Isomerization and decomposition reactions of acetaldehyde relevant to atmospheric processes from dynamics simulations on neural network-based potential energy surfaces

OH-Formation following vibrationally induced reaction dynamics of H2COO

The reaction dynamics of H2COO to form HCOOH and dioxirane as first steps for OH-elimination is quantitatively investigated. Using a machine learned potential energy surface (PES) at the CASPT2/aug-cc-pVTZ level of theory vibrational excitation along the CH-normal mode νCH with energies up to 40.0 kcal mol-1 (∼5νCH) leads almost exclusively to HCOOH which further decomposes into OH + HCO. Although the barrier to form dioxirane is only 21.4 kcal mol-1 the reaction probability to form dioxirane is two orders of magnitude lower if the CH-stretch mode is excited. Following the dioxirane-formation pathway is facile, however, if the COO-bend vibration is excited together with energies equivalent to ∼2νCH or ∼3νCOO. For OH-formation in the atmosphere the pathway through HCOOH is probably most relevant because the alternative pathways (through dioxirane or formic acid) involve several intermediates that can de-excite through collisions, relax via internal vibrational relaxation (IVR), or pass through loose and vulnerable transition states (formic acid). This work demonstrates how, by selectively exciting particular vibrational modes, it is possible to dial into desired reaction channels with a high degree of specificity.

Numerical Accuracy Matters: Applications of Machine Learned Potential Energy Surfaces

The role of numerical accuracy in training and evaluating neural network-based potential energy surfaces is examined for different experimental observables. For observables that require third- and fourth-order derivatives of the potential energy with respect to Cartesian coordinates single-precision arithmetics as is typically used in ML-based approaches is insufficient and leads to roughness of the underlying PES as is explicitly demonstrated. Increasing the numerical accuracy to double-precision gives a smooth PES with higher-order derivatives that are numerically stable and yield meaningful anharmonic frequencies and tunneling splitting as is demonstrated for H2CO and malonaldehyde. For molecular dynamics simulations, which only require first-order derivatives, single-precision arithmetics appears to be sufficient, though.

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.

Quantitative molecular simulations

All-atom simulations can provide molecular-level insights into the dynamics of gas-phase, condensed-phase and surface processes. One important requirement is a sufficiently realistic and detailed description of the underlying intermolecular interactions. The present perspective provides an overview of the present status of quantitative atomistic simulations from colleagues' and our own efforts for gas- and solution-phase processes and for the dynamics on surfaces. Particular attention is paid to direct comparison with experiment. An outlook discusses present challenges and future extensions to bring such dynamics simulations even closer to reality.

Predicting properties of periodic systems from cluster data: A case study of liquid water

The accuracy of the training data limits the accuracy of bulk properties from machine-learned potentials. For example, hybrid functionals or wave-function-based quantum chemical methods are readily available for cluster data but effectively out of scope for periodic structures. We show that local, atom-centered descriptors for machine-learned potentials enable the prediction of bulk properties from cluster model training data, agreeing reasonably well with predictions from bulk training data. We demonstrate such transferability by studying structural and dynamical properties of bulk liquid water with density functional theory and have found an excellent agreement with experimental and theoretical counterparts.

Atomistic Simulations for Reactions and Vibrational Spectroscopy in the Era of Machine Learning─Quo Vadis?

Atomistic simulations using accurate energy functions can provide molecular-level insight into functional motions of molecules in the gas and in the condensed phase. This Perspective delineates the present status of the field from the efforts of others and some of our own work and discusses open questions and future prospects. The combination of physics-based long-range representations using multipolar charge distributions and kernel representations for the bonded interactions is shown to provide realistic models for the exploration of the infrared spectroscopy of molecules in solution. For reactions, empirical models connecting dedicated energy functions for the reactant and product states allow statistically meaningful sampling of conformational space whereas machine-learned energy functions are superior in accuracy. The future combination of physics-based models with machine-learning techniques and integration into all-purpose molecular simulation software provides a unique opportunity to bring such dynamics simulations closer to reality.

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.

