Search

Machine learning potentials (MLPs) have revolutionized the field of atomistic simulations by describing atomic interactions with the accuracy of electronic structure methods at a small fraction of the cost. Most current MLPs construct the energy of a system as a sum of atomic energies, which depend on information about the atomic environments provided in the form of predefined or learnable feature vectors. If, in addition, nonlocal phenomena like long-range charge transfer are important, fourth-generation MLPs need to be used, which include a charge equilibration (Qeq) step to take the global structure of the system into account. This Qeq can significantly increase the computational cost and thus can become a computational bottleneck for large systems. In this Article, we present a highly efficient formulation of Qeq that does not require the explicit computation of the Coulomb matrix elements, resulting in a quasi-linear scaling method. Moreover, our approach also allows for the efficient calculation of energy derivatives, which explicitly consider the global structure-dependence of the atomic charges as obtained from Qeq. Due to its generality, the method is not restricted to MLPs and can also be applied within a variety of other force fields.

We present an algorithm to find first order saddle points on the potential energy surface (PES). The algorithm is formulated as a constrained optimization problem that involves two sets of atomic coordinates (images), a time-varying distance constraint and a constraint on the energy difference. Both images start in different valleys of the PES and are pulled toward each other by gradually reducing the distance. The search space is restricted to the pairs of configurations that share the same potential energy. By minimizing the energy while the distance shrinks, a minimum of the constrained search space is tracked. In simple cases, the two images are confined to their respective sides of the barrier until they finally converge near the saddle point. If one image accidentally crosses the barrier, the path is split at suitable locations and the algorithm is repeated recursively. The optimization is implemented as a combination of a quasi-Newton optimization and a linear constraint. The method was tested on a set of Lennard-Jones-38 cluster transitions and a set of 121 molecular reactions using density functional theory calculations. The efficiency in terms of energy and force evaluation is better than with competing methods as long as they do not switch to single-ended methods. The construction of a continuous search path with small steps and the ability to focus on arbitrary subsegments of the path provide an additional value in terms of robustness and flexibility., (© 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).)

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.

In this work we study isomers of several representative small clusters to find principles for their stability. Our conclusions about the principles underlying the structure of clusters are based on a huge database of 44 000 isomers generated for 58 different clusters on the density functional theory level by Minima Hopping. We explore the potential energy surface of small neutral, anionic and cationic isomers, moving left to right across the third period of the periodic table and varying the number of atoms n and the cluster charge state q (X q n , with X = {Na, Mg, Al, Si, Ge}, q = -1, 0, 1, 2). We use structural descriptors such as bond lengths and atomic coordination numbers, the surface to volume ratios and the shape factor as well as electronic descriptors such as shell filling and hardness to detect correlations with the stability of clusters. The isomers of metallic clusters are found to be structure seekers with a strong tendency to adopt compact shapes. However certain numbers of atoms can suppress the formation of nearly spherical metallic clusters. Small non-metallic clusters typically also do not adopt compact spherical shapes for their lowest energy structures. In both cases spherical jellium models are not any more applicable. Nevertheless for many structures, that frequently have a high degree of symmetry, the Kohn-Sham eigenvalues are bunched into shells and if the available electrons can completely fill such shells, a particularly stable structure can result. We call such a cluster whose shape gives rise to shells that can be completely filled by the number of available electrons an optimally matched cluster, since both the structure and the number of electrons must be special and match. In this way we can also explain the stability trends for covalent silicon and germanium cluster isomers, whose stability was previously explained by the presence of certain structural motifs. Thus we propose a unified framework to explain trends in the stability of isomers and to predict their structure for a wide range of small clusters., Competing Interests: There are no conflicts of interest to declare., (This journal is © The Royal Society of Chemistry.)

Methylammonium lead iodide is a material known for its exceptional opto-electronic properties that make it a promising candidate for many high performance applications, such as light emitting diodes or solar cells. A recent computational structure search revealed two previously unknown non-perovskite polymorphs, that are lower in energy than the experimentally observed perovskite phases. To investigate the elusiveness of the non-perovskite phases in experimental studies, we extended our Funnel Hopping Monte Carlo (FHMC) method to periodic systems and performed extensive MC simulations driven by a machine learned potential. FHMC simulations that also include these newly discovered non-perovskite phases show that above temperatures of 200 K the perovskite phases are thermodynamically preferred. A comparison with the quasi-harmonic approximation highlights the importance of anharmonic effects captured by FHMC., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

A wide-range (0 to 1044.0 g/cm^{3} and 0 to 10^{9} K) equation-of-state (EOS) table for a CH_{1.72}O_{0.37}N_{0.086} quaternary compound has been constructed based on density-functional theory (DFT) molecular-dynamics (MD) calculations using a combination of Kohn-Sham DFT MD, orbital-free DFT MD, and numerical extrapolation. The first-principles EOS data are compared with predictions of simple models, including the fully ionized ideal gas and the Fermi-degenerate electron gas models, to chart their temperature-density conditions of applicability. The shock Hugoniot, thermodynamic properties, and bulk sound velocities are predicted based on the EOS table and compared to those of C-H compounds. The Hugoniot results show the maximum compression ratio of the C-H-O-N resin is larger than that of CH polystyrene due to the existence of oxygen and nitrogen; while the other properties are similar between CHON and CH. Radiation hydrodynamic simulations have been performed using the table for inertial confinement fusion targets with a CHON ablator and compared with a similar design with CH. The simulations show CHON outperforms CH as the ablator for laser-direct-drive target designs.

