The determination of catalyst nanostructures with first-principles accuracy using genetic algorithms (GA) is very demanding due to the cubic scaling of the computational cost of density functional theory (DFT) calculations. Here, we demonstrate, for the case of Ziegler-Natta MgCl2/TiCl4nanoplates, how this structure determination can be accelerated by employing a high-dimensional neural network potential (HDNNP) of essentially DFT accuracy. First, when building HDNNPs for MgCl2/TiCl4clusters with computationally tractable sizes, we found that the structural diversity in the training set is crucial for obtaining HDNNPs reliably describing the large variety of structures generated by GA. The resulting HDNNPs dramatically accelerated the structure determination while yielding results consistent with DFT. Subsequently, we developed a multistep adaptive procedure to construct a HDNNP for MgCl2/TiCl4clusters consistent in size and TiCl4coverage with experiments where prior DFT results were scarcely collected. The structure determination and analyses underline the importance of system size and composition in order to predict some experimentally known facts such as the surface morphology and population of isospecific sites. © 2023 American Chemical Society.

In recent years, significant progress has been made in the development of machine learning potentials (MLPs) for atomistic simulations with applications in many fields from chemistry to materials science. While most current MLPs are based on environment-dependent atomic energies, the limitations of this locality approximation can be overcome, e.g., in fourth-generation MLPs, which incorporate long-range electrostatic interactions based on an equilibrated global charge distribution. Apart from the considered interactions, the quality of MLPs crucially depends on the information available about the system, i.e., the descriptors. In this work we show that including─in addition to structural information─the electrostatic potential arising from the charge distribution in the atomic environments significantly improves the quality and transferability of the potentials. Moreover, the extended descriptor allows current limitations of two- and three-body based feature vectors to be overcome regarding artificially degenerate atomic environments. The capabilities of such an electrostatically embedded fourth-generation high-dimensional neural network potential (ee4G-HDNNP), which is further augmented by pairwise interactions, are demonstrated for NaCl as a benchmark system. Employing a data set containing only neutral and negatively charged NaCl clusters, even small energy differences between different cluster geometries can be resolved, and the potential shows an impressive transferability to positively charged clusters as well as the melt.

Machine learning-based interatomic potentials, such as those provided by neural networks, are increasingly important in molecular dynamics simulations. In the present work, we consider the applicability and robustness of machine learning molecular dynamics to predict the equation of state properties of methane by using high-dimensional neural network potentials (HDNNPs). We investigate two different strategies for generating training data: one strategy based upon bulk representations using periodic cells and another strategy based upon clusters of molecules. We assess the accuracy of the trained potentials by predicting the equilibrium mass density for a wide range of thermodynamic conditions to characterize the liquid phase, supercritical fluid, and gas phase, as well as the liquid-vapor coexistence curve. Our results show an excellent agreement with reference phase diagrams, with an average error below ∼2% for all studied phases. Moreover, we confirm the applicability of models trained on cluster data sets for producing accurate and reliable results. © 2023 American Chemical Society.

The introduction of modern Machine Learning Potentials (MLPs) has led to a paradigm change in the development of potential energy surfaces for atomistic simulations. By providing efficient access to energies and forces, they allow us to perform large-scale simulations of extended systems, which are not directly accessible by demanding first-principles methods. In these simulations, MLPs can reach the accuracy of electronic structure calculations, provided that they have been properly trained and validated using a suitable set of reference data. Due to their highly flexible functional form, the construction of MLPs has to be done with great care. In this Tutorial, we describe the necessary key steps for training reliable MLPs, from data generation via training to final validation. The procedure, which is illustrated for the example of a high-dimensional neural network potential, is general and applicable to many types of MLPs. © 2023 Author(s).

Investigating atom-surface interactions is the key to an in-depth understanding of chemical processes at interfaces, which are of central importance in many fields - from heterogeneous catalysis to corrosion. In this work, we present a joint experimental and theoretical effort to gain insights into the atomistic details of hydrogen atom scattering at the α-Al2O3(0001) surface. Surprisingly, this system has been hardly studied to date, although hydrogen atoms as well as α-Al2O3 are omnipresent in catalysis as reactive species and support oxide, respectively. We address this system by performing hydrogen atom beam scattering experiments and molecular dynamics (MD) simulations based on a high-dimensional machine learning potential trained to density functional theory data. Using this combination of methods we are able to probe the properties of the multidimensional potential energy surface governing the scattering process. Specifically, we compare the angular distribution and the kinetic energy loss of the scattered atoms obtained in experiment with a large number of MD trajectories, which, moreover, allow to identify the underlying impact sites at the surface. © 2024 The Royal Society of Chemistry.

Machine learning potentials (MLP) enable atomistic simulations with first-principles accuracy at a small fraction of the costs of electronic structure calculations. Most modern MLPs rely on constructing the potential energy, or a major part of it, as a sum of atomic energies, which are given as a function of the local chemical environments up to a cutoff radius. Since analytic forces are readily available, nowadays it is common practice to make use of both, reference energies and forces, for training these MLPs. This can be computationally demanding since often large systems are required to obtain structurally converged reference forces experienced by atoms in realistic condensed phase environments. In this work we show how density-functional theory calculations of molecular fragments, which are too small to provide such structurally converged forces, can be used to learn forces exhibiting excellent transferability to extended systems. The general procedure and the accuracy of the method are illustrated for metal-organic frameworks using second-generation high-dimensional neural network potentials. © 2023 The Royal Society of Chemistry.

In recent years, many types of machine learning potentials (MLPs) have been introduced, which are able to represent high-dimensional potential-energy surfaces (PESs) with close to first-principles accuracy. Most current MLPs rely on atomic energy contributions given as a function of the local chemical environments. Frequently, in addition to total energies, atomic forces are also used to construct the potentials, as they provide detailed local information about the PES. Since many systems are too large for electronic structure calculations, obtaining reliable reference forces from smaller subsystems, such as molecular fragments or clusters, can substantially simplify the construction of the training sets. Here, we propose a method to determine structurally converged molecular fragments, providing reliable atomic forces based on an analysis of the Hessian. The method, which serves as a locality test and allows us to estimate the importance of long-range interactions, is illustrated for a series of molecular model systems and the metal-organic framework MOF-5 as an example for a complex organic-inorganic hybrid material. © 2022 Author(s).

Coupled cluster theory is a general and systematic electronic structure method, but in particular the highly accurate "gold standard"coupled cluster singles, doubles and perturbative triples, CCSD(T), can only be applied to small systems. To overcome this limitation, we introduce a framework to transfer CCSD(T) accuracy of finite molecular clusters to extended condensed phase systems using a high-dimensional neural network potential. This approach, which is automated, allows one to perform high-quality coupled cluster molecular dynamics, CCMD, as we demonstrate for liquid water including nuclear quantum effects. The machine learning strategy is very efficient, generic, can be systematically improved, and is applicable to a variety of complex systems. © 2022 American Physical Society.

In recent years, machine learning potentials (MLP) for atomistic simulations have attracted a lot of attention in chemistry and materials science. Many new approaches have been developed with the primary aim to transfer the accuracy of electronic structure calculations to large condensed systems containing thousands of atoms. In spite of these advances, the reliability of modern MLPs in reproducing the subtle details of the multi-dimensional potential-energy surface is still difficult to assess for such systems. On the other hand, moderately sized systems enabling the application of tools for thorough and systematic quality-control are nowadays rarely investigated. In this work we use benchmark-quality harmonic and anharmonic vibrational frequencies as a sensitive probe for the validation of high-dimensional neural network potentials. For the case of the formic acid dimer, a frequently studied model system for which stringent spectroscopic data became recently available, we show that high-quality frequencies can be obtained from state-of-the-art calculations in excellent agreement with coupled cluster theory and experimental data. © 2022 The Royal Society of Chemistry.

In the past two decades, machine learning potentials (MLPs) have reached a level of maturity that now enables applications to large-scale atomistic simulations of a wide range of systems in chemistry, physics, and materials science. Different machine learning algorithms have been used with great success in the construction of these MLPs. In this review, we discuss an important group of MLPs relying on artificial neural networks to establish a mapping from the atomic structure to the potential energy. In spite of this common feature, there are important conceptual differences among MLPs, which concern the dimensionality of the systems, the inclusion of long-range electrostatic interactions, global phenomena like nonlocal charge transfer, and the type of descriptor used to represent the atomic structure, which can be either predefined or learnable. A concise overview is given along with a discussion of the open challenges in the field. © 2022 Annual Reviews Inc.. All rights reserved.

In recent years the development of machine learning potentials (MLPs) has become a very active field of research. Numerous approaches have been proposed, which allow one to perform extended simulations of large systems at a small fraction of the computational costs of electronic structure calculations. The key to the success of modern MLPs is the close-To first principles quality description of the atomic interactions. This accuracy is reached by using very flexible functional forms in combination with high-level reference data from electronic structure calculations. These data sets can include up to hundreds of thousands of structures covering millions of atomic environments to ensure that all relevant features of the potential energy surface are well represented. The handling of such large data sets is nowadays becoming one of the main challenges in the construction of MLPs. In this paper we present a method, the bin-And-hash (BAH) algorithm, to overcome this problem by enabling the efficient identification and comparison of large numbers of multidimensional vectors. Such vectors emerge in multiple contexts in the construction of MLPs. Examples are the comparison of local atomic environments to identify and avoid unnecessary redundant information in the reference data sets that is costly in terms of both the electronic structure calculations as well as the training process, the assessment of the quality of the descriptors used as structural fingerprints in many types of MLPs, and the detection of possibly unreliable data points. The BAH algorithm is illustrated for the example of high-dimensional neural network potentials using atom-centered symmetry functions for the geometrical description of the atomic environments, but the method is general and can be combined with any current type of MLP. © 2021 Machine Learning: Science and Technology. All rights reserved.

Machine learning potentials have become an important tool for atomistic simulations in many fields, from chemistry via molecular biology to materials science. Most of the established methods, however, rely on local properties and are thus unable to take global changes in the electronic structure into account, which result from long-range charge transfer or different charge states. In this work we overcome this limitation by introducing a fourth-generation high-dimensional neural network potential that combines a charge equilibration scheme employing environment-dependent atomic electronegativities with accurate atomic energies. The method, which is able to correctly describe global charge distributions in arbitrary systems, yields much improved energies and substantially extends the applicability of modern machine learning potentials. This is demonstrated for a series of systems representing typical scenarios in chemistry and materials science that are incorrectly described by current methods, while the fourth-generation neural network potential is in excellent agreement with electronic structure calculations. © 2021, The Author(s).

Atomic environment fingerprints are widely used in computational materials science, from machine learning potentials to the quantification of similarities between atomic configurations. Many approaches to the construction of such fingerprints, also called structural descriptors, have been proposed. In this work, we compare the performance of fingerprints based on the overlap matrix, the smooth overlap of atomic positions, Behler–Parrinello atom-centered symmetry functions, modified Behler–Parrinello symmetry functions used in the ANI-1ccx potential and the Faber–Christensen–Huang–Lilienfeld fingerprint under various aspects. We study their ability to resolve differences in local environments and in particular examine whether there are certain atomic movements that leave the fingerprints exactly or nearly invariant. For this purpose, we introduce a sensitivity matrix whose eigenvalues quantify the effect of atomic displacement modes on the fingerprint. Further, we check whether these displacements correlate with the variation of localized physical quantities such as forces. Finally, we extend our examination to the correlation between molecular fingerprints obtained from the atomic fingerprints and global quantities of entire molecules. © 2021 The Author(s). Published by IOP Publishing Ltd

Since their introduction about 25 years ago, machine learning (ML) potentials have become an important tool in the field of atomistic simulations. After the initial decade, in which neural networks were successfully used to construct potentials for rather small molecular systems, the development of high-dimensional neural network potentials (HDNNPs) in 2007 opened the way for the application of ML potentials in simulations of large systems containing thousands of atoms. To date, many other types of ML potentials have been proposed continuously increasing the range of problems that can be studied. In this review, the methodology of the family of HDNNPs including new recent developments will be discussed using a classification scheme into four generations of potentials, which is also applicable to many other types of ML potentials. The first generation is formed by early neural network potentials designed for low-dimensional systems. High-dimensional neural network potentials established the second generation and are based on three key steps: First, the expression of the total energy as a sum of environment-dependent atomic energy contributions; second, the description of the atomic environments by atom-centered symmetry functions as descriptors fulfilling the requirements of rotational, translational, and permutation invariance; and third, the iterative construction of the reference electronic structure data sets by active learning. In third-generation HDNNPs, in addition, long-range interactions are included employing environment-dependent partial charges expressed by atomic neural networks. In fourth-generation HDNNPs, which are just emerging, in addition, nonlocal phenomena such as long-range charge transfer can be included. The applicability and remaining limitations of HDNNPs are discussed along with an outlook at possible future developments. © 2021 The Author. Published by American Chemical Society.

