A global potential energy surface for the H2 + OH ↔ H2O + H reaction using neural networks

Quantum Dynamics Studies of the Li + Na2 (V = 0, j = 0) → Na + NaLi Reaction on a New Neural Network Potential Energy Surface

The ultracold reaction offers a unique opportunity to elucidate the intricate microscopic mechanism of chemical reactions, and the Na2Li system serves as a pivotal reaction system in the investigation of ultracold reactions. In this work, a high-precision potential energy surface (PES) of the Na2Li system is constructed based on high-level ab initio energy points and the neural network (NN) method, and a proper asymptotic functional form is adopted for the long-range interaction, which is suitable for the study of cold or ultracold collisions. Based on the new NN PES, the dynamics of the Li + Na2 (v = 0, j = 0) → Na + NaLi reaction are studied in the collision energy range of 10-7 to 80 cm-1. In the high collision energy range of 8 to 80 cm-1, the dynamics of the reaction is studied using the time-dependent wave packet method and the statistical quantum mechanical (SQM) method. Comparing the results of the two methods, it is found that the SQM method provides a rough description of the product ro-vibrational state distribution but overestimates the integral cross-section values. With the decrease of collision energy, the reaction differential cross section gradually changes from forward-backward symmetric scattering to predominant forward scattering. In the low collision energy range from 10-7 to 8 cm-1, the SQM method is used to study the reaction dynamics, and the rate constant in the Wigner threshold region is estimated to be 2.87 × 10-10 cm3/s.

High vibrational excitation of the reagent transforms the late-barrier H + HOD reaction into an early-barrier reaction

Polanyi's rules predict that a late-barrier reaction yields vibrationally cold products; however, experimental studies showed that the H2 product from the late-barrier H + H2O(|04⟩-) and H + HOD(vOH = 4) reactions is vibrationally hot. Here, we report a potential-averaged five-dimensional state-to-state quantum dynamics study for the H + HOD(vOH = 0-4) → H2 + OD reactions on a highly accurate potential energy surface with the total angular momentum J = 0. It is found that with the HOD vibration excitation increasing from vOH = 1 to 4, the product H2 becomes increasingly vibrationally excited and manifests a typical characteristic of an early barrier reaction for vOH = 3 to 4. Analysis of the scattering wave functions revealed that vibrational excitation in the breaking OH bond moves the location of dynamical saddle point from product side to reactant side, transforming the reaction into an early barrier reaction. Interestingly, pronounced oscillatory structures in the total and product vibrational-state-resolved reaction probabilities were observed for the H + HOD(vOH = 3, 4) reactions, in particular at low collision energies, which originate from the Feshbach resonance states trapped in the bending/torsion excited vibrational adiabatic potential wells in the entrance region due to van der Waals interactions.

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.

A Gaussian Process Based Δ-Machine Learning Approach to Reactive Potential Energy Surfaces

The Gaussian process (GP) is an efficient nonparametric machine learning (ML) method. A distinct advantage of the GP is its ability to provide an estimate of statistical uncertainties. This is particularly useful in constructing high-dimensional potential energy surfaces (PESs) from ab initio data as it offers an optimal way to add new geometries to reduce the overall error. In this work, GP is employed in the context of Δ-machine learning (Δ-ML), in which a correction PES to an inaccurate low-level PES is constructed using a small number of high-level ab initio calculations. This new method is tested in three prototypical reactive systems, namely, the H + H2 → H + H2, OH + H2 → H2O + H, and H + CH4 → H2 + CH3 reactions. The results show that the GP-based Δ-ML approach is more efficient than its direct application in constructing high-level PESs. We also compare the new method to a previously proposed neural-network-based Δ-ML approach [Liu and Li J. Phys. Chem. Lett. 2022, 13, 4729-4738]. The results indicate that the two Δ-ML methods have comparable efficiencies in constructing accurate PESs.

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.

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.