Atomic fingerprints are commonly used for the characterization of local environments of atoms in machine learning and other contexts. In this work, we study the behavior of two widely used fingerprints, namely, the smooth overlap of atomic positions (SOAP) and the atom-centered symmetry functions (ACSFs), under finite changes of atomic positions and demonstrate the existence of manifolds of quasi-constant fingerprints. These manifolds are found numerically by following eigenvectors of the sensitivity matrix with quasi-zero eigenvalues. The existence of such manifolds in ACSF and SOAP causes a failure to machine learn four-body interactions, such as torsional energies that are part of standard force fields. No such manifolds can be found for the overlap matrix (OM) fingerprint due to its intrinsic many-body character.

We report six new dynamically stable structures of SrTiO 3 at various pressures ranging from 0 to 200 GPa. These structures were found by exploring the enthalpy surface with the Minima Hopping structure prediction method. The potential energy surface was generated by a machine learned potential, the charge equilibration via neural network technique (CENT), based on an extensive training data set of highly diverse SrTiO 3 periodic and cluster structures. All our CENT structures were validated at the level of density functional theory. For our new structures, we performed phonon calculations and NVT molecular dynamics calculations to investigate their dynamical stability. Finally, X-ray diffraction patterns were simulated to help to identify our predicted structures in experiments., (© 2021 Wiley Periodicals LLC.)

The 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.

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.

Fingerprint distances, which measure the similarity of atomic environments, are commonly calculated from atomic environment fingerprint vectors. In this work, we present the simplex method that can perform the inverse operation, i.e., calculating fingerprint vectors from fingerprint distances. The fingerprint vectors found in this way point to the corners of a simplex. For a large dataset of fingerprints, we can find a particular largest simplex, whose dimension gives the effective dimension of the fingerprint vector space. We show that the corners of this simplex correspond to landmark environments that can be used in a fully automatic way to analyze structures. In this way, we can, for instance, detect atoms in grain boundaries or on edges of carbon flakes without any human input about the expected environment. By projecting fingerprints on the largest simplex, we can also obtain fingerprint vectors that are considerably shorter than the original ones but whose information content is not significantly reduced.

The BigDFT project was started in 2005 with the aim of testing the advantages of using a Daubechies wavelet basis set for Kohn-Sham (KS) density functional theory (DFT) with pseudopotentials. This project led to the creation of the BigDFT code, which employs a computational approach with optimal features of flexibility, performance, and precision of the results. In particular, the employed formalism has enabled the implementation of an algorithm able to tackle DFT calculations of large systems, up to many thousands of atoms, with a computational effort that scales linearly with the number of atoms. In this work, we recall some of the features that have been made possible by the peculiar properties of Daubechies wavelets. In particular, we focus our attention on the usage of DFT for large-scale systems. We show how the localized description of the KS problem, emerging from the features of the basis set, is helpful in providing a simplified description of large-scale electronic structure calculations. We provide some examples on how such a simplified description can be employed, and we consider, among the case-studies, the SARS-CoV-2 main protease.

Monte Carlo simulations are a powerful tool to investigate the thermodynamic properties of atomic systems. In practice, however, sampling of the complete configuration space is often hindered by high energy barriers between different regions of configuration space, which can make ergodic sampling completely infeasible within accessible simulation times. Although several extensions to the conventional Monte Carlo scheme have been developed, which enable the treatment of such systems, these extensions often entail substantial computational cost or rely on the harmonic approximation. In this work, we propose an exact method called Funnel Hopping Monte Carlo (FHMC) that is inspired by the ideas of smart darting but is more efficient. Gaussian mixtures are used to approximate the Boltzmann distribution around local energy minima, which are then used to propose high quality Monte Carlo moves that enable the Monte Carlo simulation to directly jump between different funnels. We demonstrate the method's performance on the example of the 38 as well as the 75 atom Lennard-Jones clusters, which are well known for their double funnel energy landscapes that prevent ergodic sampling with conventional Monte Carlo simulations. By integrating FHMC into the parallel tempering scheme, we were able to reduce the number of steps required significantly until convergence of the simulation.

Finding complex reaction and transformation pathways involving many intermediate states is, in general, not possible on the density-functional theory level with existing simulation methods, due to the very large number of required energy and force evaluations. For complex reactions, it is not possible to determine which atom in the reactant is mapped onto which atom in the product. Trying out all possible atomic index mappings is not feasible because of the factorial increase in the number of possible mappings. We use a penalty function that is invariant under index permutations to bias the potential energy surface in such a way that it obtains the characteristics of a structure seeker, whose global minimum is the reaction product. By performing a minima-hopping-based global optimization on this biased potential energy surface, we rapidly find intermediate states that lead into the global minimum and allow us to then extract entire reaction pathways. We first demonstrate for a benchmark system, namely, the Lennard-Jones cluster LJ_{38}, that our method finds intermediate states relevant to the lowest energy reaction pathway, and hence we need to consider much fewer intermediate states than previous methods to find the lowest energy reaction pathway. Finally, we apply the method to two real systems, C_{60} and C_{20}H_{20}, and show that the reaction pathways found contain valuable information on how these molecules can be synthesized.

