We present a way to improve the performance of the electronic structure Vienna Ab initio Simulation Package (VASP) program. We show that high-performance computers equipped with graphics processing units (GPUs) as accelerators may reduce drastically the computation time when offloading these sections to the graphic chips. The procedure consists of (i) profiling the performance of the code to isolate the time-consuming parts, (ii) rewriting these so that the algorithms become better-suited for the chosen graphic accelerator, and (iii) optimizing memory traffic between the host computer and the GPU accelerator. We chose to accelerate VASP with NVIDIA GPU using CUDA. We compare the GPU and original versions of VASP by evaluating the Davidson and RMM-DIIS algorithms on chemical systems of up to 1100 atoms. In these tests, the total time is reduced by a factor between 3 and 8 when running on n (CPU core + GPU) compared to n CPU cores only, without any accuracy loss.Copyright © 2012 Wiley Periodicals, Inc.

Machine learning addresses the question of how to build computers that improve automatically through experience. It is one of today's most rapidly growing technical fields, lying at the intersection of computer science and statistics, and at the core of artificial intelligence and data science. Recent progress in machine learning has been driven both by the development of new learning algorithms and theory and by the ongoing explosion in the availability of online data and low-cost computation. The adoption of data-intensive machine-learning methods can be found throughout science, technology and commerce, leading to more evidence-based decision-making across many walks of life, including health care, manufacturing, education, financial modeling, policing, and marketing. Copyright © 2015, American Association for the Advancement of Science.

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.

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 for accurately predicting the properties of chemical systems, circumventing the need for explicitly solving the electronic Schrödinger equation. Because of their computational efficiency and scalability to large data sets, 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 data sets 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): The optimized geometry of helical Ala predicted by PhysNet is virtually identical to ab initio results (RMSD = 0.21 Å). By running unbiased molecular dynamics (MD) simulations of Ala on the PhysNet-PES in gas phase, it is found that instead of a helical structure, Ala folds into a "wreath-shaped" configuration, which is more stable than the helical form by 0.46 kcal mol according to the reference ab initio calculations.

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning-based PES model. This scheme, we call DP Compress, is an efficient postprocessing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, HO, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online.

Clouet, Emmanuel; Chaari, Nermine CEA, DEN, Serv Rech Met Phys, F-91191 Gif Sur Yvette, France. Caillard, Daniel CNRS, CEMES, F-31055 Toulouse, France. Onimus, Fabien CEA, DEN, Serv Rech Met Appl, F-91191 Gif Sur Yvette, France. Rodney, David Univ Lyon 1, CNRS, UMR 5306, Inst Lumiere Mat, F-69622 Villeurbanne, France.

Elemental gallium possesses several intriguing properties, such as a low melting point, a density anomaly and an electronic structure in which covalent and metallic features coexist. In order to simulate this complex system, we construct an ab initio quality interaction potential by training a neural network on a set of density functional theory calculations performed on configurations generated in multithermal-multibaric simulations. Here we show that the relative equilibrium between liquid gallium, α-Ga, β-Ga, and Ga-II is well described. The resulting phase diagram is in agreement with the experimental findings. The local structure of liquid gallium and its nucleation into α-Ga and β-Ga are studied. We find that the formation of metastable β-Ga is kinetically favored over the thermodinamically stable α-Ga. Finally, we provide insight into the experimental observations of extreme undercooling of liquid Ga.

Many phase transformations associated with solid-state precipitation look structurally simple, yet, inexplicably, take place with great difficulty. A classic case of difficult phase transformations is the nucleation of strengthening precipitates in high-strength lightweight aluminium alloys. Here, using a combination of atomic-scale imaging, simulations and classical nucleation theory calculations, we investigate the nucleation of the strengthening phase θ' onto a template structure in the aluminium-copper alloy system. We show that this transformation can be promoted in samples exhibiting at least one nanoscale dimension, with extremely high nucleation rates for the strengthening phase as well as for an unexpected phase. This template-directed solid-state nucleation pathway is enabled by the large influx of surface vacancies that results from heating a nanoscale solid. Template-directed nucleation is replicated in a bulk alloy as well as under electron irradiation, implying that this difficult transformation can be facilitated under the general condition of sustained excess vacancy concentrations.

