Fitting potential energy surfaces with fundamental invariant neural network. II. Generating fundamental invariants for molecular systems with up to ten atoms

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.

Demethylation C-C coupling reaction facilitated by the repulsive Coulomb force between two cations

Carbon chain elongation (CCE) is normally carried out using either chemical catalysts or bioenzymes. Herein we demonstrate a catalyst-free approach to promote demethylation C-C coupling reactions for advanced CCE constructed with functional groups under ambient conditions. Accelerated by the electric field, two organic cations containing a methyl group (e.g., ketones, acids, and aldehydes) approach each other with such proximity that the energy of the repulsive Coulomb interaction between these two cations exceeds the bond energy of the methyl group. This results in the elimination of a methyl cation and the coupling of the residual carbonyl carbon groups. As confirmed by high-resolution mass spectrometry and isotope-labeling experiments, the C-C coupling reactions (yields up to 76.5%) were commonly observed in the gas phase or liquid phase, for which the mechanism was further studied using molecular dynamics simulations and stationary-point calculations, revealing deep insights and perspectives of chemistry.

Gaussian Process Regression for State-to-State Integral Cross Sections: The Case of the O + O2 Collision Dissociation Reactions

Research on hypersonic vehicles has become increasingly important worldwide in recent years. However, accurately simulating the dynamics of the nonequilibrium high-temperature reactions that are in the hypersonic flow around the vehicles presents a significant challenge as a large number of states and transitions are accessible even for the smallest atom-diatom reaction systems. It is quite difficult, sometimes even impossible, to exhaustively investigate all relevant combinations or determine high-dimensional analytical representations for the state-to-state reaction probabilities. In this study, we used Gaussian process regression (GPR) to fit a model based on only 807 QCT data for training. The confidence interval of the GPR prediction and the Kullback-Leibler (KL) divergence were used to help minimize the sampling amount of data for fitting the converged GPR model. The model aims to predict the state-to-state integral cross section (ICS) of the O + O2 → 3O dissociation reaction under random initial conditions (Et, v, j). In total, it took almost a month to obtain this converged GPR model, but it took only a few seconds to predict the ICS value for any initial condition. For 330 initial conditions not included in the training set, the mean-square error (MSE) between the QCT-calculated ICSs and the GPR-predicted ones is only 0.08 Å2 and the R2 is 0.9986, indicating that the GPR model can replace the direct expensive QCT calculation with high accuracy. Finally, we calculated the equilibrium dissociation rate coefficients based on the StS ICS values predicted by the GPR model, and the results were in good agreement with available experimental and theoretical results. Thus, this study provides an effective and accurate approach to the extensive direct state-to-state reaction dynamic calculations.

"On-the-fly" Crystal : How to reliably and automatically characterize and construct potential energy surfaces

In this work, the Crystal  code, developed previously by the authors to find "holes" as well as legitimate transition states in existing potential energy surface (PES) functions [JPC Lett. 11, 6468 (2020)], is retooled to perform on-the-fly "direct dynamics"-type PES explorations, as well as automatic construction of new PES functions. In all of these contexts, the chief advantage of Crystal  over other methods is its ability to globally map the PES, thereby determining the most relevant regions of configuration space quickly and reliably-even when the dimensionality is rather large. Here, Crystal  is used to generate a uniformly spaced grid of density functional theory (DFT) or ab initio points, truncated over the relevant regions, which can then be used to either: (a) hone in precisely on PES features such as minima and transition states, or; (b) create a new PES function automatically, via interpolation. Proof of concept is demonstrated via application to three molecular systems: water (H2 O), (reduced-dimensional) methane (CH4 ), and methylene imine (CH2 NH).

Exploring the frontiers of condensed-phase chemistry with a general reactive machine learning potential

Atomistic simulation has a broad range of applications from drug design to materials discovery. Machine learning interatomic potentials (MLIPs) have become an efficient alternative to computationally expensive ab initio simulations. For this reason, chemistry and materials science would greatly benefit from a general reactive MLIP, that is, an MLIP that is applicable to a broad range of reactive chemistry without the need for refitting. Here we develop a general reactive MLIP (ANI-1xnr) through automated sampling of condensed-phase reactions. ANI-1xnr is then applied to study five distinct systems: carbon solid-phase nucleation, graphene ring formation from acetylene, biofuel additives, combustion of methane and the spontaneous formation of glycine from early earth small molecules. In all studies, ANI-1xnr closely matches experiment (when available) and/or previous studies using traditional model chemistry methods. As such, ANI-1xnr proves to be a highly general reactive MLIP for C, H, N and O elements in the condensed phase, enabling high-throughput in silico reactive chemistry experimentation.

