A reactive, scalable, and transferable model for molecular energies from a neural network approach based on local information

Despite the ever-increasing computer power, accurate ab initio calculations for large systems (thousands to millions of atoms) remain infeasible. Instead, approximate empirical energy functions are used. Most current approaches are either transferable between different chemical systems, but not particularly accurate, or they are fine-tuned to a specific application. In this work, a data-driven method to construct a potential energy surface based on neural networks is presented. Since the total energy is decomposed into local atomic contributions, the evaluation is easily parallelizable and scales linearly with system size. With prediction errors below 0.5 kcal mol −1 for both unknown molecules and configurations, the method is accurate across chemical and configurational space, which is demonstrated by applying it to datasets from nonreactive and reactive molecular dynamics simulations and a diverse database of equilibrium structures. The possibility to use small molecules as reference data to predict larger structures is also explored. Since the descriptor only uses local information, high-level ab initio methods, which are computationally too expensive for large molecules, become feasible for generating the necessary reference data used to train the neural network

PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments and Partial Charges

In recent years, machine learning (ML) methods have become increasingly popular in computational chemistry. After being trained on appropriate ab initio reference data, these methods allow to accurately predict the properties of chemical systems, circumventing the need for explicitly solving the electronic Schr\"odinger equation. Because of their computational efficiency and scalability to large datasets, deep neural networks (DNNs) are a particularly promising ML algorithm for chemical applications. This work introduces PhysNet, a DNN architecture designed for predicting energies, forces and dipole moments of chemical systems. PhysNet achieves state-of-the-art performance on the QM9, MD17 and ISO17 benchmarks. Further, two new datasets are generated in order to probe the performance of ML models for describing chemical reactions, long-range interactions, and condensed phase systems. It is shown that explicitly including electrostatics in energy predictions is crucial for a qualitatively correct description of the asymptotic regions of a potential energy surface (PES). PhysNet models trained on a systematically constructed set of small peptide fragments (at most eight heavy atoms) are able to generalize to considerably larger proteins like deca-alanine (Ala$_{10}$): The optimized geometry of helical Ala$_{10}$ predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 \r{A}). By running unbiased molecular dynamics (MD) simulations of Ala$_{10}$ on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala$_{10}$ folds into a wreath-shaped configuration, which is more stable than the helical form by 0.46 kcal mol$^{-1}$ according to the reference ab initio calculations.Comment: 23 pages, 9 figures, 7 table

Sampling reactive regions in phase space by following the minimum dynamic path

Understanding mechanistic aspects of reactivity lies at the heart of chemistry. Once the potential energy surface (PES) for a system of interest is known, reactions can be studied by computational means. While the minimum energy path (MEP) between two minima of the PES can give some insight into the topological changes required for a reaction to occur, it lacks dynamical information and is an unrealistic depiction of the reactive process. For a more realistic view, molecular dynamics (MD) simulations are required. However, this usually involves generating thousands of trajectories in order to sample a few reactive events and is therefore much more computationally expensive than calculating the MEP. In this work, it is shown that a "minimum dynamic path" (MDP) can be constructed, which, contrary to the MEP, provides insight into the reaction dynamics. It is shown that the underlying concepts can be extended to directly sample reactive regions in phase space. The sampling method and the MDP are demonstrated on the well-known 2-dimensional Müller-Brown PES and for a realistic 12-dimensional reactive PES for sulfurochloridic acid, a proxy molecule used to study vibrationally induced photodissociation of sulfuric acid

Isomerization and Decomposition Reactions of Acetaldehyde Relevant to Atmospheric Processes from Dynamics Simulations on Neural Network-Based Potential Energy Surfaces

Acetaldehyde (AA) isomerization (to vinylalcohol, VA) and decomposition (into either CO+CH$_4$ and H$_2$+H$_2$CCO) is studied using a fully dimensional, reactive potential energy surface represented as a neural network (NN). The NN, trained on 432'399 reference structures from MP2/aug-cc-pVTZ calculations has a MAE of 0.0453 kcal/mol and an RMSE of 1.186 kcal/mol for a test set of 27'399 structures. For the isomerization process AA $\rightarrow$ VA the minimum dynamical path implies that the C-H vibration, and the C-C-H (with H being the transferring H-atom) and the C-C-O angles are involved to surmount the 68.2 kcal/mol barrier. Using an excess energy of 93.6 kcal/mol - the energy available in the solar spectrum and sufficient to excite to the first electronically excited state - to initialize the molecular dynamics, no isomerization to VA is observed on the 500 ns time scale. Only with excess energies of $\sim$ 127.6 kcal/mol (including the zero point energy of the AA molecule), isomerization occurs on the nanosecond time scale. Given that collisional de-excitation at atmospheric conditions in the stratosphere occurs on the 100 ns time scale, it is concluded that formation of VA following photoexcitation of AA from actinic photons is unlikely. This also limits the relevance of this reaction pathway to be a source for formic acid

