Machine learning molecular dynamics for the simulation of infrared spectra

Machine learning dihydrogen activation in the chemical space surrounding Vaska's complex

Homogeneous catalysis using transition metal complexes is ubiquitously used for organic synthesis, as well as technologically relevant in applications such as water splitting and CO2 reduction. The key steps underlying homogeneous catalysis require a specific combination of electronic and steric effects from the ligands bound to the metal center. Finding the optimal combination of ligands is a challenging task due to the exceedingly large number of possibilities and the non-trivial ligand-ligand interactions. The classic example of Vaska's complex, trans-[Ir(PPh3)2(CO)(Cl)], illustrates this scenario. The ligands of this species activate iridium for the oxidative addition of hydrogen, yielding the dihydride cis-[Ir(H)2(PPh3)2(CO)(Cl)] complex. Despite the simplicity of this system, thousands of derivatives can be formulated for the activation of H2, with a limited number of ligands belonging to the same general categories found in the original complex. In this work, we show how DFT and machine learning (ML) methods can be combined to enable the prediction of reactivity within large chemical spaces containing thousands of complexes. In a space of 2574 species derived from Vaska's complex, data from DFT calculations are used to train and test ML models that predict the H2-activation barrier. In contrast to experiments and calculations requiring several days to be completed, the ML models were trained and used on a laptop on a time-scale of minutes. As a first approach, we combined Bayesian-optimized artificial neural networks (ANN) with features derived from autocorrelation and deltametric functions. The resulting ANNs achieved high accuracies, with mean absolute errors (MAE) between 1 and 2 kcal mol-1, depending on the size of the training set. By using a Gaussian process (GP) model trained with a set of selected features, including fingerprints, accuracy was further enhanced. Remarkably, this GP model minimized the MAE below 1 kcal mol-1, by using only 20% or less of the data available for training. The gradient boosting (GB) method was also used to assess the relevance of the features, which was used for both feature selection and model interpretation purposes. Features accounting for chemical composition, atom size and electronegativity were found to be the most determinant in the predictions. Further, the ligand fragments with the strongest influence on the H2-activation barrier were identified.

Machine-Learning X-Ray Absorption Spectra to Quantitative Accuracy

Simulations of excited state properties, such as spectral functions, are often computationally expensive and therefore not suitable for high-throughput modeling. As a proof of principle, we demonstrate that graph-based neural networks can be used to predict the x-ray absorption near-edge structure spectra of molecules to quantitative accuracy. Specifically, the predicted spectra reproduce nearly all prominent peaks, with 90% of the predicted peak locations within 1 eV of the ground truth. Besides its own utility in spectral analysis and structure inference, our method can be combined with structure search algorithms to enable high-throughput spectrum sampling of the vast material configuration space, which opens up new pathways to material design and discovery.

Hamiltonian-Reservoir Replica Exchange and Machine Learning Potentials for Computational Organic Chemistry

This work combines a machine learning potential energy function with a modular enhanced sampling scheme to obtain statistically converged thermodynamical properties of flexible medium-size organic molecules at high ab initio level. We offer a modular environment in the python package MORESIM that allows custom design of replica exchange simulations with any level of theory including ML-based potentials. Our specific combination of Hamiltonian and reservoir replica exchange is shown to be a powerful technique to accelerate enhanced sampling simulations and explore free energy landscapes with a quantum chemical accuracy unattainable otherwise (e.g., DLPNO-CCSD(T)/CBS quality). This engine is used to demonstrate the relevance of accessing the ab initio free energy landscapes of molecules whose stability is determined by a subtle interplay between variations in the underlying potential energy and conformational entropy (i.e., a bridged asymmetrically polarized dithiacyclophane and a widely used organocatalyst) both in the gas phase and in solution (implicit solvent).

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.

Machine-Learning Methods for Computational Science and Engineering

The re-kindled fascination in machine learning (ML), observed over the last few decades, has also percolated into natural sciences and engineering. ML algorithms are now used in scientific computing, as well as in data-mining and processing. In this paper, we provide a review of the state-of-the-art in ML for computational science and engineering. We discuss ways of using ML to speed up or improve the quality of simulation techniques such as computational fluid dynamics, molecular dynamics, and structural analysis. We explore the ability of ML to produce computationally efficient surrogate models of physical applications that circumvent the need for the more expensive simulation techniques entirely. We also discuss how ML can be used to process large amounts of data, using as examples many different scientific fields, such as engineering, medicine, astronomy and computing. Finally, we review how ML has been used to create more realistic and responsive virtual reality applications.

