A Full-Dimensional Global Potential Energy Surface of H3O+(ã3A) for the OH+(X̃3Σ–) + H2(X̃1Σg+) → H(2S) + H2O+(X̃2B1) Reaction

MOLPIPx: An end-to-end differentiable package for permutationally invariant polynomials in Python and Rust

In this work, we present MOLPIPx, a versatile library designed to seamlessly integrate permutationally invariant polynomials with modern machine learning frameworks, enabling the efficient development of linear models, neural networks, and Gaussian process models. These methodologies are widely employed for parameterizing potential energy surfaces across diverse molecular systems. MOLPIPx leverages two powerful automatic differentiation engines-JAX and EnzymeAD-Rust-to facilitate the efficient computation of energy gradients and higher-order derivatives, which are essential for tasks such as force field development and dynamic simulations. MOLPIPx is available at https://github.com/ChemAI-Lab/molpipx.

Effect of SiO+ Rotational Excitation on Dynamics of SiO+ + H2 → SiOH+ + H Reaction

Quasi-classical trajectory calculations and quantitative trajectory classification using DBSCAN and K-NN algorithms have been employed to study the specifics of the significant promotion of the SiO+ + H2 reaction by high rotational excitation of SiO+. There are three different reaction pathways identified. Path-I is a direct reaction process in which the product is formed when H2 collides with the O atom side of SiO+ and the H-H bond breaks. H2 first collides with the Si atom in path-II, then bounces back, and encounters the O atom to complete the reaction. Path-III is characterized by the formation of an HSiOH+ complex, is less affected by rotational excitation, and has the smallest contribution to the entire reaction. At low collision energies, rotational excitation slightly promotes the reaction, possibly due to the coupling of the rotational mode of SiO+ and the reaction coordinate of the submerged saddle point. However, this effect weakens with increasing rotational excitation, leading to a complex change in the total integral cross section. Among them, only path-I shows increased reactivity at high rotational excitation. At high collision energies, the integral cross section of the reaction is less sensitive to the rotational quantum number of the reactant, and only a slight increase is observed at the high rotational excitation of SiO+.

Higher-Order Split Operator Schemes for Solving Tetratomic Reactions Using the Time-Dependent Wave Packet Method

In this work, using the time-dependent quantum wave packet method, quite a few typical higher-order split operators (HOSOs) were for the first time applied to calculate the tetratomic reactive scattering processes in the hyperspherical coordinate. It was found that the HOSOs were hardly efficient for a tetratomic reaction calculation, unlike those for a triatomic reactive scattering calculation. We proposed an efficient HOSO with a force gradient (denoted as 2G1 in the main text) for efficiently and accurately calculating a tetratomic reaction using the quantum wave packet method. Several typical tetratomic reactions, such as H2 + OH, HF + OH, and H2 + OH+, are calculated for demonstrating the effectiveness of the proposed 2G1 in terms of (product state-resolved) reaction probability and inelastic probability, by comparing with the performance of the previously reported various HOSOs. We suggest that the 2G1 propagator could be applied to efficiently calculate a general tetratomic reaction.

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.

MLRNet: Combining the Physics-Motivated Potential Models with Neural Networks for Intermolecular Potential Energy Surface Construction

A physics-based machine learning model called MLRNet has been developed to construct the high-accuracy two-body intermolecular potential energy surface (IPES). The outputs of the neural network are integrated into the physically realistic Morse/long-range (MLR) function, which ensures that the MLRNet has meaningful extrapolation at both short and long ranges and solves the asymptotic problem in common neural network potential (NNP) models. The neural network representation of the MLR parameters is more flexible and more efficient than the polynomial expansion in the conventional mdMLR model, especially for systems containing nonrigid monomer(s). The present work illustrates the basic framework of the current MLRNet model, including (i) how to combine the physically meaningful MLR function with different possible NN structures, (ii) the preservation of permutation symmetry, and (iii) the predetermination of the long-range function u_LR. We choose two realistic systems to demonstrate the performance of MLRNet: the three-dimensional IPES of CO₂-He including the CO₂ antisymmetric vibration Q₃ and the six-dimensional IPES of the H₂O-Ar system. In both cases, the fitting errors of the MLRNet are several times smaller than those of the conventional mdMLR model. Both short-range and long-range extrapolation tests were performed to illustrate the extrapolation ability of the MLRNet and its damping function version. Moreover, for the 6-D H₂O-Ar system, the MLRNet only needs 1596 trainable parameters, which is almost equal to the number needed for the 5-D mdMLR model (1509) and half that needed for the PIP-NN model (3501) within similar accuracy, which illustrates the model efficiency in high-dimensional IPES fitting.