Quantum Gaussian process model of potential energy surface for a polyatomic molecule

With gates of a quantum computer designed to encode multi-dimensional vectors, projections of quantum computer states onto specific qubit states can produce kernels of reproducing kernel Hilbert spaces. We show that quantum kernels obtained with a fixed ansatz implementable on current quantum computers can be used for accurate regression models of global potential energy surfaces (PESs) for polyatomic molecules. To obtain accurate regression models, we apply Bayesian optimization to maximize marginal likelihood by varying the parameters of the quantum gates. This yields Gaussian process models with quantum kernels. We illustrate the effect of qubit entanglement in the quantum kernels and explore the generalization performance of quantum Gaussian processes by extrapolating global six-dimensional PESs in the energy domain.

Diabatic States of Molecules

Quantitative simulations of electronically nonadiabatic molecular processes require both accurate dynamics algorithms and accurate electronic structure information. Direct semiclassical nonadiabatic dynamics is expensive due to the high cost of electronic structure calculations, and hence it is limited to small systems, limited ensemble averaging, ultrafast processes, and/or electronic structure methods that are only semiquantitatively accurate. The cost of dynamics calculations can be made manageable if analytic fits are made to the electronic structure data, and such fits are most conveniently carried out in a diabatic representation because the surfaces are smooth and the couplings between states are smooth scalar functions. Diabatic representations, unlike the adiabatic ones produced by most electronic structure methods, are not unique, and finding suitable diabatic representations often involves time-consuming nonsystematic diabatization steps. The biggest drawback of using diabatic bases is that it can require large amounts of effort to perform a globally consistent diabatization, and one of our goals has been to develop methods to do this efficiently and automatically. In this Feature Article, we introduce the mathematical framework of diabatic representations, and we discuss diabatization methods, including adiabatic-to-diabatic transformations and recent progress toward the goal of automatization.

Femtochemistry of bimolecular reactions from weakly bound complexes: computational study of the H + H'OD → H'OH + D or HOD + H' exchange reactions

A full-dimensional wavepacket propagation describing the bimolecular exchange reactions H + H'OD → H'OH + D or HOD + H' initiated by photolysis of HCl in the hydrogen-bound complex (HCl)⋯(HOD) is reported. The dynamics of this reaction is carried out with the MCTDH method on an ab initio potential energy surface (PES) of H₃O and the initial state is derived from the ground state wavefunction of the complex obtained by relaxation on its own electronic ground state ab initio PES. The description of the system makes use of polyspherical coordinates parametrizing a set of Radau and Jacobi vectors. The calculated energy- and time-resolved reaction probabilities show, owing to the large collision energies at play stemming from the (almost full) photolysis of HCl, that the repulsion between oxygen in the H'OD molecule and the incoming hydrogen atom is the main feature of the collision and leads to non-reactive scattering. No abstraction reaction products are observed. However, both exchange processes are still observable, with a preference in O-H' bond dissociation over that of O-D. The selectivity is reversed upon vibrational pre-excitation of the O-D stretching mode in the H'OD molecule. It is shown that, after the collision, the hydrogen atom of HCl does most likely not encounter the almost stationary chlorine atom again but we also consider the limit case where the H atom is forced to collide multiple times against H'OD as a result of being pushed back by the Cl atom.

Theoretical studies on triplet-state driven dissociation of formaldehyde by quasi-classical molecular dynamics simulation on machine-learning potential energy surface

The H-atom dissociation of formaldehyde on the lowest triplet state (T1) is studied by quasi-classical molecular dynamic simulations on the high-dimensional machine-learning potential energy surface (PES) model. An atomic-energy based deep-learning neural network (NN) is used to represent the PES function, and the weighted atom-centered symmetry functions are employed as inputs of the NN model to satisfy the translational, rotational, and permutational symmetries, and to capture the geometry features of each atom and its individual chemical environment. Several standard technical tricks are used in the construction of NN-PES, which includes the application of clustering algorithm in the formation of the training dataset, the examination of the reliability of the NN-PES model by different fitted NN models, and the detection of the out-of-confidence region by the confidence interval of the training dataset. The accuracy of the full-dimensional NN-PES model is examined by two benchmark calculations with respect to ab initio data. Both the NN and electronic-structure calculations give a similar H-atom dissociation reaction pathway on the T1 state in the intrinsic reaction coordinate analysis. The small-scaled trial dynamics simulations based on NN-PES and ab initio PES give highly consistent results. After confirming the accuracy of the NN-PES, a large number of trajectories are calculated in the quasi-classical dynamics, which allows us to get a better understanding of the T1-driven H-atom dissociation dynamics efficiently. Particularly, the dynamics simulations from different initial conditions can be easily simulated with a rather low computational cost. The influence of the mode-specific vibrational excitations on the H-atom dissociation dynamics driven by the T1 state is explored. The results show that the vibrational excitations on symmetric C-H stretching, asymmetric C-H stretching, and C=O stretching motions always enhance the H-atom dissociation probability obviously.