The zinc blende (γ) phase of copper iodide holds the record hole conductivity for intrinsic transparent p-type semiconductors. In this work, we employ a high-throughput approach to systematically explore strategies for enhancing γ-CuI further by impurity incorporation. Our objectives are not only to find a practical approach to increase the hole conductivity in CuI thin films, but also to explore the possibility for ambivalent doping. In total 64 chemical elements were investigated as possible substitutionals on either the copper or the iodine site. All chalcogen elements were found to display acceptor character when substituting iodine, with sulfur and selenium significantly enhancing carrier concentrations produced by the native V Cu defects under conditions most favorable for impurity incorporation. Furthermore, eight impurities suitable for n-type doping were discovered. Unfortunately, our work also reveals that donor doping is hindered by compensating native defects, making ambipolar doping unlikely. Finally, we investigated how the presence of impurities influences the optical properties. In the majority of the interesting cases, we found no deep states in the band-gap, showing that CuI remains transparent upon doping.

In this work, surface reconstructions on the (100) surface of CaF2 are comprehensively investigated. The configurations were explored by employing the Minima Hopping Method (MHM) coupled to a machine-learning interatomic potential, that is based on a charge equilibration scheme steered by a neural network (CENT). The combination of these powerful methods revealed about 80 different morphologies for the (100) surface with very similar surface formation energies differing by not more than 0.3 J m-2. To take into account the effect of temperature on the dynamics of this surface as well as to study the solid-liquid transformation, molecular dynamics simulations were carried out in the canonical (NVT) ensemble. By analyzing the atomic mean-square displacements (MSD) of the surface layer in the temperature range of 300-1200 K, it was found that in the surface region the F sublattice is less stable and more diffusive than the Ca sublattice. Based on these results we demonstrate that not only a bulk system, but also a surface can exhibit a sublattice premelting that leads to superionicity. Both the surface sublattice premelting and surface premelting occur at temperatures considerably lower than the bulk values. The complex behaviour of the (100) surface is contrasted with the simpler behavior of other low index crystallographic surfaces.

Silicon nanowires inspire since decades a great interest for their fundamental scientific importance and their potential in new technologies. When decorated with organic molecules they form hybrid composites with applications in various fields, from sensors to life science. Specifically the diethyl 1-propylphosphonate/Si combination is considered as a promising alternative to the conventional semiconductor n-type doping methods, thanks to its solution-based processing, which is damage-free and intrinsically conformal. For these characteristics, it is a valid doping process for patterned materials and nanostructures such as the nanowires. Our joined experimental and theoretical study provides insights at atomistic level on the molecular activation, grafting and self-assembling mechanisms during the deposition process. For the first time to the best of our knowledge, by using scanning transmission electron microscopy the direct visualization of the single molecules arranged over the Si nanowire surface is reported. The results demonstrate that the molecules undergo to a sequential decomposition and self-assembling mechanism, finally forming a chemical bond with the silicon atoms. The ability to prepare well-defined molecule decorated Si nanowires opens up new opportunities for fundamental studies and nanodevice applications in diverse fields like physics, chemistry, engineering and life sciences.

Continuum models to handle solvent and electrolyte effects in an effective way have a long tradition in quantum-chemistry simulations and are nowadays also being introduced in computational condensed-matter and materials simulations. A key ingredient of continuum models is the choice of the solute cavity, i.e., the definition of the sharp or smooth boundary between the regions of space occupied by the quantum-mechanical (QM) system and the continuum embedding environment. The cavity, which should really reflect the region of space accessible to the degrees of freedom of the environmental components (the solvent), is usually defined by an exclusion approach in terms of the degrees of freedom of the system (the solute), typically, the atomic position of the QM system or its electronic density. Although most of the solute-based approaches developed lead to models with comparable and high accuracy when applied to small organic molecules, they can introduce significant artifacts when complex systems are considered. As an example, condensed-matter simulations often deal with supports that present open structures, i.e., low-density materials that have regions of space in which a continuum environment could penetrate, while a real solvent would not be able to. Similarly, unphysical pockets of continuum solvent may appear in systems featuring multiple molecular components, e.g., when dealing with hybrid QM/continuum approaches to solvation that involve introducing explicit solvent molecules around the solvated system. Here, we introduce a solvent-aware approach to eliminate the unphysical effects where regions of space smaller than the size of a single solvent molecule could still be filled with a continuum environment. We do this by defining a smoothly varying solute cavity that overcomes several of the limitations of straightforward solute-based definitions. This new approach applies to any smooth local definition of the continuum interface, it being based on the electronic density or the atomic positions of the QM system. It produces boundaries that are continuously differentiable with respect to the QM degrees of freedom, leading to accurate forces and/or Kohn-Sham potentials. The additional parameters involved in the solvent-aware interfaces can be set according to geometrical principles or can be converged to improve accuracy in complex multicomponent systems. Benchmarks on semiconductor substrates and on explicit water substrates confirm the flexibility and the accuracy of the approach and provide a general set of parameters for condensed-matter systems featuring open structures and/or explicit liquid components.