Energy- and Local-Gradient-Based Neural Network Method for Accurately Describing Long-Range Interaction: Application to the H2 + CO+ Reaction

The long-range interaction plays an important role in theoretically describing ion-molecule reaction. However, most energy-based neural network fitting methods usually introduce spurious long-range interactions. In this work, we propose an energy- and local-gradient-based neural network (ELGNN) method to fit potential energy surfaces (PESs). K-means clustering is employed to divide the whole configuration space into three regions: reactant asymptotic region, interaction region, and product asymptotic region. In the interaction region, only the energies of sampled points are computed, while in the asymptotic regions, the gradients of partially sampled configurations are calculated as well, and both the energies and energy gradients (if necessary) are used to fit long-range interactions. These regions are joined together by switching functions. The ELGNN method is first applied to fit the PES of the H₂ + CO⁺ reaction, which has significant long-range interactions. It is found that the ELGNN method works better than the energy-based NN method in describing long-range interactions. The dynamics and kinetics of the reaction are then investigated on the new PES.

Accurate many-body expansion potential energy surface for SiH2 (11 A′) using a switching function formalism

An accurate many-body expansion potential energy surface for the ground state of SiH2 is reported. To warrant the correct behavior at the Si (1D) + H2 (X1Σ+g) dissociation channels...

Mode-specific dynamics in multichannel reaction NH+ + H2

The vibrational- and rotational-mode specificity of the multichannel NH⁺ + H₂ reaction is studied on a recently constructed ab initio-based global potential energy surface using an initial state selected quasi-classical trajectory method, and the trajectories are analyzed using an isometric feature mapping and k-means approach. All excitation modes promote two reactions (R1: NH'⁺ + H₂ → NH⁺ + HH' and R4: NH'⁺ + H₂ → NH₂⁺ + H') where both NH and HH bonds are broken, but reduce the reactivity of the proton-transfer reaction R2 (NH'⁺ + H₂ → N + H'H₂⁺) at low collision energies. For the hydrogen-transfer reaction R3 (NH'⁺ + H₂ → HNH'⁺ + H), the rotational excitation of NH⁺ enhances the reactivity remarkably, while its vibrational excitation has an inhibiting effect on the reaction. The trajectory analyses show that the vibrational and rotational excitations of NH⁺ make R3 tend to go over a submerged saddle point instead of extracting hydrogen atoms directly. On the other hand, the motions of the H₂ reactant facilitate the enhancement of the reactivity but they do not affect the mechanism of R3. In addition, the results suggest that the coupling of the isometric feature mapping and the k-means approach in the trajectory analysis is an appropriate tool for reaction-dynamics studies.

Neural network potential energy surface for the low temperature ring polymer molecular dynamics of the H2CO + OH reaction

A new potential energy surface (PES) and dynamical study of the reactive process of H₂CO + OH toward the formation of HCO + H₂O and HCOOH + H are presented. In this work, a source of spurious long range interactions in symmetry adapted neural network (NN) schemes is identified, which prevents their direct application for low temperature dynamical studies. For this reason, a partition of the PES into a diabatic matrix plus a NN many-body term has been used, fitted with a novel artificial neural network scheme that prevents spurious asymptotic interactions. Quasi-classical trajectory (QCT) and ring polymer molecular dynamics (RPMD) studies have been carried on this PES to evaluate the rate constant temperature dependence for the different reactive processes, showing good agreement with the available experimental data. Of special interest is the analysis of the previously identified trapping mechanism in the RPMD study, which can be attributed to spurious resonances associated with excitations of the normal modes of the ring polymer.