Machine Learning for Molecular Simulation

Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.

IMPRESSION - prediction of NMR parameters for 3-dimensional chemical structures using machine learning with near quantum chemical accuracy

The IMPRESSION (Intelligent Machine PREdiction of Shift and Scalar information Of Nuclei) machine learning system provides an efficient and accurate method for the prediction of NMR parameters from 3-dimensional molecular structures. Here we demonstrate that machine learning predictions of NMR parameters, trained on quantum chemical computed values, can be as accurate as, but computationally much more efficient (tens of milliseconds per molecular structure) than, quantum chemical calculations (hours/days per molecular structure) starting from the same 3-dimensional structure. Training the machine learning system on quantum chemical predictions, rather than experimental data, circumvents the need for the existence of large, structurally diverse, error-free experimental databases and makes IMPRESSION applicable to solving 3-dimensional problems such as molecular conformation and stereoisomerism.

Temperature dependence of the vibrational spectrum of porphycene: a qualitative failure of classical-nuclei molecular dynamics

Approximate quantum dynamics succeed in predicting a temperature-dependent blue-shift of the high-frequency stretch bands that arise from vibrational coupling between low-frequency thermally activated modes and high-frequency quantized ones. Classical nuclei molecular dynamics fail and instead predict a red-shift.

Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions

Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force-field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for targeting electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.

A combined on-the-fly/interpolation procedure for evaluating energy values needed in molecular simulations

We propose an algorithm for molecular dynamics or Monte Carlo simulations that uses an interpolation procedure to estimate potential energy values from energies and gradients evaluated previously at points of a simplicial mesh. We chose an interpolation procedure that is exact for harmonic systems and considered two possible mesh types: Delaunay triangulation and an alternative anisotropic triangulation designed to improve performance in anharmonic systems. The mesh is generated and updated on the fly during the simulation. The procedure is tested on two-dimensional quartic oscillators and on the path integral Monte Carlo evaluation of the HCN/DCN equilibrium isotope effect.

Machine Learning in Computational Chemistry: An Evaluation of Method Performance for Nudged Elastic Band Calculations

The localization of transition states and the calculation of reaction pathways are routine tasks of computational chemists but often very CPU-intense problems, in particular for large systems. The standard algorithm for this purpose is the nudged elastic band method, but it has become obvious that an "intelligent" selection of points to be evaluated on the potential energy surface can improve its convergence significantly. This article summarizes, compares, and extends known strategies that have been heavily inspired by the machine learning developments of recent years. It presents advantages and disadvantages and provides an unbiased comparison of neural network based approaches, Gaussian process regression in Cartesian coordinates, and Gaussian approximation potentials. We test their performance on two example reactions, the ethane rotation and the activation of carbon dioxide on a metal catalyst, and provide a clear ranking in terms of usability for future implementations.

Machine learning enables long time scale molecular photodynamics simulations

Photo-induced processes are fundamental in nature but accurate simulations of their dynamics are seriously limited by the cost of the underlying quantum chemical calculations, hampering their application for long time scales. Here we introduce a method based on machine learning to overcome this bottleneck and enable accurate photodynamics on nanosecond time scales, which are otherwise out of reach with contemporary approaches. Instead of expensive quantum chemistry during molecular dynamics simulations, we use deep neural networks to learn the relationship between a molecular geometry and its high-dimensional electronic properties. As an example, the time evolution of the methylenimmonium cation for one nanosecond is used to demonstrate that machine learning algorithms can outperform standard excited-state molecular dynamics approaches in their computational efficiency while delivering the same accuracy.

A Toolbox for Organelle Mechanobiology Research-Current Needs and Challenges

Mechanobiology studies from the last decades have brought significant insights into many domains of biological research, from development to cellular signaling. However, mechano-regulation of subcellular components, especially membranous organelles, are only beginning to be unraveled. In this paper, we take mitochondrial mechanobiology as an example to discuss recent advances and current technical challenges in this field. In addition, we discuss the needs for future toolbox development for mechanobiological research of intracellular organelles.

