The fitting of potential energy and transition moment functions using neural networks: transition probabilities in OH (A2Σ+→X2Π)

High-dimensional neural network potentials for accurate vibrational frequencies: the formic acid dimer benchmark

In recent years, machine learning potentials (MLP) for atomistic simulations have attracted a lot of attention in chemistry and materials science. Many new approaches have been developed with the primary aim to transfer the accuracy of electronic structure calculations to large condensed systems containing thousands of atoms. In spite of these advances, the reliability of modern MLPs in reproducing the subtle details of the multi-dimensional potential-energy surface is still difficult to assess for such systems. On the other hand, moderately sized systems enabling the application of tools for thorough and systematic quality-control are nowadays rarely investigated. In this work we use benchmark-quality harmonic and anharmonic vibrational frequencies as a sensitive probe for the validation of high-dimensional neural network potentials. For the case of the formic acid dimer, a frequently studied model system for which stringent spectroscopic data became recently available, we show that high-quality frequencies can be obtained from state-of-the-art calculations in excellent agreement with coupled cluster theory and experimental data.

Neural Network Potentials: A Concise Overview of Methods

In the past two decades, machine learning potentials (MLPs) have reached a level of maturity that now enables applications to large-scale atomistic simulations of a wide range of systems in chemistry, physics, and materials science. Different machine learning algorithms have been used with great success in the construction of these MLPs. In this review, we discuss an important group of MLPs relying on artificial neural networks to establish a mapping from the atomic structure to the potential energy. In spite of this common feature, there are important conceptual differences among MLPs, which concern the dimensionality of the systems, the inclusion of long-range electrostatic interactions, global phenomena like nonlocal charge transfer, and the type of descriptor used to represent the atomic structure, which can be either predefined or learnable. A concise overview is given along with a discussion of the open challenges in the field.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

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.

Quantum Chemistry in the Age of Machine Learning

As the quantum chemistry (QC) community embraces machine learning (ML), the number of new methods and applications based on the combination of QC and ML is surging. In this Perspective, a view of the current state of affairs in this new and exciting research field is offered, challenges of using machine learning in quantum chemistry applications are described, and potential future developments are outlined. Specifically, examples of how machine learning is used to improve the accuracy and accelerate quantum chemical research are shown. Generalization and classification of existing techniques are provided to ease the navigation in the sea of literature and to guide researchers entering the field. The emphasis of this Perspective is on supervised machine learning.

A novel approach to describe chemical environments in high-dimensional neural network potentials

A central concern of molecular dynamics simulations is the potential energy surfaces that govern atomic interactions. These hypersurfaces define the potential energy of the system and have generally been calculated using either predefined analytical formulas (classical) or quantum mechanical simulations (ab initio). The former can accurately reproduce only a selection of material properties, whereas the latter is restricted to short simulation times and small systems. Machine learning potentials have recently emerged as a third approach to model atomic interactions, and are purported to offer the accuracy of ab initio simulations with the speed of classical potentials. However, the performance of machine learning potentials depends crucially on the description of a local atomic environment. A set of invariant, orthogonal, and differentiable descriptors for an atomic environment is proposed, implemented in a neural network potential for solid-state silicon, and tested in molecular dynamics simulations. Neural networks using the proposed descriptors are found to outperform ones using the Behler-Parinello and smooth overlap of atomic position descriptors in the literature.

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.

Neural networks and determination of diatomic molecule interatomic potential of cadmium dimer

A new method for obtaining a pointwise potential energy curve of diatomic molecule using Neural Network is reported. The method is employed to generate new characteristics of the B¹1_u(5¹P₁) electronic state of Cd₂ based on LIF excitation spectrum previously recorded using the B¹1_u←X¹0_g⁺ (5¹S₀) transition. The obtained potential provides better simulation-to-experiment agreement than those obtained using other methods. Correctness of the method is additionally tested on artificially generated LIF excitation spectra based on well characterized b³0_u⁺(5³P₁)←X¹0_g⁺ transition in Cd₂. A method for obtaining parameters of an analytical form of the potential using Neural Network applied on artificially generated Cd₂ spectra is also presented.