ConspectusThe development of first-principles-quality machine learning potentials (MLP) has seen tremendous progress, now enabling computer simulations of complex systems for which sufficiently accurate interatomic potentials have not been available. These advances and the increasing use of MLPs for more and more diverse systems gave rise to new questions regarding their applicability and limitations, which has constantly driven new developments. The resulting MLPs can be classified into several generations depending on the types of systems they are able to describe. First-generation MLPs, as introduced 25 years ago, have been applicable to low-dimensional systems such as small molecules. MLPs became a practical tool for complex systems in chemistry and materials science with the introduction of high-dimensional neural network potentials (HDNNP) in 2007, which represented the first MLP of the second generation. Second-generation MLPs are based on the concept of locality and express the total energy as a sum of environment-dependent atomic energies, which allows applications to very large systems containing thousands of atoms with linearly scaling computational costs. Since second-generation MLPs do not consider interactions beyond the local chemical environments, a natural extension has been the inclusion of long-range interactions without truncation, mainly electrostatics, employing environment-dependent charges establishing the third MLP generation. A variety of second- and, to some extent, also third-generation MLPs are currently the standard methods in ML-based atomistic simulations.In spite of countless successful applications, in recent years it has been recognized that the accuracy of MLPs relying on local atomic energies and charges is still insufficient for systems with long-ranged dependencies in the electronic structure. These can, for instance, result from nonlocal charge transfer or ionization and are omnipresent in many important types of systems and chemical processes such as the protonation and deprotonation of organic and biomolecules, redox reactions, and defects and doping in materials. In all of these situations, small local modifications can change the system globally, resulting in different equilibrium structures, charge distributions, and reactivity. These phenomena cannot be captured by second- and third-generation MLPs. Consequently, the inclusion of nonlocal phenomena has been identified as a next key step in the development of a new fourth generation of MLPs. While a first fourth-generation MLP, the charge equilibration neural network technique (CENT), was introduced in 2015, only very recently have a range of new general-purpose methods applicable to a broad range of physical scenarios emerged. In this Account, we show how fourth-generation HDNNPs can be obtained by combining the concepts of CENT and second-generation HDNNPs. These new MLPs allow for a highly accurate description of systems where nonlocal charge transfer is important. © 2021 American Chemical Society.

Machine learning potentials have emerged as a powerful tool to extend the time and length scales of first-principles quality simulations. Still, most machine learning potentials cannot distinguish different electronic spin arrangements and thus are not applicable to materials in different magnetic states. Here we propose spin-dependent atom-centered symmetry functions as a type of descriptor taking the atomic spin degrees of freedom into account. When used as an input for a high-dimensional neural network potential (HDNNP), accurate potential energy surfaces of multicomponent systems can be constructed, describing multiple collinear magnetic states. We demonstrate the performance of these magnetic HDNNPs for the case of manganese oxide, MnO. The method predicts the magnetically distorted rhombohedral structure in excellent agreement with density functional theory and experiment. Its efficiency allows to determine the Néel temperature considering structural fluctuations, entropic effects, and defects. The method is general and is expected to be useful also for other types of systems such as oligonuclear transition metal complexes. © 2021, The Author(s).

Unraveling the atomistic and the electronic structure of solid-liquid interfaces is the key to the design of new materials for many important applications, from heterogeneous catalysis to battery technology. Density functional theory (DFT) calculations can, in principle, provide a reliable description of such interfaces, but the high computational costs severely restrict the accessible time and length scales. Here, we report machine learning-driven simulations of various interfaces between water and lithium manganese oxide (LixMn2O4), an important electrode material in lithium ion batteries and a catalyst for the oxygen evolution reaction. We employ a high-dimensional neural network potential to compute the energies and forces several orders of magnitude faster than DFT without loss in accuracy. In addition, a high-dimensional neural network for spin prediction is utilized to analyze the electronic structure of the manganese ions. Combining these methods, a series of interfaces is investigated by large-scale molecular dynamics. The simulations allow us to gain insights into a variety of properties, such as the dissociation of water molecules, proton transfer processes, and hydrogen bonds, as well as the geometric and electronic structure of the solid surfaces, including the manganese oxidation state distribution, Jahn-Teller distortions, and electron hopping. © 2021 Author(s).

Abstract: In the past two and a half decades machine learning potentials have evolved from a special purpose solution to a broadly applicable tool for large-scale atomistic simulations. By combining the efficiency of empirical potentials and force fields with an accuracy close to first-principles calculations they now enable computer simulations of a wide range of molecules and materials. In this perspective, we summarize the present status of these new types of models for extended systems, which are increasingly used for materials modelling. There are several approaches, but they all have in common that they exploit the locality of atomic properties in some form. Long-range interactions, most prominently electrostatic interactions, can also be included even for systems in which non-local charge transfer leads to an electronic structure that depends globally on all atomic positions. Remaining challenges and limitations of current approaches are discussed. Graphic Abstract: [Figure not available: see fulltext.] © 2021, The Author(s).

Elemental antimony has been recently proposed as a promising material for phase change memories with improved performances with respect to the most used ternary chalcogenide alloys. The compositional simplification prevents reliability problems due to demixing of the alloy during memory operation. This is made possible by the dramatic stabilization of the amorphous phase once Sb is confined in an ultrathin film 3-5 nm thick. In this work, we shed light on the microscopic origin of this effect by means of large scale molecular dynamics simulations based on an interatomic potential generated with a machine learning technique. The simulations suggest that the dramatic reduction of the crystal growth velocity in the film with respect to the bulk is due to the effect of nanoconfinement on the fast β relaxation dynamics while the slow α relaxation is essentially unaffected. © The Royal Society of Chemistry.

Nanoparticles have become increasingly interesting for a wide range of applications because in principle it is possible to tailor their properties by controlling size, shape, and composition. One of these applications is heterogeneous catalysis, and a fundamental understanding of the structural details of the nanoparticles is essential for any knowledge-based improvement of reactivity and selectivity. In this work, we investigate the atomic structure of brass nanoparticles containing up to 5000 atoms as a typical example for a binary alloy consisting of Cu and Zn. As systems of this size are too large for electronic structure calculations, in our simulations, we use a recently parameterized machine learning potential providing close to density functional theory accuracy. This potential is employed for a structural characterization as a function of chemical composition by various types of simulations such as Monte Carlo in the semigrand canonical ensemble and simulated annealing molecular dynamics. Our analysis reveals that the distribution of both elements in the nanoparticles is inhomogeneous, and zinc accumulates in the outermost layer, while the first subsurface layer shows an enrichment of copper. Only for high zinc concentrations, alloying can be found in the interior of the nanoparticles, and regular patterns corresponding to crystalline bulk phases of α-brass can then be observed. The surfaces of the investigated clusters exhibit well-ordered single-crystal facets, which can give rise to grain boundaries inside the clusters. The melting temperature of the nanoparticles is found to decrease with increasing zinc-atom fraction, a trend which is well known also for the bulk phase diagram of brass. © 2021 The Authors. Published by American Chemical Society.

Global optimization is an active area of research in atomistic simulations, and many algorithms have been proposed to date. A prominent example is basin hopping Monte Carlo, which performs a modified Metropolis Monte Carlo search to explore the potential energy surface of the system of interest. These simulations can be very demanding due to the high-dimensional configurational search space. The effective search space can be reduced by utilizing grids for the atomic positions, but at the cost of possibly biasing the results if fixed grids are employed. In this paper, we present a flexible grid algorithm for global optimization that allows us to exploit the efficiency of grids without biasing the simulation outcome. The method is general and applicable to very heterogeneous systems, such as interfaces between two materials of different crystal structures or large clusters supported at surfaces. As a benchmark case, we demonstrate its performance for the well-known global optimization problem of Lennard-Jones clusters containing up to 100 particles. Despite the simplicity of this model potential, Lennard-Jones clusters represent a challenging test case since the global minima for some "magic" numbers of particles exhibit geometries that are very different from those of clusters with only a slightly different size. © 2020 Author(s).

The H + CH3OH reaction, which plays an important role in combustion and the interstellar medium, presents a prototypical system with multi channels and tight transition states. However, no globally reliable potential energy surface (PES) has been available to date. Here we develop global analytical PESs for this system using the permutation-invariant polynomial neural network (PIP-NN) and the high-dimensional neural network (HD-NN) methods based on a large number of data points calculated at the level of the explicitly correlated unrestricted coupled cluster single, double, and perturbative triple level with the augmented correlation corrected valence triple-ζ basis set (UCCSD(T)-F12a/AVTZ). We demonstrate that both machine learning PESs are able to accurately describe all dynamically relevant reaction channels. At a collision energy of 20 kcal/mol, quasi-classical trajectory calculations reveal that the dominant channel is the hydrogen abstraction from the methyl site, yielding H2 + CH2OH. The reaction of this major channel takes place mainly via the direct rebound mechanism. Both the vibrational and rotational states of the H2 product are relatively cold, and large portions of the available energy are converted into the product translational motion. Copyright © 2020 American Chemical Society.

We present a first principles-quality potential energy surface (PES) describing the inter-atomic forces for hydrogen atoms interacting with free-standing graphene. The PES is a high-dimensional neural network potential that has been parameterized to 75 945 data points computed with density-functional theory employing the PBE-D2 functional. Improving over a previously published PES [Jiang et al., Science, 2019, 364, 379], this neural network exhibits a realistic physisorption well and achieves a 10-fold reduction in the RMS fitting error, which is 0.6 meV per atom. The chemisorption barrier is 172 meV, which is lower than that of the REBO-EMFT PES (260 meV). We used this PES to calculate about 1.5 million classical trajectories with carefully selected initial conditions to allow for direct comparison to results of H- and D-atom scattering experiments performed at incidence translational energy of 1.9 eV and a surface temperature of 300 K. The theoretically predicted scattering angular and energy loss distributions are in good agreement with experiment, despite the fact that the experiments employed graphene grown on Pt(111). Compared to previous calculations, the agreement with experiments is improved. The remaining discrepancies between experiment and theory are likely due to the influence of the Pt substrate only present in the experiment. This journal is © the Owner Societies.

The thermal conductivity of GeTe crystalline nanowires has been computed by means of non-equilibrium molecular dynamics simulations employing a machine learning interatomic potential. This material is of interest for application in phase change non-volatile memories. The resulting lattice thermal conductivity of an ultrathin nanowire (7.3 nm diameter) of 1.57 W m-1 K-1 is sizably lower than the corresponding bulk value of 3.15 W m-1 K-1 obtained within the same framework. The analysis of the phonon dispersion relations and lifetimes reveals that the lower thermal conductivity in the nanowire is mostly due to a reduction in the phonon group velocities. We further predict the presence of a minimum in the lattice thermal conductivity for thicker nanowires. © 2019 IOP Publishing Ltd.

Highly accurate potential energy surfaces are of key interest for the detailed understanding and predictive modeling of chemical systems. In recent years, several new types of force fields, which are based on machine learning algorithms and fitted to ab initio reference calculations, have been introduced to meet this requirement. Here, we show how high-dimensional neural network potentials can be employed to automatically generate the potential energy surface of finite sized clusters at coupled cluster accuracy, namely CCSD(T*)-F12a/aug-cc-pVTZ. The developed automated procedure utilizes the established intrinsic properties of the model such that the configurations for the training set are selected in an unbiased and efficient way to minimize the computational effort of expensive reference calculations. These ideas are applied to protonated water clusters from the hydronium cation, H3O+, up to the tetramer, H9O4+, and lead to a single potential energy surface that describes all these systems at essentially converged coupled cluster accuracy with a fitting error of 0.06 kJ/mol per atom. The fit is validated in detail for all clusters up to the tetramer and yields reliable results not only for stationary points but also for reaction pathways and intermediate configurations as well as different sampling techniques. Per design, the neural network potentials (NNPs) constructed in this fashion can handle very different conditions including the quantum nature of the nuclei and enhanced sampling techniques covering very low as well as high temperatures. This enables fast and exhaustive exploration of the targeted protonated water clusters with essentially converged interactions. In addition, the automated process will allow one to tackle finite systems much beyond the present case. © 2019 American Chemical Society.