Transparent conductive oxides (TCOs) are essential in technologies coupling light and electricity. For Sn-based TCOs, oxygen deficiencies and undercoordinated Sn atoms result in an extended density of states below the conduction band edge. Although shallow states provide free carriers necessary for electrical conductivity, deeper states inside the band gap are detrimental to transparency. In zinc tin oxide (ZTO), the overall optoelectronic properties can be improved by defect passivation via annealing at high temperatures. Yet, the high thermal budget associated with such treatment is incompatible with many applications. Here, we demonstrate an alternative, low-temperature passivation method, which relies on cosputtering Sn-based TCOs with silicon dioxide (SiO 2 ). Using amorphous ZTO and amorphous/polycrystalline tin dioxide (SnO 2 ) as representative cases, we demonstrate through optoelectronic characterization and density functional theory simulations that the SiO 2 contribution is twofold. First, oxygen from SiO 2 passivates the oxygen deficiencies that form deep defects in SnO 2 and ZTO. Second, the ionization energy of the remaining deep defect centers is lowered by the presence of silicon atoms. Remarkably, we find that these ionized states do not contribute to sub-gap absorptance. This simple passivation scheme significantly improves the optical properties without affecting the electrical conductivity, hence overcoming the known transparency-conductivity trade-off in Sn-based TCOs., Competing Interests: The authors declare no competing financial interest.

Performing high accuracy hybrid functional calculations for condensed matter systems containing a large number of atoms is at present computationally very demanding or even out of reach if high quality basis sets are used. We present a highly optimized multiple graphics processing unit implementation of the exact exchange operator which allows one to perform fast hybrid functional density-functional theory (DFT) calculations with systematic basis sets without additional approximations for up to a thousand atoms. With this method hybrid DFT calculations of high quality become accessible on state-of-the-art supercomputers within a time-to-solution that is of the same order of magnitude as traditional semilocal-GGA functionals. The method is implemented in a portable open-source library.

Quantum dots are known to confine electrons within their structure. Whenever they periodically aggregate into arrays and cooperative interactions arise, novel quantum properties suitable for technological applications show up. Control over the potential barriers existing between neighboring quantum dots is therefore essential to alter their mutual crosstalk. Here we show that precise engineering of the barrier width can be experimentally achieved on surfaces by a single atom substitution in a haloaromatic compound, which in turn tunes the confinement properties through the degree of quantum dot intercoupling. We achieved this by generating self-assembled molecular nanoporous networks that confine the two-dimensional electron gas present at the surface. Indeed, these extended arrays form up on bulk surface and thin silver films alike, maintaining their overall interdot coupling. These findings pave the way to reach full control over two-dimensional electron gases by means of self-assembled molecular networks.Arrays of quantum dots can exhibit a variety of quantum properties, being sensitive to their spacing. Here, the authors fine tune interdot coupling using hexagonal molecular networks in which the dots are separated by single or double haloaromatic compounds, structurally identical but for a single atom.

We present an implicit solvation approach where the interface between the quantum-mechanical solute and the surrounding environment is described by a fully continuous permittivity built up with atomic-centered "soft" spheres. This approach combines many of the advantages of the self-consistent continuum solvation model in handling solutes and surfaces in contact with complex dielectric environments or electrolytes in electronic-structure calculations. In addition it is able to describe accurately both neutral and charged systems. The continuous function, describing the variation of the permittivity, allows to compute analytically the nonelectrostatic contributions to the solvation free energy that are described in terms of the quantum surface. The whole methodology is computationally stable, provides consistent energies and forces, and keeps the computational efforts and runtimes comparable to those of standard vacuum calculations. The capabilitiy to treat arbitrary molecular or slab-like geometries as well as charged molecules is key to tackle electrolytes within mixed explicit/implicit frameworks. We show that, with given, fixed atomic radii, two parameters are sufficient to give a mean absolute error of only 1.12 kcal/mol with respect to the experimental aqueous solvation energies for a set of 274 neutral solutes. For charged systems, the same set of parameters provides solvation energies for a set of 60 anions and 52 cations with an error of 2.96 and 2.13 kcal/mol, respectively, improving upon previous literature values. To tackle elements not present in most solvation databases, a new benchmark scheme on wettability and contact angles is proposed for solid-liquid interfaces and applied to the investigation of the stable terminations of a CdS (112̅0) surface in an electrochemical medium.

The experimental discovery of borospherene, the only non-carbon fullerene observed in nature, has generated a lot of interest in the scientific community and led to the theoretical prediction of various endohedrally and exohedrally decorated borospherene. We apply Minima Hopping Method (MHM), a global geometry optimization algorithm at the density functional level to check the stability of recently proposed exohedrally decorated borospherenes M 6 @B 40 for (M = Li, Na, K, Rb, Be, Mg, Ca, Sr, Sc and Ti). By performing short MHM runs, we find that the proposed fullerene structures are not global minima. Our new lowest energy structures are significantly deformed and of much lower symmetry. These low energy structures spontaneously aggregate by forming chemical bonds when they are brought together. Therefore, it would be challenging to synthesize bulk materials made out of the theoretically postulated exohedrally decorated borospherenes such as B 40 M 6 which might have technologically useful properties.

