From ab Initio Potential Energy Surfaces to State-Resolved Reactivities: X + H2O ↔ HX + OH [X = F, Cl, and O(3P)] Reactions

Tell Machine Learning Potentials What They Are Needed For: Simulation-Oriented Training Exemplified for Glycine

Machine learning potentials (MLPs) are widely applied as an efficient alternative way to represent potential energy surfaces (PESs) in many chemical simulations. The MLPs are often evaluated with the root-mean-square errors on the test set drawn from the same distribution as the training data. Here, we systematically investigate the relationship between such test errors and the simulation accuracy with MLPs on an example of a full-dimensional, global PES for the glycine amino acid. Our results show that the errors in the test set do not unambiguously reflect the MLP performance in different simulation tasks, such as relative conformer energies, barriers, vibrational levels, and zero-point vibrational energies. We also offer an easily accessible solution for improving the MLP quality in a simulation-oriented manner, yielding the most precise relative conformer energies and barriers. This solution also passed the stringent test by diffusion Monte Carlo simulations.

State-to-State Dynamics in Mode-Selective Polyatomic Reactions

Chemical reactions are intrinsically quantum mechanical transformations of reactants to products. Recent experimental and theoretical advances have enabled the exploration of reaction dynamics with a quantum state resolution for both reactants and products. To this end, reactions involving more than three atoms are of particular interest, because they exhibit rich dynamics concerning the role of different reactant modes in controlling reactivity and product energy disposal. A clear understanding of the state-to-state dynamics requires new paradigms. In this Perspective, we examine some new concepts that have emerged from recent state-to-state studies of polyatomic reactions and illustrate the key role played by the transition state.

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.

Global Potential Energy Surfaces by Compressed-State Multistate Pair-Density Functional Theory: The Lowest Doublet States Responsible for the N(4Su) + C2(a 3Πu) → CN(X 2Σ+) + C(3Pg) Reaction

Global potential energy surfaces (PESs) for the 1 ²A' and 1 ²A″ states of the C₂N system responsible for the N(⁴S_u) + C₂(a ³Π_u) → CN(X ²Σ⁺) + C(³P_g) reaction are mapped using compressed-state multistate pair-density functional theory (CMS-PDFT), which is a multi-state version of multiconfiguration pair-density functional theory (MC-PDFT). Calculations are also performed at selected geometries by explicitly correlated multireference configuration interaction with quadruple corrections, MRCI-F12+Q, and the comparison of the two sets of calculations shows that CMS-PDFT describes the globally reactive PESs well, including the bond-breaking asymptotes. We conclude that CMS-PDFT is an efficient method for constructing PESs for strongly correlated reactive systems. The PESs for producing CN + C are found to be barrierless and proceed through intermediate complexes. The CMS-PDFT PESs were fitted with a neural network method, and quasiclassical trajectories were computed on the resulting analytic PESs. These trajectories predict that the reaction produces vibrationally excited CN.

Machine Learning Applications for Chemical Reactions

Machine learning (ML) approaches have enabled rapid and efficient molecular property predictions as well as the design of new novel materials. In addition to great success for molecular problems, ML techniques are applied to various chemical reaction problems that require huge costs to solve with the existing experimental and simulation methods. In this review, starting with basic representations of chemical reactions, we summarized recent achievements of ML studies on two different problems; predicting reaction properties and synthetic routes. The various ML models are used to predict physical properties related to chemical reaction properties (e. g. thermodynamic changes, activation barriers, and reaction rates). Furthermore, the predictions of reactivity, self-optimization of reaction, and designing retrosynthetic reaction paths are also tackled by ML approaches. Herein we illustrate various ML strategies utilized in the various context of chemical reaction studies.

Strong non-Arrhenius behavior at low temperatures in the OH + HCl → H2O + Cl reaction due to resonance induced quantum tunneling

The OH + HCl reaction possesses many Feshbach resonances trapped in the hydrogen bond well in the entrance channel, which substantially enhance the reaction rates at low temperatures.