Many positive electrode materials in lithium ion batteries include transition metals, which are difficult to describe by electronic structure methods like density functional theory (DFT) due to the presence of multiple oxidation states. A prominent example is the lithium manganese oxide spinel LixMn2O4 with 0≤x≤2. While DFT, employing the local hybrid functional PBE0r, provides a reliable description, the need for extended computer simulations of large structural models remains a significant challenge. Here, we close this gap by constructing a DFT-based high-dimensional neural network potential (HDNNP) providing accurate energies and forces at a fraction of the computational costs. As different oxidation states and the resulting Jahn-Teller distortions represent a new level of complexity for HDNNPs, the potential is carefully validated by performing x-ray diffraction experiments. We demonstrate that the HDNNP provides atomic level details and is able to predict a series of properties like the lattice parameters and expansion with increasing Li content or temperature, the orthorhombic to cubic transition, the lithium diffusion barrier, and the phonon frequencies. We show that for understanding these properties access to large time and length scales as enabled by the HDNNP is essential to close the gap between theory and experiment. © 2020 American Physical Society.

We have discovered an error in the published paper for the discussion on the significance of inclusion of the angular symmetry functions. As a result, the paragraph below eqn (14) needs be modified. All other conclusions are not affected by this correction. For consistency and clarity, the following equations are given without relabeling. They provide descriptions for the local chemical environments of the central atom i being 1, 2, 3, and 4.(Formula Presented). © the Owner Societies.

The determination of the most stable structures of metal clusters supported at solid surfaces by computer simulations represents a formidable challenge due to the complexity of the potential-energy surface. Here, we combine a high-dimensional neural network potential, which allows us to predict the energies and forces of a large number of structures with first-principles accuracy, with a global optimization scheme employing genetic algorithms. This very efficient setup is used to identify the global minima and low-energy local minima for a series of copper clusters containing between four and ten atoms adsorbed at the ZnO(101¯0) surface. A series of structures with common structural features resembling the Cu(111) and Cu(110) surfaces at the metal-oxide interface has been identified, and the geometries of the emerging clusters are characterized in detail. We demonstrate that the frequently employed approximation of a frozen substrate surface in global optimization can result in missing the most relevant structures. © 2020 Author(s).

High-dimensional neural network potentials, proposed by Behler and Parrinello in 2007, have become an established method to calculate potential energy surfaces with first-principles accuracy at a fraction of the computational costs. The method is general and can describe all types of chemical interactions (e.g., covalent, metallic, hydrogen bonding, and dispersion) for the entire periodic table, including chemical reactions, in which bonds break or form. Typically, many-body atom-centered symmetry functions, which incorporate the translational, rotational, and permutational invariances of the potential energy surface exactly, are used as descriptors for the atomic environments. This chapter describes how such symmetry functions and high-dimensional neural network potentials are constructed and validated. © 2020, The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG.

The lithium manganese oxide spinel LixMn2O4, with 0≤x≤2, is an important example for cathode materials in lithium ion batteries. However, an accurate description of LixMn2O4 by first-principles methods like density functional theory is far from trivial due to its complex electronic structure, with a variety of energetically close electronic and magnetic states. It was found that the local density approximation as well as the generalized gradient approximation (GGA) are unable to describe LixMn2O4 correctly. Here, we report an extensive benchmark for different LixMnyOz systems using the hybrid functionals PBE0 and HSE06, as well as the recently introduced local hybrid functional PBE0r. We find that all of these functionals yield energetic, structural, electronic, and magnetic properties in good agreement with experimental data. The notable benefit of the PBE0r functional, which relies on onsite Hartree-Fock exchange only, is a much reduced computational effort that is comparable to GGA functionals. Furthermore, the Hartree-Fock mixing factors in PBE0r are smaller than in PBE0, which improves the results for (lithium) manganese oxides. The investigation of LixMn2O4 shows that two Mn oxidation states, +III and +IV, coexist. The MnIII ions are in the high-spin state and the corresponding MnO6 octahedra are Jahn-Teller distorted. The ratio between MnIII and MnIV and thus the electronic structure changes with the Li content while no major structural changes occur in the range from x=0 to 1. This work demonstrates that the PBE0r functional provides an equally accurate and efficient description of the investigated LixMnyOz systems. © 2020 American Physical Society.

Water permeation between stacked layers of hBN sheets forming 2D nanochannels is investigated using large-scale ab initio-quality molecular dynamics simulations. A high-dimensional neural network potential trained on density-functional theory calculations is employed. We simulate water in van der Waals nanocapillaries and study the impact of nanometric confinement on the structure and dynamics of water using both equilibrium and nonequilibrium methods. At an interlayer distance of 10.2 Å confinement induces a first-order phase transition resulting in a well-defined AA-stacked bilayer of hexagonal ice. In contrast, for h < 9 Å, the 2D water monolayer consists of a mixture of different locally ordered patterns of squares, pentagons, and hexagons. We found a significant change in the transport properties of confined water, particularly for monolayer water where the water-solid friction coefficient decreases to half and the diffusion coefficient increases by a factor of 4 as compared to bulk water. Accordingly, the slip-velocity is found to increase under confinement and we found that the overall permeation is dominated by monolayer water adjacent to the hBN membranes at extreme confinements. We conclude that monolayer water in addition to bilayer ice has a major contribution to water transport through 2D nanochannels. Copyright © 2020 American Chemical Society.

Machine learning of the quantitative relationship between local environment descriptors and the potential energy surface of a system of atoms has emerged as a new frontier in the development of interatomic potentials (IAPs). Here, we present a comprehensive evaluation of machine learning IAPs (ML-IAPs) based on four local environment descriptors - atom-centered symmetry functions (ACSF), smooth overlap of atomic positions (SOAP), the spectral neighbor analysis potential (SNAP) bispectrum components, and moment tensors - using a diverse data set generated using high-throughput density functional theory (DFT) calculations. The data set comprising bcc (Li, Mo) and fcc (Cu, Ni) metals and diamond group IV semiconductors (Si, Ge) is chosen to span a range of crystal structures and bonding. All descriptors studied show excellent performance in predicting energies and forces far surpassing that of classical IAPs, as well as predicting properties such as elastic constants and phonon dispersion curves. We observe a general trade-off between accuracy and the degrees of freedom of each model and, consequently, computational cost. We will discuss these trade-offs in the context of model selection for molecular dynamics and other applications. © 2020 American Chemical Society.

Lithium ion batteries often contain transition metal oxides such as LixMn2O4 (0 ≤ x ≤ 2). Depending on the Li content, different ratios of MnIII to MnIV ions are present. In combination with electron hopping, the Jahn-Teller distortions of the MnIIIO6 octahedra can give rise to complex phenomena such as structural transitions and conductance. While for small model systems oxidation and spin states can be determined using density functional theory (DFT), the investigation of dynamical phenomena by DFT is too demanding. Previously, we have shown that a high-dimensional neural network potential can extend molecular dynamics (MD) simulations of LixMn2O4 to nanosecond time scales, but these simulations did not provide information about the electronic structure. Here, we extend the use of neural networks to the prediction of atomic oxidation and spin states. The resulting high-dimensional neural network is able to predict the spins of the Mn ions with an error of only 0.03 We find that the Mn eg electrons are correctly conserved and that the number of Jahn-Teller distorted MnIIIO6 octahedra is predicted precisely for different Li loadings. A charge ordering transition is observed between 280 K and 300 K, which matches resistivity measurements. Moreover, the activation energy of the electron hopping conduction above the phase transition is predicted to be 0.18 eV, deviating only 0.02 eV from experiment. This work demonstrates that machine learning is able to provide an accurate representation of both the geometric and the electronic structure dynamics of LixMn2O4 on time and length scales that are not accessible by ab initio MD. © 2020 Author(s).

Binary metal clusters are of high interest for applications in heterogeneous catalysis and have received much attention in recent years. To gain insights into their structure and composition at the atomic scale, computer simulations can provide valuable information if reliable interatomic potentials are available. In this paper we describe the construction of a high-dimensional neural network potential (HDNNP) intended for simulations of large brass nanoparticles with thousands of atoms, which is also applicable to bulk α-brass and its surfaces. The HDNNP, which is based on reference data obtained from density-functional theory calculations, is very accurate with a root-mean-square error of 1.7 meV/atom for total energies and 39 meV Å-1 for the forces of structures not included in the training set. The potential has been thoroughly validated for a wide range of energetic and structural properties of bulk α-brass, its surfaces as well as clusters of different size and composition demonstrating its suitability for large-scale molecular dynamics and Monte Carlo simulations with first-principles accuracy. © 2020 American Chemical Society.

Alkaline electrolyte solutions are important components in rechargeable batteries and alkaline fuel cells. As the ionic conductivity is thought to be a limiting factor in the performance of these devices, which are often operated at elevated temperatures, its temperature dependence is of significant interest. Here we use NaOH as a prototypical example of alkaline electrolytes, and for this system we have carried out reactive molecular dynamics simulations with an experimentally verified high-dimensional neural network potential derived from density-functional theory calculations. It is found that in concentrated NaOH solutions elevated temperatures enhance both the contributions of proton transfer to the ionic conductivity and deviations from the Nernst-Einstein relation. These findings are expected to be of practical relevance for electrochemical devices based on alkaline electrolyte solutions. This journal is © the Owner Societies.

Germanium manganese compounds exhibit a variety of stable and metastable phases with different stoichiometries. These materials entail interesting electronic, magnetic, and thermal properties both in their bulk form and as heterostructures. Here, we develop and validate a transferable machine learning potential, based on the high-dimensional neural network formalism, to enable the study of Mn xGe y materials over a wide range of compositions. We show that a neural network potential fitted on a minimal training set reproduces successfully the structural and vibrational properties and the thermal conductivity of systems with different local chemical environments, and it can be used to predict phononic effects in nanoscale heterostructures. © 2020 Author(s).

The availability of accurate full-dimensional potential energy surfaces (PESs) is a mandatory condition for efficient computer simulations of molecular systems. Much effort has been devoted to developing reliable PESs with physically sound properties, such as the invariance of the energy with respect to the permutation of chemically identical atoms. In this work, we compare the performance of four neural network (NN)-based approaches with a rigorous permutation symmetry for fitting five typical reaction systems: OH + CO, H + H2S, H + NH3, H + CH4 and OH + CH4. The methods can be grouped into two categories, invariant polynomial based NNs and high-dimensional NN potentials (HD-NNPs). For the invariant polynomial based NNs, three types of polynomials, permutation invariant polynomials (PIPs), non-redundant PIPs (NRPIPs) and fundamental invariants (FIs), are used in the input layer of the NN. In HD-NNPs, the total energy is the sum of atomic contributions, each of which is given by an individual atomic NN with input vectors consisting of sets of atom-centered symmetry functions. Our results show that all methods exhibit a similar level of accuracy for the energies with respect to ab initio data obtained at the explicitly correlated coupled cluster level of theory (CCSD(T)-F12a). The HD-NNP method allows study of systems with larger numbers of atoms, making it more generally applicable than invariant polynomial based approaches, which in turn are computationally more efficient for smaller systems. To illustrate the applicability of the obtained potentials, quasi-classical trajectory calculations have been performed for the OH + CH4 → H2O + CH3 reaction to reveal its complicated mode specificity. © the Owner Societies 2019.

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations, and proton disorder. This is made possible by combining advanced free-energy methods and state-of-the-art machine-learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments and reliable estimates of the melting points of light and heavy water. We observe that nuclear-quantum effects contribute a crucial 0.2 meV/H 2 O to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine-learning potentials as an intermediate step. © 2019 National Academy of Sciences. All rights reserved.