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

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

Accurate fundamental invariant-neural network representation of ab initio potential energy surfaces

Highly accurate potential energy surfaces are critically important for chemical reaction dynamics. The large number of degrees of freedom and the intricate symmetry adaption pose a big challenge to accurately representing potential energy surfaces (PESs) for polyatomic reactions. Recently, our group has made substantial progress in this direction by developing the fundamental invariant-neural network (FI-NN) approach. Here, we review these advances, demonstrating that the FI-NN approach can represent highly accurate, global, full-dimensional PESs for reactive systems with even more than 10 atoms. These multi-channel reactions typically involve many intermediates, transition states, and products. The complexity and ruggedness of this potential energy landscape present even greater challenges for full-dimensional PES representation. These PESs exhibit a high level of complexity, molecular size, and accuracy of fit. Dynamics simulations based on these PESs have unveiled intriguing and novel reaction mechanisms, providing deep insights into the intricate dynamics involved in combustion, atmospheric, and organic chemistry.

Accuracy Assessment of Atomistic Neural Network Potentials: The Impact of Cutoff Radius and Message Passing

Atomistic neural network potentials have achieved great success in accelerating atomistic simulations in complicated systems in recent years. They are typically based on the atomic decomposition of total properties, truncating the interatomic correlations to a local environment within a given cutoff radius. A more recently developed message passing (MP) neural network framework can, in principle, incorporate nonlocal effects through iteratively correlating some atoms outside the cutoff sphere with atoms inside, a process referred to as MP. However, how the model accuracy depends on the cutoff radius and the MP process has rarely been discussed. In this work, we investigate this dependence using a recursively embedded atom neural network method that possesses both local and MP features, in two representative systems: liquid H2O and solid Al2O3. We focus on how these settings influence predictions for structural and vibrational properties, namely, radial distribution functions (RDFs) and vibrational density of states (VDOSs). We find that while MP lowers test errors of energy and forces in general, it may not improve the prediction for RDFs and/or VDOSs if direct interatomic correlations in the local environment are insufficiently described. A cutoff radius exceeding the first neighbor shell is necessary, beyond which involving MP quickly enhances the model accuracy until convergence. This is a potentially more efficient way to increase the model accuracy than directly increasing the cutoff radius, especially with more memory savings in the GPU implementation. Our findings also suggest that using the mean test error as the measure of the model accuracy alone is inadequate.

Roaming Dynamics in Hydroxymethyl Hydroperoxide Decomposition Revealed by the Full-Dimensional Potential Energy Surface of the CH2OO + H2O Reaction

The CH2OO + H2O reaction is an important atmospheric process that leads to the formation of formic acid (HCOOH) and water via the intermediate hydroxymethyl hydroperoxide (HOCH2OOH, HMHP). We investigated the intricacies of this process by employing quasiclassical trajectory calculations on an accurate, full-dimensional ab initio potential energy surface (PES). In addition to the direct mechanism via the transition state (TS), an interesting roaming mechanism was found to play the predominant role in producing H2O and HCOOH. This roaming pathway is featured as the near direct dissociation of HMHP into OH and hydroxymethoxy radical, followed by the retraction of OH and abstraction of the H atom, culminating in the formation of H2O. Due to the longer interaction time of the roaming mechanism, less product translational energy was released, but more internal energies of HCOOH were obtained, as compared with the direct TS mechanism. The enhanced yield of H2O and formic acid achieved through roaming dynamics underscores the significance of dynamics simulations based on an accurate full-dimensional PES. This work provides new insights into the dynamics of the CH2OO + H2O reaction and its implications for atmospheric chemistry.

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

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

Molecular dynamics-driven global potential energy surfaces: Application to the AlF dimer

In this work, we present a full-dimensional potential energy surface for AlF-AlF. We apply a general machine learning approach for full-dimensional potential energy surfaces, employing an active learning scheme trained on ab initio points, whose size grows based on the accuracy required. The training points are selected based on molecular dynamics simulations, choosing the most suitable configurations for different collision energy and mapping the most relevant part of the potential energy landscape of the system. The present approach does not require long-range information and is entirely general. As a result, it is possible to provide the full-dimensional AlF-AlF potential energy surface, requiring ≲0.01% of the configurations to be calculated ab initio. Furthermore, we analyze the general properties of the AlF-AlF system, finding critical differences with other reported results on CaF or bi-alkali dimers.