Gradient domain machine learning with composite kernels: improving the accuracy of PES and force fields for large molecules

The generalization accuracy of machine learning models of potential energy surfaces (PES) and force fields (FF) for large polyatomic molecules can be improved either by increasing the number of training points or by improving the models. In order to build accurate models based on expensive ab initio calculations, much of recent work has focused on the latter. In particular, it has been shown that gradient domain machine learning (GDML) models produce accurate results for high-dimensional molecular systems with a small number of ab initio calculations. The present work extends GDML to models with composite kernels built to maximize inference from a small number of molecular geometries. We illustrate that GDML models can be improved by increasing the complexity of underlying kernels through a greedy search algorithm using Bayesian information criterion as the model selection metric. We show that this requires including anisotropy into kernel functions and produces models with significantly smaller generalization errors. The results are presented for ethanol, uracil, malonaldehyde and aspirin. For aspirin, the model with composite kernels trained by forces at 1000 randomly sampled molecular geometries produces a global 57-dimensional PES with the mean absolute accuracy 0.177 kcal mol−1 (61.9 cm−1) and FFs with the mean absolute error 0.457 kcal mol−1 Å−1.

Permutationally Invariant Polynomial Expansions with Unrestricted Complexity

A general strategy is presented for constructing and validating permutationally invariant polynomial (PIP) expansions for chemical systems of any stoichiometry. Demonstrations are made for three categories of gas-phase dynamics and kinetics: collisional energy-transfer trajectories for predicting pressure-dependent kinetics, three-body collisions for describing transient van der Waals adducts relevant to atmospheric chemistry, and nonthermal reactivity via quasiclassical trajectories. In total, 30 systems are considered with up to 15 atoms and 39 degrees of freedom. Permutational invariance is enforced in PIP expansions with as many as 13 million terms and 13 permutationally distinct atom types by taking advantage of petascale computational resources. The quality of the PIP expansions is demonstrated through the systematic convergence of in-sample and out-of-sample errors with respect to both the number of training data and the order of the expansion, and these errors are shown to predict errors in the dynamics for both reactive and nonreactive applications. The parallelized code distributed as part of this work enables the automation of PIP generation for complex systems with multiple channels and flexible user-defined symmetry constraints and for automatically removing unphysical unconnected terms from the basis set expansions, all of which are required for simulating complex reactive systems.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Full-dimensional quantum stereodynamics of the non-adiabatic quenching of OH(A2Σ+) by H2

The Born–Oppenheimer approximation, assuming separable nuclear and electronic motion, is widely adopted for characterizing chemical reactions in a single electronic state. However, the breakdown of the Born–Oppenheimer approximation is omnipresent in chemistry, and a detailed understanding of the non-adiabatic dynamics is still incomplete. Here we investigate the non-adiabatic quenching of electronically excited OH(A²Σ⁺) molecules by H₂ molecules using full-dimensional quantum dynamics calculations for zero total nuclear angular momentum using a high-quality diabatic-potential-energy matrix. Good agreement with experimental observations is found for the OH(X²Π) ro-vibrational distribution, and the non-adiabatic dynamics are shown to be controlled by stereodynamics, namely the relative orientation of the two reactants. The uncovering of a major (in)elastic channel, neglected in a previous analysis but confirmed by a recent experiment, resolves a long-standing experiment–theory disagreement concerning the branching ratio of the two electronic quenching channels.

