SchNet: A continuous-filter convolutional neural network for modeling quantum interactions

Deep learning has the potential to revolutionize quantum chemistry as it is ideally suited to learn representations for structured data and speed up the exploration of chemical space. While convolutional neural networks have proven to be the first choice for images, audio and video data, the atoms in molecules are not restricted to a grid. Instead, their precise locations contain essential physical information, that would get lost if discretized. Thus, we propose to use continuous-filter convolutional layers to be able to model local correlations without requiring the data to lie on a grid. We apply those layers in SchNet: a novel deep learning architecture modeling quantum interactions in molecules. We obtain a joint model for the total energy and interatomic forces that follows fundamental quantum-chemical principles. This includes rotationally invariant energy predictions and a smooth, differentiable potential energy surface. Our architecture achieves state-of-the-art performance for benchmarks of equilibrium molecules and molecular dynamics trajectories. Finally, we introduce a more challenging benchmark with chemical and structural variations that suggests the path for further work

Quantum-Chemical Insights from Interpretable Atomistic Neural Networks

With the rise of deep neural networks for quantum chemistry applications, there is a pressing need for architectures that, beyond delivering accurate predictions of chemical properties, are readily interpretable by researchers. Here, we describe interpretation techniques for atomistic neural networks on the example of Behler–Parrinello networks as well as the end-to-end model SchNet. Both models obtain predictions of chemical properties by aggregating atom-wise contributions. These latent variables can serve as local explanations of a prediction and are obtained during training without additional cost. Due to their correspondence to well-known chemical concepts such as atomic energies and partial charges, these atom-wise explanations enable insights not only about the model but more importantly about the underlying quantum-chemical regularities. We generalize from atomistic explanations to 3d space, thus obtaining spatially resolved visualizations which further improve interpretability. Finally, we analyze learned embeddings of chemical elements that exhibit a partial ordering that resembles the order of the periodic table. As the examined neural networks show excellent agreement with chemical knowledge, the presented techniques open up new venues for data-driven research in chemistry, physics and materials science.EC/H2020/792572/EU/Machine Learning for Catalytic Carbon Dioxide Activation/MachineCatBMBF, 01IS14013A, Verbundprojekt: BBDC - Berliner Kompetenzzentrum für Big DataBMBF, 01IS18037A, Verbundprojekt BIFOLD-BZML: Berlin Institute for the Foundations of Learning and DataEC/H2020/725291/EU/Beyond Static Molecules: Modeling Quantum Fluctuations in Complex Molecular Environments/BeStM

SchNet - a deep learning architecture for molecules and materials

Deep learning has led to a paradigm shift in artificial intelligence, including web, text and image search, speech recognition, as well as bioinformatics, with growing impact in chemical physics. Machine learning in general and deep learning in particular is ideally suited for representing quantum-mechanical interactions, enabling to model nonlinear potential-energy surfaces or enhancing the exploration of chemical compound space. Here we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chemical space for \emph{molecules and materials} where our model learns chemically plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for molecular dynamics simulations of small molecules and perform an exemplary study of the quantum-mechanical properties of C$_{20}$-fullerene that would have been infeasible with regular ab initio molecular dynamics

Machine learning of accurate energy-conserving molecular force fields

Using conservation of energy - a fundamental property of closed classical and quantum mechanical systems - we develop an efficient gradient-domain machine learning (GDML) approach to construct accurate molecular force fields using a restricted number of samples from ab initio molecular dynamics (AIMD) trajectories. The GDML implementation is able to reproduce global potential energy surfaces of intermediate-sized molecules with an accuracy of 0.3 kcal mol−1 for energies and 1 kcal mol−1 Å̊−1 for atomic forces using only 1000 conformational geometries for training. We demonstrate this accuracy for AIMD trajectories of molecules, including benzene, toluene, naphthalene, ethanol, uracil, and aspirin. The challenge of constructing conservative force fields is accomplished in our work by learning in a Hilbert space of vector-valued functions that obey the law of energy conservation. The GDML approach enables quantitative molecular dynamics simulations for molecules at a fraction of cost of explicit AIMD calculations, thereby allowing the construction of efficient force fields with the accuracy and transferability of high-level ab initio methods.BMBF, 01IS14013A, Verbundprojekt: BBDC - Berliner Kompetenzzentrum für Big DataDFG, MU 987/20-

Thermal and electronic fluctuations of flexible adsorbed molecules : azobenzene on Ag(111)

We investigate the thermal and electronic collective fluctuations that contribute to the finite-temperature adsorption properties of flexible adsorbates on surfaces on the example of the molecular switch azobenzene C12H10N2 on the Ag(111) surface. Using first-principles molecular dynamics simulations, we obtain the free energy of adsorption that accurately accounts for entropic contributions, whereas the inclusion of many-body dispersion interactions accounts for the electronic correlations that govern the adsorbate binding. We find the adsorbate properties to be strongly entropy driven, as can be judged by a kinetic molecular desorption prefactor of 10^24 s−1 that largely exceeds previously reported estimates. We relate this effect to sizable fluctuations across structural and electronic observables. A comparison of our calculations to temperature-programed desorption measurements demonstrates that finite-temperature effects play a dominant role for flexible molecules in contact with polarizable surfaces, and that recently developed first-principles methods offer an optimal tool to reveal novel collective behavior in such complex systems

Exploring the Bonding of Large Hydrocarbons on Noble Metals: Diindoperylene on Cu(111), Ag(111), and Au(111)

We present a benchmark study for the adsorption of a large pi-conjugated organic molecule on different noble metal surfaces, which is based on X-ray standing wave (XSW) measurements and density functional theory calculations with van der Waals (vdW) interactions. The bonding distances of diindenoperylene on Cu(111), Ag(111), and Au(111) surfaces (2.51 A, 3.01 A, and 3.10 A, respectively) determined with the normal incidence XSW technique are compared with calculations. Excellent agreement with the experimental data, i.e. deviations less than 0.1 A, is achieved using the Perdew-Burke-Ernzerhof functional with vdW interactions that include the collective response of substrate electrons (PBE+vdW^{surf} method). Noteworthy, the calculations show that the vdW contribution to the adsorption energy increases in the order Au(111) < Ag(111) < Cu(111).Comment: 6 pages, 4 figures, accepted by Phys. Rev.