Showing 1–31 of 31 results for author: Hammer, B

Efficient Grand Canonical Global Optimization with On-the-fly-trained Machine-learning Interatomic Potentials

Authors: Jon Eunan Quinlivan Dominguez, Mads-Peter Verner Christiansen, Konstantin M. Neyman, Bøjrk Hammer, Albert Bruix

Abstract: 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, especiall… ▽ More 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 \textit{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. △ Less

Submitted 29 June, 2026; v1 submitted 24 September, 2025; originally announced September 2025.

Gradient-based grand canonical optimization enabled by graph neural networks with fractional atomic existence

Authors: Mads-Peter Verner Christiansen, Bjørk Hammer

Abstract: 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 i… ▽ More 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. △ Less

Submitted 28 September, 2025; v1 submitted 25 July, 2025; originally announced July 2025.

Journal ref: Mach. Learn.: Sci. Technol. 6, 045049 (2025)

Active Δ-learning with universal potentials for global structure optimization

Authors: Joe Pitfield, Mads-Peter Verner Christiansen, Bjørk Hammer

Abstract: 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 gradu… ▽ More 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. △ Less

Submitted 24 July, 2025; originally announced July 2025.

Cascading symmetry constraint during machine learning-enabled structural search for sulfur induced Cu(111)-$(\sqrt{43}\times\sqrt{43})$ surface reconstruction

Authors: Florian Brix, Mads-Peter Verner Christiansen, Bjørk Hammer

Abstract: 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 s… ▽ More 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) $(\sqrt{43}\times\sqrt{43})$ surface reconstruction for which we identify a new highly stable structure which conforms with experimental evidence. △ Less

Submitted 1 April, 2025; originally announced April 2025.

Journal ref: J. Chem. Phys. 160, 174107 (2024)

$Δ$-model correction of Foundation Model based on the models own understanding

Authors: Mads-Peter Verner Christiansen, Bjørk Hammer

Abstract: Foundation models of interatomic potentials, 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 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 Regressio… ▽ More Foundation models of interatomic potentials, 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 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 to that discussed in recent DFT-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 the 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 similar behavior, but with varying degrees of error, demonstrating the general need for augmentation schemes for universal potential models. △ Less

Submitted 31 March, 2025; v1 submitted 28 February, 2025; originally announced February 2025.

Comments: 10 pages, 9 figures

Journal ref: J. Chem. Phys. 162, 184701 (2025)

Augmentation of Universal Potentials for Broad Applications

Authors: Joe Pitfield, Florian Brix, Zeyuan Tang, Andreas Møller Slavensky, Nikolaj Rønne, Mads-Peter Verner Christiansen, Bjørk Hammer

Abstract: 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, CHGNet\cite{deng2023chgnet} 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… ▽ More 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, CHGNet\cite{deng2023chgnet} 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 its formation. △ Less

Submitted 19 July, 2024; originally announced July 2024.

Journal ref: Phys. Rev. Lett. 134, 056201 (2025)

Accelerating structure search using atomistic graph-based classifiers

Authors: Andreas Møller Slavensky, Bjørk Hammer

Abstract: 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… ▽ More 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 2-dimensional pyroxene, 3-dimensional olivine, Au12, and Lennard-Jones LJ55 and LJ75 nanoparticles. △ Less

Submitted 18 July, 2024; originally announced July 2024.

Comments: 12 pages, 10 figures

Journal ref: J. Chem. Phys. 161, 014713 (2024)

Generating candidates in global optimization algorithms using complementary energy landscapes

Authors: Andreas Møller Slavensky, Mads-Peter V. Christensen, Bjørk Hammer

Abstract: Global optimization of atomistic structure rely on the generation of new candidate structures in order to drive the exploration of the potential energy surface (PES) in search for the global minimum energy (GM) 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 d… ▽ More Global optimization of atomistic structure rely on the generation of new candidate structures in order to drive the exploration of the potential energy surface (PES) in search for the global minimum energy (GM) 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 few local minima. This means that local optimization in the CE landscapes may facilitate identification of new funnels in the true PES. We discuss how to construct the CE landscapes and we test their influence on global optimization of a reduced rutile SnO2(110)-(4x1) surface, and an olivine (Mg2SiO4)4 cluster for which we report a new global minimum energy structure. △ Less

Submitted 28 February, 2024; originally announced February 2024.

