Machine learning enhanced global optimization by clustering local environments to enable bundled atomic energies.

We show how to speed up global optimization of molecular structures using machine learning methods. To represent the molecular structures, we introduce the auto-bag feature vector that combines (i) a local feature vector for each atom, (ii) an unsupervised clustering of such feature vectors for many atoms across several structures, and (iii) a count for a given structure of how many times each cluster is represented. During subsequent global optimization searches, accumulated structure-energy relations of relaxed structural candidates are used to assign local energies to each atom using supervised learning. Specifically, the local energies follow from assigning energies to each cluster of local feature vectors and demanding the sum of local energies to amount to the structural energies in the least squares sense. The usefulness of the method is demonstrated in basin hopping searches for 19-atom structures described by single- or double-well Lennard-Jones type potentials and for 24-atom carbon structures described by density functional theory. In all cases, utilizing the local energy information derived on-the-fly enhances the rate at which the global minimum energy structure is found.

Supramolecular Corrals on Surfaces Resulting from Aromatic Interactions of Nonplanar Triazoles.

Interaction forces between aromatic moieties, often referred to as π-π interactions, are an important element in stabilizing complex supramolecular structures. For supramolecular self-assembly occurring on surfaces, where aromatic moieties are typically forced to adsorb coplanar with the surface, the possible role of intermolecular aromatic interactions is much less explored. Here, we report on unusual, ring-shaped supramolecular corral surface structures resulting from adsorption of a molecule with nonplanar structure, allowing for intermolecular aromatic interactions. The discrete corral structures are observed using high-resolution scanning tunneling microscopy, and the energetic driving forces for their formation are elucidated using density functional theory calculations and Monte Carlo simulations. The individual corrals involve between 11 and 18 molecules bound through triazole moieties to a ring-shaped ensemble of bridge site positions on (111) surfaces of copper, silver, or gold. The curvature required to form the corrals is identified to result from the angle dependence of aromatic interactions between molecular phenanthrene moieties. The study provides detailed quantitative insights into triazole-surface and aromatic interactions and illustrates how they may be used to drive surface supramolecular self-assembly.

An automated nudged elastic band method.

A robust, efficient, dynamic, and automated nudged elastic band (AutoNEB) algorithm to effectively locate transition states is presented. The strength of the algorithm is its ability to use fewer resources than the nudged elastic band (NEB) method by focusing first on converging a rough path before improving upon the resolution around the transition state. To demonstrate its efficiency, it has been benchmarked using a simple diffusion problem and a dehydrogenation reaction. In both cases, the total number of force evaluations used by the AutoNEB method is significantly less than the NEB method. Furthermore, it is shown that for a fast and robust relaxation to the transition state, a climbing image elastic band method where the full spring force, rather than only the component parallel to the local tangent to the path, is preferred especially for pathways through energy landscapes with multiple local minima. The resulting corner cutting does not affect the accuracy of the transition state as long as this is located with the climbing image method. Finally, a number of pitfalls often encountered while locating the true transition state of a reaction are discussed in terms of systematically exploring the multidimensional energy landscape of a given process.

Pyridine adsorption and diffusion on Pt(111) investigated with density functional theory.

The adsorption, diffusion, and dissociation of pyridine, C5H5N, on Pt(111) are investigated with van der Waals-corrected density functional theory. An elaborate search for local minima in the adsorption potential energy landscape reveals that the intact pyridine adsorbs with the aromatic ring parallel to the surface. Piecewise interconnections of the local minima in the energy landscape reveal that the most favourable diffusion path for pyridine has a barrier of 0.53 eV. In the preferred path, the pyridine remains parallel to the surface while performing small single rotational steps with a carbon-carbon double bond hinged above a single Pt atom. The origin of the diffusion pathway is discussed in terms of the C2-Pt π-bond being stronger than the corresponding CN-Pt π-bond. The energy barrier and reaction enthalpy for dehydrogenation of adsorbed pyridine into an adsorbed, upright bound α-pyridyl species are calculated to 0.71 eV and 0.18 eV, respectively (both zero-point energy corrected). The calculations are used to rationalize previous experimental observations from the literature for pyridine on Pt(111).