A Status Report on "Gold Standard" Machine-Learned Potentials for Water

Owing to the central importance of water to life as well as its unusual properties, potentials for water have been the subject of extensive research over the past 50 years. Recently, five potentials based on different machine learning approaches have been reported that are at or near the "gold standard" CCSD(T) level of theory. The development of such high-level potentials enables efficient and accurate simulations of water systems using classical and quantum dynamical approaches. This Perspective serves as a status report of these potentials, focusing on their methodology and applications to water systems across different phases. Their performances on the energies of gas phase water clusters, as well as condensed phase structural and dynamical properties, are discussed.

Fitting Potential Energy Surfaces by Learning the Charge Density Matrix with Permutationally Invariant Polynomials

The electronic energy in the Hartree-Fock (HF) theory is the trace of the product of the charge density matrix (CDM) with the one-electron and two-electron matrices represented in an atomic orbital basis, where the two-electron matrix is also a function of the same CDM. In this work, we examine a formalism of analytic representation of a generic molecular potential energy surface (PES) as a sum of a linearly parameterized HF and a correction term, the latter formally representing the electron correlation energy, also linearly parameterized, by expressing the elements of CDM using permutationally invariant polynomials (PIPs). We show on a variety of numerical examples, ranging from exemplary two-electron systems HeH+ and H3+ to the more challenging cases of methanium (CH5+) fragmentation and high-energy tautomerization of formamide to formimidic acid that such a formulation requires significantly fewer, 10-20% of PIPs, to accomplish the same accuracy of the fit as the conventional representation at practically the same computational cost.

Neural network potential energy surfaces and dipole moment surfaces for SO2(H2O) and SO2(H2O)2 complexes

Full-dimensional, ab initio-based many-body potential energy surfaces and dipole moment surfaces constructed using the neural network method for SO2(H2O)n (n = 1,2) complexes are reported. The database of the SO2 1-body PES, SO2(H2O) 2-body PES and SO2(H2O)2 3-body PES consists of 11 952, 79 882 and 84 159 ab initio energies, respectively. All 1-body energies were calculated at the CCSD(T)/CBS(AVTZ:AVQZ) level and all 2,3-body energies were calculated at the DSD-PBEP86/AVTZ level. The database of DMSs is the same as that of PESs and all dipole moments were calculated at the MP2/AVTZ level. Harmonic frequencies and dissociation energies of SO2(H2O) and SO2(H2O)2 were calculated on these PESs and compared with ab initio results to examine the fidelity of these PESs.

Direct mass spectrometry analysis of exhaled human breath in real-time

The molecular composition of exhaled human breath can reflect various physiological and pathological conditions. Considerable progress has been achieved over the past decade in real-time analysis of exhaled human breath using direct mass spectrometry methods, including selected ion flow tube mass spectrometry, proton transfer reaction mass spectrometry, extractive electrospray ionization mass spectrometry, secondary electrospray ionization mass spectrometry, acetone-assisted negative photoionization mass spectrometry, atmospheric pressure photoionization mass spectrometry, and low-pressure photoionization mass spectrometry. Here, recent developments in direct mass spectrometry analysis of exhaled human breath are reviewed with regard to analytical performance (chemical sensitivity, selectivity, quantitative capabilities) and applications of the developed methods in disease diagnosis, targeted molecular detection, and real-time metabolic monitoring.

An Ab Initio Neural Network Potential Energy Surface for the Dimer of Formic Acid and Further Quantum Tunneling Dynamics

We construct a full-dimensional ab initio neural network potential energy surface (PES) for the isomerization system of the formic acid dimer (FAD). This is based upon ab initio calculations using the DLPNO-CCSD(T) approach with the aug-cc-pVTZ basis set, performed at over 14000 symmetry-unique geometries. An accurate fit to the obtained energies is generated using a general neural network fitting procedure combined with the fundamental invariant method, and the overall energy-weighted root-mean-square fitting error is about 6.4 cm^-1. Using this PES, we present a multidimensional quantum dynamics study on tunneling splittings with an efficient theoretical scheme developed by our group. The ground-state tunneling splitting of FAD calculated with a four-mode coupled method is in good agreement with the most recent experimental measurements. The PES can be applied for further dynamics studies. The effectiveness of the present scheme for constructing a high-dimensional PES is demonstrated, and this scheme is expected to be feasible for larger molecular systems.