An interatomic potential for the Al-Tb alloy around the composition of AlTb is developed using the deep neural network (DNN) learning method. The atomic configurations and the corresponding total potential energies and forces on each atom obtained from ab initio molecular dynamics (AIMD) simulations are collected to train a DNN model to construct the interatomic potential for the Al-Tb alloy. We show that the obtained DNN model can well reproduce the energies and forces calculated by AIMD simulations. Molecular dynamics (MD) simulations using the DNN interatomic potential also accurately describe the structural properties of the AlTb liquid, such as partial pair correlation functions (PPCFs) and bond angle distributions, in comparison with the results from AIMD simulations. Furthermore, the developed DNN interatomic potential predicts the formation energies of the crystalline phases of the Al-Tb system with an accuracy comparable to ab initio calculations. The structure factors of the AlTb metallic liquid and glass obtained by MD simulations using the developed DNN interatomic potential are also in good agreement with the experimental X-ray diffraction data. The development of short-range order (SRO) in the AlTb liquid and the undercooled liquid is also analyzed and three dominant SROs, i.e., Al-centered distorted icosahedron (DISICO) and Tb-centered '3661' and '15551' clusters, respectively, are identified.

It has long been proposed that the hydrated excess proton in water (aka the solvated "hydronium" cation) likely has two limiting forms, that of the Eigen cation (HO) and that of the Zundel cation (HO). There has been debate over which of these two is the more dominant species and/or whether intermediate (or "distorted") structures between these two limits are the more realistic representation. Spectroscopy experiments have recently provided further results regarding the excess proton. These experiments show that the hydrated proton has an anisotropy reorientation time scale on the order of 1-2 ps. This time scale has been suggested to possibly contradict the picture of the more rapid "special pair dance" phenomenon for the hydrated excess proton, which is a signature of a distorted Eigen cation. The special pair dance was predicted from prior computational studies in which the hydrated central core hydronium structure continually switches (O-H···O)* special pair hydrogen-bond partners with the closest three water molecules, yielding on average a distorted Eigen cation with three equivalent and dynamically exchanging distortions. Through state-of-art simulations it is shown here that anisotropy reorientation time scales of the same magnitude are obtained that also include structural reorientations associated with the special pair dance, leading to a reinterpretation of the experimental results. These results and additional analyses point to a distorted and dynamic Eigen cation as the most prevalent hydrated proton species in aqueous acid solutions of dilute to moderate concentration, as opposed to a stabilized or a distorted (but not "dancing") Zundel cation.

We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio density functional theory calculations. In combination with a neural network representation of the interatomic potential energy surface, the scheme allows us to calculate the Raman spectra along 2-nanosecond classical trajectories at different temperatures for HO and DO. The vast gains in efficiency provided by the machine learning approach enable longer trajectories and larger system sizes relative to ab initio methods, reducing the statistical error and improving the resolution of the low-frequency Raman spectra. Decomposing the spectra into intramolecular and intermolecular contributions elucidates the mechanisms behind the temperature dependence of the low-frequency and stretch modes.

The possible existence of a metastable liquid-liquid transition (LLT) and a corresponding liquid-liquid critical point (LLCP) in supercooled liquid water remains a topic of much debate. An LLT has been rigorously proved in three empirically parametrized molecular models of water, and evidence consistent with an LLT has been reported for several other such models. In contrast, experimental proof of this phenomenon has been elusive due to rapid ice nucleation under deeply supercooled conditions. In this work, we combined density functional theory (DFT), machine learning, and molecular simulations to shed additional light on the possible existence of an LLT in water. We trained a deep neural network (DNN) model to represent the ab initio potential energy surface of water from DFT calculations using the Strongly Constrained and Appropriately Normed (SCAN) functional. We then used advanced sampling simulations in the multithermal-multibaric ensemble to efficiently explore the thermophysical properties of the DNN model. The simulation results are consistent with the existence of an LLCP, although they do not constitute a rigorous proof thereof. We fit the simulation data to a two-state equation of state to provide an estimate of the LLCP's location. These combined results-obtained from a purely first-principles approach with no empirical parameters-are strongly suggestive of the existence of an LLT, bolstering the hypothesis that water can separate into two distinct liquid forms.