We investigate the possibility of achieving high-temperature superconductivity in hydrides under pressure by inducing metallization of otherwise insulating phases through doping, a path previously used to render standard semiconductors superconducting at ambient pressure. Following this idea, we study H 2 O, one of the most abundant and well-studied substances, we identify nitrogen as the most likely and promising substitution/dopant. We show that for realistic levels of doping of a few percent, the phase X of ice becomes superconducting with a critical temperature of about 60 K at 150 GPa. In view of the vast number of hydrides that are strongly covalent bonded, but that remain insulating up to rather large pressures, our results open a series of new possibilities in the quest for novel high-temperature superconductors.

Using multiwavelets, we have obtained total energies and corresponding atomization energies for the GGA-PBE and hybrid-PBE0 density functionals for a test set of 211 molecules with an unprecedented and guaranteed μHartree accuracy. These quasi-exact references allow us to quantify the accuracy of standard all-electron basis sets that are believed to be highly accurate for molecules, such as Gaussian-type orbitals (GTOs), all-electron numeric atom-centered orbitals (NAOs), and full-potential augmented plane wave (APW) methods. We show that NAOs are able to achieve the so-called chemical accuracy (1 kcal/mol) for the typical basis set sizes used in applications, for both total and atomization energies. For GTOs, a triple-ζ quality basis has mean errors of ∼10 kcal/mol in total energies, while chemical accuracy is almost reached for a quintuple-ζ basis. Due to systematic error cancellations, atomization energy errors are reduced by almost an order of magnitude, placing chemical accuracy within reach also for medium to large GTO bases, albeit with significant outliers. In order to check the accuracy of the computed densities, we have also investigated the dipole moments, where in general only the largest NAO and GTO bases are able to yield errors below 0.01 D. The observed errors are similar across the different functionals considered here.

A new intermetallic compound, the first to be structurally identified in the Cu-Bi binary system, is reported. This compound is accessed by high-pressure reaction of the elements. Its detailed characterization, physical property measurements, and ab initio calculations are described. The commensurate crystal structure of Cu 11 Bi 7 is a unique variation of the NiAs structure type. Temperature-dependent electrical resistivity and heat capacity measurements reveal a bulk superconducting transition at T c =1.36 K. Density functional theory calculations further demonstrate that Cu 11 Bi 7 can be stabilized (relative to decomposition into the elements) at high pressure and temperature. These results highlight the ability of high-pressure syntheses to allow for inroads into heretofore-undiscovered intermetallic systems for which no thermodynamically stable binaries are known., (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The on-surface Ullmann-type chemical reaction synthesizes polymers by linking carbons of adjacent molecules on solid surfaces. Although an organometallic compound is recently identified as the reaction intermediate, little is known about the detailed structure of the bonded organometallic species and its influence on the molecule and the reaction. Herein atomic force microscopy at low temperature is used to study the reaction with 3,9-diiododinaphtho[2,3-b:2',3'-d]thiophene (I-DNT-VW), which is polymerized on Ag(111) in vacuum. Thermally sublimated I-DNT-VW picks up a Ag surface atom, forming a CAg bond at one end after removing an iodine. The CAg bond is usually short-lived, and a CAgC organometallic bond immediately forms with an adjacent molecule. The existence of the bonded Ag atoms strongly affects the bending angle and adsorption height of the molecular unit. Density functional theory calculations reveal the bending mechanism, which reveals that charge from the terminus of the molecule is transferred via the Ag atom into the organometallic bond and strengths the local adsorption to the substrate. Such deformations vanish when the Ag atoms are removed by annealing and CC bonds are established., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

Semiconducting half and, to a lesser extent, full Heusler compounds are promising thermoelectric materials due to their compelling electronic properties with large power factors. However, intrinsically high thermal conductivity resulting in a limited thermoelectric efficiency has so far impeded their widespread use in practical applications. Here, we report the computational discovery of a class of hitherto unknown stable semiconducting full Heusler compounds with ten valence electrons (X_{2}YZ, X=Ca, Sr, and Ba; Y=Au and Hg; Z=Sn, Pb, As, Sb, and Bi) through high-throughput ab initio screening. These new compounds exhibit ultralow lattice thermal conductivity κ_{L} close to the theoretical minimum due to strong anharmonic rattling of the heavy noble metals, while preserving high power factors, thus resulting in excellent phonon-glass electron-crystal materials.

An analysis of the network defined by the potential energy minima of multi-atomic systems and their connectivity via reaction pathways that go through transition states allows us to understand important characteristics like thermodynamic, dynamic, and structural properties. Unfortunately computing the transition states and reaction pathways in addition to the significant energetically low-lying local minima is a computationally demanding task. We here introduce a computationally efficient method that is based on a combination of the minima hopping global optimization method and the insight that uphill barriers tend to increase with increasing structural distances of the educt and product states. This method allows us to replace the exact connectivity information and transition state energies with alternative and approximate concepts. Without adding any significant additional cost to the minima hopping global optimization approach, this method allows us to generate an approximate network of the minima, their connectivity, and a rough measure for the energy needed for their interconversion. This can be used to obtain a first qualitative idea on important physical and chemical properties by means of a disconnectivity graph analysis. Besides the physical insight obtained by such an analysis, the gained knowledge can be used to make a decision if it is worthwhile or not to invest computational resources for an exact computation of the transition states and the reaction pathways. Furthermore it is demonstrated that the here presented method can be used for finding physically reasonable interconversion pathways that are promising input pathways for methods like transition path sampling or discrete path sampling.