Comments: 13 pages, 9 figures

Journal ref: J. Chem. Phys. 159, 024123 (2023)

Generative diffusion model for surface structure discovery

Authors: Nikolaj Rønne, Alán Aspuru-Guzik, Bjørk Hammer

Abstract: 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 masked 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 force-field for guided sampl… ▽ More 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 masked 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 force-field for guided sampling of low-energy surface phases. An effective data-augmentation scheme for training the denoiser-network is proposed to scale 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 previously unknown silver-oxide domain-boundary of unprecedented size. △ Less

Submitted 2 July, 2024; v1 submitted 27 February, 2024; originally announced February 2024.

Journal ref: Phys. Rev. B 110, 235427 (2024)

Machine learning based approach for solving atomic structures of nanomaterials combining pair distribution functions with density functional theory

Authors: Magnus Kløve, Sanna Sommer, Bo B. Iversen, Bjørk Hammer, Wilke Dononelli

Abstract: Determination of crystal structures of nanocrystalline or amorphous compounds is a great challenge in solid states 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 starting configuration for structure refinements. Here,… ▽ More Determination of crystal structures of nanocrystalline or amorphous compounds is a great challenge in solid states 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 starting configuration for structure refinements. Here, we present 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 that combines density functional theory (DFT) calculations with comparison of calculated and measured PDFs for global optimization in an artificial landscape. Due to the nature of this landscape, even metastable configurations can be determined. △ Less

Submitted 14 September, 2022; v1 submitted 3 September, 2022; originally announced September 2022.

Dimerization of dehydrogenated polycyclic aromatic hydrocarbons on graphene

Authors: Zeyuan Tang, Bjørk Hammer

Abstract: 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 for… ▽ More 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. △ Less

Submitted 12 April, 2022; originally announced April 2022.

Comments: 8 pages, 6 figures

Journal ref: J. Chem. Phys. 156, 134703 (2022)

Atomistic Global Optimization X: A Python package for optimization of atomistic structures

Authors: Mads-Peter Verner Christiansen, Nikolaj Rønne, Bjørk Hammer

Abstract: Modelling and understanding properties of materials from first principles require knowledge of the underlying atomistic structure. This entails knowing the individual identity and position of all involved atoms. Obtaining such information for macro-molecules, nano-particles, clusters, and for the surface, interface, and bulk phases of amorphous and solid materials represents a difficult high dimen… ▽ More Modelling and understanding properties of materials from first principles require knowledge of the underlying atomistic structure. This entails knowing the individual identity and position of all involved atoms. Obtaining such information for macro-molecules, nano-particles, 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 such structure searches. The complexity of the new methods have established the necessity for an efficient way of experimenting with and assembling them into global optimization algorithms. In this paper we introduce the Atomistic Global Optimization X (AGOX) framework and code, as a customizable approach to building efficient 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. Two examples of global optimization problems are analyzed: One that is computationally inexpensive which is used to showcase that AGOX enables the expression of multiple global optimization algorithms. As the other example, AGOX is used for solving a complex atomistic optimization problem for a metal-nitride nano-cluster embedded in a graphene sheet as described at the density functional theory (DFT) level. △ Less

Submitted 19 August, 2022; v1 submitted 4 April, 2022; originally announced April 2022.