Rapid prediction of NMR spectral properties with quantified uncertainty

Accurate calculation of specific spectral properties for NMR is an important step for molecular structure elucidation. Here we report the development of a novel machine learning technique for accurately predicting chemical shifts of both \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${^1\mathrm{H}}$$\end{document}1H   and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${^{13}\mathrm{C}}$$\end{document}13C nuclei which exceeds DFT-accessible accuracy for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${^{13}\mathrm{C}}$$\end{document}13C and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${^1\mathrm{H}}$$\end{document}1H for a subset of nuclei, while being orders of magnitude more performant. Our method produces estimates of uncertainty, allowing for robust and confident predictions, and suggests future avenues for improved performance.

Accurate and transferable multitask prediction of chemical properties with an atoms-in-molecules neural network

Atomic and molecular properties could be evaluated from the fundamental Schrodinger's equation and therefore represent different modalities of the same quantum phenomena. Here, we present AIMNet, a modular and chemically inspired deep neural network potential. We used AIMNet with multitarget training to learn multiple modalities of the state of the atom in a molecular system. The resulting model shows on several benchmark datasets state-of-the-art accuracy, comparable to the results of orders of magnitude more expensive DFT methods. It can simultaneously predict several atomic and molecular properties without an increase in the computational cost. With AIMNet, we show a new dimension of transferability: the ability to learn new targets using multimodal information from previous training. The model can learn implicit solvation energy (SMD method) using only a fraction of the original training data and an archive median absolute deviation error of 1.1 kcal/mol compared to experimental solvation free energies in the MNSol database.

Approaching coupled cluster accuracy with a general-purpose neural network potential through transfer learning

Computational modeling of chemical and biological systems at atomic resolution is a crucial tool in the chemist's toolset. The use of computer simulations requires a balance between cost and accuracy: quantum-mechanical methods provide high accuracy but are computationally expensive and scale poorly to large systems, while classical force fields are cheap and scalable, but lack transferability to new systems. Machine learning can be used to achieve the best of both approaches. Here we train a general-purpose neural network potential (ANI-1ccx) that approaches CCSD(T)/CBS accuracy on benchmarks for reaction thermochemistry, isomerization, and drug-like molecular torsions. This is achieved by training a network to DFT data then using transfer learning techniques to retrain on a dataset of gold standard QM calculations (CCSD(T)/CBS) that optimally spans chemical space. The resulting potential is broadly applicable to materials science, biology, and chemistry, and billions of times faster than CCSD(T)/CBS calculations.

From Molecular Fragments to the Bulk: Development of a Neural Network Potential for MOF-5

The development of first-principles-quality reactive atomistic potentials for organic-inorganic hybrid materials is still a substantial challenge because of the very different physics of the atomic interactions-from covalent via ionic bonding to dispersion-that have to be described in an accurate and balanced way. In this work we used a prototypical metal-organic framework, MOF-5, as a benchmark case to investigate the applicability of high-dimensional neural network potentials (HDNNPs) to this class of materials. In HDNNPs, which belong to the class of machine learning potentials, the energy is constructed as a sum of environment-dependent atomic energy contributions. We demonstrate that by the use of this approach it is possible to obtain a high-quality potential for the periodic MOF-5 crystal using density functional theory (DFT) reference calculations of small molecular fragments only. The resulting HDNNP, which has a root-mean-square error (RMSE) of 1.6 meV/atom for the energies of molecular fragments not included in the training set, is able to provide the equilibrium lattice constant of the bulk MOF-5 structure with an error of about 0.1% relative to DFT, and also, the negative thermal expansion behavior is accurately predicted. The total energy RMSE of periodic structures that are completely absent in the training set is about 6.5 meV/atom, with errors on the order of 2 meV/atom for energy differences. We show that in contrast to energy differences, achieving a high accuracy for total energies requires careful variation of the stoichiometries of the training structures to avoid energy offsets, as atomic energies are not physical observables. The forces, which have RMSEs of about 94 meV/ a₀ for the molecular fragments and 130 meV/ a₀ for bulk structures not included in the training set, are insensitive to such offsets. Therefore, forces, which are the relevant properties for molecular dynamics simulations, provide a realistic estimate of the accuracy of atomistic potentials.