Full-dimensional neural network potential energy surface and dynamics of the CH2OO + H2O reaction

An accurate global full-dimensional machine learning-based potential energy surface (PES) of the simplest Criegee intermediate (CH₂OO) reaction with water monomer was developed based on the high level of extensive CCSD(T)-F12a/aug-cc-pVTZ calculations. This analytical global PES not only covers the regions of reactants to hydroxymethyl hydroperoxide (HMHP) intermediates, but also different end product channels, which facilities both the reliable and efficient kinetics and dynamics calculations. The rate coefficients calculated by the transition state theory with the interface to the full-dimensional PES agree well with the experimental results, indicating the accuracy of the current PES. Extensive quasi-classical trajectory (QCT) calculations were performed both from the bimolecular reaction CH₂OO + H₂O and from HMHP intermediate on the new PES. The product branching ratios of hydroxymethoxy radical (HOCH₂O, HMO) + OH radical, formaldehyde (CH₂O) + H₂O₂ and formic acid (HCOOH) + H₂O were calculated. The reaction yields dominantly HMO + OH, because of the barrierless pathway from HMHP to this channel. The computed dynamical results for this product channel show the total available energy was deposited into the internal rovibrational excitation of HMO, and the energy release in OH and translational energy is limited. The large amount of OH radical found in the current study implies that the CH₂OO + H₂O reaction can provide crucially OH yield in Earth's atmosphere.

A highly accurate full-dimensional ab initio potential surface for the rearrangement of methylhydroxycarbene (H3C-C-OH)

We report here a full-dimensional machine learning global potential surface (PES) for the rearrangement of methylhydroxycarbene (H₃C-C-OH, 1t). The PES is trained with the fundamental invariant neural network (FI-NN) method on 91 564 ab initio energies calculated at the UCCSD(T)-F12a/cc-pVTZ level of theory, covering three possible product channels. FI-NN PES has the correct symmetry properties with respect to permutation of four identical hydrogen atoms and is suitable for dynamics studies of the 1t rearrangement. The averaged root mean square error (RMSE) is 11.4 meV. Six important reaction pathways, as well as the energies and vibrational frequencies at the stationary geometries on these pathways are accurately preproduced by our FI-NN PES. To demonstrate the capacity of the PES, we calculated the rate coefficient of hydrogen migration in -CH₃ (path A) and hydrogen migration of -OH (path B) with instanton theory on this PES. Our calculations predicted the half-life of 1t to be 95 min, which is excellent in agreement with experimental observations.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Observation of Competitive Nonadiabatic Photodissociation Dynamics of H2S+ Cations

A comprehensive understanding of dissociation mechanisms is of fundamental importance in the photochemistry of small molecules. Here, we investigated the detailed photodissociation dynamics of H₂S⁺ near 337 nm by using the velocity map ion imaging technique together with the theoretical characterizations by developing global full-dimensional potential energy surfaces (PESs). Rotational state resolved images were acquired for the S⁺(⁴S) + H₂ product channel. Significant changes in product total kinetic energy release distributions and angular distributions have been observed within a small excitation photon energy range of 5 wavenumbers. Analysis based on the full-dimensional PESs reveals that two nonadiabatic pathways determined by the transition state connecting two minima on the 1²A' state are responsible for the dramatic variation of observed product distributions. The current study has directly witnessed the competitive photodissociation mechanisms controlled by a critical energy point on the PES, thereby providing in-depth insight into the nonadiabatic dynamics in photochemistry.

