282 ab initio energy points at the level of UCCSD(T)-F12/aug-cc-pVTZ. The flexible fundamental invariant-neural network method is applied in the fitting, resulting in a total root mean square error of 0.13 kcal mol^-1. On one hand, the calculated differential cross sections agree reasonably well with the experimental results and indicate that the reaction is dominated by the direct abstraction and stripping mechanisms while a considerable amount of reaction takes place by the indirect "yo-yo" mechanism. The product energy partition also reproduces well the experimental result, which can be understood according to the geometry change along the minimum energy path. On the other hand, the obtained vibrational state distribution of the product HF follows P_νHF=2≈P_νHF=1 > P_νHF=0 > P_νHF=3, less consistent with the scattered experimental results. In addition, the calculated thermal rate coefficients have practically no temperature dependence within the statistical errors.

Bridging the Gap between Direct Dynamics and Globally Accurate Reactive Potential Energy Surfaces Using Neural Networks

Direct dynamics simulations become increasingly popular in studying reaction dynamics for complex systems where analytical potential energy surfaces (PESs) are unavailable. Yet, the number and/or the propagation time of trajectories are often limited by high computational costs, and numerous energies and forces generated on-the-fly become wasted after simulations. We demonstrate here an example of reusing only a very small portion of existing direct dynamics data to reconstruct a 90-dimensional globally accurate reactive PES describing the interaction of CO₂ with a movable Ni(100) surface based on a machine learning approach. In addition to reproducing previous results with much better statistics, we predict scattering probabilities of CO₂ at the state-to-state level, which is extremely demanding for direct dynamics. We propose this unified way to investigate gaseous and gas-surface reactions of medium size, initiating with hundreds of preliminary direct dynamics trajectories, followed by low-cost and high-quality simulations on full-dimensional analytical PESs.

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.

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.

Chirality in molecular collision dynamics

Chirality is a phenomenon that permeates the natural world, with implications for atomic and molecular physics, for fundamental forces and for the mechanisms at the origin of the early evolution of life and biomolecular homochirality. The manifestations of chirality in chemistry and biochemistry are numerous, the striking ones being chiral recognition and asymmetric synthesis with important applications in molecular sciences and in industrial and pharmaceutical chemistry. Chiral discrimination phenomena, due to the existence of two enantiomeric forms, very well known in the case of interaction with light, but still nearly disregarded in molecular collision studies. Here we review some ideas and recent advances about the role of chirality in molecular collisions, designing and illustrating molecular beam experiments for the demonstration of chiral effects and suggesting a scenario for a stereo-directional origin of chiral selection.

Role of an ethyl radical and the problem of HF(v) bimodal vibrational distribution in the F(2P) + C2H6 → HF(v) + C2H5 reaction

A theoretical study of the dynamics of the F(²P) + C₂H₆ hydrogen abstraction reaction was presented using quasi-classical trajectories propagated on an ab initio fitted global potential energy surface, PES-2018.

Simulation of the experimental imaging results for the OH + CHD3 reaction with a simple and accurate theoretical approach

The OH + CHD₃ reaction is among the largest one ever studied at the high-resolution level permitted by imaging techniques [B. Zhang et al., J. Phys. Chem. A, 2005, 109, 8989]. This process involves eighteen configuration space coordinates, which are large enough to make exact quantum scattering calculations beyond reach. Moreover, freezing some degrees-of-freedom in order to render these calculations feasible may lead to unrealistic predictions. However, we have found it possible to reproduce for the first time the pair-correlated measurements of Zhang et al. at a nearly quantitative level by means of full-dimensional classical trajectory calculations in a quantum spirit on a recent ab initio potential energy surface. These calculations combine the classical description of the dynamics, well suited to polyatomic systems, with Bohr quantization of both reagent and product vibrational motions. While this pseudo-quantization is exactly imposed to the reagents, it is approximately imposed to the products in a first step through energy-based Gaussian binning (1GB). In a second step, we show that the original action-based Gaussian binning (GB), long thought to be inapplicable in practice to polyatomic reactions, yields in fact results comparable in accuracy and numerical cost to those obtained by means of 1GB, provided that Gaussian weights are properly widened. This new finding clearly extends the scope of GB in theoretical reactive scattering.

High-level ab initio potential energy surface and dynamics of the F- + CH3I SN2 and proton-transfer reactions

Bimolecular nucleophilic substitution (S_N2) and proton transfer are fundamental processes in chemistry and F^- + CH₃I is an important prototype of these reactions. Here we develop the first full-dimensional ab initio analytical potential energy surface (PES) for the F^- + CH₃I system using a permutationally invariant fit of high-level composite energies obtained with the combination of the explicitly-correlated CCSD(T)-F12b method, the aug-cc-pVTZ basis, core electron correlation effects, and a relativistic effective core potential for iodine. The PES accurately describes the S_N2 channel producing I^- + CH₃F via Walden-inversion, front-side attack, and double-inversion pathways as well as the proton-transfer channel leading to HF + CH₂I^-. The relative energies of the stationary points on the PES agree well with the new explicitly-correlated all-electron CCSD(T)-F12b/QZ-quality benchmark values. Quasiclassical trajectory computations on the PES show that the proton transfer becomes significant at high collision energies and double-inversion as well as front-side attack trajectories can occur. The computed broad angular distributions and hot internal energy distributions indicate the dominance of indirect mechanisms at lower collision energies, which is confirmed by analyzing the integration time and leaving group velocity distributions. Comparison with available crossed-beam experiments shows usually good agreement.

QCT dynamics study of OH/OD + GeH4 reactions. The problem of water bending excitation

The difficulties in the description of the water bending population could be related to the zero-point violation problem in QCT calculations.

Mode-specific multi-channel dynamics of the F- + CHD2Cl reaction on a global ab initio potential energy surface

We report a detailed quasiclassical trajectory study for the dynamics of the ground-state and CH/CD stretching-excited F^- + CHD₂Cl(v_CH/CD = 0, 1) → Cl^- + CHD₂F, HF + CD₂Cl^-, and DF + CHDCl^- S_N2, proton-, and deuteron-abstraction reactions using a full-dimensional global ab initio analytical potential energy surface. The simulations show that (a) CHD₂Cl(v_CH/CD = 1), especially for v_CH = 1, maintains its mode-specific excited character prior to interaction, (b) the S_N2 reaction is vibrationally mode-specific,