Comments: 18 pages, 19 figures

Journal ref: J. Chem. Phys. 157, 054701 (2022)

Global optimization of atomistic structure enhanced by machine learning

Authors: Malthe K. Bisbo, Bjørk Hammer

Abstract: Global Optimization with First-principles Energy Expressions (GOFEE) is an efficient method for identifying low energy structures in computationally expensive energy landscapes such as the ones described by density functional theory (DFT), van der Waals-enabled DFT, or even methods beyond DFT. GOFEE relies on a machine learned surrogate model of energies and forces, trained on-the-fly, to explore… ▽ More Global Optimization with First-principles Energy Expressions (GOFEE) is an efficient method for identifying low energy structures in computationally expensive energy landscapes such as the ones described by density functional theory (DFT), van der Waals-enabled DFT, or even methods beyond DFT. GOFEE relies on a machine learned surrogate model of energies and forces, trained on-the-fly, to explore configuration space, eliminating the need for expensive relaxations of all candidate structures using first-principles methods. In this paper we elaborate on the importance of the use of a Gaussian kernel with two length scales in the Gaussian Process Regression (GPR) surrogate model. We further explore the role of the use in GOFEE of the lower confidence bound for relaxation and selection of candidate structures. In addition, we present two improvements to the method: 1) the population generation now relies on a clustering of all low-energy structures evaluated with DFT, with the lowest energy member of each cluster making up the population. 2) the very final relaxations in well-sampled basins of the energy landscape, the final exploitation steps, are now performed as continued relaxation paths within the first-principles method, to allow for arbitrarily fine relaxations of the best structures, independently of the predictive resolution of the surrogate model. The versatility of the GOFEE method is demonstrated by applying it to identify the low-energy structures of gas-phase fullerene-type 24-atom carbon clusters and of dome-shaped 18-atom carbon clusters supported on Ir(111). △ Less

Submitted 30 December, 2020; originally announced December 2020.

Journal ref: Phys. Rev. B 105, 245404 (2022)

Atomistic Structure Learning Algorithm with surrogate energy model relaxation

Authors: Henrik Lund Mortensen, Søren Ager Meldgaard, Malthe Kjær Bisbo, Mads-Peter V. Christiansen, Bjørk Hammer

Abstract: The recently proposed Atomistic Structure Learning Algorithm (ASLA) builds on neural network enabled image recognition and reinforcement learning. It enables fully autonomous structure determination when used in combination with a first-principles total energy calculator, e.g. a density functional theory (DFT) program. To save on the computational requirements, ASLA utilizes the DFT program in a s… ▽ More The recently proposed Atomistic Structure Learning Algorithm (ASLA) builds on neural network enabled image recognition and reinforcement learning. It enables fully autonomous structure determination when used in combination with a first-principles total energy calculator, e.g. a density functional theory (DFT) program. To save on the computational requirements, ASLA utilizes the DFT program in a single-point mode, i.e. without allowing for relaxation of the structural candidates according to the force information at the DFT level. In this work, we augment ASLA to establish a surrogate energy model concurrently with its structure search. This enables approximative but computationally cheap relaxation of the structural candidates before the single-point energy evaluation with the computationally expensive DFT program. We demonstrate a significantly increased performance of ASLA for building benzene while utilizing a surrogate energy landscape. Further we apply this model-enhanced ASLA in a thorough investigation of the c(4x8) phase of the Ag(111) surface oxide. ASLA successfully identifies a surface reconstruction which has previously only been guessed on the basis of scanning tunnelling microscopy images. △ Less

Submitted 15 July, 2020; originally announced July 2020.

Journal ref: Phys. Rev. B 102, 075427 (2020)

Supervised Learning in the Presence of Concept Drift: A modelling framework

Authors: Michiel Straat, Fthi Abadi, Zhuoyun Kan, Christina Göpfert, Barbara Hammer, Michael Biehl

