Structure and stability of small H clusters on graphene

The structure and stability of small hydrogen clusters adsorbed on graphene is studied by means of Density Functional Theory (DFT) calculations. Clusters containing up to six H atoms are investigated systematically -- the clusters having either all H atoms on one side of the graphene sheet (\textit{cis}-clusters) or having the H atoms on both sides in an alternating manner (\textit{trans}-cluster). The most stable cis-clusters found have H atoms in ortho- and para-positions with respect to each other (two H's on neighboring or diagonally opposite carbon positions within one carbon hexagon) while the most stable trans-clusters found have H atoms in ortho-trans-positions with respect to each other (two H's on neighboring carbon positions, but on opposite sides of the graphene). Very stable trans-clusters with 13-22 H atoms were identified by optimizing the number of H atoms in ortho-trans-positions and thereby the number of closed, H-covered carbon hexagons. For the cis-clusters, the associative H$_2$ desorption was investigated. Generally, the desorption with the lowest activation energy proceeds via para-cis-dimer states, i.e.\ involving somewhere in the H clusters two H atoms that are positioned on opposite sites within one carbon hexagon. H$_2$ desorption from clusters lacking such H pairs is calculated to occur via hydrogen diffusion causing the formation of para-cis-dimer states. Studying the diffusion events showed a strong dependence of the diffusion energy barriers on the reaction energies and a general odd-even dependence on the number of H atoms in the cis-clusters.Comment: 11 pages, 11 figures, to appear in Phys. Rev.

Global optimization of atomistic structure enhanced by machine learning

Global Optimization with First-principles Energy Expressions (GOFEE) is an efficient method for identifying low energy structures in computationally expensive energy landscapes such as the ones described by density functional theory (DFT), van der Waals-enabled DFT, or even methods beyond DFT. GOFEE relies on a machine learned surrogate model of energies and forces, trained on-the-fly, to explore configuration space, eliminating the need for expensive relaxations of all candidate structures using first-principles methods. In this paper we elaborate on the importance of the use of a Gaussian kernel with two length scales in the Gaussian Process Regression (GPR) surrogate model. We further explore the role of the use in GOFEE of the lower confidence bound for relaxation and selection of candidate structures. In addition, we present two improvements to the method: 1) the population generation now relies on a clustering of all low-energy structures evaluated with DFT, with the lowest energy member of each cluster making up the population. 2) the very final relaxations in well-sampled basins of the energy landscape, the final exploitation steps, are now performed as continued relaxation paths within the first-principles method, to allow for arbitrarily fine relaxations of the best structures, independently of the predictive resolution of the surrogate model. The versatility of the GOFEE method is demonstrated by applying it to identify the low-energy structures of gas-phase fullerene-type 24-atom carbon clusters and of dome-shaped 18-atom carbon clusters supported on Ir(111)

Atomistic Global Optimization X: A Python package for optimization of atomistic structures

Modelling and understanding properties of materials from first principles require knowledge of the underlying atomistic structure. This entails knowing the individual identity and position of all involved atoms. Obtaining such information for macro-molecules, nano-particles, clusters, and for the surface, interface, and bulk phases of amorphous and solid materials represents a difficult high dimensional global optimization problem. The rise of machine learning techniques in materials science has, however, led to many compelling developments that may speed up such structure searches. The complexity of the new methods have established the necessity for an efficient way of experimenting with and assembling them into global optimization algorithms. In this paper we introduce the Atomistic Global Optimization X (AGOX) framework and code, as a customizable approach to building efficient global optimization algorithms. A modular way of expressing global optimization algorithms is described and modern programming practices are used to enable that modularity in the freely available AGOX python package. Two examples of global optimization problems are analyzed: One that is computationally inexpensive which is used to showcase that AGOX enables the expression of multiple global optimization algorithms. As the other example, AGOX is used for solving a complex atomistic optimization problem for a metal-nitride nano-cluster embedded in a graphene sheet as described at the density functional theory (DFT) level.Comment: 12 pages, 11 figure