The widespread popularity of density functional theory has given rise to an extensive range of dedicated codes for predicting molecular and crystalline properties. However, each code implements the formalism in a different way, raising questions about the reproducibility of such predictions. We report the results of a community-wide effort that compared 15 solid-state codes, using 40 different potentials or basis set types, to assess the quality of the Perdew-Burke-Ernzerhof equations of state for 71 elemental crystals. We conclude that predictions from recent codes and pseudopotentials agree very well, with pairwise differences that are comparable to those between different high-precision experiments. Older methods, however, have less precise agreement. Our benchmark provides a framework for users and developers to document the precision of new applications and methodological improvements., (Copyright © 2016, American Association for the Advancement of Science.)

Measuring similarities/dissimilarities between atomic structures is important for the exploration of potential energy landscapes. However, the cell vectors together with the coordinates of the atoms, which are generally used to describe periodic systems, are quantities not directly suitable as fingerprints to distinguish structures. Based on a characterization of the local environment of all atoms in a cell, we introduce crystal fingerprints that can be calculated easily and define configurational distances between crystalline structures that satisfy the mathematical properties of a metric. This distance between two configurations is a measure of their similarity/dissimilarity and it allows in particular to distinguish structures. The new method can be a useful tool within various energy landscape exploration schemes, such as minima hopping, random search, swarm intelligence algorithms, and high-throughput screenings.

Density functional theory calculations are computationally extremely expensive for systems containing many atoms due to their intrinsic cubic scaling. This fact has led to the development of so-called linear scaling algorithms during the last few decades. In this way it becomes possible to perform ab initio calculations for several tens of thousands of atoms within reasonable walltimes. However, even though the use of linear scaling algorithms is physically well justified, their implementation often introduces some small errors. Consequently most implementations offering such a linear complexity either yield only a limited accuracy or, if one wants to go beyond this restriction, require a tedious fine tuning of many parameters. In our linear scaling approach within the BigDFT package, we were able to overcome this restriction. Using an ansatz based on localized support functions expressed in an underlying Daubechies wavelet basis - which offers ideal properties for accurate linear scaling calculations - we obtain an amazingly high accuracy and a universal applicability while still keeping the possibility of simulating large system with linear scaling walltimes requiring only a moderate demand of computing resources. We prove the effectiveness of our method on a wide variety of systems with different boundary conditions, for single-point calculations as well as for geometry optimizations and molecular dynamics.

Functionalized materials consisting of inorganic substrates with organic adsorbates play an increasing role in emerging technologies like molecular electronics or hybrid photovoltaics. For such applications, the adsorption geometry of the molecules under operating conditions, e.g., ambient temperature, is crucial because it influences the electronic properties of the interface, which in turn determine the device performance. So far detailed experimental characterization of adsorbates at room temperature has mainly been done using a combination of complementary methods like photoelectron spectroscopy together with scanning tunneling microscopy. However, this approach is limited to ensembles of adsorbates. In this paper, we show that the characterization of individual molecules at room temperature, comprising the determination of the adsorption configuration and the electrostatic interaction with the surface, can be achieved experimentally by atomic force microscopy (AFM) and Kelvin probe force microscopy (KPFM). We demonstrate this by identifying two different adsorption configurations of isolated copper(ii) meso-tetra (4-carboxyphenyl) porphyrin (Cu-TCPP) on rutile TiO2 (110) in ultra-high vacuum. The local contact potential difference measured by KPFM indicates an interfacial dipole due to electron transfer from the Cu-TCPP to the TiO2. The experimental results are verified by state-of-the-art first principles calculations. We note that the improvement of the AFM resolution, achieved in this work, is crucial for such accurate calculations. Therefore, high resolution AFM at room temperature is promising for significantly promoting the understanding of molecular adsorption.

The structure of metallic glasses is a long-standing question because the lack of long-range order makes diffraction based techniques difficult to be applied. Here, we used scanning tunneling microscopy with large tunneling resistance of 6 GΩ at low temperature in order to minimize forces between probe and sample and reduce thermal fluctuations of metastable structures. Under these extremely gentle conditions, atomic structures of Ni40Ta60 metallic glasses are revealed with unprecedented lateral resolution. In agreement with previous models and experiments, icosahedral-like clusters are observed. The clusters show a high degree of mobility, which explains the need of low temperatures for stable imaging. In addition to icosahedrons, chain-like structures are resolved and comparative density functional theory (DFT) calculations confirm that these structures are meta-stable. The co-existence of icosahedral and chain-like structures might be an key ingredient for the understanding of the mechanical properties of metallic glasses.

Halogen bonding is a noncovalent interaction where an electrophilic cap on a halogen atom, the so-called σ-hole, attracts a nucleophilic site on an adjacent molecule. The polarizability of halogens relates to the strength of the σ-hole, and accordingly the halogen-halogen distance becomes shorter in the order of Cl, Br, and I. Fully fluoro-substituted aromatic molecules, on the contrary, are generally believed not to form halogen bonds due to the absence of a σ-hole. Here, we study atomic-scale in-plane F-F contacts with high-resolution force microscopy. Our ab initio calculations show that the attractive dispersion forces can overcome the electrostatic repulsion between the fluorine atoms, while the anisotropic distribution of the negative electrostatic potential leads the directional bond and even changes the gap. The coexistence of these two competing forces results in the formation of a "windmill" structure, containing three C-F···F bonds among neighboring molecules. While the σ-hole is absent, the scheme of the C-F···F bonding has a high similarity to halogen bonding.