The breakdown of the Born–Oppenheimer approximation is omnipresent in chemistry and detailed understanding of non-adiabatic dynamics is still incomplete. Now, the non-adiabatic quenching of electronically excited OH(A²Σ⁺) molecules by H₂ has been investigated using full-dimensional quantum dynamics calculations and a high-quality diabatic-potential-energy matrix, providing insight into the branching ratio of the two electronic quenching channels.

Searching Configurations in Uncertainty Space: Active Learning of High-Dimensional Neural Network Reactive Potentials

Neural network (NN) potential energy surfaces (PESs) have been widely used in atomistic simulations with ab initio accuracy. While constructing NN PESs, their training data points are often sampled by molecular dynamics trajectories. This strategy can be however inefficient for reactive systems involving rare events. Here, we develop an uncertainty-driven active learning strategy to automatically and efficiently generate high-dimensional NN-based reactive potentials, taking a gas-surface reaction as an example. The difference between two independent NN models is used as a simple and differentiable uncertainty metric, allowing us to quickly search in the uncertainty space and place new samples at which the PES is less reliable. By interfacing this algorithm with the first-principles simulation package, we demonstrate that a globally accurate NN potential of the H₂ + Ag(111) system can be constructed with merely ∼150 data points. This PES can be further refined to describe H₂ dissociation on Ag(100) by adding ∼130 more configurations on this facet. The entire process is completely automatic and self-terminated once the relative error criterion is fulfilled. Impressively, data points sampled by this uncertainty-driven strategy are substantially fewer than by the traditional trajectory-based sampling. The final NN PES not only converges well the quantum dissociation probability of the molecule but also well-reproduces the phonon properties of the substrate and is capable of describing surface temperature effects. These results show the potential of this active learning approach in developing high-dimensional NN reactive potentials in gas and condensed phases.

First-Principles Reaction Dynamics beyond Six-Atom Systems

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

A neural network potential energy surface for the F + H2O ↔ HF + OH reaction and quantum dynamics study of the isotopic effect

We report here a global and full dimensional neural network potential energy surface for the F + CH₄ reaction and investigate the isotopic effect on the total reaction probabilities using the time-dependent wave packet method.

Time-Dependent Wave Packet Dynamics Calculations of Cross Sections for Ultracold Four-Atom Reactions

We report here the first time-dependent wave packet dynamics study for an ultracold four-atom reaction. Our calculations provide accurate integral cross sections and rate constants all the way down to the Bethe-Wigner threshold regime for the benchmark OH + H₂(v = 2, j = 0) → H₂O + H reaction, indicating that the time-dependent wave packet method is a powerful tool for studying ultracold four-atom reactions.

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.

High-Fidelity Potential Energy Surfaces for Gas-Phase and Gas-Surface Scattering Processes from Machine Learning

In this Perspective, we review recent advances in constructing high-fidelity potential energy surfaces (PESs) from discrete ab initio points, using machine learning tools. Such PESs, albeit with substantial initial investments, provide significantly higher efficiency than direct dynamics methods and/or high accuracy at a level that is not affordable by on-the-fly approaches. These PESs not only are a necessity for quantum dynamical studies because of delocalization of wave packets but also enable the study of low-probability and long-time events in (quasi-)classical treatments. Our focus here is on inelastic and reactive scattering processes, which are more challenging than bound systems because of the involvement of continua. Relevant applications and developments for dynamical processes in both the gas phase and at gas-surface interfaces are discussed.

On the nonadiabatic collisional quenching of OH(A) by H2: a four coupled quasi-diabatic state description

1²A, 2²A, and 3²A electronic states of OH(A) + H₂ where conical intersections facilitate the quenching of OH(A) by H₂.

Integrating Machine Learning with the Multilayer Energy-Based Fragment Method for Excited States of Large Systems

In this work we have combined machine learning techniques with our recently developed multilayer energy-based fragment method for studying excited states of large systems. The photochemically active and inert regions are separately treated with the complete active space self-consistent field method and the trained models. This method is demonstrated to provide accurate energies and gradients leading to essentially the same excited-state potential energy surfaces and nonadiabatic dynamics compared with full ab initio results. Furthermore, in conjunction with the use of machine learning models, this method is highly parallel and exhibits low-scaling computational cost. Finally, the present work could encourage the marriage of machine learning with fragment-based electronic structure methods to explore photochemistry of large systems.