Full-dimensional quantum dynamics study of isotope effects for the H2 + NH2/ND2/NHD and H2/D2/HD + NH2 reactions

A full-dimensional quantum dynamical study for the bimolecular reactions of hydrogen molecules with amino radicals for different isotopologues is reported. The nonreactive amino radical is described by two Radau vectors that are very close to the valence bond coordinates. Potential-optimized discrete variable representation basis is used for the vibrational coordinates of the amino radical. Starting from the reaction H₂ + NH₂, we study the isotope effects for the two reagents separately, i.e., H₂ + NH₂/ND₂/NHD and H₂/D₂/HD + NH₂. The effects of different vibrational mode excitations of the reagents on the reactivities are studied. Physical explanations about the isotope effects are also provided thoroughly including the influence of vibrational energy differences between the different isotopologues and the impact of the tunneling effect.

An accurate full-dimensional potential energy surface for the reaction OH + SO → H + SO2

An accurate full-dimensional PES for the OH + SO ↔ H + SO₂ reaction is developed by the permutation invariant polynomial-neural network approach.

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.

Full-dimensional quantum mechanical calculations of the reaction probability of the H + CH4 reaction based on a mixed Jacobi and Radau description

A full-dimensional time-dependent wave packet study using mixed polyspherical Jacobi and Radau coordinates for the title reaction has been reported. The non-reactive moiety CH₃ has been described using three Radau vectors, whereas two Jacobi vectors have been used for the bond breaking/formation process. A potential-optimized discrete variable representation basis has been employed to describe the vibrational coordinates of the reagent CH₄. About one hundred billion basis functions have been necessary to achieve converged results. The reaction probabilities for some initial vibrational states are given. A comparison between the present approach and other methods, including reduced and full-dimensional ones, is also presented.

Benchmark ab initio and dynamical characterization of the stationary points of reactive atom + alkane and SN2 potential energy surfaces

We review composite ab initio and dynamical methods and their applications to characterize stationary points of atom/ion + molecule reactions.

Universal crossed beam imaging studies of polyatomic reaction dynamics

Crossed-beam imaging studies of polyatomic reactions show surprising dynamics not anticipated by extrapolation from smaller model systems.

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

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

Probing the Partial Activation of Water by Open-Shell Interactions, Cl(H2O)1-4

The partial chemical activation of water by reactive radicals was examined computationally for small clusters of chlorine and water, Cl^•(H₂O)_n=1-4. Using an automated isomer-search procedure, dozens of unique, stable structures were computed. Among the resulting structural classes were intact, hydrated-chlorine isomers, as well as hydrogen-abstracted (HCl)(OH)(H₂O)_n-1 configurations. The latter showed increased stability as the degree of hydration increased, until n = 4, where a new class of structures was discovered with a chloride ion bound to an oxidized water network. The electronic structure of these three structural classes was investigated, and spectral signatures of this hydration-based evolution were connected to these electronic properties. An ancillary outcome of this detailed computational analysis, including coupled-cluster benchmarks, was the calibration of cost-effective quantum chemistry methods for future studies of these radical-water complexes.

Globally Accurate Full-Dimensional Potential Energy Surface for H2 + HCl Inelastic Scattering

A globally accurate full-dimensional potential energy surface (PES) for the inelastic scattering between H₂ and HCl is developed on the basis of a large number of points calculated at the coupled-cluster singles, doubles, and perturbative triples level of theory. The machine-learned PES is trained with 42 417 ab initio points using the permutation invariant polynomial-neural network method, resulting in a root-mean-square fitting error of 5.6 cm^-1. Both full- and reduced-dimensional quantum calculations for rotationally inelastic scattering are performed on this new PES and good agreement is obtained with previous quantum dynamical results on a reduced-dimensional model. Furthermore, strong resonances are identified at collision energies below 100 K, including cold conditions. This new PES provides a reliable platform for future studies of scattering dynamics with vibrationally excited collision partners in a wide range of collision energies extending to cold and ultracold conditions.