An accurate description of reactive scattering of molecules on metal surfaces often requires the modeling of energy transfer between the molecule and the surface phonons. Although ab initio molecular dynamics (AIMD) can describe this energy transfer, AIMD is at present untractable for reactions with reaction probabilities smaller than 1%. Here, we show that it is possible to use a neural network potential to describe a polyatomic molecule reacting on a mobile metal surface with considerably reduced computational effort compared to AIMD. The highly activated reaction of CHD 3 on Cu(111) is used as a test case for this method. It is observed that the reaction probability is influenced considerably by dynamical effects such as the bobsled effect and surface recoil. A special dynamical effect for CHD 3 + Cu(111) is that a higher vibrational efficacy is obtained for two quanta in the CH stretch mode than for a single quantum. Copyright © 2019 American Chemical Society.

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. © 2019 American Chemical Society.

Machine-learning methods have become increasingly popular for describing potential energy surfaces for molecular and materials simulations, and they are even beginning to challenge the present-day dominance of force fields for this task. This chapter reviews high-dimensional neural network potentials (HDNNPs), which are a general-purpose reactive potential method that can be used for simulations of an arbitrary number of atoms, can describe all types of chemical interactions (e.g., covalent, metallic, and dispersion), and includes the breaking and forming of chemical bonds. Before an HDNNP can be applied, it must be parameterized using electronic structure data, and great care must be taken at the parameterization stage to ensure that all pertinent parts of the potential energy surface are adequately covered. Typically, this is done iteratively through the addition of more training data and refitting of parameters. This chapter illustrates these points through the use of two case studies from our recent work for aqueous NaOH solutions and the ZnO/water interface. © 2019 American Chemical Society. All rights reserved.

Neural networks and other machine learning approaches have been successfully used to accurately represent atomic interaction potentials derived from computationally demanding electronic structure calculations. Due to their low computational cost, such representations open the possibility for large scale reactive molecular dynamics simulations of processes with bonding situations that cannot be described accurately with traditional empirical force fields. Here, we present a library of functions developed for the implementation of neural network potentials. Written in C++, this library incorporates several strategies resulting in a very high efficiency of neural network potential-energy and force evaluations. Based on this library, we have developed an implementation of the neural network potential within the molecular dynamics package LAMMPS and demonstrate its performance using liquid water as a test system. © 2019 American Chemical Society.

An extensive characterization of Co3(PO4)2 was performed by topological analysis according to Bader‘s Quantum Theory of Atoms in Molecules from the experimentally and theoretically determined electron density. This study sheds light on the reactivity of cobalt orthophosphate as a solid-state heterogeneous oxidative-dehydration and -dehydrogenation catalyst. Various faces of the bulk catalyst were identified as possible reactive sites given their topological properties. The charge accumulations and depletions around the two independent five- and sixfold-coordinated cobalt atoms, found in the topological analysis, are correlated to the orientation and population of the d-orbitals. It is shown that the (011) face has the best structural features for catalysis. Fivefold-coordinated ions in close proximity to advantageously oriented vacant coordination sites and electron depletions suit the oxygen lone pairs of the reactant, mainly for chemisorption. This is confirmed both from the multipole refinement as well as from density functional theory calculations. Nearby basic phosphate ions are readily available for C−H activation. © 2019 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.

Long-range charge transport is important for many applications like batteries, fuel cells, sensors, and catalysis. Obtaining microscopic insights into the atomistic mechanism is challenging, in particular if the underlying processes involve protons as the charge carriers. Here, large-scale reactive molecular dynamics simulations employing an efficient density-functional-theory-based neural network potential are used to unravel long-range proton transport mechanisms at solid-liquid interfaces, using the zinc oxide-water interface as a prototypical case. We find that the two most frequently occurring ZnO surface facets, (1010) and (1120), that typically dominate the morphologies of zinc oxide nanowires and nanoparticles, show markedly different proton conduction behaviors along the surface with respect to the number of possible proton transfer mechanisms, the role of the solvent for long-range proton migration, as well as the proton transport dimensionality. Understanding such surface-facet-specific mechanisms is crucial for an informed bottom-up approach for the functionalization and application of advanced oxide materials. © 2019 The Royal Society of Chemistry.

Electron-hole pair (ehp) excitation is thought to substantially affect the dynamics of molecules on metal surfaces, but it is not clear whether this can be better addressed by orbital-dependent friction (ODF) or the local density friction approximation (LDFA). We investigate the effect of ehp excitation on the dissociative chemisorption of N2 on and its inelastic scattering from Ru(0001), which is the benchmark system of highly activated dissociation, with these two different models. ODF is in better agreement with the best experimental estimates for the reaction probabilities than LDFA, yields results for vibrational excitation in better agreement with experiment, but slightly overestimates the translational energy loss during scattering. N2 on Ru(0001) is thus the first system for which the ODF and LDFA approaches are shown to yield substantially different results for easily accessible experimental observables, including reaction probabilities. © 2019 American Chemical Society.

Over the past years high-dimensional neural network potentials (HDNNPs), fitted to accurately reproduce ab initio potential energy surfaces, have become a powerful tool in chemistry, physics and materials science. Here, we focus on the training of the neural networks that lies at the heart of the HDNNP method. We present an efficient approach for optimizing the weight parameters of the neural network via multistream Kalman filtering, using potential energies and forces as reference data. In this procedure, the choice of the free parameters of the Kalman filter can have a significant impact on the fit quality. Carrying out a large parameter study, we determine optimal settings and demonstrate how to optimize training results of HDNNPs. Moreover, we illustrate our HDNNP training approach by revisiting previously presented fits for water and developing a new potential for copper sulfide. This material, accessible in computer simulations so far only via first-principles methods, forms a particularly complex solid structure at low temperatures and undergoes a phase transition to a superionic state upon heating. Analyzing MD simulations carried out with the Cu 2 S HDNNP, we confirm that the underlying ab initio reference method indeed reproduces this behavior. © 2019 American Chemical Society.

Strategies to reduce the incubation time for crystal nucleation and thus the stochasticity of the set process are of relevance for the operation of phase change memories in ultra-scaled geometries. With these premises, in this work we investigate the crystallization kinetics of the phase change compound GeTe. We have performed large scale molecular dynamics simulations using an interatomic potential, generated previously from a neural network fitting of a database of ab initio energies. We have addressed the crystallization of models of amorphous GeTe annealed at different temperatures above the glass transition. The results on the distribution of subcritical nuclei and on the crystal growth velocity of postcritical ones are compared with our previous simulations of the supercooled liquid quenched from the melt. We find that a large population of subcritical nuclei can form at the lower temperatures where the nucleation rate is large. This population partially survives upon fast annealing, which leads to a dramatic reduction of the incubation time at high temperatures where the crystal growth velocity is maximal. This priming effect could be exploited to enhance the speed of the set process in phase change memories. © 2019 The Royal Society of Chemistry.

Interfaces between water and metal oxides exhibit many interesting phenomena like dissociation and recombination of water molecules and water exchange between the interface and the bulk liquid. Moreover, a variety of structural motifs can be found, differing in hydrogen-bonding patterns and molecular orientations. Here, we report the structure and dynamics of liquid water interacting with the two most stable ZnO surfaces, (101Ì) and (112Ì), by means of reactive molecular dynamics simulations based on a machine learning high-dimensional neural network potential. For both surfaces, three distinct hydration layers can be observed within 10 Å from the surface with the first hydration layer (nearest to the surface) representing the most interesting region to investigate. There, water molecules dynamically dissociate and recombine, leading to a variety of chemical species at the interface. We characterized these species and their molecular environments by analyzing the properties of the hydrogen bonds and local geometries. At ZnO(112Ì0), some of the adsorbed hydroxide ions bridge two surface Zn ions, which is not observed at ZnO(101Ì0). For both surfaces, adsorbed water molecules always bind to a single Zn ion, and those located in proximity of the substrate are mostly "H-down" oriented for ZnO(101Ì0) and "flat-lying", i.e., parallel to the surface, for ZnO(112Ì0). The time scales for proton-transfer (PT) reactions are quite similar at the two surfaces, with the average lifetime of adsorbed hydroxide ions being around 41 ± 3 ps until recombination. However, water exchange events, in which adsorbed water molecules leave the surface and enter the bulk liquid, happen more frequently at ZnO(112Ì0) than at ZnO(101Ì0). © 2018 American Chemical Society.

The temperature dependence of vibrational spectra can provide information about structural changes of a system and also serve as a probe to identify different vibrational mode couplings. Fully anharmonic temperature-dependent calculations of these quantities are challenging due to the cost associated with statistically converging trajectory-based methods, especially when accounting for nuclear quantum effects. Here, we train a high-dimensional neural network potential energy surface for the porphycene molecule based on data generated with DFT-B3LYP, including pairwise van der Waals interactions. In addition, we fit a kernel ridge regression model for the molecular dipole moment surface. The combination of this machinery with thermostatted path integral molecular dynamics (TRPMD) allows us to obtain well-converged, full-dimensional, fully-anharmonic vibrational spectra including nuclear quantum effects, without sacrificing the first-principles quality of the potential-energy surface or the dipole surface. Within this framework, we investigate the temperature and isotopologue dependence of the high-frequency vibrational fingerprints of porphycene. While classical-nuclei dynamics predicts a red shift of the vibrations encompassing the NH and CH stretches, TRPMD predicts a strong blue shift in the NH-stretch region and a smaller one in the CH-stretch region. We explain this behavior by analyzing the modulation of the effective potential with temperature, which arises from vibrational coupling between quasi-classical thermally activated modes and high-frequency quantized modes. © 2019 Royal Society of Chemistry. All rights reserved.

The excitation of electron-hole pairs in reactive scattering of molecules at metal surfaces often affects the physical and dynamical observables of interest, including the reaction probability. Here, we study the influence of electron-hole pair excitation on the dissociative chemisorption of N2 on Ru(0001) using the local density friction approximation method. The effect of surface atom motion has also been taken into account by a high-dimensional neural network potential. Our nonadiabatic molecular dynamics simulations with electronic friction show that the reaction of N2 is more strongly affected by the energy transfer to surface phonons than by the energy loss to electron-hole pairs. The discrepancy between the computed reaction probabilities and experimental results is within the experimental error both with and without friction; however, the incorporation of electron-hole pairs yields somewhat better agreement with experiments, especially at high collision energies. We also calculate the vibrational efficacy for the N2 + Ru(0001) reaction and demonstrate that the N2 reaction is more enhanced by exciting the molecular vibrations than by adding an equivalent amount of energy into translation. © 2018 American Chemical Society.

Machine learning of atomic-scale properties is revolutionizing molecular modeling, making it possible to evaluate inter-atomic potentials with first-principles accuracy, at a fraction of the costs. The accuracy, speed, and reliability of machine learning potentials, however, depend strongly on the way atomic configurations are represented, i.e., the choice of descriptors used as input for the machine learning method. The raw Cartesian coordinates are typically transformed in "fingerprints," or "symmetry functions," that are designed to encode, in addition to the structure, important properties of the potential energy surface like its invariances with respect to rotation, translation, and permutation of like atoms. Here we discuss automatic protocols to select a number of fingerprints out of a large pool of candidates, based on the correlations that are intrinsic to the training data. This procedure can greatly simplify the construction of neural network potentials that strike the best balance between accuracy and computational efficiency and has the potential to accelerate by orders of magnitude the evaluation of Gaussian approximation potentials based on the smooth overlap of atomic positions kernel. We present applications to the construction of neural network potentials for water and for an Al-Mg-Si alloy and to the prediction of the formation energies of small organic molecules using Gaussian process regression. © 2018 Author(s).

The accurate representation of multidimensional potential energy surfaces is a necessary requirement for realistic computer simulations of molecular systems. The continued increase in computer power accompanied by advances in correlated electronic structure methods nowadays enables routine calculations of accurate interaction energies for small systems, which can then be used as references for the development of analytical potential energy functions (PEFs) rigorously derived from many-body (MB) expansions. Building on the accuracy of the MB-pol many-body PEF, we investigate here the performance of permutationally invariant polynomials (PIPs), neural networks, and Gaussian approximation potentials (GAPs) in representing water two-body and three-body interaction energies, denoting the resulting potentials PIP-MB-pol, Behler-Parrinello neural network-MB-pol, and GAP-MB-pol, respectively. Our analysis shows that all three analytical representations exhibit similar levels of accuracy in reproducing both two-body and three-body reference data as well as interaction energies of small water clusters obtained from calculations carried out at the coupled cluster level of theory, the current gold standard for chemical accuracy. These results demonstrate the synergy between interatomic potentials formulated in terms of a many-body expansion, such as MB-pol, that are physically sound and transferable, and machine-learning techniques that provide a flexible framework to approximate the short-range interaction energy terms. © 2018 Author(s).

