Accelerating structure search using atomistic graph-based classifiers.

We introduce an atomistic classifier based on a combination of spectral graph theory and a Voronoi tessellation method. This classifier allows for the discrimination between structures from different minima of a potential energy surface, making it a useful tool for sorting through large datasets of atomic systems. We incorporate the classifier as a filtering method in the Global Optimization with First-principles Energy Expressions (GOFEE) algorithm. Here, it is used to filter out structures from exploited regions of the potential energy landscape, whereby the risk of stagnation during the searches is lowered. We demonstrate the usefulness of the classifier by solving the global optimization problem of two-dimensional pyroxene, three-dimensional olivine, Au12, and Lennard-Jones LJ55 and LJ75 nanoparticles.

Cascading symmetry constraint during machine learning-enabled structural search for sulfur-induced Cu(111)-(43×43) surface reconstruction.

In this work, we investigate how exploiting symmetry when creating and modifying structural models may speed up global atomistic structure optimization. We propose a search strategy in which models start from high symmetry configurations and then gradually evolve into lower symmetry models. The algorithm is named cascading symmetry search and is shown to be highly efficient for a number of known surface reconstructions. We use our method for the sulfur-induced Cu (111) (43×43) surface reconstruction for which we identify a new highly stable structure that conforms with the experimental evidence.

Origin of hydroxyl pair formation on reduced anatase TiO2(101).

The interaction of water with metal oxide surfaces is of key importance to several research fields and applications. Because of its ability to photo-catalyze water splitting, reducible anatase TiO2 (a-TiO2) is of particular interest. Here, we combine experiments and theory to study the dissociation of water on bulk-reduced a-TiO2(101). Following large water exposures at room temperature, point-like protrusions appear on the a-TiO2(101) surface, as shown by scanning tunneling microscopy (STM). These protrusions originate from hydroxyl pairs, consisting of terminal and bridging OH groups, OHt/OHb, as revealed by infrared reflection absorption spectroscopy (IRRAS) and valence band experiments. Utilizing density functional theory (DFT) calculations, we offer a comprehensive model of the water/a-TiO2(101) interaction. This model also explains why the hydroxyl pairs are thermally stable up to ∼480 K.

A machine learning potential for simulating infrared spectra of nanosilicate clusters.

The use of machine learning (ML) in chemical physics has enabled the construction of interatomic potentials having the accuracy of ab initio methods and a computational cost comparable to that of classical force fields. Training an ML model requires an efficient method for the generation of training data. Here, we apply an accurate and efficient protocol to collect training data for constructing a neural network-based ML interatomic potential for nanosilicate clusters. Initial training data are taken from normal modes and farthest point sampling. Later on, the set of training data is extended via an active learning strategy in which new data are identified by the disagreement between an ensemble of ML models. The whole process is further accelerated by parallel sampling over structures. We use the ML model to run molecular dynamics simulations of nanosilicate clusters with various sizes, from which infrared spectra with anharmonicity included can be extracted. Such spectroscopic data are needed for understanding the properties of silicate dust grains in the interstellar medium and in circumstellar environments.

Generating candidates in global optimization algorithms using complementary energy landscapes.

Global optimization of atomistic structure relies on the generation of new candidate structures in order to drive the exploration of the potential energy surface (PES) in search of the global minimum energy structure. In this work, we discuss a type of structure generation, which locally optimizes structures in complementary energy (CE) landscapes. These landscapes are formulated temporarily during the searches as machine learned potentials (MLPs) using local atomistic environments sampled from collected data. The CE landscapes are deliberately incomplete MLPs that rather than mimicking every aspect of the true PES are sought to become much smoother, having only a few local minima. This means that local optimization in the CE landscapes may facilitate the identification of new funnels in the true PES. We discuss how to construct the CE landscapes and we test their influence on the global optimization of a reduced rutile SnO2(110)-(4  × 1) surface and an olivine (Mg2SiO4)4 cluster for which we report a new global minimum energy structure.

Dimerization of dehydrogenated polycyclic aromatic hydrocarbons on graphene.