Unexpected steric hindrance failure in the gas phase F- + (CH3)3CI SN2 reaction

Base-induced elimination (E2) and bimolecular nucleophilic substitution (S_N2) reactions are of significant importance in physical organic chemistry. The textbook example of the retardation of S_N2 reactivity by bulky alkyl substitution is widely accepted based on the static analysis of molecular structure and steric environment. However, the direct dynamical evidence of the steric hindrance of S_N2 from experiment or theory remains rare. Here, we report an unprecedented full-dimensional (39-dimensional) machine learning-based potential energy surface for the 15-atom F⁻ + (CH₃)₃CI reaction, facilitating the reliable and efficient reaction dynamics simulations that can reproduce well the experimental outcomes and examine associated atomic-molecular level mechanisms. Moreover, we found surprisingly high “intrinsic” reactivity of S_N2 when the E2 pathway is completely blocked, indicating the reaction that intends to proceed via E2 transits to S_N2 instead, due to a shared pre-reaction minimum. This finding indicates that the competing factor of E2 but not the steric hindrance determines the small reactivity of S_N2 for the F⁻ + (CH₃)₃CI reaction. Our study provides new insight into the dynamical origin that determines the intrinsic reactivity in gas-phase organic chemistry.

Base-induced elimination (E2) and bimolecular nucleophilic substitution (SN2) are of significant importance in physical organic chemistry. Here, the authors show that the competing factor of E2 as opposed to steric hindrance determines the low reactivity of SN2 in the F⁻ + (CH₃)₃CI reaction.

Adiabatic models for the quantum dynamics of surface scattering with lattice effects

In this contribution, we review models for the lattice effects in quantum dynamics calculations on surface scattering, which is important to modeling heterogeneous catalysis for achieving an interpretation of experimental measurements. Unlike dynamics models for reactions in the gas phase, those for heterogeneous reactions have to include the effects of the surface. For manageable computational costs in calculations, the effects of static surface (SS) are firstly modeled as this is simply and easily implemented. Then, the SS model has to be improved to include the effects of the flexible surface, that is the lattice effects. To do this, various surface models have been designed where the coordinates of the surface atoms are introduced in the Hamiltonian operator, especially those of the top surface atom. Based on this model Hamiltonian operator, extensive multi-dimension quantum dynamics calculations can be performed to recover the lattice effects. Here, we first review an overview of the techniques in constructing the Hamiltonian operator, which is a sum of the kinetic energy operator (KEO) and potential energy surface (PES). Since the PES containing the coordinates of the surface atoms in a cell is still expensive, the SS model is often accepted. We consider a mathematical model, called the coupled harmonic oscillator (CHO) model, to introduce the concepts of adiabatic and diabatic representations for separating the molecule and surface. Under the adiabatic model, we further introduce the expansion model where the potential function is Taylor expanded around the optimized geometry of the surface. By an expansion model truncated at the first and second order, various coupling surface models between the molecule and surface are derived. Moreover, by further and deeply understanding the adiabatic representation, an effective Hamiltonian operator is obtained by optimizing the total wave function in factorized form. By this factorized form of wave function and effective Hamiltonian operator, the geometry phase of the surface wave function is theoretically found. This theoretical prediction may be measured by carefully designing experiments. Finally, discussions on the adiabatic representation, the PES construction, and possibility of the classical-dynamics solutions are given. Based on these discussions, a simple outlook on the dynamics of photocatalytics is finally given.

Dynamical Effects of SN2 Reactivity Suppression by Microsolvation: Dynamics Simulations of the F-(H2O) + CH3I Reaction on a 21-Dimensional Potential Energy Surface

A comparison of atomistic dynamics between microsolvated and unsolvated reactions can expose the precise role of solvent molecules and thus provide deep insight into how solvation influences chemical reactions. Here we developed the first full-dimensional analytical potential energy surface of the F-(H2O) + CH3I reaction, which facilitates the efficient dynamics simulations on a quantitatively accurate level. The computed SN2 reactivity suppression ratio of the monosolvated F-(H2O) + CH3I reaction relative to the unsolvated F- + CH3I reaction as a function of collision energy first increases and then decreases steadily, forming an inverted-V shape, due to the combined dynamical effects of interaction time, steric hindrance, and collision-induced dehydration. Moreover, further analysis reveals that the steric effect of the F-(H2O) + CH3I reaction resulting from the single water molecule is manifested mainly in dragging the F- anion away from the central C atom, rather than shielding F- from C. Our study shows there is great potential in rigorously studying the role of the solvent in more complicated reactions.