Using molecular dynamics simulations based on ab initio trained high-dimensional neural network potentials, we study the equation of state of liquid water at negative pressures. From density isobars computed for various pressures down to p = -230 MPa we determine the line of density maxima for two potentials based on the BLYP and the RPBE functionals, respectively. In both cases, dispersion corrections are included to account for non-local long-range correlations that give rise to van der Waals forces. We have followed the density maximum down to negative pressures close to the spinodal instability. For both functionals, the temperature of maximum density increases with decreasing pressure under moderate stretching, but changes slope at P ≈ -200 MPa and p ≈ -20 MPa for BLYP and RPBE, respectively. Our calculations confirm qualitatively the retracing shape of the line of density maxima found for empirical water models, indicating that the spinodal line maintains a positive slope even at strongly negative pressures. © 2018 IOP Publishing Ltd.

The design of accurate helium-solute interaction potentials for the simulation of chemically complex molecules solvated in superfluid helium has long been a cumbersome task due to the rather weak but strongly anisotropic nature of the interactions. We show that this challenge can be met by using a combination of an effective pair potential for the He-He interactions and a flexible high-dimensional neural network potential (NNP) for describing the complex interaction between helium and the solute in a pairwise additive manner. This approach yields an excellent agreement with a mean absolute deviation as small as 0.04 kJ mol-1 for the interaction energy between helium and both hydronium and Zundel cations compared with coupled cluster reference calculations with an energetically converged basis set. The construction and improvement of the potential can be performed in a highly automated way, which opens the door for applications to a variety of reactive molecules to study the effect of solvation on the solute as well as the solute-induced structuring of the solvent. Furthermore, we show that this NNP approach yields very convincing agreement with the coupled cluster reference for properties like many-body spatial and radial distribution functions. This holds for the microsolvation of the protonated water monomer and dimer by a few helium atoms up to their solvation in bulk helium as obtained from path integral simulations at about 1 K. © 2018 Author(s).

Unraveling the atomistic details of solid/liquid interfaces, e.g., by means of vibrational spectroscopy, is of vital importance in numerous applications, from electrochemistry to heterogeneous catalysis. Water-oxide interfaces represent a formidable challenge because a large variety of molecular and dissociated water species are present at the surface. Here, we present a comprehensive theoretical analysis of the anharmonic OH stretching vibrations at the water/ZnO(1010) interface as a prototypical case. Molecular dynamics simulations employing a reactive high-dimensional neural network potential based on density functional theory calculations have been used to sample the interfacial structures. In the second step, one-dimensional potential energy curves have been generated for a large number of configurations to solve the nuclear Schrödinger equation. We find that (i) the ZnO surface gives rise to OH frequency shifts up to a distance of about 4 Å from the surface; (ii) the spectrum contains a number of overlapping signals arising from different chemical species, with the frequencies decreasing in the order ν(adsorbed hydroxide) > ν(non-adsorbed water) > ν(surface hydroxide) > ν(adsorbed water); (iii) stretching frequencies are strongly influenced by the hydrogen bond pattern of these interfacial species. Finally, we have been able to identify substantial correlations between the stretching frequencies and hydrogen bond lengths for all species. © 2018 Author(s).

Nuclear quantum effects (NQEs) cause the nuclei of light elements like hydrogen to delocalize, affecting numerous properties of water and aqueous solutions, such as hydrogen-bonding and proton transfer barriers. Here, we address the prototypical case of aqueous NaOH solutions by investigating the effects of quantum nuclear fluctuations on radial distribution functions, hydrogen-bonding geometries, power spectra, proton transfer barriers, proton transfer rates, water self-exchange rates around the Na+ cations, and diffusion coefficients, for the full room-temperature solubility range. These properties were calculated from classical and ring-polymer molecular dynamics simulations employing a reactive high-dimensional neural network potential based on dispersion-corrected density functional theory reference calculations. We find that NQEs have a very small impact on the solvation structure around Na+, slightly strengthen the water-water and water-hydroxide hydrogen bonds, and lower the peak positions in the power spectra for the HOH bending and OH stretching modes by about 50 and 100 cm-1, respectively. Moreover, NQEs significantly lower the proton transfer barriers, thus increasing the proton transfer rates, resulting in an increase of the diffusion coefficient in particular of OH-, as well as a decrease of the mean residence time of molecules in the first hydration shell around Na+ at high NaOH concentrations. © 2018 American Chemical Society.

Ab initio molecular dynamics (AIMD) simulations enable the accurate description of reactive molecule-surface scattering especially if energy transfer involving surface phonons is important. However, presently, the computational expense of AIMD rules out its application to systems where reaction probabilities are smaller than about 1%. Here we show that this problem can be overcome by a high-dimensional neural network fit of the molecule-surface interaction potential, which also incorporates the dependence on phonons by taking into account all degrees of freedom of the surface explicitly. As shown for N2 + Ru(0001), which is a prototypical case for highly activated dissociative chemisorption, the method allows an accurate description of the coupling of molecular and surface atom motion and accurately accounts for vibrational properties of the employed slab model of Ru(0001). The neural network potential allows reaction probabilities as low as 10-5 to be computed, showing good agreement with experimental results. © 2017 American Chemical Society.

Nanowires made of chalcogenide alloys are of interest for use in phase-change nonvolatile memories. For this application, insights into the thermal properties of such nanowires and, in particular, into the crystallization kinetics at the atomic level are crucial. Toward this end, we have performed large-scale atomistic simulations of ultrathin nanowires (9 nm in diameter) of the prototypical phase-change compound GeTe. We made use of an interatomic potential generated by the neural network fitting of a large ab initio database to compute the thermal properties of the nanowires. By melting a portion of a nanowire, we investigated the velocity of recrystallization as a function of temperature. The simulations show that the melting temperature of the nanowire is about 100 K below the melting temperature of the bulk, which yields a reduction by about a factor of 2 of the maximum crystallization speed. Further, analysis of the structural properties of the amorphous phase of the nanowire suggests a possible origin of the reduction of the resistance drift observed experimentally in nanowires with respect to the bulk. © 2017 American Chemical Society.

Modern simulation techniques have reached a level of maturity which allows a wide range of problems in chemistry and materials science to be addressed. Unfortunately, the application of first principles methods with predictive power is still limited to rather small systems, and despite the rapid evolution of computer hardware no fundamental change in this situation can be expected. Consequently, the development of more efficient but equally reliable atomistic potentials to reach an atomic level understanding of complex systems has received considerable attention in recent years. A promising new development has been the introduction of machine learning (ML) methods to describe the atomic interactions. Once trained with electronic structure data, ML potentials can accelerate computer simulations by several orders of magnitude, while preserving quantum mechanical accuracy. This Review considers the methodology of an important class of ML potentials that employs artificial neural networks. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Machine learning has emerged as an invaluable tool in many research areas. In the present work, we harness this power to predict highly accurate molecular infrared spectra with unprecedented computational efficiency. To account for vibrational anharmonic and dynamical effects-typically neglected by conventional quantum chemistry approaches-we base our machine learning strategy on ab initio molecular dynamics simulations. While these simulations are usually extremely time consuming even for small molecules, we overcome these limitations by leveraging the power of a variety of machine learning techniques, not only accelerating simulations by several orders of magnitude, but also greatly extending the size of systems that can be treated. To this end, we develop a molecular dipole moment model based on environment dependent neural network charges and combine it with the neural network potential approach of Behler and Parrinello. Contrary to the prevalent big data philosophy, we are able to obtain very accurate machine learning models for the prediction of infrared spectra based on only a few hundreds of electronic structure reference points. This is made possible through the use of molecular forces during neural network potential training and the introduction of a fully automated sampling scheme. We demonstrate the power of our machine learning approach by applying it to model the infrared spectra of a methanol molecule, n-alkanes containing up to 200 atoms and the protonated alanine tripeptide, which at the same time represents the first application of machine learning techniques to simulate the dynamics of a peptide. In all of these case studies we find an excellent agreement between the infrared spectra predicted via machine learning models and the respective theoretical and experimental spectra. © 2017 The Royal Society of Chemistry.

The dissociation of water is an important step in many chemical processes at solid surfaces. In particular, water often spontaneously dissociates near metal oxide surfaces, resulting in a mixture of H2O, H+, and OH- at the interface. Ubiquitous proton-transfer (PT) reactions cause these species to dynamically interconvert, but the underlying mechanisms are poorly understood. Here, we develop and use a reactive high-dimensional neural-network potential based on density functional theory data to elucidate the structural and dynamical properties of the interfacial species at the liquid-water-metal-oxide interface, using the nonpolar ZnO(101̅0) surface as a prototypical case. Molecular dynamics simulations reveal that water dissociation and recombination proceed via two types of PT reactions: (i) to and from surface oxide and hydroxide anions (“surface-PT”) and (ii) to and from neighboring adsorbed hydroxide ions and water molecules (“adlayer-PT”). We find that the adlayer-PT rate is significantly higher than the surface-PT rate. Water dissociation is, for both types of PT, governed by a predominant presolvation mechanism, i.e., thermal fluctuations that cause the adsorbed water molecules to occasionally accept a hydrogen bond, resulting in a decreased PT barrier and an increased dissociation rate as compared to when no hydrogen bond is present. Consequently, we are able to show that hydrogen bond fluctuations govern PT events at the water-metal-oxide interface in a way similar to that in acidic and basic aqueous bulk solutions. © 2017 American Chemical Society.

Ligand exchange plays an important role for organic and inorganic chemical reactions. We demonstrate the existence of a novel water exchange mechanism, the "proton transfer pathway" (PTP), around Na+(aq) in basic (high pH) solution, using reactive molecular dynamics simulations employing a high-dimensional neural network potential. An aqua ligand in the first solvation (hydration) shell around a sodium ion is only very weakly acidic, but if a hydroxide ion is present in the second solvation shell, thermal fluctuations can cause the aqua ligand to transfer a proton to the neighboring OH-, resulting in a transient direct-contact ion pair, Na+-OH-, which is only weakly bound and easily dissociates. The extent to which water exchange events follow the PTP is pH-dependent: in dilute NaOH(aq) solutions, only very few exchanges occur, whereas in saturated NaOH(aq) solutions up to a third of water self-exchange events are induced by proton transfer. The principles and results outlined here are expected to be relevant for chemical synthesis involving bases and alkali metal cations. © 2017 American Chemical Society.

Solid-liquid interfaces play an important role in many fields like electrochemistry, corrosion, and heterogeneous catalysis. For understanding the related processes, detailed insights into the elementary steps at the atomic level are mandatory. Here we unravel the properties of prototypical surface-defects like adatoms and vacancies at a number of copper-water interfaces including the low-index Cu(111), Cu(100), and Cu(110), as well as the stepped Cu(211) and Cu(311) surfaces. Using a first-principles quality neural network potential constructed from density functional theory reference data in combination with molecular dynamics and metadynamics simulations, we investigate the defect diffusion mechanisms and the associated free energy barriers. Further, the solvent structure and the mobility of the interfacial water molecules close to the defects are analyzed and compared to the defect-free surfaces. We find that, like at the copper-vacuum interface, hopping mechanisms are preferred compared to exchange mechanisms, while the associated barriers for hopping are reduced in the presence of liquid water. The water structure close to adatoms and vacancies exhibits pronounced local features and differs strongly from the structure at the ideal low-index surfaces. Moreover, in particular at Cu(111) the adatoms are very mobile and hopping events along the surface are more frequent than the exchange of coordinating water molecules in their local environment. Consequently, adatom self-diffusion processes at Cu(111) involve entities of adatoms and their associated solvation shells. © 2017 American Chemical Society.