Optimizations of atomic positions belong to the most commonly performed tasks in electronic structure calculations. Many simulations like global minimum searches or characterizations of chemical reactions require performing hundreds or thousands of minimizations or saddle computations. To automatize these tasks, optimization algorithms must not only be efficient but also very reliable. Unfortunately, computational noise in forces and energies is inherent to electronic structure codes. This computational noise poses a severe problem to the stability of efficient optimization methods like the limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. We here present a technique that allows obtaining significant curvature information of noisy potential energy surfaces. We use this technique to construct both, a stabilized quasi-Newton minimization method and a stabilized quasi-Newton saddle finding approach. We demonstrate with the help of benchmarks that both the minimizer and the saddle finding approach are superior to comparable existing methods.

Intermetallic Li-Al compounds are on the one hand key materials for light-weight engineering, and on the other hand, they have been proposed for high-capacity electrodes for Li batteries. We determine from first-principles the phase diagram of Li-Al binary crystals using the minima hopping structural prediction method. Beside reproducing the experimentally reported phases (LiAl, Li3Al2, Li9Al4, LiAl3, and Li2Al), we unveil a structural variety larger than expected by discovering six unreported binary phases likely to be thermodynamically stable. Finally, we discuss the behavior of the elastic constants and of the electric potential profile of all Li-Al stable compounds as a function of their stoichiometry.

Using the minima hopping global optimization method at the density functional level, we found low-energy nanostructures for neutral Au26 and its anion. The local-density and a generalized gradient approximation of the exchange–correlation functional predict different nanoscale motifs. We found a vast number of isomers within a small energy range above the respective putative global minima with each method. Photoelectron spectroscopy of Au26(-) under different experimental conditions revealed definitive evidence of the presence of multiple isomers, consistent with the theoretical predictions. Comparison between the experimental and simulated photoelectron spectra suggests that the photoelectron spectra of Au26(-) contain a mixture of three isomers, all of which are low-symmetry core–shell-type nanoclusters with a single internal Au atom. We present a disconnectivity graph for Au26(-) that has been computed completely at the density functional level. The transition states used to build this disconnectivity graph are complete enough to predict Au26(-) to have a possible fluxional shell, which facilitates the understanding of its catalytic activity.

The Minima Hopping global optimization method uses physically realizable molecular dynamics moves in combination with an energy feedback that guarantees the escape from any potential energy funnel. For the purpose of finding reaction pathways, we argue that Minima Hopping is particularly suitable as a guide through the potential energy landscape and as a generator for pairs of minima that can be used as input structures for methods capable of finding transition states between two minima. For Lennard-Jones benchmark systems we compared this Minima Hopping guided path search method to a known approach for the exploration of potential energy landscapes that is based on deterministic mode-following. Although we used a stabilized mode-following technique that reliably allows to follow distinct directions when escaping from a local minimum, we observed that Minima Hopping guided path search is far superior in finding lowest-barrier reaction pathways. We, therefore, suggest that Minima Hopping guided path search can be used as a simple and efficient way to identify energetically low-lying chemical reaction pathways. Finally, we applied the Minima Hopping guided path search approach to 75-atom and 102-atom Lennard-Jones systems. For the 75-atom system we found pathways whose highest energies are significantly lower than the highest energy along the previously published lowest-barrier pathway. Furthermore, many of these pathways contain a smaller number of intermediate transition states than the previously publish lowest-barrier pathway. In case of the 102-atom system Minima Hopping guided path search found a previously unknown and energetically low-lying funnel.

We demonstrate that Daubechies wavelets can be used to construct a minimal set of optimized localized adaptively contracted basis functions in which the Kohn-Sham orbitals can be represented with an arbitrarily high, controllable precision. Ground state energies and the forces acting on the ions can be calculated in this basis with the same accuracy as if they were calculated directly in a Daubechies wavelets basis, provided that the amplitude of these adaptively contracted basis functions is sufficiently small on the surface of the localization region, which is guaranteed by the optimization procedure described in this work. This approach reduces the computational costs of density functional theory calculations, and can be combined with sparse matrix algebra to obtain linear scaling with respect to the number of electrons in the system. Calculations on systems of 10,000 atoms or more thus become feasible in a systematic basis set with moderate computational resources. Further computational savings can be achieved by exploiting the similarity of the adaptively contracted basis functions for closely related environments, e.g., in geometry optimizations or combined calculations of neutral and charged systems.

