Universal machine learning interatomic potentials (uMLIPs) have recently been formulated and shown to generalize well. When applied out-of-sample, further data collection for improvement of the uMLIPs may, however, be required. In this work we demonstrate that, whenever the envisaged use of the MLIPs is global optimization, the data acquisition can follow an active learning scheme in which a gradually updated uMLIP directs the finding of new structures, which are subsequently evaluated at the density functional theory (DFT) level. In the scheme, we augment foundation models using a Δ-model based on this new data using local SOAP-descriptors, Gaussian kernels, and a sparse Gaussian process regression model. We compare the efficacy of the approach with different global optimization algorithms, random structure search, basin hopping, a Bayesian approach with competitive candidates (GOFEE), and a replica exchange formulation (REX). We further compare several foundation models, CHGNet, MACE-MP0, and MACE-MPA. The test systems are silver-sulfur clusters and sulfur-induced surface reconstructions on Ag(111) and Ag(100). Judged by the fidelity of identifying global minima, active learning with GPR-based Δ-models appears to be a robust approach. Judged by the total CPU time spent, the REX approach stands out as being the most efficient.

The characterization of nanostructured materials under reactive environments is challenging due to the complexity of the structural motifs involved and their chemical transformations. Global optimization approaches allow predicting stable structures for targeted materials, but addressing the configurational and compositional search spaces is both computationally demanding and inefficient, especially when first-principles calculations are required. In this work, we implement and evaluate a computationally efficient grand canonical global optimization algorithm able to identify stable structures and chemical states of targeted systems under given reaction conditions (e.g., reactant pressure and temperature). The algorithm leverages an on-the-fly trained machine-learning interatomic potential based on sparse Gaussian process regression and the smooth overlap of atomic positions descriptor to reduce the number of first-principles energy evaluations carried out during global optimization searches. The ab initio thermodynamics framework is incorporated to approximate the Gibbs energy of evaluated candidates, performing environment-aware optimizations over multiple stoichiometries. We demonstrate the computational performance of this approach and its ability to reproduce some literature examples.

We present a study the initial stages of ice growth on pristine and oxygen-functionalized highly oriented pyrolytic graphite (O-HOPG), combining low-temperature scanning tunneling microscopy (LT-STM) and machine-learning structural searches. LT-STM images show that oxygen atoms act as nucleation sites for ice growth, and that the size, structure and porosity of the nanometer-sized ice clusters depend strongly on the growth temperature. Machine learning-assisted structural searches and first-principles energy calculations confirm that clusters of water molecules are likely to bind to chemisorbed oxygen atoms through hydrogen bonding. During the early stages of the cluster growth clusters of water molecules are likely to be immobilized by binding to more than one chemisorbed oxygen atom through hydrogen bonding. However, the energy gain by hydrogen bond formation of a molecule, upon incorporation into smaller clusters only bound to a single oxygen atom, is large enough to induce cluster diffusion and favor the growth of larger ice clusters. Our results demonstrate that the mobility of water molecules is significantly lowered in the presence of defects on the surface. The observed lower mobility on defected carbon presented here offers an enhanced understanding of macroscopic anti-icing properties observed for functionalized HOPG under ambient conditions and provides insight into the early stages of ice growth on dust grain surfaces in interstellar space.

We present a generative modeling framework for atomistic systems that combines score-based diffusion for atomic positions with a novel continuous-time discrete diffusion process for atomic types. This approach enables flexible and physically grounded generation of atomic structures across chemical and structural domains. Applied to metallic clusters and two-dimensional materials using the QCD and C2DB datasets, our models achieve strong performance in fidelity and diversity, evaluated using precision-recall metrics against synthetic baselines. We demonstrate atomic type interpolation for generating bimetallic clusters beyond the training distribution, and use classifier-free guidance to steer sampling toward specific crystallographic symmetries in two-dimensional materials. These capabilities are implemented in Atomistic Generative Diffusion (AGeDi), an open-source, extensible software package for atomistic generative diffusion modeling.