Sodium hydroxide, NaOH, is one of the most widely-used chemical reagents, but the structural properties of its aqueous solutions have only sparingly been characterized. Here, we automatically classify the cation coordination polyhedra obtained from molecular dynamics simulations. We find that, for example, with increasing concentration, octahedral coordination geometries become less favored, while the opposite is true for the trigonal prism. At high concentrations, the coordination polyhedra frequently deviate considerably from "ideal" polyhedra, because of an increased extent of interligand hydrogen-bonding, in which hydrogen bonds between two ligands, either OH2 or OH-, around the same Na+ are formed. In saturated solutions, with concentrations of about 19 mol L-1, ligands are frequently shared between multiple Na+ ions as a result of the deficiency of solvent molecules. This results in more complex structural patterns involving certain "characteristic" polyhedron connectivities, such as octahedra sharing ligands with capped trigonal prisms, and tetrahedra sharing ligands with trigonal bipyramids. The simulations were performed using a density-functional-theory-based reactive high-dimensional neural network potential, that was extensively validated against available neutron and X-ray diffraction data from the literature. © the Owner Societies 2017.

Density functional theory (DFT) is routinely used to calculate the adsorption energies of molecules on solid surfaces, which can be employed to derive surface phase diagrams. Such calculations become computationally expensive if the number of substrate atoms is large, which happens whenever the adsorbate coverage is small. Here, we propose an efficient method for calculating surface phase diagrams for redox-active adsorbates on semiconductors, that we apply to the important example of proton (H+) and hydride (H-) adsorbates on a ZnO surface. We identify the leading cause for the coverage dependence of the adsorption energies to be the filling and depletion of the disperse substrate conduction band. From only four DFT calculations, coupled with an analysis of the substrate electronic band structure and changes in the electrostatic potential within the substrate upon adsorption, we derive a phenomenological model that well describes the coverage-dependent adsorption energies. Moreover, our model allows us to extrapolate to the "infinite" supercell limit, where additional H adsorption leads to an arbitrarily small increase of the surface coverage. With this tool we are able to derive a surface phase diagram containing structures with extremely small H coverages (&lt;0.002 ML), that have so far been unattainable. We expect that such models can be applied to a wide range of semiconductor substrates and redox-active adsorbates. © 2017 the Owner Societies.

Phase change memories rest on the ability of some chalcogenide alloys to undergo a fast and reversible transition between the crystalline and amorphous phases upon Joule heating. The fast crystallization is due to a high nucleation rate and a large crystal growth velocity which are actually possible thanks to the fragility of the supercooled liquid that allows for the persistence of a high atomic mobility at high supercooling where the thermodynamical driving force for crystallization is also high. Since crystallization in the devices occurs by rapidly heating the amorphous phase, hysteretic effects might arise with a different diffusion coefficient and viscosity on heating than on cooling. In this work, we have quantified these hysteretic effects in the phase change compound GeTe by means of molecular dynamics simulations. The atomic mobility in the overheated amorphous phase is lower than in supercooled liquid at the same temperature and the viscosity is consequently higher. Still, the simulations of the overheated amorphous phase reveal a breakdown of the Stokes-Einstein relation between the diffusion coefficient and the viscosity, similarly to what we found previously in the supercooled liquid. Evidences are provided that the breakdown is due to the emergence of dynamical heterogeneities at high supercooling. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Many approaches, which have been developed to express the potential energy of large systems, exploit the locality of the atomic interactions. A prominent example is the fragmentation methods in which the quantum chemical calculations are carried out for overlapping small fragments of a given molecule that are then combined in a second step to yield the system's total energy. Here we compare the accuracy of the systematic molecular fragmentation approach with the performance of high-dimensional neural network (HDNN) potentials introduced by Behler and Parrinello. HDNN potentials are similar in spirit to the fragmentation approach in that the total energy is constructed as a sum of environment-dependent atomic energies, which are derived indirectly from electronic structure calculations. As a benchmark set, we use all-trans alkanes containing up to eleven carbon atoms at the coupled cluster level of theory. These molecules have been chosen because they allow to extrapolate reliable reference energies for very long chains, enabling an assessment of the energies obtained by both methods for alkanes including up to 10 000 carbon atoms. We find that both methods predict high-quality energies with the HDNN potentials yielding smaller errors with respect to the coupled cluster reference. © 2016 Author(s).

Proton transfer processes play an important role in many fields of chemistry. In dilute basic aqueous solutions, proton transfer from water molecules to hydroxide ions is aided by "presolvation", i.e., thermal fluctuations that modify the hydrogen-bonding environment around the proton-receiving OH- ion to become more similar to that of a neutral H2O molecule. In particular at high concentrations, however, the underlying mechanisms and especially the role of the counterions are little understood. As a prototypical case, we investigate aqueous NaOH solutions using molecular dynamics simulations employing a reactive high-dimensional neural-network potential constructed from density functional theory reference data. We find that with increasing concentration the predominant proton transfer mechanism changes from being "acceptor-driven", i.e., governed by the presolvation of OH-, to "donor-driven", i.e., governed by the presolvation of H2O, and back to acceptor-driven near the room-temperature solubility limit of 19 mol/L, which corresponds to an extremely solvent-deficient system containing only about one H2O molecule per ion. Specifically, we identify concentration ranges where the proton transfer rate is mostly affected by OH- losing an accepted hydrogen bond, OH- forming a donated hydrogen bond, H2O forming an accepted hydrogen bond, or H2O losing a coordinated Na+. Presolvation also manifests itself in the shortening of the Na+-OH2 distances, in that the Na+ "pushes" one of the H2O protons away. © 2016 American Chemical Society.

There is a misprint in the references of the paper.1 Reference 72 should be as follows: J. S. Elias, N. Artrith, M. Bugnet, L. Giordano, G. A. Botton, A. M. Kolpak, and Y. Shao-Horn, ACS Catal. 6, 1675 (2016)2. © 2016 Author(s).

The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the system. Many approaches have been suggested to reduce the required number of replicas. Among these, high-order factorizations of the Boltzmann operator are particularly attractive for high-precision and low-temperature scenarios. Unfortunately, to date, several technical challenges have prevented a widespread use of these approaches to study the nuclear quantum effects in condensed-phase systems. Here we introduce an inexpensive molecular dynamics scheme that overcomes these limitations, thus making it possible to exploit the improved convergence of high-order path integrals without having to sacrifice the stability, convenience, and flexibility of conventional second-order techniques. The capabilities of the method are demonstrated by simulations of liquid water and ice, as described by a neural-network potential fitted to the dispersion-corrected hybrid density functional theory calculations. © 2016 Author(s).

Whereas the interactions between water molecules are dominated by strongly directional hydrogen bonds (HBs), it was recently proposed that relatively weak, isotropic van der Waals (vdW) forces are essential for understanding the properties of liquid water and ice. This insight was derived from ab initio computer simulations, which provide an unbiased description of water at the atomic level and yield information on the underlying molecular forces. However, the high computational cost of such simulations prevents the systematic investigation of the influence of vdW forces on the thermodynamic anomalies of water. Here, we develop efficient ab initio-quality neural network potentials and use them to demonstrate that vdW interactions are crucial for the formation of water's density maximum and its negative volume of melting. Both phenomena can be explained by the flexibility of the HB network, which is the result of a delicate balance of weak vdW forces, causing, e.g., a pronounced expansion of the second solvation shell upon cooling that induces the density maximum.

Full-dimensional coupled-channel quantum scattering and quasi-classical trajectory calculations have been carried out and analyzed to unravel the mode specific dynamics in the H2 + SH → H + H2S reaction employing two different accurate neural network representations of an ab initio global potential energy surface at the coupled cluster level. Strong mode selectivity was found and partially rationalized by the sudden vector projection model. Specifically, the vibrational excitation of H2 remarkably enhances the reactivity while its rotational excitation only slightly promotes the reaction. On the other hand, the reactant SH acts as a good spectator, whose vibrational and rotational excitations have a negligible effect on the reaction. © the Owner Societies 2016.

Solid-liquid interfaces have received considerable attention in recent years due to their central role in many technologically relevant fields like electrochemistry, heterogeneous catalysis and corrosion. As the chemical processes in these examples take place primarily at the interface, understanding the structural and dynamical properties of the interfacial water molecules is of vital importance. Here, we use a first-principles quality high-dimensional neural network potential built from dispersion-corrected density functional theory data in molecular dynamics simulations to investigate water-copper interfaces as a prototypical case. After performing convergence tests concerning the required supercell size and water film diameter, we investigate numerous properties of the interfacial water molecules at the low-index copper (111), (100) and (110) surfaces. These include density profiles, hydrogen bond properties, lateral mean squared displacements and residence times of the water molecules at the surface. We find that in general the copper-water interaction is rather weak with the strongest interactions observed at the Cu(110) surface, followed by the Cu(100) and Cu(111) surfaces. The distribution of the water molecules in the first hydration layer exhibits a double peak structure. In all cases, the molecules closest to the surface are predominantly allocated on top of the metal sites and are aligned nearly parallel with the oxygen pointing slightly to the surface. The more distant molecules in the first hydration layer at the Cu(111) and Cu(100) surfaces are mainly found in between the top sites, whereas at the Cu(110) surface most of these water molecules are found above the trenches of the close packed atom rows at the surface. © 2016 the Owner Societies.

One of the most prominent consequences of the quantum nature of light atomic nuclei is that their kinetic energy does not follow a Maxwell-Boltzmann distribution. Deep inelastic neutron scattering (DINS) experiments can measure this effect. Thus, the nuclear quantum kinetic energy can be probed directly in both ordered and disordered samples. However, the relation between the quantum kinetic energy and the atomic environment is a very indirect one, and cross-validation with theoretical modeling is therefore urgently needed. Here, we use state of the art path integral molecular dynamics techniques to compute the kinetic energy of hydrogen and oxygen nuclei in liquid, solid, and gas-phase water close to the triple point, comparing three different interatomic potentials and validating our results against equilibrium isotope fractionation measurements. We will then show how accurate simulations can draw a link between extremely precise fractionation experiments and DINS, therefore establishing a reliable benchmark for future measurements and providing key insights to increase further the accuracy of interatomic potentials for water. © 2016 American Chemical Society.

Nowadays, computer simulations have become a standard tool in essentially all fields of chemistry, condensed matter physics, and materials science. In order to keep up with state-of-the-art experiments and the ever growing complexity of the investigated problems, there is a constantly increasing need for simulations of more realistic, i.e., larger, model systems with improved accuracy. In many cases, the availability of sufficiently efficient interatomic potentials providing reliable energies and forces has become a serious bottleneck for performing these simulations. To address this problem, currently a paradigm change is taking place in the development of interatomic potentials. Since the early days of computer simulations simplified potentials have been derived using physical approximations whenever the direct application of electronic structure methods has been too demanding. Recent advances in machine learning (ML) now offer an alternative approach for the representation of potential-energy surfaces by fitting large data sets from electronic structure calculations. In this perspective, the central ideas underlying these ML potentials, solved problems and remaining challenges are reviewed along with a discussion of their current applicability and limitations. © 2016 Author(s).

A lot of progress has been made in recent years in the development of atomistic potentials using machine learning (ML) techniques. In contrast to most conventional potentials, which are based on physical approximations and simplifications to derive an analytic functional relation between the atomic configuration and the potential-energy, ML potentials rely on simple but very flexible mathematical terms without a direct physical meaning. Instead, in case of ML potentials the topology of the potential-energy surface is "learned" by adjusting a number of parameters with the aim to reproduce a set of reference electronic structure data as accurately as possible. Due to this bias-free construction, they are applicable to a wide range of systems without changes in their functional form, and a very high accuracy close to the underlying first-principles data can be obtained. Neural network potentials (NNPs), which have first been proposed about two decades ago, are an important class of ML potentials. Although the first NNPs have been restricted to small molecules with only a few degrees of freedom, they are now applicable to high-dimensional systems containing thousands of atoms, which enables addressing a variety of problems in chemistry, physics, and materials science. In this tutorial review, the basic ideas of NNPs are presented with a special focus on developing NNPs for high-dimensional condensed systems. A recipe for the construction of these potentials is given and remaining limitations of the method are discussed. © 2015 Wiley Periodicals, Inc.