Stereodynamical control of product branching in multi-channel barrierless hydrogen abstraction of CH3OH by F

Comprehensive dynamical simulations of a prototypical multi-channel reaction on a globally accurate potential energy surface show that the non-statistical product branching is dictated by unique stereodynamics in the entrance channels.

Hydrogen abstraction from methanol (CH₃OH) by F atoms presents an ideal proving ground to investigate dynamics of multi-channel reactions, because two types of hydrogen can be abstracted from the methanol molecule leading to the HF + CH₃O and HF + CH₂OH products. Using the quasi-classical trajectory approach on a globally accurate potential energy surface based on high-level ab initio calculations, this work reports a comprehensive dynamical investigation of this multi-channel reaction, yielding measurable attributes including integral and differential cross sections, as well as branching ratios. It is shown that while complex-forming and direct mechanisms coexist at low collision energies, these barrierless reaction channels are dominated at high energies by the direct mechanism, in which the reaction is only possible for trajectories entering into the respective dynamical cones of acceptance. Perhaps more importantly, the non-statistical product branching is found to be dictated by unique stereodynamics in the entrance channels.

Imaging pair-correlated reaction cross sections in F + CH3D(νb = 0, 1) → CH2D(ν4 = 1) + HF(ν)

The title reactions were studied in a crossed-beam experiment at collisional energies (Ec) from 0.5 to 4.7 kcal mol-1. The νb (ν4) vibrational mode denotes the bending (umbrella) motion of the CH3D reactant (CH2D product). Using a time-sliced, velocity-map imaging technique, we extracted the state-specific, pair-correlated integral and differential cross sections. As with other isotopically analogous ground-state reactions, an inverted vibrational population of the HF coproduct was observed. Both the step-like excitation function near the threshold and the oscillatory forward-backward peakings in the Ec-evolution of the two dominant pair-correlated angular distributions at lower Ec suggest a resonance-mediated, time-delay mechanism. As Ec increases, the angular distribution of the HF(ν = 2) product evolves into a smooth and broad swath in the backward hemisphere, indicative of a direct rebound mechanism. One quantum excitation of the bending modes of CH3D(νb = 1) promotes the reaction rate by two- to three-fold up to Ec = 2.1 kcal mol-1. Broadly speaking, all major findings are qualitatively in line with previous results in the reactions of the F atom with other isotopologues. However, the rainbow feature recently observed in the CH2D(00) + HF(ν = 3) product channel is entirely absent. A possible rationale is put forward, which reinforces the previous reactive rainbow conjecture and calls for future theoretical investigations.

Mode-specific quantum dynamics and kinetics of the hydrogen abstraction reaction OH + H2O → H2O + OH

The synergistic effect between the reactant stretching and bending modes on promoting the reaction.

Understanding mode-specific dynamics in the local mode representation

Mode specificity is a main characteristic of transition state control of reaction dynamics. The normal mode representation has been widely employed to describe the mode specificity in elementary chemical reactions. However, spectroscopists have demonstrated that the local mode representation has advantages in analyzing the overtone and combination band spectra. In this work, the mode-specific reaction dynamics between the hydrogen atom and the molecules H2S and H2O is studied using a full-dimensional quantum scattering model in the (2 + 1) Radau-Jacobi coordinates. The mode specificities in the reactions that violates our physical intuition in the normal mode representation are well rationalized in the local mode representation. The energy flow between different XH bonds resulting from the intramolecular interaction and/or intermolecular interaction is unveiled, together with its impacts on dynamics of the abstraction and exchange reactions.