Universal potentials open the door for DFT level calculations at a fraction of their cost. We find that for application to systems outside the scope of its training data, pretrained CHGNet [Deng et al., Nat. Mach. Intell. 5, 1031 (2023)] has the potential to succeed out of the box, but can also fail significantly in predicting the ground state configuration. We demonstrate that via fine-tuning or a Δ-learning approach it is possible to augment the overall performance of universal potentials for specific cluster and surface systems. We utilize this to investigate and explain experimentally observed defects in the Ag(111)-O surface reconstruction and explain the mechanics behind their formation.

Studying the anharmonicity in the infrared (IR) spectra of polycyclic aromatic hydrocarbons (PAHs) at elevated temperatures is important to understand the vibrational features and chemical properties of interstellar dust, especially in the James Webb Space Telescope (JWST) era. We take pyrene as an example PAH and investigate how different degrees of superhydrogenation affect the applicability of the harmonic approximation and the role of temperature in the IR spectra of PAHs. This is achieved by comparing the theoretical IR spectra generated by classical molecular dynamics (MD) simulations and the experimental IR spectra obtained via gas-phase action spectroscopy, which utilizes the infrared multiple photon dissociation. All simulations are accelerated by a machine learning interatomic potential, in order to reach first-principles accuracies while keeping computational costs low. We have found that the harmonic approximation with empirical scaling factors is able to reproduce experimental band profile of pristine and partially superhydrogenated pyrene cations. However, a MD-based anharmonic treatment is mandatory in the case of fully superhydrogenated pyrene cation for matching theory and experiment. In addition, band shifts and broadenings as the temperature increases are investigated in detail. These findings may aid in the interpretation of JWST observations on the variations in band positions and widths of interstellar dust.

Machine learning interatomic potentials have become an indispensable tool for materials science, enabling the study of larger systems and longer timescales. State-of-the-art models are generally graph neural networks that employ message passing to iteratively update atomic embeddings that are ultimately used for predicting properties. In this work we extend the message passing formalism with the inclusion of a continuous variable that accounts for fractional atomic existence. This allows us to calculate the gradient of the Gibbs free energy with respect to both the Cartesian coordinates of atoms and their existence. Using this we propose a gradient-based grand canonical optimization method and document its capabilities for a Cu(110) surface oxide.

Foundation models of interatomic potentials, the so called universal potentials, may require fine-tuning or residual corrections when applied to specific subclasses of materials. In the present work, we demonstrate how such an augmentation can be accomplished via Δ-learning based on the representation already embedded in the universal potentials. The Δ-model introduced is a Gaussian Process Regression (GPR) model, and various types of aggregation (global, species-separated, and atomic) of the representation vector are discussed. Employing a specific universal potential, CHGNet [Deng et al., Nat. Mach. Intell. 5, 1031 (2023)], in a global structure optimization setting, we find that it correctly describes the energetics of the “8” Cu oxide, which is an ultra-thin oxide film on Cu(111). The universal potential model even predicts a more favorable structure compared with that discussed in recent density functional theory-based literature. Moving to sulfur adatom overlayers on Cu(111), Ag(111), and Au(111), the CHGNet model, however, requires corrections. We demonstrate that these are efficiently provided via the GPR-based Δ-model formulated on CHGNet’s own internal atomic embedding representation. The need for corrections is tracked to the scarcity of metal–sulfur atomic environments in the materials project database that CHGNet is trained on, leading to an overreliance on sulfur–sulfur atomic environments. Other universal potentials trained on the same data, MACE-MP0, SevenNet-0, and ORB-v2-only-MPtrj, show a similar behavior but with varying degrees of error, demonstrating the general need for augmentation schemes for universal potential models.