Abstract: We present a modelling framework for the investigation of supervised learning in non-stationary environments. Specifically, we model two example types of learning systems: prototype-based Learning Vector Quantization (LVQ) for classification and shallow, layered neural networks for regression tasks. We investigate so-called student teacher scenarios in which the systems are trained from a stream o… ▽ More We present a modelling framework for the investigation of supervised learning in non-stationary environments. Specifically, we model two example types of learning systems: prototype-based Learning Vector Quantization (LVQ) for classification and shallow, layered neural networks for regression tasks. We investigate so-called student teacher scenarios in which the systems are trained from a stream of high-dimensional, labeled data. Properties of the target task are considered to be non-stationary due to drift processes while the training is performed. Different types of concept drift are studied, which affect the density of example inputs only, the target rule itself, or both. By applying methods from statistical physics, we develop a modelling framework for the mathematical analysis of the training dynamics in non-stationary environments. Our results show that standard LVQ algorithms are already suitable for the training in non-stationary environments to a certain extent. However, the application of weight decay as an explicit mechanism of forgetting does not improve the performance under the considered drift processes. Furthermore, we investigate gradient-based training of layered neural networks with sigmoidal activation functions and compare with the use of rectified linear units (ReLU). Our findings show that the sensitivity to concept drift and the effectiveness of weight decay differs significantly between the two types of activation function. △ Less

Submitted 27 February, 2021; v1 submitted 21 May, 2020; originally announced May 2020.

Comments: 17 pages in twocolumn

Journal ref: Neural Computing and Applications 2021

Efficient global structure optimization with a machine learned surrogate model

Authors: Malthe K. Bisbo, Bjørk Hammer

Abstract: We propose a scheme for global optimization with first-principles energy expressions (GOFEE) 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, an acquisition function is used to… ▽ More We propose a scheme for global optimization with first-principles energy expressions (GOFEE) 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, an acquisition function is used to decide on which of the resulting structures is the more promising. Subsequently, a single point first-principles energy calculation is conducted for that structure. The method is demonstrated to outperform by two orders of magnitude a well established first-principles based evolutionary algorithm in finding surface reconstructions. Finally, GOFEE is utilized to identify initial stages of the edge oxidation and oxygen intercalation of graphene sheets on the Ir(111) surface. △ Less

Submitted 12 July, 2019; originally announced July 2019.

Journal ref: Phys. Rev. Lett. 124, 086102 (2020)

Prototype-based classifiers in the presence of concept drift: A modelling framework

Authors: Michael Biehl, Fthi Abadi, Christina Göpfert, Barbara Hammer

Abstract: We present a modelling framework for the investigation of prototype-based classifiers in non-stationary environments. Specifically, we study Learning Vector Quantization (LVQ) systems trained from a stream of high-dimensional, clustered data.We consider standard winner-takes-all updates known as LVQ1. Statistical properties of the input data change on the time scale defined by the training process… ▽ More We present a modelling framework for the investigation of prototype-based classifiers in non-stationary environments. Specifically, we study Learning Vector Quantization (LVQ) systems trained from a stream of high-dimensional, clustered data.We consider standard winner-takes-all updates known as LVQ1. Statistical properties of the input data change on the time scale defined by the training process. We apply analytical methods borrowed from statistical physics which have been used earlier for the exact description of learning in stationary environments. The suggested framework facilitates the computation of learning curves in the presence of virtual and real concept drift. Here we focus on timedependent class bias in the training data. First results demonstrate that, while basic LVQ algorithms are suitable for the training in non-stationary environments, weight decay as an explicit mechanism of forgetting does not improve the performance under the considered drift processes. △ Less

Submitted 18 March, 2019; originally announced March 2019.