Optical Control of Reactions between Water and Laser-Cooled Be+ Ions

We investigate reactions between laser-cooled Be⁺ ions and room-temperature water molecules using an integrated ion trap and high-resolution time-of-flight mass spectrometer. This system allows simultaneous measurement of individual reaction rates that are resolved by reaction product. The rate coefficient of the Be⁺(²S_1/2) + H₂O → BeOH⁺ + H reaction is measured for the first time and is found to be approximately two times smaller than predicted by an ion-dipole capture model. Zero-point-corrected quasi-classical trajectory calculations on a highly accurate potential energy surface for the ground electronic state reveal that the reaction is capture-dominated, but a submerged barrier in the product channel lowers the reactivity. Furthermore, laser excitation of the ions from the ²S_1/2 ground state to the ²P_3/2 state opens new reaction channels, and we report the rate and branching ratio of the Be⁺(²P_3/2) + H₂O → BeOH⁺ + H and H₂O⁺ + Be reactions. The excited-state reactions are nonadiabatic in nature.

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.

Combined Experimental-Theoretical Study of the OH + CO → H + CO2 Reaction Dynamics

A combined experimental-theoretical study is performed to advance our understanding of the dynamics of the prototypical tetra-atom, complex-forming reaction OH + CO → H + CO₂, which is also of great practical relevance in combustion, Earth's atmosphere, and, potentially, Mars's atmosphere and interstellar chemistry. New crossed molecular beam experiments with mass spectrometric detection are analyzed together with the results from previous experiments and compared with quasi-classical trajectory (QCT) calculations on a new, full-dimensional potential energy surface (PES). Comparisons between experiment and theory are carried out both in the center-of-mass and laboratory frames. Good agreement is found between experiment and theory, both for product angular and translational energy distributions, leading to the conclusion that the new PES is the most accurate at present in elucidating the dynamics of this fundamental reaction. Yet, small deviations between experiment and theory remain and are presumably attributable to the QCT treatment of the scattering dynamics.

Probing the rate-determining region of the potential energy surface for a prototypical ion-molecule reaction

We report a joint experimental-theoretical study of the F^- + HCl → HF + Cl^- reaction kinetics. The experimental measurement of the rate coefficient at several temperatures was made using the selected ion flow tube method. Theoretical rate coefficients are calculated using the quasi-classical trajectory method on a newly developed global potential energy surface, obtained by fitting a large number of high-level ab initio points with augmentation of long-range electrostatic terms. In addition to good agreement between experiment and theory, analyses suggest that the ion-molecule reaction rate is significantly affected by shorter-range interactions, in addition to the traditionally recognized ion-dipole and ion-induced dipole terms. Furthermore, the statistical nature of the reaction is assessed by comparing the measured and calculated HF product vibrational state distributions to that predicted by the phase space theory.This article is part of the theme issue 'Modern theoretical chemistry'.

Quantum dynamics of ClH2O- photodetachment: Isotope effect and impact of anion vibrational excitation

Photodetachment of the ClH₂O^- anion is investigated using full-dimensional quantum mechanics on accurate potential energy surfaces of both the anion and neutral species. Detailed analysis of the photoelectron spectrum and the corresponding wavefunctions reveals that the photodetachment leads to, in the product channel of the exothermic HCl + OH → Cl + H₂O reaction, the formation of numerous Feshbach resonances due apparently to slow energy transfer from H₂O vibrational modes to the dissociation coordinate. These long-lived resonances can be grouped into two broad peaks in the low-resolution photoelectron spectrum, which is in good agreement with available experiments, and they are assigned to the ground and first excited OH stretching vibrational manifolds of H₂O complexed with Cl. In addition, effects of isotope substitution on the photoelectron spectrum were small. Finally, photodetachment of the vibrationally excited ClH₂O^- in the ionic hydrogen bond mode is found to lead to Feshbach resonances with higher stretching vibrational excitations in H₂O.

Fermi resonance controlled product branching in the H + HOD reaction

Excitation of the first overtone of bending mode results in a significant enhancement in the HD + OH channel due to the 1 : 2 Fermi resonance between the fundamental OD stretch and the first overtone of the bend.