Validating experiments for the reaction H2 + NH2- by dynamical calculations on an accurate full-dimensional potential energy surface

Ion-molecule reactions play key roles in the field of ion related chemistry. As a prototypical multi-channel ion-molecule reaction, the reaction H₂ + NH₂^- → NH₃ + H^- has been studied for decades. In this work, we develop a new globally accurate potential energy surface (PES) for the title system based on hundreds of thousands of sampled points over a wide dynamically relevant region that covers long-range interacting configuration space. The permutational invariant polynomial-neural network (PIP-NN) method is used for fitting and the resulting total root mean squared error (RMSE) is extremely small, 0.026 kcal mol^-1. Extensive dynamical and kinetic calculations are carried out on this PIP-NN PES. Impressively, a unique phenomenon of significant reactivity suppression by exciting the rotational mode of H₂ is reported, supported by both the quasi-classical trajectory (QCT) and quantum dynamics (QD) calculations. Further analysis uncovers that exciting the H₂ rotational mode would prevent the formation of the reactant complex and thus suppress the reactivity. The calculated rate coefficients for H₂/D₂ + NH₂^- agree well with the experimental results, which show an inverse temperature dependence from 50 to 300 K, consistent with the capture nature of this barrierless reaction. The significant kinetic isotope effect observed by experiments is well reproduced by the QCT computations as well.

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

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

REANN: A PyTorch-based end-to-end multi-functional deep neural network package for molecular, reactive, and periodic systems

In this work, we present a general purpose deep neural network package for representing energies, forces, dipole moments, and polarizabilities of atomistic systems. This so-called recursively embedded atom neural network model takes advantages of both the physically inspired atomic descriptor based neural networks and the message-passing based neural networks. Implemented in the PyTorch framework, the training process is parallelized on both the central processing unit and the graphics processing unit with high efficiency and low memory in which all hyperparameters can be optimized automatically. We demonstrate the state-of-the-art accuracy, high efficiency, scalability, and universality of this package by learning not only energies (with or without forces) but also dipole moment vectors and polarizability tensors in various molecular, reactive, and periodic systems. An interface between a trained model and LAMMPs is provided for large scale molecular dynamics simulations. We hope that this open-source toolbox will allow for future method development and applications of machine learned potential energy surfaces and quantum-chemical properties of molecules, reactions, and materials.

All-Atom Nonadiabatic Dynamics Simulation of Hybrid Graphene Nanoribbons Based on Wannier Analysis and Machine Learning

Trajectory surface hopping combined with ab initio electronic structure calculations is a popular and powerful approach for on-the-fly nonadiabatic dynamics simulations. For large systems, however, this remains a significant challenge because of the unaffordable computational cost of large-scale electronic structure calculations. Here, we present an efficient divide-and-conquer approach to construct the system Hamiltonian based on Wannier analysis and machine learning. In detail, the large system under investigation is first decomposed into small building blocks, and then all possible segments formed by building blocks within a cutoff distance are found out. Ab initio molecular dynamics is carried out to generate a sequence of geometries for each equivalent segment with periodicity. The Hamiltonian matrices in the maximum localized Wannier function (MLWF) basis are obtained for all geometries and utilized to train artificial neural networks (ANNs) for the structure-dependent Hamiltonian elements. Taking advantage of the orthogonality and spatial locality of MLWFs, the one-electron Hamiltonian of a large system at arbitrary geometry can be directly constructed by the trained ANNs. As demonstrations, we study charge transport in a zigzag graphene nanoribbon (GNR), a coved GNR, and a series of hybrid GNRs with a state-of-the-art surface hopping method. The interplay between delocalized and localized states is found to determine the electron dynamics in hybrid GNRs. Our approach has successfully studied GNRs with >10 000 atoms, paving the way for efficient and reliable all-atom nonadiabatic dynamics simulation of general systems.

Kinetic and dynamic studies of the NH2+ + H2 reaction on a high-level ab initio potential energy surface

The dynamics and kinetics of the NH2+ + H2 reaction are investigated on a newly developed ab initio potential energy surface using the quasi-classical trajectory method.

A full-dimensional ab initio potential energy and dipole moment surfaces for (NH3)2

A full-dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS) for the ammonia dimer (NH₃)₂ are reported. The database of the PES consists of 27 736 ab initio energy points and all of these points were calculated at the UCCSD(T)-F12a/AVTZ level. The PES was fitted by using the fundamental invariant neural network (FI-NN) method that satisfies the permutational symmetry of identical atoms, and the root mean square fitting error for the PES is very small as low as 0.562 meV. The geometries for the (NH₃)₂ DMS are the same as those used for the PES and are calculated at the XYG3/AVTZ level. This PES can describe a variety of internal floppy motions, including all kinds of vibrational modes no matter intermolecular or intramolecular. The CCSD(T)-PES can dissociate correctly to two NH₃ monomers, with D_e = 1135.55 cm^-1 (13.58 kJ/mol) which agrees accurately with the 13.5 ± 0.3 kJ/mol predicted by previous work.