While polycyclic aromatic hydrocarbons (PAHs) are now accepted to be abundant in interstellar space, the abundance and influence of superhydrogenated PAHs (HPAHs) in the interstellar medium (ISM) are still under investigation. HPAHs may act as catalysts for or reactants in small-molecule formation via hydrogen abstraction reactions, H _2 evaporation, and carbon skeleton fragmentation. Here, we present a gas-phase infrared (IR) action spectroscopy study of the HPAH 4, 5, 9, 10-tetrahydropyrene (THP; C _16 H _14 ), performed at the Free Electron Lasers for Infrared eXperiments facility. IR action spectroscopy was performed on the THP cation, protonated THP, and their fragments produced by collision-induced dissociation in the range from 600 to 1800 cm ^−1 . Calculated IR spectra, at the density functional theory level, agree with experimental IR spectra to a high degree and were utilized to determine molecular structures of the HPAH fragments. Molecular dynamics simulations compared with experimental mass spectra reveal favorable HPAH fragmentation pathways. Molecular hydrogen (H _2 ) is observed to be a primary fragment of [THP+H] ^+ with superhydrogenated duo groups. This contrasts the notion that HPAHs typically undergo carbon skeleton fragmentation leading to C _x H _y formation. These observations show that lowered symmetry and duo or trio aliphatic groups on HPAHs uniquely change their IR spectra, stability, and fragmentation patterns. As a result, these species may contribute to H _2 formation in the ISM.

Reliable uncertainty measures are required when using data-based machine learning interatomic potentials (MLIPs) for atomistic simulations. In this work, we propose for sparse Gaussian process regression (GPR) type MLIPs a stochastic uncertainty measure akin to the query-by-committee approach often used in conjunction with neural network based MLIPs. The uncertainty measure is coined ‘label noise’ ensemble uncertainty as it emerges from adding noise to the energy labels in the training data. We find that this method of calculating an ensemble uncertainty is as well calibrated as the one obtained from the closed-form expression for the posterior variance when the sparse GPR is treated as a projected process. Comparing the two methods, our proposed ensemble uncertainty is, however, faster to evaluate than the closed-form expression. Finally, we demonstrate that the proposed uncertainty measure acts better to support a Bayesian search for optimal structure of Au _20 clusters.

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.

We present a generative diffusion model specifically tailored to the discovery of surface structures. The generative model takes into account substrate registry and periodicity by including fixed substrate atoms and z-directional confinement. Using a rotational equivariant neural network architecture, we design a method that trains a denoiser network for diffusion alongside a forcefield for guided sampling of low-energy surface phases. An effective data-augmentation scheme for training the denoiser network is introduced to allow for scaling the structure generation far beyond structure sizes represented in the training data. We showcase the generative model by investigating multiple surface systems and propose an atomistic structure model for a silver-oxide domain boundary of unprecedented size.

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.

We present gas-phase infrared (IR) spectra of protonated dihydropentacene, the hydrogen functionalised form of the linear, catacondensed, polycyclic aromatic hydrocarbon (PAH), pentacene. Experimental IR spectra are obtained by IR multiple-photon dissociation spectroscopy measurements, while density functional theory calculations provide theoretical spectra. The comparison with the gas-phase spectrum of protonated pentacene reveals the effect of H-atom functionalisation on the IR spectra of PAHs thereby enabling the identification of such species in the interstellar medium.

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.

The high performance of platinum-tin catalysts for oxidation reactions has been linked to the formation of tin oxides at the metal surface, but little is known about the structure of these oxides or the chemical behavior that determines their catalytic properties. We show here how surface oxides on Pt3Sn(111) incorporate oxygen at the metal interface, which may be subsequently removed by reaction with CO. The storage mechanism, where oxygen uptake occurs without loss of interfacial Pt-Sn bonds, is enabled by the peculiar asymmetrical coordination state of Sn2+. O atoms are bound at pocket sites in the 2D oxide sheet between these outward-buckled Sn atoms and metallic Sn in the alloy surface below.

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.

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.

The honeycomb lattice of silicene exhibits a variety of nontrivial reconstructions on the Ag(111) surface, whose diversity hampers the theoretical prediction of experimentally unidentified structures using computationally expensive density functional theory (DFT) calculations. We here apply an efficient method based on an evolutionary algorithm and a Gaussian process, which is trained on the fly with DFT calculations, to the search for the stable structures of silicene on Ag(111). We demonstrate that the structure search method can not only reproduce the well-known structures, but also predict the existence of metastable structures that are close in stability to the most stable ones. Detailed analyses of the obtained results reveal that such metastable structures play crucial roles in the stabilization of less ordered phases often observed experimentally. The present method can replace the conventional manual search based on intuition and is widely applicable to the investigations of new systems such as emerging two-dimensional materials.

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.