Embedded Atom Neural Network Potentials: Efficient and Accurate Machine Learning with a Physically Inspired Representation

We propose a simple, but efficient and accurate, machine learning (ML) model for developing a high-dimensional potential energy surface. This so-called embedded atom neural network (EANN) approach is inspired by the well-known empirical embedded atom method (EAM) model used in the condensed phase. It simply replaces the scalar embedded atom density in EAM with a Gaussian-type orbital based density vector and represents the complex relationship between the embedded density vector and atomic energy by neural networks. We demonstrate that the EANN approach is equally accurate as several established ML models in representing both big molecular and extended periodic systems, yet with much fewer parameters and configurations. It is highly efficient as it implicitly contains the three-body information without an explicit sum of the conventional costly angular descriptors. With high accuracy and efficiency, EANN potentials can vastly accelerate molecular dynamics and spectroscopic simulations in complex systems at ab initio level.

A Machine Learning Approach for Prediction of Rate Constants

We report a machine learning approach to train and predict bimolecular thermal rate constants over a large temperature range. The approach uses Gaussian process (GP) regression to evaluate the difference between accurate quantum results and Eckart-corrected conventional transition state theory, mostly for collinear reactions. Training is done on a database of rate constants for 13 reaction/potential surface combinations, and testing is performed on a set of 39 reaction/potential surface combinations. Averaged over all test reactions, the GP method is within 80% of the accurate answer, whereas transition state theory (TST) is only within 330% and Eckart-corrected TST (ECK) is within 110%. In the tunneling region, GP is generally (with a few exceptions) more accurate and sometimes much more accurate. In the high-temperature recrossing region, GP is significantly more accurate than either TST or ECK, neither of which addresses the possibility of recrossing. The GP predictions for the 3D reactions O(³P) + H₂, OH + H₂, O(³P) + CH₄, and H + CH₄, for which accurate quantum results are available, provide further encouragement to the machine learning approach.

Instanton rate constant calculations using interpolated potential energy surfaces in nonredundant, rotationally and translationally invariant coordinates

A trivial flaw in the utilization of artificial neural networks in interpolating chemical potential energy surfaces (PES) whose descriptors are Cartesian coordinates is their dependence on simple translations and rotations of the molecule under consideration. A different set of descriptors can be chosen to circumvent this problem, internuclear distances, inverse internuclear distances or z-matrix coordinates are three such descriptors. The objective is to use an interpolated PES in instanton rate constant calculations, hence information on the energy, gradient, and Hessian is required at coordinates in the vicinity of the tunneling path. Instanton theory relies on smoothly fitted Hessians, therefore we use energy, gradients, and Hessians in the training procedure. A major challenge is presented in the proper back-transformation of the output gradients and Hessians from internal coordinates to Cartesian coordinates. We perform comparisons between our method, a previous approach and on-the-fly rate constant calcuations on the hydrogen abstraction from methanol and on the hydrogen addition to isocyanic acid. © 2018Wiley Periodicals, Inc.

A critical comparison of neural network potentials for molecular reaction dynamics with exact permutation symmetry

Several symmetry strategies have been compared in fitting full dimensional accurate potentials for reactive systems based on a neural network approach.

Bayesian machine learning for quantum molecular dynamics

This article discusses applications of Bayesian machine learning for quantum molecular dynamics.

Two-state diabatic potential energy surfaces of ClH2 based on nonadiabatic couplings with neural networks

A neural network-fitting procedure based on nonadiabatic couplings is proposed to generate two-state diabatic PESs with conical intersections.

Kinetic isotope effects in the water forming reaction H2/D2 + OH from rigorous close-coupling quantum dynamics simulations

Rigorous quantum dynamics simulations of thermal rate constants and kinetic isotope effects for the water-forming H₂/D₂ + OH reaction are presented, which show increased tunneling below 300 K and can serve as benchmarks for approximate methods.