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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. [ABSTRACT FROM AUTHOR]

It is uncontested that a machine learning scheme cannot correctly reproduce physical properties that vary on a manifold in configuration space if the fingerprint, used as an input for the machine learning scheme, is constant on this manifold. In our original paper, we found several manifolds whose fingerprint variation is sufficiently small to prevent machine learning based on a standard training scheme even if some 40 configurations on the manifold are included in the training set. Response to "Comment on 'Manifolds of quasi-constant SOAP and ACSF fingerprints and the resulting failure to machine learn four-body interactions'" [J. Chem. Phys. [Extracted from the article]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We report six new dynamically stable structures of SrTiO3 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 SrTiO3 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. [ABSTRACT FROM AUTHOR]

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. Machine learning potentials do not account for long-range charge transfer. Here the authors introduce a fourth-generation high-dimensional neural network potential including non-local information of charge populations that is able to provide forces, charges and energies in excellent agreement with DFT data. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 minimahopping 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We present modifications for the method recently developed by Granot and Baer [J. Chem. Phys. 128, 184111 (2008)]. These modifications significantly enhance the efficiency and reliability of the method. In addition, we discuss some specific features of this method. These features provide important flexibilities which are crucial for a double-ended saddle point search method in order to be applicable to complex reaction mechanisms. Furthermore, it is discussed under what circumstances this methods might fail to find the transition state and remedies to avoid such situations are provided. We demonstrate the performance of the enhanced splined saddle method on several examples with increasing complexity, isomerization of ammonia, ethane and cyclopropane molecules, tautomerization of cytosine, the ring opening of cyclobutene, the Stone-Wales transformation of the C60 fullerene, and finally rolling a small NaCl cube on NaCl(001) surface. All of these calculations are based on density functional theory. The efficiency of the method is remarkable in regard to the reduction of the total computational time. [ABSTRACT FROM AUTHOR]

We re-examine the question of whether the geometrical ground state of neutral and ionized clusters are identical. Using a well defined criterion for being 'identical' together, the extensive sampling methods on a potential energy surface calculated by density functional theory, we show that the ground states are in general different. This behavior is to be expected whenever there are metastable configurations which are close in energy to the ground state, but it disagrees with previous studies. [ABSTRACT FROM AUTHOR]

We show that molecular dynamics based moves in the minima hopping method are more efficient than saddle point crossing moves. For binary systems we incorporate identity exchange moves in a way that allows one to avoid the generation of high energy configurations. Using this modified minima hopping method, we re-examine the binary Lennard-Jones benchmark system with up to 100 atoms and we find a large number of new putative global minima. [ABSTRACT FROM AUTHOR]

A structure prediction method is presented based on the minima hopping method. To escape local minima, moves on the configurational enthalpy surface are performed by variable cell shape molecular dynamics. To optimize the escape steps the initial atomic and cell velocities are aligned to low curvature directions of the current local minimum. The method is applied to both silicon crystals and well-studied binary Lennard-Jones mixtures. For the latter new putative ground state structures are presented. It is shown that a high success rate is achieved and a reliable prediction of unknown ground state structures is possible. [ABSTRACT FROM AUTHOR]

We present the implementation of a full electronic structure calculation code on a hybrid parallel architecture with graphic processing units (GPUs). This implementation is performed on a free software code based on Daubechies wavelets. Such code shows very good performances, systematic convergence properties, and an excellent efficiency on parallel computers. Our GPU-based acceleration fully preserves all these properties. In particular, the code is able to run on many cores which may or may not have a GPU associated, and thus on parallel and massive parallel hybrid machines. With double precision calculations, we may achieve considerable speedup, between a factor of 20 for some operations and a factor of 6 for the whole density functional theory code. [ABSTRACT FROM AUTHOR]

We compare evolutionary algorithms with minima hopping for global optimization in the field of cluster structure prediction. We introduce a new average offspring recombination operator and compare it with previously used operators. Minima hopping is improved with a softening method and a stronger feedback mechanism. Test systems are atomic clusters with Lennard-Jones interaction as well as silicon and gold clusters described by force fields. The improved minima hopping is found to be well-suited to all these homoatomic problems. The evolutionary algorithm is more efficient for systems with compact and symmetric ground states, including LJ150, but it fails for systems with very complex energy landscapes and asymmetric ground states, such as LJ75 and silicon clusters with more than 30 atoms. Both successes and failures of the evolutionary algorithm suggest ways for its improvement. [ABSTRACT FROM AUTHOR]

Daubechies wavelets are a powerful systematic basis set for electronic structure calculations because they are orthogonal and localized both in real and Fourier space. We describe in detail how this basis set can be used to obtain a highly efficient and accurate method for density functional electronic structure calculations. An implementation of this method is available in the ABINIT free software package. This code shows high systematic convergence properties, very good performances, and an excellent efficiency for parallel calculations. [ABSTRACT FROM AUTHOR]