Comments: Accepted contribution to WSOM+ 2019, Barcelona/Spain, June 2019 13th International Workshop on Self-Organizing Maps and Learning Vector Quantization, Clustering and Data Visualization 11 pages

Atomistic structure learning

Authors: Mathias S. Jørgensen, Henrik L. Mortensen, Søren A. Meldgaard, Esben L. Kolsbjerg, Thomas L. Jacobsen, Knud H. Sørensen, Bjørk Hammer

Abstract: One endeavour of modern physical chemistry is to use bottom-up approaches to design materials and drugs with desired properties. Here we introduce an atomistic structure learning algorithm (ASLA) that utilizes a convolutional neural network to build 2D compounds and layered structures atom by atom. The algorithm takes no prior data or knowledge on atomic interactions but inquires a first-principle… ▽ More One endeavour of modern physical chemistry is to use bottom-up approaches to design materials and drugs with desired properties. Here we introduce an atomistic structure learning algorithm (ASLA) that utilizes a convolutional neural network to build 2D compounds and layered structures atom by atom. The algorithm takes no prior data or knowledge on atomic interactions but inquires a first-principles quantum mechanical program for physical properties. Using reinforcement learning, the algorithm accumulates knowledge of chemical compound space for a given number and type of atoms and stores this in the neural network, ultimately learning the blueprint for the optimal structural arrangement of the atoms for a given target property. ASLA is demonstrated to work on diverse problems, including grain boundaries in graphene sheets, organic compound formation and a surface oxide structure. This approach to structure prediction is a first step toward direct manipulation of atoms with artificially intelligent first principles computer codes. △ Less

Submitted 27 February, 2019; originally announced February 2019.

Viscosity independent diffusion mediated by death and reproduction in biofilms

Authors: Arben Kalziqi, Siu Lung Ng, David Yanni, Gabi Steinbach, Brian K. Hammer, Peter J. Yunker

Abstract: Bacterial biofilms, surface-attached communities of cells, are in some respects similar to colloidal solids; both are densely packed with non-zero yield stresses. However, unlike non-living materials, bacteria reproduce and die, breaking mechanical equilibrium and inducing collective dynamic responses. We report experiments and theory investigating the motion of immotile Vibrio cholerae, which can… ▽ More Bacterial biofilms, surface-attached communities of cells, are in some respects similar to colloidal solids; both are densely packed with non-zero yield stresses. However, unlike non-living materials, bacteria reproduce and die, breaking mechanical equilibrium and inducing collective dynamic responses. We report experiments and theory investigating the motion of immotile Vibrio cholerae, which can kill each other and reproduce in biofilms. We vary viscosity by using bacterial variants that secrete different amounts of extracellular matrix polymers, but are otherwise identical. Unlike thermally-driven diffusion, in which diffusivity decreases with increased viscosity, we find that cellular motion mediated by death and reproduction is independent of viscosity over timescales relevant to bacterial reproduction. To understand this surprising result, we use two separate modeling approaches. First we perform explicitly mechanical simulations of one-dimensional chains of Voigt-Kelvin elements that can die and reproduce. Next, we perform an independent statistical approach, modeling Brownian motion with the classic Langevin equation under an effective temperature that depends on cellular division rate. The diffusion of cells in both approaches agrees quite well, supporting a kinetic interpretation for the effective temperature used here and developed in previous work. As the viscoelastic behavior of biofilms is believed to play a large role in their anomalous biological properties, such as antibiotic resistance, the independence of cellular diffusive motion --- important for biofilm growth and remodeling --- on viscoelastic properties likely holds ecological, medical, and industrial relevance. △ Less

Submitted 4 January, 2019; originally announced January 2019.

Size-dependent phase transitions in MoS2 nanoparticles controlled by a metal substrate

Authors: Albert Bruix, Jeppe Vang Lauritsen, Bjørk Hammer

Abstract: Nanomaterials based on MoS2 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 dimens… ▽ More Nanomaterials based on MoS2 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. This work demonstrates how the properties of nanostructured MoS2 and similar layered systems can be modified by the choice of supporting metal. △ Less

Submitted 3 May, 2018; originally announced May 2018.

