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.

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.

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.

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-Based Approach for Solving Atomic Structures of Nanomaterials Combining Pair Distribution Functions with Density Functional Theory.

Determination of crystal structures of nanocrystalline or amorphous compounds is a great challenge in solid-state chemistry and physics. Pair distribution function (PDF) analysis of X-ray or neutron total scattering data has proven to be a key element in tackling this challenge. However, in most cases, a reliable structural motif is needed as a starting configuration for structure refinements. Here, an algorithm that is able to determine the crystal structure of an unknown compound by means of an on-the-fly trained machine learning model, which combines density functional theory calculations with comparison of calculated and measured PDFs for global optimization in an artificial landscape, is presented. Due to the nature of this landscape, even metastable configurations and stacking disorders can be identified.

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.

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.

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.

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.

Water Chemistry beneath Graphene: Condensation of a Dense OH-H2O Phase under Graphene.

Room temperature oxygen hydrogenation below graphene flakes supported by Ir(111) is investigated through a combination of X-ray photoelectron spectroscopy, scanning tunneling microscopy, and density functional theory calculations using an evolutionary search algorithm. We demonstrate how the graphene cover and its doping level can be used to trap and characterize dense mixed O-OH-H2O phases that otherwise would not exist. Our study of these graphene-stabilized phases and their response to oxygen or hydrogen exposure reveals that additional oxygen can be dissolved into them at room temperature creating mixed O-OH-H2O phases with an increased areal coverage underneath graphene. In contrast, additional hydrogen exposure converts the mixed O-OH-H2O phases back to pure OH-H2O with a reduced areal coverage underneath graphene.

Structure of an Ultrathin Oxide on Pt3Sn(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 Pt3Sn(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.

Size-dependent phase stability in transition metal dichalcogenide nanoparticles controlled by metal substrates.

Nanomaterials based on MoS2 and related transition metal dichalcogenides (TMDCs) are remarkably versatile; MoS2 nanoparticles are proven catalysts for processes such as hydrodesulphurization and the hydrogen evolution reaction, and transition metal dichalcogenides in general have recently emerged as novel 2D components for nanoscale electronics and optoelectronics. The properties of such materials are intimately related to their structure and dimensionality. For example, only the edges exposed by MoS2 nanoparticles (NPs) are catalytically active, and extended MoS2 systems show different character (direct or indirect gap semiconducting, or metallic) depending on their thickness and crystallographic phase. In this work, we show how particle size and interaction with a metal surface affect the stability and properties of different MoS2 NPs and the resulting phase diagrams. By means of calculations based on the Density Functional Theory (DFT), we address how support interactions affect MoS2 nanoparticles of varying size, composition, and structure. We demonstrate that interaction with Au modifies the relative stability of the different nanoparticle types so that edge terminations and crystallographic phases that are metastable for free-standing nanoparticles and monolayers are expressed in the supported system. These support-effects are strongly size-dependent due to the mismatch between Au and MoS2 lattices, which explains experimentally observed transitions in the structural phases for supported MoS2 NPs. Accounting for vdW interactions and the contraction of the Au(111) surface underneath the MoS2 is further found to be necessary for quantitatively reproducing experimental results. We finally find that support-induced effects on the stability of nanoparticle structures are general to TMDC nanoparticles on metal surfaces, which we demonstrate also for MoS2 on Au(111), WS2 on Au(111), and WS2 on Ag(111). This work demonstrates how the properties of nanostructured transition metal dichalcogenides and similar layered systems can be modified by the choice of supporting metal.

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.

Structure prediction of surface reconstructions by deep reinforcement learning.

We demonstrate how image recognition and reinforcement learning combined may be used to determine the atomistic structure of reconstructed crystalline surfaces. A deep neural network represents a reinforcement learning agent that obtains training rewards by interacting with an environment. The environment contains a quantum mechanical potential energy evaluator in the form of a density functional theory program. The agent handles the 3D atomistic structure as a series of stacked 2D images and outputs the next atom type to place and the atomic site to occupy. Agents are seen to require 1000-10 000 single point density functional theory evaluations, to learn by themselves how to build the optimal surface reconstructions of anatase TiO2(001)-(1 × 4) and rutile SnO2(110)-(4 × 1).

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.

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.

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.

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.

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.