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.

Study on the kinetics and dynamics of the H2 + NH2- reaction on a high-level ab initio potential energy surface

Gas-phase ion-molecule reactions play major roles in many fields of chemistry and physics. The reaction of an amino radical anion with a hydrogen molecule is one of the simplest proton transfer reactions involving anions. A globally accurate full-dimensional potential energy surface (PES) for the NH₂^- + H₂ reaction is developed by the fundamental invariant-neural network method, resulting in a root mean square error of 0.116 kcal mol^-1. Quasi-classical trajectory calculations are then carried out on the newly developed PES to give integral cross sections, differential cross sections and thermal rate coefficients. This reaction has two reaction channels, proton transfer and hydrogen exchange. The reactivity of the proton transfer channel is about one or two orders of magnitude stronger than that of the hydrogen exchange channel in the energy range studied. Vibrational excitation of H₂ promotes the proton transfer reaction, while fundamental excitation of each vibrational mode of NH₂^- has a negligible effect. In addition, the theoretical rate coefficients of the proton transfer reaction on the PES show inverse temperature dependence from 150 to 750 K, in accordance with the available experimental results.

Quantum Wave Packet Study of the H + Br2 → HBr + Br Reaction on a New Ab Initio Potential Energy Surface

An accurate global potential energy surface (PES) for the HBr₂ system has been constructed using the fundamental invariant neural network fitting method based upon 11 698 ab initio energies at the UCCSD(T)/CBS level of theory, with the spin-orbit coupling of the ²P_3/2 orbit of the Br atom properly included. The time-dependent wave packet calculations have been performed to study the H + Br₂ → HBr + Br reaction on the new PES. The total reaction probabilities for total angular momentum J = 0 for the ground initial state show no threshold due to the submerged barrier height (-0.351 kcal/mol) of the PES. The total integral cross sections (ICS) for reactant Br₂ in ro-vibrational states (v₀ = 0, j₀ = 0, 10, 20, 30; v₀ = 1-5, j₀ = 0) were calculated for collision energy of up to 0.5 eV. It is found that the initial rotational excitation has a negligible effect on the ICS, and the initial vibrational excitation depresses the reactivity to some extent. The thermal rate constants for the title reaction in the temperature range of 100-1000 K were calculated from the Boltzmann averaging of the v₀ = 0-5 rate constants, which overestimated the experimental results to some extent.

GPU-Accelerated Neural Network Potential Energy Surfaces for Diffusion Monte Carlo

Diffusion Monte Carlo (DMC) provides a powerful method for understanding the vibrational landscape of molecules that are not well-described by conventional methods. The most computationally demanding step of these calculations is the evaluation of the potential energy. In this work, a general approach is developed in which a neural network potential energy surface is trained by using data generated from a small-scale DMC calculation. Once trained, the neural network can be evaluated by using highly parallelizable calls to a graphics processing unit (GPU). The power of this approach is demonstrated for DMC simulations on H₂O, CH₅⁺, and (H₂O)₂. The need to include permutation symmetry in the neural network potentials is explored and incorporated into the molecular descriptors of CH₅⁺ and (H₂O)₂. It is shown that the zero-point energies and wave functions obtained by using the neural network potentials are nearly identical to the results obtained when using the potential energy surfaces that were used to train the neural networks at a substantial savings in the computational requirements of the simulations.

Double-Roaming Dynamics in the H + C2H2 → H2 + C2H Reaction: Acetylene-Facilitated Roaming and Vinylidene-Facilitated Roaming

We report two novel roaming pathways for the H + C₂H₂ → H₂ + C₂H reaction by performing extensive quasiclassical trajectory calculations on a new, global, high-level machine learning-based potential energy surface. One corresponds to the acetylene-facilitated roaming pathway, where the H atom turns back from the acetylene + H channel and abstracts another H atom from acetylene. The other is the vinylidene-facilitated roaming, where the H atom turns back from the vinylidene + H channel and abstracts another H from vinylidene. The "double-roaming" pathways account for roughly 95% of the total cross section of the H₂ + C₂H products at the collision energy of 70 kcal/mol. These computational results give valuable insights into the significance of the two isomers (acetylene and vinylidene) in chemical reaction dynamics and also the experimental search for roaming dynamics in this bimolecular reaction.