Contact-Induced Semiconductor-to-Metal Transition in Single-Layer WS$_2$

Authors: Maciej Dendzik, Albert Bruix, Matteo Michiardi, Arlette S. Ngankeu, Marco Bianchi, Jill A. Miwa, Bjørk Hammer, Philip Hofmann, Charlotte E. Sanders

Abstract: Low-resistance ohmic contacts are a challenge for electronic devices based on two-dimensional materials. We show that an atomically precise junction between a two-dimensional semiconductor and a metallic contact can lead to a semiconductor-to-metal transition in the two-dimensional material--a finding which points the way to a possible method of achieving low-resistance junctions. Specifically, si… ▽ More Low-resistance ohmic contacts are a challenge for electronic devices based on two-dimensional materials. We show that an atomically precise junction between a two-dimensional semiconductor and a metallic contact can lead to a semiconductor-to-metal transition in the two-dimensional material--a finding which points the way to a possible method of achieving low-resistance junctions. Specifically, single-layer WS$_2$ undergoes a semiconductor-to-metal transition when epitaxially grown on Ag(111), while it remains a direct band gap semiconductor on Au(111). The metallicity of the single layer on Ag(111) is established by lineshape analysis of core level photoemission spectra. Angle-resolved photoemission spectroscopy locates the metallic states near the Q point of the WS$_2$ Brillouin zone. Density functional theory calculations show that the metallic states arise from hybridization between Ag bulk bands and the local conduction band minimum of WS$_2$ near the Q point. △ Less

Submitted 9 August, 2017; originally announced August 2017.

Comments: Main text: 21 pages, 4 figures. Supplement: 7 pages, 4 figures, 1 table

Journal ref: Phys. Rev. B 96, 235440 (2017)

Life in the coffee-ring: how evaporation-driven density gradients dictate the outcome of inter-bacterial competition

Authors: David Yanni, Arben Kalziqi, Jacob Thomas, Siu Lung Ng, Skanda Vivek, William C. Ratcliff, Brian K. Hammer, Peter J. Yunker

Abstract: When a drop dries, it often leaves a ring-shaped stain through a ubiquitous phenomenon known as the coffee-ring effect. This also occurs when the liquid contains suspended microbes; evaporation leaves cells at higher concentrations in the ring than the drop interior. Using biofilm experiments and cellular automata simulations, we show that the physical structure created by the coffee-ring effect c… ▽ More When a drop dries, it often leaves a ring-shaped stain through a ubiquitous phenomenon known as the coffee-ring effect. This also occurs when the liquid contains suspended microbes; evaporation leaves cells at higher concentrations in the ring than the drop interior. Using biofilm experiments and cellular automata simulations, we show that the physical structure created by the coffee-ring effect can dramatically alter the outcome of inter-bacterial competition. We experimentally study this effect using two strains of $\textit{Vibrio cholerae}$ that compete using a contact-dependent killing mechanism termed the type 6 secretion system. By creating a heterogeneous density profile, the coffee-ring effect changes the outcome of competition: the bacterial strain that wins in the low-density interior loses in the far denser ring. Through simulations parameterized with experimentally-determined density profiles, we recapitulate our experimental findings. We examine the role of a $\textit{V. cholerae}$ strain's frequency, its relative efficacy at killing competitors, and the initial concentration of cells in the droplet in determining the outcome of competition. By scaling from individual cellular interactions to overall changes in strain frequency, our work demonstrates how the coffee-ring effect plays a powerful role in structuring microbial communities, indirectly driving ecological changes in community composition. △ Less

Submitted 11 July, 2017; originally announced July 2017.

Crystalline and electronic structure of single-layer TaS$_2$

Authors: Charlotte E. Sanders, Maciej Dendzik, Arlette S. Ngankeu, Andreas Eich, Albert Bruix, Marco Bianchi, Jill A. Miwa, Bjørk Hammer, Alexander A. Khajetoorians, Philip Hofmann

