Thermodynamically stable polymorphs of nitrogen-rich carbon nitrides: a C3N5 study.

We have carried out an extensive search for stable polymorphs of carbon nitride with C3N5 stoichiometry using the minima hopping method. Contrary to the widely held opinion that stacked, planar, graphite-like structures are energetically the most stable carbon nitride polymorphs for various nitrogen contents, we find that this does not apply for nitrogen-rich materials owing to the high abundance of N-N bonds. In fact, our results disclose novel morphologies with moieties not previously considered for C3N5. We demonstrate that nitrogen-rich compounds crystallize in a large variety of different structures due to particular characteristics of their energy landscapes. The newly found low-energy structures of C3N5 have band gaps within good agreement with the values measured in experimental studies.

New strontium titanate polymorphs under high pressure.

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.

Artificial neural networks for the kinetic energy functional of non-interacting fermions.

A novel approach to find the fermionic non-interacting kinetic energy functional with chemical accuracy using machine learning techniques is presented. To that extent, we apply machine learning to an intermediate quantity rather than targeting the kinetic energy directly. We demonstrate the performance of the method for three model systems containing three and four electrons. The resulting kinetic energy functional remarkably accurately reproduces self-consistently the ground state electron density and total energy of reference Kohn-Sham calculations with an error of less than 5 mHa. This development opens a new avenue to advance orbital-free density functional theory by means of machine learning.

Surface reconstructions and premelting of the (100) CaF2 surface.

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.

Optimized symmetry functions for machine-learning interatomic potentials of multicomponent systems.

Current machine-learning methods to reproduce ab initio potential energy landscapes suffer from an unfavorable computational scaling with respect to the number of chemical species. In this work, we propose a new approach by using optimized symmetry functions to explore similarities of structures in multicomponent systems in order to yield linear complexity. We combine these symmetry functions with the charge equilibration via neural network technique, a reliable artificial neural network potential for ionic materials, and apply this method to study alkali-halide materials MX with 6 chemical species (M = {Li, Na, K} and X = {F, Cl, Br}). Our results show that our approach provides good agreement both with experimental and DFT reference data of many physical and structural properties for any chemical combination.

A neural-network potential through charge equilibration for WS2: From clusters to sheets.

In the present work, we use a machine learning method to construct a high-dimensional potential for tungsten disulfide using a charge equilibration neural-network technique. A training set of stoichiometric WS2 clusters is prepared in the framework of density functional theory. After training the neural-network potential, the reliability and transferability of the potential are verified by performing a crystal structure search on bulk phases of WS2 and by plotting energy-area curves of two different monolayers. Then, we use the potential to investigate various triangular nano-clusters and nanotubes of WS2. In the case of nano-structures, we argue that 2H atomic configurations with sulfur rich edges are thermodynamically more stable than the other investigated configurations. We also studied a number of WS2 nanotubes which revealed that 1T tubes with armchair chirality exhibit lower bending stiffness.

A highly accurate and efficient algorithm for electrostatic interactions of charged particles confined by parallel metallic plates.

We present an accurate and efficient algorithm to calculate the electrostatic interaction of charged point particles with partially periodic boundary conditions that are confined along the non-periodic direction by two parallel metallic plates. The method preserves the original boundary conditions, leading to an exact solution of the problem. In addition, the scaling complexity is quasilinear O(Nln(N)), where N is the number of particles in the simulation box. Based on the superposition principle in electrostatics, the problem is split into two electrostatic problems where each can be calculated by the appropriate Poisson solver. The method is applied to NaCl ultra-thin films where its dielectric response with respect to an external bias voltage is investigated. Furthermore, the total charge induced on the metallic boundaries can be calculated to an arbitrary precision.

A fingerprint based metric for measuring similarities of crystalline structures.

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.

Metrics for measuring distances in configuration spaces.

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.

Crystal structure of cold compressed graphite.

Through a systematic structural search we found an allotrope of carbon with Cmmm symmetry which we predict to be more stable than graphite for pressures above 10 GPa. This material, which we refer to as Z-carbon, is formed by pure sp(3) bonds and it provides an explanation to several features in experimental x-ray diffraction and Raman spectra of graphite under pressure. The transition from graphite to Z-carbon can occur through simple sliding and buckling of graphene sheets. Our calculations predict that Z-carbon is a transparent wide band-gap semiconductor with a hardness comparable to diamond.

An enhanced splined saddle method.

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 C(60) 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.

The effect of ionization on the global minima of small and medium sized silicon and magnesium clusters.

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.

Ubiquitous mechanisms of energy dissipation in noncontact atomic force microscopy.

Atomistic simulations considering larger tip structures than hitherto assumed reveal novel dissipation mechanisms in noncontact atomic force microscopy. The potential energy surfaces of realistic silicon tips exhibit many energetically close local minima that correspond to different structures. Most of them easily deform, thus causing dissipation arising from hysteresis in force versus distance characteristics. Furthermore, saddle points which connect local minima can suddenly switch to connect different minima. Configurations driven into metastability by the tip motion can thus suddenly access lower energy structures when thermal activation becomes allowed within the time required to detect the resulting average dissipation.

Particle-particle, particle-scaling function algorithm for electrostatic problems in free boundary conditions.

An algorithm for fast calculation of the Coulombic forces and energies of point particles with free boundary conditions is proposed. Its calculation time scales as N log N for N particles. This novel method has lower crossover point with the full O(N(2)) direct summation than the fast multipole method. The forces obtained by our algorithm are analytical derivatives of the energy which guarantees energy conservation during a molecular dynamics simulation. Our algorithm is very simple. A version of the code parallelized with the Message Passing Interface can be downloaded under the GNU General Public License from the website of our group.