Phonon dispersion relations and electron-phonon coupling of hole-doped trigonal GeTe have been computed by density functional perturbation theory. This compound is a prototypical phase change material of interest for applications in phase change non-volatile memories. The calculations allowed us to estimate the electron-phonon contribution to the thermal boundary resistance at the interface between the crystalline and amorphous phases present in the device. The lattice contribution to the thermal boundary resistance has been computed by non-equilibrium molecular dynamics simulations with an interatomic potential based on a neural network scheme. We find that the electron-phonon term contributes to the thermal boundary resistance to an extent which is strongly dependent on the concentration and mobility of the holes. Further, for measured values of the holes concentration and electrical conductivity, the electron-phonon term is larger than the contribution from the lattice. It is also shown that the presence of Ge vacancies, responsible for the p-type degenerate character of the semiconductor, strongly affects the lattice thermal conductivity of the crystal. © 2015 AIP Publishing LLC.

Phase change materials are the active compounds in optical disks and in nonvolatile phase change memory devices. These applications rest on the fast and reversible switching between the amorphous and the crystalline phases, which takes place in the nano domain in both the time and the length scales. The fast crystallization is a key feature for the applications of phase change materials. In this work, we have investigated by means of large scale molecular dynamics simulations the crystal growth of the prototypical phase change compound GeTe at the interface between the crystalline and the supercooled liquid reached in the device upon heating the amorphous phase. A neural network interatomic potential, markedly faster with respect to first-principles methods, allowed us to consider high-symmetry crystalline surfaces as well as polycrystalline models that are very close to the actual geometry of the memory devices. We have found that the crystal growth from the interface is dominant at high temperatures while it is competing with homogeneous crystallization in the melt at lower temperatures. The crystal growth velocity markedly depends on the crystallographic plane exposed at the interface, the (100) surface being kinetically dominant with respect to the (111) surface. Polycrystalline interfaces, representative of realistic conditions in phase change memory devices, grow at significantly slower pace because of the presence of grain boundaries. © 2015 American Chemical Society.

Aging is a common feature of the glassy state. In the case of phase-change chalcogenide alloys the aging of the amorphous state is responsible for an increase of the electrical resistance with time. This phenomenon called drift is detrimental in the application of these materials in phase-change nonvolatile memories, which are emerging as promising candidates for storage class memories. By means of combined molecular dynamics and electronic structure calculations based on density functional theory, we have unraveled the atomistic origin of the resistance drift in the prototypical phase-change compound GeTe. The drift results from a widening of the band gap and a reduction of Urbach tails due to structural relaxations leading to the removal of chains of Ge-Ge homopolar bonds. The same structural features are actually responsible for the high mobility above the glass transition which boosts the crystallization speed exploited in the device. © 2015 American Physical Society.

An emerging route to nanostructured hybrid organic-metal interfaces with tailored properties is their manipulation by nanomechanical forces as exerted by STM and AFM tips. Yet, despite impressive experimental progress, close to nothing is known about the underlying atomistic mechanisms of such nanomechanical techniques, thus hindering predictive, rational approaches. Here, we identify "surface peeling" as an important new mechanism for the modification of surfaces. Using density-functional calculations of thiolate self-assembled monolayers at gold and silver, we find that this phenomenon is very sensitive to the force vector, resulting in a high anisotropy in the systems' response that can be exploited for the selective creation of novel hybrid surfaces. © 2015 American Physical Society. © 2015 American Physical Society.

Investigating the properties of protons in water is essential for understanding many chemical processes in aqueous solution. While important insights can in principle be gained by accurate and well-established methods like ab initio molecular dynamics simulations, the computational costs of these techniques are often very high. This prevents studying large systems on long time scales, which is severely limiting the applicability of computer simulations to address a wide range of interesting phenomena. Developing more efficient potentials enabling the simulation of water including dissociation and recombination events with first-principles accuracy is a very challenging task. In particular protonated water clusters have become important model systems to assess the reliability of such potentials, as the presence of the excess proton induces substantial changes in the local hydrogen bond patterns and many energetically similar isomers exist, which are extremely difficult to describe. In recent years it has been demonstrated for a number of systems including neutral water clusters of varying size that neural networks (NNs) can be used to construct potentials with close to first-principles accuracy. Based on density-functional theory (DFT) calculations, here we present a reactive full-dimensional NN potential for protonated water clusters up to the octamer. A detailed investigation of this potential shows that the energetic, structural, and vibrational properties are in excellent agreement with DFT results making the NN approach a very promising candidate for developing a high-quality potential for water. This finding is further supported by first preliminary but very encouraging NN-based simulations of the bulk liquid. This journal is © the Owner Societies 2015.

A contending technology for nonvolatile memories of the next generation is based on a remarkable property of chalcogenide alloys known as phase change materials, namely their ability to undergo a fast and reversible transition between the amorphous and crystalline phases upon heating. The fast crystallization has been ascribed to the persistence of a high atomic mobility in the supercooled liquid phase, down to temperatures close to the glass transition. In this work we unravel the atomistic, structural origin of this feature in the supercooled liquid state of GeTe, a prototypical phase change compound, by means of molecular dynamic simulations. To this end, we employed an interatomic potential based on a neural network framework, which allows simulating thousands of atoms for tens of ns by keeping an accuracy close to that of the underlying first-principles framework. Our findings demonstrate that the high atomic mobility is related to the presence of clusters of slow and fast moving atoms. The latter contain a large fraction of chains of homopolar Ge-Ge bonds, which at low temperatures have a tendency to move by discontinuous cage-jump rearrangements. This structural fingerprint of dynamical heterogeneity provides an explanation of the breakdown of the Stokes-Einstein relation in GeTe, which is the ultimate origin of the fast crystallization of phase change materials exploited in the devices. © 2014 American Chemical Society.

The computer simulation of condensed systems is a challenging task. While electronic structure methods like density-functional theory (DFT) usually provide a good compromise between accuracy and efficiency, they are computationally very demanding and thus applicable only to systems containing up to a few hundred atoms. Unfortunately, many interesting problems require simulations to be performed on much larger systems involving thousands of atoms or more. Consequently, more efficient methods are urgently needed, and a lot of effort has been spent on the development of a large variety of potentials enabling simulations with significantly extended time and length scales. Most commonly, these potentials are based on physically motivated functional forms and thus perform very well for the applications they have been designed for. On the other hand, they are often highly system-specific and thus cannot easily be transferred from one system to another. Moreover, their numerical accuracy is restricted by the intrinsic limitations of the imposed functional forms. In recent years, several novel types of potentials have emerged, which are not based on physical considerations. Instead, they aim to reproduce a set of reference electronic structure data as accurately as possible by using very general and flexible functional forms. In this review we will survey a number of these methods. While they differ in the choice of the employed mathematical functions, they all have in common that they provide high-quality potential-energy surfaces, while the efficiency is comparable to conventional empirical potentials. It has been demonstrated that in many cases these potentials now offer a very interesting new approach to study complex systems with hitherto unreached accuracy. © EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2014.

The development of interatomic potentials employing artificial neural networks has seen tremendous progress in recent years. While until recently the applicability of neural network potentials (NNPs) has been restricted to low-dimensional systems, this limitation has now been overcome and high-dimensional NNPs can be used in large-scale molecular dynamics simulations of thousands of atoms. NNPs are constructed by adjusting a set of parameters using data from electronic structure calculations, and in many cases energies and forces can be obtained with very high accuracy. Therefore, NNP-based simulation results are often very close to those gained by a direct application of first-principles methods. In this review, the basic methodology of high-dimensional NNPs will be presented with a special focus on the scope and the remaining limitations of this approach. The development of NNPs requires substantial computational effort as typically thousands of reference calculations are required. Still, if the problem to be studied involves very large systems or long simulation times this overhead is regained quickly. Further, the method is still limited to systems containing about three or four chemical elements due to the rapidly increasing complexity of the configuration space, although many atoms of each species can be present. Due to the ability of NNPs to describe even extremely complex atomic configurations with excellent accuracy irrespective of the nature of the atomic interactions, they represent a general and therefore widely applicable technique, e.g. for addressing problems in materials science, for investigating properties of interfaces, and for studying solvation processes. © 2014 IOP Publishing Ltd.

The fundamental importance of water for many chemical processes has motivated the development of countless efficient but approximate water potentials for large-scale molecular dynamics simulations, from simple empirical force fields to very sophisticated flexible water models. Accurate and generally applicable water potentials should fulfill a number of requirements. They should have a quality close to quantum chemical methods, they should explicitly depend on all degrees of freedom including all relevant many-body interactions, and they should be able to describe molecular dissociation and recombination. In this work, we present a high-dimensional neural network (NN) potential for water clusters based on density-functional theory (DFT) calculations, which is constructed using clusters containing up to 10 monomers and is in principle able to meet all these requirements. We investigate the reliability of specific parametrizations employing two frequently used generalized gradient approximation (GGA) exchange-correlation functionals, PBE and RPBE, as reference methods. We find that the binding energy errors of the NN potentials with respect to DFT are significantly lower than the typical uncertainties of DFT calculations arising from the choice of the exchange-correlation functional. Further, we examine the role of van der Waals interactions, which are not properly described by GGA functionals. Specifically, we incorporate the D3 scheme suggested by Grimme (J. Chem. Phys. 2010, 132, 154104) in our potentials and demonstrate that it can be applied to GGA-based NN potentials in the same way as to DFT calculations without modification. Our results show that the description of small water clusters provided by the RPBE functional is significantly improved if van der Waals interactions are included, while in case of the PBE functional, which is well-known to yield stronger binding than RPBE, van der Waals corrections lead to overestimated binding energies. © 2013 American Chemical Society.

Water clusters have attracted a lot of attention as prototype systems to study hydrogen bonded molecular aggregates but also to gain deeper insights into the properties of liquid water, the solvent of life. All these studies depend on an accurate description of the atomic interactions and countless potentials have been proposed in the literature in the past decades to represent the potential-energy surface (PES) of water. Many of these potentials employ drastic approximations like rigid water monomers and fixed point charges, while on the other hand also several attempts have been made to derive very accurate PESs by fitting data obtained in high-level electronic structure calculations. In recent years artificial neural networks (NNs) have been established as a powerful tool to construct high-dimensional PESs of a variety of systems, but to date no full-dimensional NN PES for water has been reported. Here, we present NN potentials for water clusters containing two to six water molecules trained to density functional theory (DFT) data employing two different exchange-correlation functionals, PBE and RPBE. In contrast to other potentials fitted to first principles data, these NN potentials are not based on a truncated many-body expansion of the energy but consider the interactions between all water molecules explicitly. For both functionals an excellent agreement with the underlying DFT calculations has been found with binding energy errors of only about 1%.© by Oldenbourg Wissenschaftsverlag, München.

Density-functional theory calculations have been carried out to study the adsorption of methanethiolate and atomic sulfur as a nonmolecular reference at the Cu(111) surface. A large number of surface models have been investigated considering a variety of binding sites and coverages at the ideal and reconstructed surface. For methanethiolate, we find that the proposed [5013] supercell commonly used to approximate the experimentally observed noncommensurate pseudo(100) reconstruction yields the lowest surface energy, but several similar local minima exist differing in the positions of the copper atoms. None of these structures show the regular nearly square coordination of the thiolate species observed in scanning tunneling microscopy (STM). Modifying the chemical composition of the relaxed layer, e.g., by adding another copper atom, yields structures of comparable stability. It is thus very likely that the proposed supercell is not a good approximation to the true pseudo(100) phase and that larger unit cells are needed to allow for a realistic relaxation of the reconstructed layer. For atomic sulfur, it is well established that the most stable phase at Cu(111) is a (√7 × √7)R19.1 reconstruction. Its structure, however, has been discussed controversially in the literature for many years. While there is a consensus that the unit cell contains three sulfur atoms, there are still several competing models differing in the number of copper adatoms in the reconstructed layer. We find that three models have a very similar stability, and a three-copper adatom model is only marginally preferred. These results will be of importance for many fields from heterogeneous catalysis to covalent mechanochemistry and molecular nanomechanics. © 2012 American Chemical Society.