Neural Network Potential Energy Surfaces for Small Molecules and Reactions

We review progress in neural network (NN)-based methods for the construction of interatomic potentials from discrete samples (such as ab initio energies) for applications in classical and quantum dynamics including reaction dynamics and computational spectroscopy. The main focus is on methods for building molecular potential energy surfaces (PES) in internal coordinates that explicitly include all many-body contributions, even though some of the methods we review limit the degree of coupling, due either to a desire to limit computational cost or to limited data. Explicit and direct treatment of all many-body contributions is only practical for sufficiently small molecules, which are therefore our primary focus. This includes small molecules on surfaces. We consider direct, single NN PES fitting as well as more complex methods that impose structure (such as a multibody representation) on the PES function, either through the architecture of one NN or by using multiple NNs. We show how NNs are effective in building representations with low-dimensional functions including dimensionality reduction. We consider NN-based approaches to build PESs in the sums-of-product form important for quantum dynamics, ways to treat symmetry, and issues related to sampling data distributions and the relation between PES errors and errors in observables. We highlight combinations of NNs with other ideas such as permutationally invariant polynomials or sums of environment-dependent atomic contributions, which have recently emerged as powerful tools for building highly accurate PESs for relatively large molecular and reactive systems.

Analytic intermolecular potential energy surface and first-principles prediction of the rotational profiles for a symmetric top ion-atom complex: A case study of H3O+-Ar

We presented the first three-dimensional (3D) ab initio intermolecular potential energy surface (PES) for the H₃O⁺-Ar complex. The electronic structure computations were carried out at the explicitly correlated coupled cluster theory-F12 with an augmented correlation-consistent triple zeta basis set. Analytic 3D PES was obtained by least-squares fitting the multi-dimensional Morse/Long-Range (mdMLR) potential model to interaction energies, where the mdMLR function form was applied to the nonlinear ion-atom case for the first time. The 3D PES fitting to 1708 points has root-mean-square deviations of 0.19 cm^-1 with only 108 parameters for interaction energies less than 500 cm^-1. With the 3D PES of the H₃O⁺-Ar complex, we employed the combined radial discrete variable representation/angular finite basis representation method and Lanczos algorithm to calculate rovibrational energy levels. The rotational profiles of the O-H anti-stretching vibrational bands of v₃ ⁺(S)←0⁺ and v₃ ^-(A)←0^- for the H₃O⁺-Ar complex were predicted and were in good agreement with the experimental results.

Quasi-classical trajectory analysis with isometric feature mapping and locally linear embedding: deep insights into the multichannel reaction on an NH3+(4A) potential energy surface

Two manifold learning methods, isometric feature mapping and locally linear embedding, are applied to the analysis of quasi-classical trajectories for multi-channel reaction NH⁺ + H₂ → N + H₃⁺/NH₂⁺ + H.

New diabatic potential energy surfaces of the NaH2 system and dynamics studies for the Na(3p) + H2 → NaH + H reaction

The Na(3p) + H2(X1Σg+) → NaH(X1Σ+) + H(2S) reaction plays an important role in the field of diabatic reaction dynamics. A set of new diabatic potential energy surfaces (PESs) of the NaH2 system are structured, which include the diabatic coupling between the lowest two adiabatic states. The electronic structure calculations are performed on the multi-reference configuration interaction level with the cc-pwCVQZ and aug-cc-PVQZ basis sets for Na and H atoms. 32402 geometries are chosen to construct the diabatic data by a unitary transformation based on the molecular property method. The diabatic matrix elements of [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) are fitted by the artificial neural network model. The spectroscopic constants of diatoms obtained from the present PESs are consistent with the experimental data. The topographical and intersection characteristics of the [Formula: see text] and [Formula: see text] surfaces are discussed. Based on the new PESs, the time-dependent quantum wave packet calculations are carried out to study the reaction mechanism of the title reaction in detail.