Dimerization of polycyclic aromatic hydrocarbons (PAHs) is an important, yet poorly understood, step in the on-surface synthesis of graphene (nanoribbon), soot formation, and growth of carbonaceous dust grains in the interstellar medium (ISM). The on-surface synthesis of graphene and the growth of carbonaceous dust grains in the ISM require the chemical dimerization in which chemical bonds are formed between PAH monomers. An accurate and cheap method of exploring structure rearrangements is needed to reveal the mechanism of chemical dimerization on surfaces. This work has investigated the chemical dimerization of two dehydrogenated PAHs (coronene and pentacene) on graphene via an evolutionary algorithm augmented by machine learning surrogate potentials and a set of customized structure operators. Different dimer structures on surfaces have been successfully located by our structure search methods. Their binding energies are within the experimental errors of temperature programmed desorption measurements. The mechanism of coronene dimer formation on graphene is further studied and discussed.

Atomistic global optimization X: A Python package for optimization of atomistic structures.

Modeling and understanding properties of materials from first principles require knowledge of the underlying atomistic structure. This entails knowing the individual chemical identity and position of all atoms involved. Obtaining such information for macro-molecules, nano-particles, and 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 structure searches. The complexity of such new methods has prompted a need for an efficient way of assembling them into global optimization algorithms that can be experimented with. In this paper, we introduce the Atomistic Global Optimization X (AGOX) framework and code as a customizable approach that enables efficient building and testing of 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. A number of examples of global optimization approaches are implemented and analyzed. This ranges from random search and basin-hopping to machine learning aided approaches with on-the-fly learnt surrogate energy landscapes. The methods are applied to problems ranging from supported clusters over surface reconstructions to large carbon clusters and metal-nitride clusters incorporated into graphene sheets.

Atomistic structure search using local surrogate model.

We describe a local surrogate model for use in conjunction with global structure search methods. The model follows the Gaussian approximation potential formalism and is based on the smooth overlap of atomic positions descriptor with sparsification in terms of a reduced number of local environments using mini-batch k-means. The model is implemented in the Atomistic Global Optimization X framework and used as a partial replacement of the local relaxations in basin hopping structure search. The approach is shown to be robust for a wide range of atomistic systems, including molecules, nanoparticles, surface supported clusters, and surface thin films. The benefits in a structure search context of a local surrogate model are demonstrated. This includes the ability to benefit from transfer learning from smaller systems as well as the possibility to perform concurrent multi-stoichiometry searches.

Structure of an Ultrathin Oxide on Pt3 Sn(111) Solved by Machine Learning Enhanced Global Optimization.

Determination of the atomic structure of solid surfaces typically depends on comparison of measured properties with simulations based on hypothesized structural models. For simple structures, the models may be guessed, but for more complex structures there is a need for reliable theory-based search algorithms. So far, such methods have been limited by the combinatorial complexity and computational expense of sufficiently accurate energy estimation for surfaces. However, the introduction of machine learning methods has the potential to change this radically. Here, we demonstrate how an evolutionary algorithm, utilizing machine learning for accelerated energy estimation and diverse population generation, can be used to solve an unknown surface structure-the (4×4) surface oxide on Pt3 Sn(111)-based on limited experimental input. The algorithm is efficient and robust, and should be broadly applicable in surface studies, where it can replace manual, intuition based model generation.

Efficient Global Structure Optimization with a Machine-Learned Surrogate Model.

We propose a scheme for global optimization with first-principles energy expressions of atomistic structure. While unfolding its search, the method actively learns a surrogate model of the potential energy landscape on which it performs a number of local relaxations (exploitation) and further structural searches (exploration). Assuming Gaussian processes, deploying two separate kernel widths to better capture rough features of the energy landscape while retaining a good resolution of local minima, an acquisition function is used to decide on which of the resulting structures is the more promising and should be treated at the first-principles level. The method is demonstrated to outperform by 2 orders of magnitude a well established first-principles based evolutionary algorithm in finding surface reconstructions. Finally, global optimization with first-principles energy expressions is utilized to identify initial stages of the edge oxidation and oxygen intercalation of graphene sheets on the Ir(111) surface.

The mechanism of Mg2+ conduction in ammine magnesium borohydride promoted by a neutral molecule.