Representing potential energy surfaces by high-dimensional neural network potentials

The development of interatomic potentials employing artificial neural networks has seen tremendous progress in recent years. While until recently the applicability of neural network potentials (NNPs) has been restricted to low-dimensional systems, this limitation has now been overcome and high-dimensional NNPs can be used in large-scale molecular dynamics simulations of thousands of atoms. NNPs are constructed by adjusting a set of parameters using data from electronic structure calculations, and in many cases energies and forces can be obtained with very high accuracy. Therefore, NNP-based simulation results are often very close to those gained by a direct application of first-principles methods. In this review, the basic methodology of high-dimensional NNPs will be presented with a special focus on the scope and the remaining limitations of this approach. The development of NNPs requires substantial computational effort as typically thousands of reference calculations are required. Still, if the problem to be studied involves very large systems or long simulation times this overhead is regained quickly. Further, the method is still limited to systems containing about three or four chemical elements due to the rapidly increasing complexity of the configuration space, although many atoms of each species can be present. Due to the ability of NNPs to describe even extremely complex atomic configurations with excellent accuracy irrespective of the nature of the atomic interactions, they represent a general and therefore widely applicable technique, e.g. for addressing problems in materials science, for investigating properties of interfaces, and for studying solvation processes.

Efficient hybrid evolutionary optimization of interatomic potential models

The lack of adequately predictive atomistic empirical models precludes meaningful simulations for many materials systems. We describe advances in the development of a hybrid, population based optimization strategy intended for the automated development of material specific interatomic potentials. We compare two strategies for parallel genetic programming and show that the Hierarchical Fair Competition algorithm produces better results in terms of transferability, despite a lower training set accuracy. We evaluate the use of hybrid local search and several fitness models using system energies and/or particle forces. We demonstrate a drastic reduction in the computation time with the use of a correlation-based fitness statistic. We show that the problem difficulty increases with the number of atoms present in the systems used for model development and demonstrate that vectorization can help to address this issue. Finally, we show that with the use of this method, we are able to "rediscover" the exact model for simple known two- and three-body interatomic potentials using only the system energies and particle forces from the supplied atomic configurations.

Ab initio molecular dynamics of hydrogen dissociation on metal surfaces using neural networks and novelty sampling

We outline a hybrid multiscale approach for the construction of ab initio potential energy surfaces (PESs) useful for performing six-dimensional (6D) classical or quantum mechanical molecular dynamics (MD) simulations of diatomic molecules reacting at single crystal surfaces. The algorithm implements concepts from the corrugation reduction procedure, which reduces energetic variation in the PES, and uses neural networks for interpolation of smoothed ab initio data. A novelty sampling scheme is implemented and used to identify configurations that are most likely to be predicted inaccurately by the neural network. This hybrid multiscale approach, which couples PES construction at the electronic structure level to MD simulations at the atomistic scale, reduces the number of density functional theory (DFT) calculations needed to specify an accurate PES. Due to the iterative nature of the novelty sampling algorithm, it is possible to obtain a quantitative measure of the convergence of the PES with respect to the number of ab initio calculations used to train the neural network. We demonstrate the algorithm by first applying it to two analytic potentials, which model the H2/Pt(111) and H2/Cu(111) systems. These potentials are of the corrugated London-Eyring-Polanyi-Sato form, which are based on DFT calculations, but are not globally accurate. After demonstrating the convergence of the PES using these simple potentials, we use DFT calculations directly and obtain converged semiclassical trajectories for the H2/Pt(111) system at the PW91/generalized gradient approximation level. We obtain a converged PES for a 6D hydrogen-surface dissociation reaction using novelty sampling coupled directly to DFT. These results, in excellent agreement with experiments and previous theoretical work, are compared to previous simulations in order to explore the sensitivity of the PES (and therefore MD) to the choice of exchange and correlation functional. Despite having a lower energetic corrugation in our PES, we obtain a broader reaction probability curve than previous simulations, which is attributed to increased geometric corrugation in the PES and the effect of nonparallel dissociation pathways.

Representing molecule-surface interactions with symmetry-adapted neural networks

The accurate description of molecule-surface interactions requires a detailed knowledge of the underlying potential-energy surface (PES). Recently, neural networks (NNs) have been shown to be an efficient technique to accurately interpolate the PES information provided for a set of molecular configurations, e.g., by first-principles calculations. Here, we further develop this approach by building the NN on a new type of symmetry functions, which allows to take the symmetry of the surface exactly into account. The accuracy and efficiency of such symmetry-adapted NNs is illustrated by the application to a six-dimensional PES describing the interaction of oxygen molecules with the Al(111) surface.