Low temperature rates for key steps of interstellar gas-phase water formation

The gas-phase formation of water molecules in the diffuse interstellar medium (ISM) proceeds mainly via a series of reactions involving the molecular ions OH⁺, H₂O⁺, and H₃O⁺ and molecular hydrogen. These reactions form the backbone for the chemistry leading to the formation of several complex molecular species in space. A comprehensive understanding of the mechanisms involved in these reactions in the ISM necessitates an accurate knowledge of the rate coefficients at the relevant temperatures (10 to 100 K). We present measurements of the rate coefficients for two key reactions below 100 K, which, in both cases, are significantly higher than the values used in astronomical models thus far. The experimental rate coefficients show excellent agreement with dedicated theoretical calculations using a novel ring-polymer molecular dynamics approach that offers a first-principles treatment of low-temperature barrierless gas-phase reactions, which are prevalent in interstellar chemical networks.

Diabatic potential energy surfaces of MgH2+ and dynamic studies for the Mg+(3p) + H2 → MgH+ + H reaction

The global diabatic potential energy surfaces for the Mg⁺(3p) + H₂ → MgH⁺ + H reaction are structured for the first time.

Dynamics of the O + H2+ → OH+ + H, OH + H+ proton and hydrogen atom transfer reactions on the two lowest potential energy surfaces

The dynamics of the title reaction was studied using mainly the quasiclassical trajectory (QCT) method on the ground 1²A'' (OH⁺ channel) and first excited 1²A' (OH channel) potential energy surfaces (PESs) employing ab initio analytical representations of the PESs developed by us. Both PESs correspond to exoergic reactions, are barrierless and present a deep minimum along the minimum energy path (MEP). Some extra calculations (cross sections) were also performed with the time dependent quantum real wave packet method at the centrifugal sudden level (RWP-CS method). A broad set of properties as a function of collision energy (E_col ≤ 0.5 eV) was considered using the QCT method: cross sections, average fractions of energy, product rovibrational distributions, two- and three-vector properties, and the microscopic mechanisms analyzing their influence on the dynamics. The proton transfer channel dominates the reactivity of the system and significant differences between the two reaction channels are found for the vibrational distributions and microscopic mechanisms. The results were interpreted according to the properties of the ground and excited PESs. Moreover, the QCT and RWP-CS cross sections are in rather good agreement for both reaction channels. We hope that this study will encourage the experimentalists to investigate the dynamics of this interesting but scarcely studied system, whose two lowest PESs include the ground and first excited electronic states of the H₂O⁺ cation.

Recent Advances in Quantum Dynamics of Bimolecular Reactions

In this review, we survey the latest advances in theoretical understanding of bimolecular reaction dynamics in the past decade. The remarkable recent progress in this field has been driven by more accurate and efficient ab initio electronic structure theory, effective potential-energy surface fitting techniques, and novel quantum scattering algorithms. Quantum mechanical characterization of bimolecular reactions continues to uncover interesting dynamical phenomena in atom-diatom reactions and beyond, reaching an unprecedented level of sophistication. In tandem with experimental explorations, these theoretical developments have greatly advanced our understanding of key issues in reaction dynamics, such as microscopic reaction mechanisms, mode specificity, product energy disposal, influence of reactive resonances, and nonadiabatic effects.

Comparison of experimental and theoretical quantum-state-selected integral cross-sections for the H2O+ + H2 (D2) reactions in the collision energy range of 0.04–10.00 eV

A combined experimental–theoretical study of the rovibrationally state-selected ion–molecule reactions H₂O⁺(X²B₁; v₁⁺v₂⁺v₃⁺; N_Ka+Kc+⁺) + H₂ (D₂) → H₃O⁺ (H₂DO⁺) + H (D), where (v₁⁺v₂⁺v₃⁺) = (000), (020), and (100) and N_Ka+Kc+⁺ = 0₀₀, 1₁₁, and 2₁₁.