How machine learning can assist the interpretation of ab initio molecular dynamics simulations and conceptual understanding of chemistry

Molecular dynamics simulations are often key to the understanding of the mechanism, rate and yield of chemical reactions. One current challenge is the in-depth analysis of the large amount of data produced by the simulations, in order to produce valuable insight and general trends. In the present study, we propose to employ recent machine learning analysis tools to extract relevant information from simulation data without a priori knowledge on chemical reactions. This is demonstrated by training machine learning models to predict directly a specific outcome quantity of ab initio molecular dynamics simulations - the timescale of the decomposition of 1,2-dioxetane. The machine learning models accurately reproduce the dissociation time of the compound. Keeping the aim of gaining physical insight, it is demonstrated that, in order to make accurate predictions, the models evidence empirical rules that are, today, part of the common chemical knowledge. This opens the way for conceptual breakthroughs in chemistry where machine analysis would provide a source of inspiration to humans.

Toward Building Protein Force Fields by Residue-Based Systematic Molecular Fragmentation and Neural Network

Accurate force fields are crucial for molecular dynamics investigation of complex biological systems. Building accurate protein force fields from quantum mechanical (QM) calculations is challenging due to the complexity of proteins and high computational costs of QM methods. In order to overcome these two difficulties, here we developed the residue-based systematic molecular fragmentation method to partition general proteins into only 20 types of amino acid dipeptides and one type of peptide bond at level 1. The total energy of proteins is the combination of the energies of these fragments. Each type of the fragments is then parametrized using neural network (NN) representation of the QM reference. Adopting NN representation can circumvent the limitation of the analytic form of classical molecular mechanics (MM) force fields. Using MM force fields as the baseline, our method adds NN representation of QM corrections at the length scale of amino acid dipeptides. We tested our force fields for both homogeneous and heterogeneous polypeptides. Energy and forces predicted by our force fields compare favorably with full QM calculations from tripeptides to decapeptides. Our development provides an efficient and accurate method of building protein force fields fully from ab initio QM calculations.

Insight into the adsorption mechanisms of methylene blue and chromium(iii) from aqueous solution onto pomelo fruit peel

In this study, the biosorption mechanisms of methylene blue (MB) and Cr(iii) onto pomelo peel collected from our local fruits are investigated by combining experimental analysis with ab initio simulations.

Highly efficient surface hopping dynamics using a linear vibronic coupling model

We report an implementation of the linear vibronic coupling (LVC) model within the surface hopping dynamics approach and present utilities for parameterizing this model in a blackbox fashion. This results in an extremely efficient method to obtain qualitative and even semi-quantitative information about the photodynamical behavior of a molecule, and provides a new route toward benchmarking the results of surface hopping computations. The merits and applicability of the method are demonstrated in a number of applications. First, the method is applied to the SO2 molecule showing that it is possible to compute its absorption spectrum beyond the Condon approximation, and that all the main features and timescales of previous on-the-fly dynamics simulations of intersystem crossing are reproduced while reducing the computational effort by three orders of magnitude. The dynamics results are benchmarked against exact wavepacket propagations on the same LVC potentials and against a variation of the electronic structure level. Four additional test cases are presented to exemplify the broader applicability of the model. The photodynamics of the isomeric adenine and 2-aminopurine molecules are studied and it is shown that the LVC model correctly predicts ultrafast decay in the former and an extended excited-state lifetime in the latter. Futhermore, the method correctly predicts ultrafast intersystem crossing in the modified nucleobase 2-thiocytosine and its absence in 5-azacytosine while it fails to describe the ultrafast internal conversion to the ground state in the latter.

SchNetPack: A Deep Learning Toolbox For Atomistic Systems

SchNetPack is a toolbox for the development and application of deep neural networks that predict potential energy surfaces and other quantum-chemical properties of molecules and materials. It contains basic building blocks of atomistic neural networks, manages their training, and provides simple access to common benchmark datasets. This allows for an easy implementation and evaluation of new models. For now, SchNetPack includes implementations of (weighted) atom-centered symmetry functions and the deep tensor neural network SchNet, as well as ready-to-use scripts that allow one to train these models on molecule and material datasets. Based on the PyTorch deep learning framework, SchNetPack allows one to efficiently apply the neural networks to large datasets with millions of reference calculations, as well as parallelize the model across multiple GPUs. Finally, SchNetPack provides an interface to the Atomic Simulation Environment in order to make trained models easily accessible to researchers that are not yet familiar with neural networks.