Esben L. Kolsbjerg

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).

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.

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.

Rotation and diffusion of naphthalene on Pt(111)

The behavior of naphthalene on Pt(111) surfaces is studied by combining insight from scanning tunneling microscopy (STM) and van der Waals enabled density functional theory. Adsorption, diffusion, and rotation are investigated by a series of variable temperature STM experiments revealing naphthalene ability to rotate on-site with ease with a rotational barrier of 0.69 eV. Diffusion to neighbouring sites is found to be more difficult. The experimental results are in good agreement with the theoretical investigations which confirm that the barrier for diffusion is slightly higher than the one for rotation. The theoretical barriers for rotation and translation are found to be 0.75 and 0.78 eV, respectively. An automatic mapping of the possible diffusion pathways reveals very detailed diffusion paths with many small local minima that would have been practically impossible to find manually. This automated procedure provides detailed insight into the preferred diffusion pathways that are important for our understanding of molecule-substrate interactions.

NH3 adsorption on anatase-TiO2(101)

The adsorption of ammonia on anatase TiO2 is of fundamental importance for several catalytic applications of TiO2 and for probing acid-base interactions. Utilizing high-resolution scanning tunneling microscopy (STM), synchrotron X-ray photoelectron spectroscopy, temperature-programmed desorption (TPD), and density functional theory (DFT), we identify the adsorption mode and quantify the adsorption strength on the anatase TiO2(101) surface. It was found that ammonia adsorbs non-dissociatively as NH3 on regular five-fold coordinated titanium surface sites (5f-Ti) with an estimated exothermic adsorption energy of 1.2 eV for an isolated ammonia molecule. For higher adsorbate coverages, the adsorption energy progressively shifts to smaller values, due to repulsive intermolecular interactions. The repulsive adsorbate-adsorbate interactions are quantified using DFT and autocorrelation analysis of STM images, which both showed a repulsive energy of ∼50 meV for nearest neighbor sites and a lowering in binding energy for an ammonia molecule in a full monolayer of 0.28 eV, which is in agreement with TPD spectra.

Exciting H2 Molecules for Graphene Functionalization

Hydrogen functionalization of graphene by exposure to vibrationally excited H2 molecules is investigated by combined scanning tunneling microscopy, high-resolution electron energy loss spectroscopy, X-ray photoelectron spectroscopy measurements, and density functional theory calculations. The measurements reveal that vibrationally excited H2 molecules dissociatively adsorb on graphene on Ir(111) resulting in nanopatterned hydrogen functionalization structures. Calculations demonstrate that the presence of the Ir surface below the graphene lowers the H2 dissociative adsorption barrier and allows for the adsorption reaction at energies well below the dissociation threshold of the H–H bond. The first reacting H2 molecule must contain considerable vibrational energy to overcome the dissociative adsorption barrier. However, this initial adsorption further activates the surface resulting in reduced barriers for dissociative adsorption of subsequent H2 molecules. This enables functionalization by H2 molecules with lower vibrational energy, yielding an avalanche effect for the hydrogenation reaction. These results provide an example of a catalytically active graphene-coated surface and additionally set the stage for a re-interpretation of previous experimental work involving elevated H2 background gas pressures in the presence of hot filaments.