Transfer learned potential energy surfaces: accurate anharmonic vibrational dynamics and dissociation energies for the formic acid monomer and dimer

The vibrational dynamics of the formic acid monomer (FAM) and dimer (FAD) is investigated from machine-learned potential energy surfaces at the MP2 (PES_MP2) and transfer-learned (PES_TL) to the CCSD(T) levels of theory. The normal mode (MAEs of 17.6 and 25.1 cm⁻¹) and second order vibrational perturbation theory (VPT2, MAEs of 6.7 and 17.1 cm⁻¹) frequencies from PES_TL for all modes below 2000 cm⁻¹ for FAM and FAD agree favourably with experiment. For the OH stretch mode the experimental frequencies are overestimated by more than 150 cm⁻¹ for both FAM and FAD from normal mode calculations. Conversely, VPT2 calculations on PES_TL for FAM reproduce the experimental OH frequency to within 22 cm⁻¹. For FAD the VPT2 calculations find the high-frequency OH stretch at 3011 cm⁻¹, compared with an experimentally reported, broad (∼100 cm⁻¹) absorption band with center frequency estimated at ∼3050 cm⁻¹. In agreement with earlier reports, MD simulations at higher temperature shift the position of the OH-stretch in FAM to the red, consistent with improved sampling of the anharmonic regions of the PES. However, for FAD the OH-stretch shifts to the blue and for temperatures higher than 1000 K the dimer partly or fully dissociates using PES_TL. Including zero-point energy corrections from diffusion Monte Carlo simulations for FAM and FAD and corrections due to basis set superposition and completeness errors yields a dissociation energy of D₀ = −14.23 ± 0.08 kcal mol⁻¹ compared with an experimentally determined value of −14.22 ± 0.12 kcal mol⁻¹.

Neural network based PESs are constructed for formic acid monomer and dimer at the MP2 and transfer learned to the CCSD(T) level of theory. The PESs are used to study the vibrational dynamics and dissociation energy of the molecules.

Learning intermolecular forces at liquid-vapor interfaces

By adopting a perspective informed by contemporary liquid-state theory, we consider how to train an artificial neural network potential to describe inhomogeneous, disordered systems. We find that neural network potentials based on local representations of atomic environments are capable of describing some properties of liquid-vapor interfaces but typically fail for properties that depend on unbalanced long-ranged interactions that build up in the presence of broken translation symmetry. These same interactions cancel in the translationally invariant bulk, allowing local neural network potentials to describe bulk properties correctly. By incorporating explicit models of the slowly varying long-ranged interactions and training neural networks only on the short-ranged components, we can arrive at potentials that robustly recover interfacial properties. We find that local neural network models can sometimes approximate a local molecular field potential to correct for the truncated interactions, but this behavior is variable and hard to learn. Generally, we find that models with explicit electrostatics are easier to train and have higher accuracy. We demonstrate this perspective in a simple model of an asymmetric dipolar fluid, where the exact long-ranged interaction is known, and in an ab initio water model, where it is approximated.

Machine Learning Force Fields

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

Impact of the Characteristics of Quantum Chemical Databases on Machine Learning Prediction of Tautomerization Energies

An essential aspect for adequate predictions of chemical properties by machine learning models is the database used for training them. However, studies that analyze how the content and structure of the databases used for training impact the prediction quality are scarce. In this work, we analyze and quantify the relationships learned by a machine learning model (Neural Network) trained on five different reference databases (QM9, PC9, ANI-1E, ANI-1, and ANI-1x) to predict tautomerization energies from molecules in Tautobase. For this, characteristics such as the number of heavy atoms in a molecule, number of atoms of a given element, bond composition, or initial geometry on the quality of the predictions are considered. The results indicate that training on a chemically diverse database is crucial for obtaining good results and also that conformational sampling can partly compensate for limited coverage of chemical diversity. The overall best-performing reference database (ANI-1x) performs on average by 1 kcal/mol better than PC9, which, however, contains about 2 orders of magnitude fewer reference structures. On the other hand, PC9 is chemically more diverse by a factor of ∼5 as quantified by the number of atom-in-molecule-based fragments (amons) it contains compared with the ANI family of databases. A quantitative measure for deficiencies is the Kullback-Leibler divergence between reference and target distributions. It is explicitly demonstrated that when certain types of bonds need to be covered in the target database (Tautobase) but are undersampled in the reference databases, the resulting predictions are poor. Examples of this include the poor performance of all databases analyzed to predict C(sp²)-C(sp²) double bonds close to heteroatoms and azoles containing N-N and N-O bonds. Analysis of the results with a Tree MAP algorithm provides deeper understanding of specific deficiencies in predicting tautomerization energies by the reference datasets due to inadequate coverage of chemical space. Capitalizing on this information can be used to either improve existing databases or generate new databases of sufficient diversity for a range of machine learning (ML) applications in chemistry.