In this work, an investigation of supercritical water is presented combining inelastic and deep inelastic neutron scattering experiments and molecular dynamics simulations based on a machine-learned potential of quality. The local hydrogen dynamics is investigated at 250 bar and in the temperature range of 553-823 K, covering the evolution from subcritical liquid to supercritical gas-like water. The evolution of libration, bending, and stretching motions in the vibrational density of states is studied, analyzing the spectral features by a mode decomposition. Moreover, the hydrogen nuclear momentum distribution is measured, and its anisotropy is probed experimentally. It is shown that hydrogen bonds survive up to the higher temperatures investigated, and we discuss our results in the framework of the coupling between intramolecular modes and intermolecular librations. Results show that the local potential affecting hydrogen becomes less anisotropic within the molecular plane in the supercritical phase, and we attribute this result to the presence of more distorted hydrogen bonds.

Machine learning models are rapidly becoming widely used to simulate complex physicochemical phenomena with accuracy. Here, we use one such model as well as direct density functional theory (DFT) calculations to investigate the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an eye toward studying ice nucleation. The machine learning model is based on deep neural networks and has been trained on DFT data obtained using the SCAN exchange and correlation functional. We use this model to drive enhanced sampling simulations aimed at calculating a number of complex properties that are out of reach of DFT-driven simulations and then employ an appropriate reweighting procedure to compute the corresponding properties for the SCAN functional. This approach allows us to calculate the melting temperature of both ice polymorphs, the driving force for nucleation, the heat of fusion, the densities at the melting temperature, the relative stability of ices Ih and Ic, and other properties. We find a correct qualitative prediction of all properties of interest. In some cases, quantitative agreement with experiment is better than for state-of-the-art semiempirical potentials for water. Our results also show that SCAN correctly predicts that ice Ih is more stable than ice Ic.

In this work the high pressure region of the phase diagram of water has been studied by computer simulation by using the TIP4P/2005 model of water. Free energy calculations were performed for ices VII and VIII and for the fluid phase to determine the melting curve of these ices. In addition, molecular dynamics simulations were performed at high temperatures (440 K) observing the spontaneous freezing of the liquid into a solid phase at pressures of about 80,000 bar. The analysis of the structure obtained lead to the conclusion that a plastic crystal phase was formed. In the plastic crystal phase the oxygen atoms were arranged forming a body center cubic structure, as in ice VII, but the water molecules were able to rotate almost freely. Free energy calculations were performed for this new phase, and it was found that for TIP4P/2005 this plastic crystal phase is thermodynamically stable with respect to ices VII and VIII for temperatures higher than about 400 K, although the precise value depends on the pressure. By using Gibbs-Duhem simulations, all coexistence lines were determined, and the phase diagram of the TIP4P/2005 model was obtained, including ices VIII and VII and the new plastic crystal phase. The TIP4P/2005 model is able to describe qualitatively the phase diagram of water. It would be of interest to study if such a plastic crystal phase does indeed exist for real water. The nearly spherical shape of water makes possible the formation of a plastic crystal phase at high temperatures. The formation of a plastic crystal phase at high temperatures (with a bcc arrangements of oxygen atoms) is fast from a kinetic point of view occurring in about 2 ns. This is in contrast to the nucleation of ice Ih which requires simulations of the order of hundreds of ns.

Ionic solvation phenomena in liquids involve intense interactions in the inner solvation shell. For interactions beyond the first shell, the ion-solvent interaction energies result from the sum of many smaller-magnitude contributions that can still include polarization effects. Deep neural network (DNN) methods have recently found wide application in developing efficient molecular models that maintain near-quantum accuracy. Here we extend the DeePMD-kit code to produce accurate molecular multipole moments in the bulk and near interfaces. The new method is validated by comparing the DNN moments with those generated by simulations. The moments are used to compute the electrostatic potential at the center of a molecular-sized hydrophobic cavity in water. The results show that the fields produced by the DNN models are in quantitative agreement with the AIMD-derived values. These efficient methods will open the door to more accurate solvation models for large solutes such as proteins.