Interatomic potentials for ionic systems with density functional accuracy based on charge densities obtained by a neural network

Based on an analysis of the short range chemical environment of each atom in a system, standard machine learning based approaches to the construction of interatomic potentials aim at determining directly the central quantity which is the total energy. This prevents for instance an accurate description of the energetics of systems where long range charge transfer is important as well as of ionized systems. We propose therefore not to target directly with machine learning methods the total energy but an intermediate physical quantity namely the charge density, which then in turn allows to determine the total energy. By allowing the electronic charge to distribute itself in an optimal way over the system, we can describe not only neutral but also ionized systems with unprecedented accuracy. We demonstrate the power of our approach for both neutral and ionized NaCl clusters where charge redistribution plays a decisive role for the energetics. We are able to obtain chemical accuracy, i.e. errors of less than a milli Hartree per atom compared to the reference density functional results. The introduction of physically motivated quantities which are determined by the short range atomic environment via a neural network leads also to an increased stability of the machine learning process and transferability of the potential.Comment: 4 figure

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.Comment: 7 pages, 7 figure

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

Structural Metastability of Endohedral Silicon Fullerenes

Endohedrally doped Si20 fullerenes appear as appealing building blocks for nanoscale materials. We investigate their structural stability with an unbiased and systematic global geometry optimization method within density-functional theory. For a wide range of metal doping atoms, it was sufficient to explore the Born Oppenheimer surface for only a moderate number of local minima to find structures that clearly differ from the initial endohedral cages, but are considerably more favorable in terms of energy. Previously proposed structures are thus all metastable.Comment: 4 pages, 1 figur

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. We show that these metrics correlate well with the RMSD between two configurations if this RMSD is obtained from a global minimization over all translations, rotations and permutations of atomic indices. We introduce a Monte Carlo approach to obtain this global minimum of the RMSD between configurations

Particle-Particle, Particle-Scaling function (P3S) 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. An MPI parallelised version of the code can be downloaded under the GNU General Public License from the website of our group.Comment: 19 pages, 11 figures, submitted to: Journal of Chemical Physic