Machine Learning for Chemical Reactions

Machine learning (ML) techniques applied to chemical reactions have a long history. The present contribution discusses applications ranging from small molecule reaction dynamics to computational platforms for reaction planning. ML-based techniques can be particularly relevant for problems involving both computation and experiments. For one, Bayesian inference is a powerful approach to develop models consistent with knowledge from experiments. Second, ML-based methods can also be used to handle problems that are formally intractable using conventional approaches, such as exhaustive characterization of state-to-state information in reactive collisions. Finally, the explicit simulation of reactive networks as they occur in combustion has become possible using machine-learned neural network potentials. This review provides an overview of the questions that can and have been addressed using machine learning techniques, and an outlook discusses challenges in this diverse and stimulating field. It is concluded that ML applied to chemistry problems as practiced and conceived today has the potential to transform the way with which the field approaches problems involving chemical reactions, in both research and academic teaching.

Transfer Learning to CCSD(T): Accurate Anharmonic Frequencies from Machine Learning Models

The calculation of the anharmonic modes of small- to medium-sized molecules for assigning experimentally measured frequencies to the corresponding type of molecular motions is computationally challenging at sufficiently high levels of quantum chemical theory. Here, a practical and affordable way to calculate coupled-cluster quality anharmonic frequencies using second-order vibrational perturbation theory (VPT2) from machine-learned models is presented. The approach, referenced as "NN + VPT2", uses a high-dimensional neural network (PhysNet) to learn potential energy surfaces (PESs) at different levels of theory from which harmonic and VPT2 frequencies can be efficiently determined. The NN + VPT2 approach is applied to eight small- to medium-sized molecules (H₂CO, trans-HONO, HCOOH, CH₃OH, CH₃CHO, CH₃NO₂, CH₃COOH, and CH₃CONH₂) and frequencies are reported from NN-learned models at the MP2/aug-cc-pVTZ, CCSD(T)/aug-cc-pVTZ, and CCSD(T)-F12/aug-cc-pVTZ-F12 levels of theory. For the largest molecules and at the highest levels of theory, transfer learning (TL) is used to determine the necessary full-dimensional, near-equilibrium PESs. Overall, NN + VPT2 yields anharmonic frequencies to within 20 cm^-1 of experimentally determined frequencies for close to 90% of the modes for the highest quality PES available and to within 10 cm^-1 for more than 60% of the modes. For the MP2 PESs only ∼60% of the NN + VPT2 frequencies were within 20 cm^-1 of the experiment, with outliers up to ∼150 cm^-1, compared to the experiment. It is also demonstrated that the approach allows to provide correct assignments for strongly interacting modes such as the OH bending and the OH torsional modes in formic acid monomer and the CO-stretch and OH-bend mode in acetic acid.

Machine learning meets chemical physics

Over recent years, the use of statistical learning techniques applied to chemical problems has gained substantial momentum. This is particularly apparent in the realm of physical chemistry, where the balance between empiricism and physics-based theory has traditionally been rather in favor of the latter. In this guest Editorial for the special topic issue on "Machine Learning Meets Chemical Physics," a brief rationale is provided, followed by an overview of the topics covered. We conclude by making some general remarks.