Light weight and cheap electrolytes with fast multi-valent ion conductivity can pave the way for future high-energy density solid-state batteries, beyond the lithium-ion battery. Here we present the mechanism of Mg-ion conductivity of monoammine magnesium borohydride, Mg(BH4)2·NH3. Density functional theory calculations (DFT) reveal that the neutral molecule (NH3) in Mg(BH4)2·NH3 is exchanged between the lattice and interstitial Mg2+ facilitated by a highly flexible structure, mainly owing to a network of di-hydrogen bonds, N-Hδ+-δH-B and the versatile coordination of the BH4- ligand. DFT shows that di-hydrogen bonds in inorganic matter and hydrogen bonds in bio-materials have similar bond strengths and bond lengths. As a result of the high structural flexibiliy, the Mg-ion conductivity is dramatically improved at moderate temperature, e.g. σ(Mg2+) = 3.3 × 10-4 S cm-1 at T = 80 °C for Mg(BH4)2·NH3, which is approximately 8 orders of magnitude higher than that of Mg(BH4)2. Our results may inspire a new approach for the design and discovery of unprecedented multivalent ion conductors.

Gaussian representation for image recognition and reinforcement learning of atomistic structure.

The success of applying machine learning to speed up structure search and improve property prediction in computational chemical physics depends critically on the representation chosen for the atomistic structure. In this work, we investigate how different image representations of two planar atomistic structures (ideal graphene and graphene with a grain boundary region) influence the ability of a reinforcement learning algorithm [the Atomistic Structure Learning Algorithm (ASLA)] to identify the structures from no prior knowledge while interacting with an electronic structure program. Compared to a one-hot encoding, we find a radial Gaussian broadening of the atomic position to be beneficial for the reinforcement learning process, which may even identify the Gaussians with the most favorable broadening hyperparameters during the structural search. Providing further image representations with angular information inspired by the smooth overlap of atomic positions method, however, is not found to cause further speedup of ASLA.

Chemically-resolved determination of hydrogenated graphene-substrate interaction.

Functionalization of graphene on Ir(111) is a promising route to modify graphene by chemical means in a controlled fashion at the nanoscale. Yet, the nature of such functionalized sp3 nanodots remains unknown. Density functional theory (DFT) calculations alone cannot differentiate between two plausible structures, namely true graphane and substrate stabilized graphane-like nanodots. These two structures, however, interact dramatically differently with the underlying substrate. Discriminating which type of nanodots forms on the surface is thus of paramount importance for the applications of such prepared nanostructures. By comparing X-ray standing wave measurements against theoretical model structures obtained by DFT calculations we are able to exclude the formation of true graphane nanodots and clearly show the formation graphane-like nanodots.

Structure and Dynamics of Individual Diastereomeric Complexes on Platinum: Surface Studies Related to Heterogeneous Enantioselective Catalysis.

The modification of heterogeneous catalysts through the chemisorption of chiral molecules is a method to create catalytic sites for enantioselective surface reactions. The chiral molecule is called a chiral modifier by analogy to the terms chiral auxiliary or chiral ligand used in homogeneous asymmetric catalysis. While there has been progress in understanding how chirality transfer occurs, the intrinsic difficulties in determining enantioselective reaction mechanisms are compounded by the multisite nature of heterogeneous catalysts and by the challenges facing stereospecific surface analysis. However, molecular descriptions have now emerged that are sufficiently detailed to herald rapid advances in the area. The driving force for the development of heterogeneous enantioselective catalysts stems, at the minimum, from the practical advantages they might offer over their homogeneous counterparts in terms of process scalability and catalyst reusability. The broader rewards from their study lie in the insights gained on factors controlling selectivity in heterogeneous catalysis. Reactions on surfaces to produce a desired enantiomer in high excess are particularly challenging since at room temperature, barrier differences as low as ∼2 kcal/mol between pathways to R and S products are sufficient to yield an enantiomeric ratio (er) of 90:10. Such small energy differences are comparable to weak interadsorbate interaction energies and are much smaller than chemisorption or even most physisorption energies. In this Account, we describe combined experimental and theoretical surface studies of individual diastereomeric complexes formed between chiral modifiers and prochiral reactants on the Pt(111) surface. Our work is inspired by the catalysis literature on the enantioselective hydrogenation of activated ketones on cinchona-modified Pt catalysts. Using scanning tunneling microscopy (STM) measurements and density functional theory (DFT) calculations, we probe the structures and relative abundances of non-covalently bonded complexes formed between three representative prochiral molecules and (R)-(+)-1-(1-naphthyl)ethylamine ((R)-NEA). All three prochiral molecules, 2,2,2-trifluoroacetophenone (TFAP), ketopantolactone (KPL), and methyl 3,3,3-trifluoropyruvate (MTFP), are found to form multiple complexation configurations around the ethylamine group of chemisorbed (R)-NEA. The principal intermolecular interaction is NH···O H-bonding. In each case, submolecularly resolved STM images permit the determination of the prochiral ratio (pr), pro-R to pro-S, proper to specific locations around the ethylamine group. The overall pr observed in experiments on large ensembles of KPL-(R)-NEA complexes is close to the er reported in the literature for the hydrogenation of KPL to pantolactone on (R)-NEA-modified Pt catalysts at 1 bar H2. The results of independent DFT and STM studies are merged to determine the geometries of the most abundant complexation configurations. The structures reveal the hierarchy of chemisorption and sometimes multiple H-bonding interactions operating in complexes. In particular, privileged complexes formed by KPL and MTFP reveal the participation of secondary CH···O interactions in stereocontrol. State-specific STM measurements on individual TFAP-(R)-NEA complexes show that complexation states interconvert through processes including prochiral inversion. The state-specific information on structure, prochirality, dynamics, and energy barriers delivered by the combination of DFT and STM provides insight on how to design better chiral modifiers.