According to previous interpretations of experimental data, sodium-scandium double-cation borohydride NaSc(BH4)4 crystallizes in the crystallographic space group Cmcm where each sodium (scandium) atom is surrounded by six scandium (sodium) atoms. A careful investigation of this phase based on ab initio calculations indicates that the structure is dynamically unstable and gives rise to an energetically and dynamically more favorable phase with C2221 symmetry and nearly identical x-ray diffraction pattern. By additionally performing extensive structural searches with the minima-hopping method we discover a class of new low-energy structures exhibiting a novel structural motif in which each sodium (scandium) atom is surrounded by four scandium (sodium) atoms arranged at the corners of either a rectangle with nearly equal sides or a tetrahedron. These new phases are all predicted to be insulators with band gaps of 7.9-8.2 eV. Finally, we estimate the influence of these structures on the hydrogen-storage performance of NaSc(BH4)4.

Individual in situ polymerized fluorene chains 10-100 nm long linked by C-C bonds are pulled vertically from an Au(111) substrate by the tip of a low-temperature atomic force microscope. The conformation of the selected chains is imaged before and after manipulation using scanning tunneling microscopy. The measured force gradient shows strong and periodic variations that correspond to the step-by-step detachment of individual fluorene repeat units. These variations persist at constant intensity until the entire polymer is completely removed from the surface. Calculations based on an extended Frenkel-Kontorova model reproduce the periodicity and magnitude of these features and allow us to relate them to the detachment force and desorption energy of the repeat units. The adsorbed part of the polymer slides easily along the surface during the pulling process, leading to only small oscillations as a result of the high stiffness of the fluorenes and of their length mismatch with respect to the substrate surface structure. A significant lateral force also is caused by the sequential detachment of individual units. The gained insight into the molecule-surface interactions during sliding and pulling should aid the design of mechanoresponsive nanosystems and devices.

In order to characterize molecular structures we introduce configurational fingerprint vectors which are counterparts of quantities used experimentally to identify structures. The Euclidean distance between the configurational fingerprint vectors satisfies the properties of a metric and can therefore safely be used to measure dissimilarities between configurations in the high dimensional configuration space. In particular we show that these metrics are a perfect and computationally cheap replacement for the root-mean-square distance (RMSD) when one has to decide whether two noise contaminated configurations are identical or not. We introduce a Monte Carlo approach to obtain the global minimum of the RMSD between configurations, which is obtained from a global minimization over all translations, rotations, and permutations of atomic indices.

State-of-the art experimental techniques such as scanning tunneling microscopy have great difficulties in extracting detailed structural information about molecules adsorbed on surfaces. By combining atomic force microscopy and Kelvin probe force microscopy with ab initio calculations, we demonstrate that we can obtain a wealth of detailed structural information about the molecule itself and its environment. Studying an FFPB molecule on a gold surface, we are able to determine its exact location on the surface, the nature of its bonding properties with neighboring molecules that lead to the growth of one-dimensional strips, and the internal torsions and bendings of the molecule.

Systematic ab initio structure prediction was applied for the first time to predict low energy surface reconstructions by employing the minima hopping method on the α-boron (111) surface. Novel reconstruction geometries were identified and carefully characterized in terms of structural and electronic properties. Our calculations predict the formation of a planar, monolayer sheet at the surface, which is responsible for conductive surface states. Furthermore, the isolated boron sheet is shown to be the ground state 2D structure in vacuum at a hole density of η=1/5 and is therefore a potential candidate as a precursor for boron nanostructures.

Low-energy structures of alanates are currently known to be described by patterns of isolated, nearly ideal tetrahedral [AlH4] anions and metal cations. We discover that the novel polymeric motif recently proposed for LiAlH4 plays a dominant role in a series of alanates, including LiAlH4, NaAlH4, KAlH4, Mg(AlH4)2, Ca(AlH4)2, and Sr(AlH4)2. In particular, most of the low-energy structures discovered for the whole series are characterized by networks of corner-sharing [AlH6] octahedra, forming wires and/or planes throughout the materials. Finally, for Mg(AlH4)2 and Sr(AlH4)2, we identify two polymeric phases to be lowest in energy at low temperatures.

By adding a nonlinear core correction to the well established dual space Gaussian type pseudopotentials for the chemical elements up to the third period, we construct improved pseudopotentials for the Perdew-Burke-Ernzerhof [J. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996)] functional and demonstrate that they exhibit excellent accuracy. Our benchmarks for the G2-1 test set show average atomization energy errors of only half a kcal/mol. The pseudopotentials also remain highly reliable for high pressure phases of crystalline solids. When supplemented by empirical dispersion corrections [S. Grimme, J. Comput. Chem. 27, 1787 (2006); S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, J. Chem. Phys. 132, 154104 (2010)] the average error in the interaction energy between molecules is also about half a kcal/mol. The accuracy that can be obtained by these pseudopotentials in combination with a systematic basis set is well superior to the accuracy that can be obtained by commonly used medium size Gaussian basis sets in all-electron calculations.

We identify a class of novel low energy phases of the hydrogen storage material LiAlH4 by using the ab initio minima hopping crystal structure prediction method. These phases are, unlike previous predictions and known structures of similar materials, characterized by polymeric networks consisting of Al atoms interlinked with H atoms. The most stable structure is a layered ionic crystal with P21/c symmetry, and it has lower free energy than the previously reported structure over a wide range of temperatures. Furthermore, we carry out x-ray diffraction, phonon, and GW band-structure analysis in order to characterize this phase. Its experimental synthesis would have profound implications for the study of dehydrogenation and rehydrogenation processes and the stability problem of LiAlH4 for hydrogen storage applications.