Values of the melting temperature at normal pressure $T_m$, of the slope of the melting line, and of the activation energies for the diffusion coefficient and viscosity are corrected. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Phase change materials are of great interest as active layers in rewritable optical disks and novel electronic nonvolatile memories. These applications rest on a fast and reversible transformation between the amorphous and crystalline phases upon heating, taking place on the nanosecond time scale. In this work, we investigate the microscopic origin of the fast crystallization process by means of large-scale molecular dynamics simulations of the phase change compound GeTe. To this end, we use an interatomic potential generated from a Neural Network fitting of a large database of ab initio energies. We demonstrate that in the temperature range of the programming protocols of the electronic memories (500-700 K), nucleation of the crystal in the supercooled liquid is not rate-limiting. In this temperature range, the growth of supercritical nuclei is very fast because of a large atomic mobility, which is, in turn, the consequence of the high fragility of the supercooled liquid and the associated breakdown of the Stokes-Einstein relation between viscosity and diffusivity. © 2013 American Chemical Society.

Density-functional theory calculations of propanethiolate self-assembled monolayers at the Au(111) surface have been carried out to study the response properties of organic adlayers at metal surfaces to externally applied mechanical forces. Force maps are introduced in order to systematically quantify the system's nanomechanical response to both the magnitude and direction of the external forces applied here in an isotensional setup. Depending on the direction and magnitude of the forces we find that there are two dominant phenomena for the most stable c(4 × 2) structure containing two propanethiolate gold adatom adsorbate complexes C3S-Au ad-SC3 per unit cell: a sliding of the complete topmost metal layer including adsorbates or the detachment of the thiolate-adatom complexes only. Investigations of the atomistic mechanisms show that the initial configuration of the bulky C3S-Auad-SC3 complexes is responsible for sizable variations in the effective barrier heights for different force directions. A lateral force along the [110] direction with magnitude between 0.6 nN and 1.4 nN induces a plane sliding of the complete outermost Au(111) layer. In contrast, a force normal to the surface induces a detachment of the thiolate complexes if the force exceeds a threshold value of about 1.4 nN, which is in excellent agreement with experimental results. The use of tilted pulling directions, i.e., applying forces with nonzero normal and lateral components, facilitates the removal of the adsorbate complexes even at notably smaller force magnitudes. This mechanochemical promotion is traced back to a destabilization of the molecule-metal interface as a result of a (slight) lateral displacement to energetically unfavorable sites, thereby weakening chemical bonding of adsorbate complexes to the substrate. These observations are vastly different from what has been found for single molecule pulling normal to the surface, where nanowire formation is typically observed. Overall, a rich spectrum of nanomechanical response scenarios is revealed by these explorative calculations, which is expected to significantly grow upon varying further parameters such as the chain length, surface plane, and substrate metal. © 2013 The Owner Societies.

The development of reliable interatomic potentials for large-scale molecular dynamics (MD) simulations of chemical processes at surfaces and interfaces is a formidable challenge because a wide range of atomic environments and very different types of bonding can be present. In recent years interatomic potentials based on artificial neural networks (NNs) have emerged offering an unbiased approach to the construction of potential energy surfaces (PESs) for systems that are difficult to describe by conventional potentials. Here, we review the basic properties of NN potentials and describe their construction for materials like metals and oxides. The accuracy and efficiency are demonstrated using copper and zinc oxide as benchmark systems. First results for a potential of the combined ternary CuZnO system aiming at the description of oxide-supported copper clusters are reported. Model of a copper cluster at the ZnO($10\overline {1} 0$) surface. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Understanding the unique properties of water still represents a significant challenge for theory and experiment. Computer simulations by molecular dynamics require a reliable description of the atomic interactions, and in recent decades countless water potentials have been reported in the literature. Still, most of these potentials contain significant approximations, for instance a frozen internal structure of the individual water monomers. Artificial neural networks (NNs) offer a promising way for the construction of very accurate potential-energy surfaces taking all degrees of freedom explicitly into account. These potentials are based on electronic structure calculations for representative configurations, which are then interpolated to a continuous energy surface that can be evaluated many orders of magnitude faster. We present a full-dimensional NN potential for the water dimer as a first step towards the construction of a NN potential for liquid water. This many-body potential is based on environment-dependent atomic energy contributions, and long-range electrostatic interactions are incorporated employing environment-dependent atomic charges. We show that the potential and derived properties like vibrational frequencies are in excellent agreement with the underlying reference density-functional theory calculations. © 2012 American Institute of Physics.

An accurate determination of the potential energy is the crucial step in computer simulations of chemical processes, but using electronic structure methods on-the-fly in molecular dynamics (MD) is computationally too demanding for many systems. Constructing more efficient interatomic potentials becomes intricate with increasing dimensionality of the potential-energy surface (PES), and for numerous systems the accuracy that can be achieved is still not satisfying and far from the reliability of first-principles calculations. Feed-forward neural networks (NNs) have a very flexible functional form, and in recent years they have been shown to be an accurate tool to construct efficient PESs. High-dimensional NN potentials based on environment-dependent atomic energy contributions have been presented for a number of materials. Still, these potentials may be improved by a more detailed structural description, e.g., in form of atom pairs, which directly reflect the atomic interactions and take the chemical environment into account. We present an implementation of an NN method based on atom pairs, and its accuracy and performance are compared to the atom-based NN approach using two very different systems, the methanol molecule and metallic copper. We find that both types of NN potentials provide an excellent description of both PESs, with the pair-based method yielding a slightly higher accuracy making it a competitive alternative for addressing complex systems in MD simulations. © 2012 American Institute of Physics.

The atomic environments at metal surfaces differ strongly from the bulk, and, in particular, in case of reconstructions or imperfections at "real surfaces," very complicated atomic configurations can be present. This structural complexity poses a significant challenge for the development of accurate interatomic potentials suitable for large-scale molecular dynamics simulations. In recent years, artificial neural networks (NN) have become a promising new method for the construction of potential-energy surfaces for difficult systems. In the present work, we explore the applicability of such high-dimensional NN potentials to metal surfaces using copper as a benchmark system. A detailed analysis of the properties of bulk copper and of a wide range of surface structures shows that NN potentials can provide results of almost density functional theory (DFT) quality at a small fraction of the computational costs. © 2012 American Physical Society.

X-ray diffraction experiments have shown that sodium exhibits a dramatic pressure-induced drop in melting temperature, which extends from 1000?K at ∼30GPa to as low as room temperature at ∼120GPa. Despite significant theoretical effort to understand the anomalous melting, its origins are still debated. In this work, we reconstruct the sodium phase diagram by using an ab?initio quality neural-network potential. Furthermore, we demonstrate that the reentrant behavior results from the screening of interionic interactions by conduction electrons, which at high pressure induces a softening in the short-range repulsion. © 2012 American Physical Society.

GeTe is a prototypical phase change material of high interest for applications in optical and electronic nonvolatile memories. We present an interatomic potential for the bulk phases of GeTe, which is created using a neural network (NN) representation of the potential-energy surface obtained from reference calculations based on density functional theory. It is demonstrated that the NN potential provides a close to ab initio quality description of a number of properties of liquid, crystalline, and amorphous GeTe. The availability of a reliable classical potential allows addressing a number of issues of interest for the technological applications of phase change materials, which are presently beyond the capability of first-principles molecular dynamics simulations. © 2012 American Physical Society.

We computed the thermal conductivity (κ) of amorphous GeTe by means of classical molecular dynamics and lattice dynamics simulations. GeTe is a phase change material of interest for applications in nonvolatile memories. An interatomic potential with close-to-ab initio accuracy was used as generated by fitting a huge ab initio database with a neural network method. It turns out that the majority of heat carriers are nonpropagating vibrations (diffusons), the small percentage of propagating modes giving a negligible contribution to the total value of κ. This result is in contrast with the properties of other amorphous semiconductors such as Si for which nonpropagating and propagating vibrations account for about one half of the value of κ each. This outcome suggests that the value of κ measured for the bulk amorphous phase can be used to model the thermal transport of GeTe and possibly of other materials in the same class also in nanoscaled memory devices. Actually, the contribution from propagating modes, which may endure ballistic transport at the scale of 10-20 nm, is negligible. © 2012 American Physical Society.

Neural networks offer an unbiased and numerically very accurate approach to represent high-dimensional ab initio potential-energy surfaces. Once constructed, neural network potentials can provide the energies and forces many orders of magnitude faster than electronic structure calculations, and thus enable molecular dynamics simulations of large systems. However, Cartesian coordinates are not a good choice to represent the atomic positions, and a transformation to symmetry functions is required. Using simple benchmark systems, the properties of several types of symmetry functions suitable for the construction of high-dimensional neural network potential-energy surfaces are discussed in detail. The symmetry functions are general and can be applied to all types of systems such as molecules, crystalline and amorphous solids, and liquids. © 2011 American Institute of Physics.

Artificial neural networks represent an accurate and efficient tool to construct high-dimensional potential-energy surfaces based on first-principles data. However, so far the main drawback of this method has been the limitation to a single atomic species. We present a generalization to compounds of arbitrary chemical composition, which now enables simulations of a wide range of systems containing large numbers of atoms. The required incorporation of long-range interactions is achieved by combining the numerical accuracy of neural networks with an electrostatic term based on environment-dependent charges. Using zinc oxide as a benchmark system we show that the neural network potential-energy surface is in excellent agreement with density-functional theory reference calculations, while the evaluation is many orders of magnitude faster. © 2011 American Physical Society.

The accuracy of the results obtained in molecular dynamics or Monte Carlo simulations crucially depends on a reliable description of the atomic interactions. A large variety of efficient potentials has been proposed in the literature, but often the optimum functional form is difficult to find and strongly depends on the particular system. In recent years, artificial neural networks (NN) have become a promising new method to construct potentials for a wide range of systems. They offer a number of advantages: they are very general and applicable to systems as different as small molecules, semiconductors and metals; they are numerically very accurate and fast to evaluate; and they can be constructed using any electronic structure method. Significant progress has been made in recent years and a number of successful applications demonstrate the capabilities of neural network potentials. In this Perspective, the current status of NN potentials is reviewed, and their advantages and limitations are discussed. © the Owner Societies 2011.

Graphite and diamond have comparable free energies, yet forming diamond from graphite in the absence of a catalyst requires pressures that are significantly higher than those at equilibrium coexistence. At lower temperatures, the formation of the metastable hexagonal polymorph of diamond is favoured instead of the more stable cubic diamond. These phenomena cannot be explained by the concerted mechanism suggested in previous theoretical studies. Using an ab initio quality neural-network potential, we carried out a large-scale study of the graphite-to-diamond transition assuming that it occurs through nucleation. The nucleation mechanism accounts for the observed phenomenology and reveals its microscopic origins. We demonstrate that the large lattice distortions that accompany the formation of diamond nuclei inhibit the phase transition at low pressure, and direct it towards the hexagonal diamond phase at higher pressure. The proposed nucleation mechanism should improve our understanding of structural transformations in a wide range of carbon-based materials. © 2011 Macmillan Publishers Limited. All rights reserved.

An interatomic potential for high-pressure high-temperature (HPHT) crystalline and liquid phases of sodium is created using a neural-network (NN) representation of the ab initio potential-energy surface. It is demonstrated that the NN potential provides an ab initio quality description of multiple properties of liquid sodium and bcc, fcc, and cI16 crystal phases in the P-T region up to 120 GPa and 1200 K. The unique combination of computational efficiency of the NN potential and its ability to reproduce quantitatively experimental properties of sodium in the wide P-T range enables molecular-dynamics simulations of physicochemical processes in HPHT sodium of unprecedented quality. © 2010 The American Physical Society.

An interatomic potential for the diamond and graphite phases of carbon has been created using a neural-network (NN) representation of the ab initio potential energy surface. The NN potential combines the accuracy of a first-principles description of both phases with the efficiency of empirical force fields and allows one to perform a molecular-dynamics study, of ab initio quality, of the thermodynamics of graphite-diamond coexistence. Good agreement between the experimental and calculated coexistence curves is achieved if nuclear quantum effects are included in the simulation. © 2010 The American Physical Society.

Recently, spin selection rules have been invoked to explain the discrepancy between measured and calculated adsorption probabilities of molecular oxygen reacting with Al(111). In this work, we inspect the impact of nonadiabatic spin transitions on the dynamics of this system from first principles. For this purpose, the motion on two distinct potential-energy surfaces associated to different spin configurations and possible transitions between them are inspected by means of the fewest-switches algorithm. Within this framework, we especially focus on the influence of such spin transitions on observables accessible to molecular-beam experiments. On this basis, we suggest experimental setups that can validate the occurrence of such transitions and discuss their feasibility. © 2010 The American Physical Society.