Vibrational Signature of Dynamic Coupling of a Strong Hydrogen Bond

Elucidating the dynamic couplings of hydrogen bonds remains an important and challenging goal for spectroscopic studies of bulk systems, because their vibrational signatures are masked by the collective effects of the fluctuation of many hydrogen bonds. Here we utilize size-selected infrared spectroscopy based on a tunable vacuum ultraviolet free electron laser to unmask the vibrational signatures for the dynamic couplings in neutral trimethylamine-water and trimethylamine-methanol complexes, as microscopic models with only one single hydrogen bond holding two molecules. Surprisingly broad progression of OH stretching peaks with distinct intensity modulation over ∼700 cm^-1 is observed for trimethylamine-water, while the dramatic reduction of this progression in the trimethylamine-methanol spectrum offers direct experimental evidence for the dynamic couplings. State-of-the-art quantum mechanical calculations reveal that such dynamic couplings are originated from strong Fermi resonance between the stretches of hydrogen-bonded OH and several motions of the solvent water/methanol, such as translation, rocking, and bending, which are significant in various solvated complexes commonly found in atmospheric and biological systems.

A Full-Dimensional Potential Energy Surface and Dynamics of the Multichannel Reaction between H and HO2

In addition to its vital significance in combustion and atmospheric chemistry, the reaction between H' and HO₂ on the ground triplet state represents a prototype with multiple product channels, including H₂ + O₂, OH + OH, O + H₂O, and H + H'O₂. In this work, a full-dimensional accurate potential energy surface (PES) for the title reaction was developed to provide reliable descriptions for all dynamically relevant regions. Using this PES, we adopted the quasi-classical trajectory approach to study the corresponding reaction dynamics, including the reactivity of each product channel and the associated product branching ratio, the product energy distributions, product angular distributions, and associated microscopic mechanisms. For representing distributions of the product energies, such as product translational energy as well as product rotational and vibrational energies, both the traditional histogram and the kernel density estimation (KDE) methods were used and compared. It seems that the features of the resulting distributions in this work are very similar to each other among different methods. The KDE method is suggested for statistics, particularly for those populations with small oscillations in the histogram plot.

Supercollisions of fast H-atom with ethylene on an accurate full-dimensional potential energy surface

The collisions transferring large portions of energy are often called supercollisions. In the H + C₂H₂ reactive system, the rovibrationally cold C₂H₂ molecule can be activated with substantial internal excitations by its collision with a translationally hot H atom. It is interesting to investigate the mechanisms of collisional energy transfer in other important reactions of H with hydrocarbons. Here, an accurate, global, full-dimensional potential energy surface (PES) of H + C₂H₄ was constructed by the fundamental invariant neural network fitting based on roughly 100 000 UCCSD(T)-F12a/aug-cc-pVTZ data points. Extensive quasi-classical trajectory calculations were carried out on the full-dimensional PES to investigate the energy transfer process in collisions of the translationally hot H atoms with C₂H₄ in a wide range of collision energies. The computed function of the energy-transfer probability is not a simple exponential decay function but exhibits large magnitudes in the region of a large amount of energy transfer, indicating the signature of supercollisions. The supercollisions among non-complex-forming nonreactive (prompt) trajectories are frustrated complex-forming processes in which the incoming H atom penetrates into C₂H₄ with a small C-H distance but promptly and directly leaves C₂H₄. The complex-forming supercollisions, in which either the attacking H atom leaves (complex-forming nonreactive collisions) or one of the original H atoms of C₂H₄ leaves (complex-forming reactive trajectories), dominate large energy transfer from the translational energy to internal excitation of molecule. The current work sheds valuable light on the energy transfer of this important reaction in the combustion and may motivate related experimental investigations.

Full-dimensional potential energy surface for acetylacetone and tunneling splittings

New, full-dimensional potential energy surface for acetylacetone allows for description of H-tunneling dynamics and characterization of stationary points.

A fundamental invariant-neural network representation of quasi-diabatic Hamiltonians for the two lowest states of H3

The FI-NN approach is capable of representing highly accurate diabatic PESs with particular and complicated symmetry problems.