Reactive Dynamics and Spectroscopy of Hydrogen Transfer from Neural Network-Based Reactive Potential Energy Surfaces

The in silico exploration of chemical, physical and biological systems requires accurate and efficient energy functions to follow their nuclear dynamics at a molecular and atomistic level. Recently, machine learning tools gained a lot of attention in the field of molecular sciences and simulations and are increasingly used to investigate the dynamics of such systems. Among the various approaches, artificial neural networks (NNs) are one promising tool to learn a representation of potential energy surfaces. This is done by formulating the problem as a mapping from a set of atomic positions $\mathbf{x}$ and nuclear charges $Z_i$ to a potential energy $V(\mathbf{x})$. Here, a fully-dimensional, reactive neural network representation for malonaldehyde (MA), acetoacetaldehyde (AAA) and acetylacetone (AcAc) is learned. It is used to run finite-temperature molecular dynamics simulations, and to determine the infrared spectra and the hydrogen transfer rates for the three molecules. The finite-temperature infrared spectrum for MA based on the NN learned on MP2 reference data provides a realistic representation of the low-frequency modes and the H-transfer band whereas the CH vibrations are somewhat too high in frequency. For AAA it is demonstrated that the IR spectroscopy is sensitive to the position of the transferring hydrogen at either the OCH- or OCCH$_3$ end of the molecule. For the hydrogen transfer rates it is demonstrated that the O-O vibration is a gating mode and largely determines the rate at which the hydrogen is transferred between the donor and acceptor. Finally, possibilities to further improve such NN-based potential energy surfaces are explored. They include the transferability of an NN-learned energy function across chemical species (here methylation) and transfer learning from a lower level of reference data (MP2) to a higher level of theory (pair natural orbital-LCCSD(T))

Exhaustive state-to-state cross sections for reactive molecular collisions from importance sampling simulation and a neural network representation

High-temperature, reactive gas flow is inherently nonequilibrium in terms of energy and state population distributions. Modeling such con- ditions is challenging even for the smallest molecular systems due to the extremely large number of accessible states and transitions between them. Here, neural networks (NNs) trained on explicitly simulated data are constructed and shown to provide quantitatively realistic descrip- tions which can be used in mesoscale simulation approaches such as Direct Simulation Monte Carlo to model gas flow at the hypersonic regime. As an example, the state-to-state cross sections for N( 4 S) + NO( 2 Π ) → O( 3 P) + N 2 (X 1 Σ + g ) are computed from quasiclassical trajectory (QCT) simulations. By training NNs on a sparsely sampled noisy set of state-to-state cross sections, it is demonstrated that independently generated reference data are predicted with high accuracy. State-specific and total reaction rates as a function of temperature from the NN are in quantitative agreement with explicit QCT simulations and confirm earlier simulations, and the final state distributions of the vibra- tional and rotational energies agree as well. Thus, NNs trained on physical reference data can provide a viable alternative to computationally demanding explicit evaluation of the microscopic information at run time. This will considerably advance the ability to realistically model nonequilibrium ensembles for network-based simulations

Collision-induced rotational excitation in N2 (+)((2)Σg (+),v=0)-Ar: Comparison of computations and experiment

The collisional dynamics of N2 (+)((2)Σg (+)) cations with Ar atoms is studied using quasi-classical simulations. N2 (+)-Ar is a proxy to study cooling of molecular ions and interesting in its own right for molecule-to-atom charge transfer reactions. An accurate potential energy surface (PES) is constructed from a reproducing kernel Hilbert space (RKHS) interpolation based on high-level ab initio data. The global PES including the asymptotics is fully treated within the realm of RKHS. From several ten thousand trajectories, the final state distribution of the rotational quantum number of N2 (+) after collision with Ar is determined. Contrary to the interpretation of previous experiments which indicate that up to 98% of collisions are elastic and conserve the quantum state, the present simulations find a considerably larger number of inelastic collisions which supports more recent findings

Automatic identification of chemical moieties

In recent years, the prediction of quantum mechanical observables with machine learning methods has become increasingly popular. Message-passing neural networks (MPNNs) solve this task by constructing atomic representations, from which the properties of interest are predicted. Here, we introduce a method to automatically identify chemical moieties (molecular building blocks) from such representations, enabling a variety of applications beyond property prediction, which otherwise rely on expert knowledge. The required representation can either be provided by a pretrained MPNN, or be learned from scratch using only structural information. Beyond the data-driven design of molecular fingerprints, the versatility of our approach is demonstrated by enabling the selection of representative entries in chemical databases, the automatic construction of coarse-grained force fields, as well as the identification of reaction coordinates