Unified Representation of Molecules and Crystals for Machine Learning

Accurate simulations of atomistic systems from first principles are limited by computational cost. In high-throughput settings, machine learning can potentially reduce these costs significantly by accurately interpolating between reference calculations. For this, kernel learning approaches crucially require a single Hilbert space accommodating arbitrary atomistic systems. We introduce a many-body tensor representation that is invariant to translations, rotations and nuclear permutations of same elements, unique, differentiable, can represent molecules and crystals, and is fast to compute. Empirical evidence is presented for energy prediction errors below 1 kcal/mol for 7k organic molecules and 5 meV/atom for 11k elpasolite crystals. Applicability is demonstrated for phase diagrams of Pt-group/transition-metal binary systems.Comment: Revised version, minor changes throughou

Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the approximate free energies of complex statistical systems. The analysis is centered around the variational principle of N. N. Bogoliubov for free energy in the context of its applications to various problems of statistical mechanics and condensed matter physics. The review presents a terse discussion of selected works carried out over the past few decades on the theory of many-particle interacting systems in terms of the variational inequalities. It is the purpose of this paper to discuss some of the general principles which form the mathematical background to this approach, and to establish a connection of the variational technique with other methods, such as the method of the mean (or self-consistent) field in the many-body problem, in which the effect of all the other particles on any given particle is approximated by a single averaged effect, thus reducing a many-body problem to a single-body problem. The method is illustrated by applying it to various systems of many-particle interacting systems, such as Ising and Heisenberg models, superconducting and superfluid systems, strongly correlated systems, etc. It seems likely that these technical advances in the many-body problem will be useful in suggesting new methods for treating and understanding many-particle interacting systems. This work proposes a new, general and pedagogical presentation, intended both for those who are interested in basic aspects, and for those who are interested in concrete applications.Comment: 60 pages, Refs.25

First-principles kinetic Monte Carlo simulations for heterogeneous catalysis, applied to the CO oxidation at RuO2(110)

We describe a first-principles statistical mechanics approach enabling us to simulate the steady-state situation of heterogeneous catalysis. In a first step density-functional theory together with transition-state theory is employed to obtain the energetics of all relevant elementary processes. Subsequently the statistical mechanics problem is solved by the kinetic Monte Carlo method, which fully accounts for the correlations, fluctuations, and spatial distributions of the chemicals at the surface of the catalyst under steady-state conditions. Applying this approach to the catalytic oxidation of CO at RuO2(110), we determine the surface atomic structure and composition in reactive environments ranging from ultra-high vacuum (UHV) to technologically relevant conditions, i.e. up to pressures of several atmospheres and elevated temperatures. We also compute the CO2 formation rates (turnover frequencies). The results are in quantitative agreement with all existing experimental data. We find that the high catalytic activity of this system is intimately connected with a disordered, dynamic surface ``phase'' with significant compositional fluctuations. In this active state the catalytic function results from a self-regulating interplay of several elementary processes.Comment: 18 pages including 9 figures; related publications can be found at http://www.fhi-berlin.mpg.de/th/th.htm