Abstract: Single-layer TaS$_2$ is epitaxially grown on Au(111) substrates. The resulting two-dimensional crystals adopt the 1H polymorph. The electronic structure is determined by angle-resolved photoemission spectroscopy and found to be in excellent agreement with density functional theory calculations. The single layer TaS$_2$ is found to be strongly n-doped, with a carrier concentration of 0.3(1) extra e… ▽ More Single-layer TaS$_2$ is epitaxially grown on Au(111) substrates. The resulting two-dimensional crystals adopt the 1H polymorph. The electronic structure is determined by angle-resolved photoemission spectroscopy and found to be in excellent agreement with density functional theory calculations. The single layer TaS$_2$ is found to be strongly n-doped, with a carrier concentration of 0.3(1) extra electrons per unit cell. No superconducting or charge density wave state is observed by scanning tunneling microscopy at temperatures down to 4.7 K. △ Less

Submitted 19 June, 2016; originally announced June 2016.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. B 94, 081404 (2016)

Band gap engineering by Bi intercalation of graphene on Ir(111)

Authors: Jonas Warmuth, Albert Bruix, Matteo Michiardi, Torben Hänke, Marco Bianchi, Jens Wiebe, Roland Wiesendanger, Bjørk Hammer, Philip Hofmann, Alexander A. Khajetoorians

Abstract: We report on the structural and electronic properties of a single bismuth layer intercalated underneath a graphene layer grown on an Ir(111) single crystal. Scanning tunneling microscopy (STM) reveals a hexagonal surface structure and a dislocation network upon Bi intercalation, which we attribute to a $\sqrt{3}\times\sqrt{3}R30°$ Bi structure on the underlying Ir(111) surface. Ab-initio calculati… ▽ More We report on the structural and electronic properties of a single bismuth layer intercalated underneath a graphene layer grown on an Ir(111) single crystal. Scanning tunneling microscopy (STM) reveals a hexagonal surface structure and a dislocation network upon Bi intercalation, which we attribute to a $\sqrt{3}\times\sqrt{3}R30°$ Bi structure on the underlying Ir(111) surface. Ab-initio calculations show that this Bi structure is the most energetically favorable, and also illustrate that STM measurements are most sensitive to C atoms in close proximity to intercalated Bi atoms. Additionally, Bi intercalation induces a band gap ($E_g=0.42\,$eV) at the Dirac point of graphene and an overall n-doping ($\sim 0.39\,$eV), as seen in angular-resolved photoemission spectroscopy. We attribute the emergence of the band gap to the dislocation network which forms favorably along certain parts of the moiré structure induced by the graphene/Ir(111) interface. △ Less

Submitted 29 March, 2016; originally announced March 2016.

Comments: 5 figures

Single-layer MoS$_2$ on Au(111): band gap renormalization and substrate interaction

Authors: Albert Bruix, Jill A. Miwa, Nadine Hauptmann, Daniel Wegner, Søren Ulstrup, Signe S. Grønborg, Charlotte E. Sanders, Maciej Dendzik, Antonija Grubišić Čabo, Marco Bianchi, Jeppe V. Lauritsen, Alexander A. Khajetoorians, Bjørk Hammer, Philip Hofmann

Abstract: The electronic structure of epitaxial single-layer MoS$_2$ on Au(111) is investigated by angle-resolved photoemission spectroscopy, scanning tunnelling spectroscopy, and first principles calculations. While the band dispersion of the supported single-layer is close to a free-standing layer in the vicinity of the valence band maximum at $\bar{K}$ and the calculated electronic band gap on Au(111) is… ▽ More The electronic structure of epitaxial single-layer MoS$_2$ on Au(111) is investigated by angle-resolved photoemission spectroscopy, scanning tunnelling spectroscopy, and first principles calculations. While the band dispersion of the supported single-layer is close to a free-standing layer in the vicinity of the valence band maximum at $\bar{K}$ and the calculated electronic band gap on Au(111) is similar to that calculated for the free-standing layer, significant modifications to the band structure are observed at other points of the two-dimensional Brillouin zone: At $\barΓ$, the valence band maximum has a significantly higher binding energy than in the free MoS$_2$ layer and the expected spin-degeneracy of the uppermost valence band at the $\bar{M}$ point cannot be observed. These band structure changes are reproduced by the calculations and can be explained by the detailed interaction of the out-of-plane MoS$_2$ orbitals with the substrate. △ Less

Submitted 1 January, 2016; originally announced January 2016.