State-to-state mode specificity in H + DOH(νOH = 1) → HD + OH(ν2 = 0) reaction: vibrational non-adiabaticity or local-mode excitation?

State-of-the-art full dimensional state-to-state quantum dynamics reveal a startling observation in which the DOH(ν_OH = 1) molecule reacts with a H atom to produce a vibrationless OH product. This interesting observation is attributed to a small OD excited local-mode component in the reactant wavefunction.

Effects of vibrational excitation on the F + H2O → HF + OH reaction: dissociative photodetachment of overtone-excited [F-H-OH]. Chem Sci 2017;8:7821-7833. [PMID: 29163919 PMCID: PMC5674243 DOI: 10.1039/c7sc03364h]

Photodetaching vibrationally excited FH₂O^– channels energy into the reaction coordinate of the F + H₂O reaction, as shown in this joint experimental-theoretical study.

The reaction F + H₂O → HF + OH is a four-atom system that provides an important benchmark for reaction dynamics. Hydrogen atom transfer at the transition state for this reaction is expected to exhibit a strong dependence on reactant vibrational excitation. In the present study, the vibrational effects are examined by photodetachment of vibrationally excited F^–(H₂O) precursor anions using photoelectron-photofragment coincidence (PPC) spectroscopy and compared with full six-dimensional quantum dynamical calculations on ab initio potential energy surfaces. Prior to photodetachment at hν_UV = 4.80 eV, the overtone of the ionic hydrogen bond mode in the precursor F^–(H₂O), 2ν_IHB at 2885 cm^–1, was excited using a tunable IR laser. Experiment and theory show that vibrational energy in the anion can be effectively carried away by the photoelectron upon a Franck–Condon photodetachment, and also show evidence for an increase of branching into the F + H₂O reactant channel. The experimental results suggest a greater role for product rotational excitation than theory. Improved potential energy surfaces and longer wavepacket propagation times would be helpful to further examine the nature of the discrepancy.

Dynamics and Novel Mechanisms of SN2 Reactions on ab Initio Analytical Potential Energy Surfaces

We describe a novel theoretical approach to the bimolecular nucleophilic substitution (S_N2) reactions that is based on analytical potential energy surfaces (PESs) obtained by fitting a few tens of thousands high-level ab initio energy points. These PESs allow computing millions of quasi-classical trajectories thereby providing unprecedented statistical accuracy for S_N2 reactions, as well as performing high-dimensional quantum dynamics computations. We developed full-dimensional ab initio PESs for the F^- + CH₃Y [Y = F, Cl, I] systems, which describe the direct and indirect, complex-forming Walden-inversion, the frontside attack, and the new double-inversion pathways as well as the proton-transfer channels. Reaction dynamics simulations on the new PESs revealed (a) a novel double-inversion S_N2 mechanism, (b) frontside complex formation,

Accurate Determination of Tunneling-Affected Rate Coefficients: Theory Assessing Experiment

The thermal rate coefficients of a prototypical bimolecular reaction are determined on an accurate ab initio potential energy surface (PES) using ring polymer molecular dynamics (RPMD). It is shown that quantum effects such as tunneling and zero-point energy (ZPE) are of critical importance for the HCl + OH reaction at low temperatures, while the heavier deuterium substitution renders tunneling less facile in the DCl + OH reaction. The calculated RPMD rate coefficients are in excellent agreement with experimental data for the HCl + OH reaction in the entire temperature range of 200-1000 K, confirming the accuracy of the PES. On the other hand, the RPMD rate coefficients for the DCl + OH reaction agree with some, but not all, experimental values. The self-consistency of the theoretical results thus allows a quality assessment of the experimental data.

Kinetics and dynamics of the C(3P) + H2O reaction on a full-dimensional accurate triplet state potential energy surface

A full-dimensional accurate PES for the C(³P) + H₂O reaction is developed using the PIP-NN method.