Water Dissociation and Hydroxyl Ordering on Anatase TiO_{2}(001)-(1×4).

We studied the interaction of water with the anatase TiO_{2}(001) surface by means of scanning tunneling microscopy, x-ray photoelectron spectroscopy, and density functional theory calculations. Water adsorbs dissociatively on the ridges of a (1×4) reconstructed surface, resulting in a (3×4) periodic structure of hydroxyl pairs. We observed this process at 120 K, and the created hydroxyls desorb from the surface by recombination to water, which occurs below 300 K. Our calculations reveal the water dissociation mechanism and uncover a very pronounced dependence on the coverage. This strong coverage dependence is explained through water-induced reconstruction on anatase TiO_{2}(001)-(1×4). The high intrinsic reactivity of the anatase TiO_{2}(001) surface towards water observed here is fundamentally different from that seen on other surfaces of titania and may explain its high catalytic activity in heterogeneous catalysis and photocatalysis.

Exploration versus Exploitation in Global Atomistic Structure Optimization.

The ability to navigate vast energy landscapes of molecules, clusters, and solids is a necessity for discovering novel compounds in computational chemistry and materials science. For high-dimensional systems, it is only computationally feasible to search a small portion of the landscape, and hence, the search strategy is of critical importance. Introducing Bayesian optimization concepts in an evolutionary algorithm framework, we quantify the concepts of exploration and exploitation in global minimum searches. The method allows us to control the balance between probing unknown regions of the landscape (exploration) and investigating further regions of the landscape known to have low-energy structures (exploitation). The search for global minima structures proves significantly faster with the optimal balance for three test systems (molecular compounds) and to a lesser extent also for a crystalline surface reconstruction. In addition, global search behaviors are analyzed to provide reasonable grounds for an optimal balance for different problems.

An extended chiral surface coordination network based on Ag7-clusters.

We present an extended metal-coordinated structure obtained by deposition of trimesic acid (TMA) onto the Ag(111) surface under ultra-high vacuum conditions followed by annealing to 510 K. Scanning tunneling microscopy and density functional theory calculations reveal the structure to consist of metal clusters containing seven Ag atoms each, coordinated by six dehydrogenated TMA molecules. The molecules are asymmetrically arranged, resulting in a chiral structure. The calculations confirm that this structure has a lower free energy under the experimental conditions than the hydrogen-bonded structures observed after annealing at lower temperatures. We show that the formation of such large metal clusters is possible due to the low adatom formation energy on silver and the relatively strong Ag-O bond in combination with a good lattice match between the structure and the Ag surface.

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.

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.

Structure of the SnO_{2}(110)-(4×1) Surface.

Using surface x-ray diffraction (SXRD), quantitative low-energy electron diffraction (LEED), and density-functional theory (DFT) calculations, we have determined the structure of the (4×1) reconstruction formed by sputtering and annealing of the SnO_{2}(110) surface. We find that the reconstruction consists of an ordered arrangement of Sn_{3}O_{3} clusters bound atop the bulk-terminated SnO_{2}(110) surface. The model was found by application of a DFT-based evolutionary algorithm with surface compositions based on SXRD, and shows excellent agreement with LEED and with previously published scanning tunneling microscopy measurements. The model proposed previously consisting of in-plane oxygen vacancies is thus shown to be incorrect, and our result suggests instead that Sn(II) species in interstitial positions are the more relevant features of reduced SnO_{2}(110) surfaces.