Comments: 10 pages, 6 figures

Journal ref: Phys. Rev. B 93, 165422 (2016)

In Situ Detection of Active Edge Sites in Single-Layer MoS$_2$ Catalysts

Authors: Albert Bruix, Henrik G. Füchtbauer, Anders K. Tuxen, Alex S. Walton, Mie Andersen, Søren Porsgaard, Flemming Besenbacher, Bjørk Hammer, Jeppe V. Lauritsen

Abstract: MoS2 nanoparticles are proven catalysts for processes such as hydrodesulphurization and hydrogen evolution, but unravelling their atomic-scale structure under catalytic working conditions has remained significantly challenging. Ambient pressure X-ray Photoelectron Spectroscopy (AP-XPS) allows us to follow in-situ the formation of the catalytically relevant MoS2 edge sites in their active state. Th… ▽ More MoS2 nanoparticles are proven catalysts for processes such as hydrodesulphurization and hydrogen evolution, but unravelling their atomic-scale structure under catalytic working conditions has remained significantly challenging. Ambient pressure X-ray Photoelectron Spectroscopy (AP-XPS) allows us to follow in-situ the formation of the catalytically relevant MoS2 edge sites in their active state. The XPS fingerprint is described by independent contributions to the Mo3d core level spectrum whose relative intensity is sensitive to the thermodynamic conditions. Density Functional Theory (DFT) is used to model the triangular MoS2 particles on Au(111) and identify the particular sulphidation state of the edge sites. A consistent picture emerges in which the core level shifts for the edge Mo atoms evolve counter-intuitively towards higher binding energies when the active edges are reduced. The shift is explained by a surprising alteration in the metallic character of the edge sites, which is a distinct spectroscopic signature of the MoS2 edges under working conditions. △ Less

Submitted 13 November, 2015; originally announced November 2015.

Journal ref: ACS Nano, 2015, 9 (9), pp 9322-9330

High Crystallinity and Decoupling of Graphene on a Metal: Reduced Coulomb Screening and Tunable pn-Junctions

Authors: Søren Ulstrup, Mie Andersen, Marco Bianchi, Lucas Barreto, Bjørk Hammer, Liv Hornekær, Philip Hofmann

Abstract: High quality epitaxial graphene films can be applied as templates for tailoring graphene-substrate interfaces that allow for precise control of the charge carrier behavior in graphene through doping and many-body effects. By combining scanning tunneling microscopy, angle-resolved photoemission spectroscopy and density functional theory we demonstrate that oxygen intercalated epitaxial graphene on… ▽ More High quality epitaxial graphene films can be applied as templates for tailoring graphene-substrate interfaces that allow for precise control of the charge carrier behavior in graphene through doping and many-body effects. By combining scanning tunneling microscopy, angle-resolved photoemission spectroscopy and density functional theory we demonstrate that oxygen intercalated epitaxial graphene on Ir(111) has high structural quality, is quasi free-standing, and shows signatures of many-body interactions. Using this system as a template, we show that tunable pn-junctions can be patterned by adsorption and intercalation of rubidium, and that the n-doped graphene regions exhibit a reduced Coulomb screening via enhanced electron-plasmon coupling. These findings are central for understanding and tailoring the properties of graphene-metal contacts e.g. for realizing quantum tunneling devices. △ Less

Submitted 24 April, 2014; originally announced April 2014.

Comments: 22 pages, 6 figures, 1 table

Steps on Rutile TiO2(110): Active Sites for Water and Methanol Dissociation

Authors: Umberto Martinez, Lasse B. Vilhelmsen, Henrik H. Kristoffersen, Jess Stausholm-Møller, Bjørk Hammer

Abstract: We present a detailed investigation of the structure and activity of extended defects namely monoatomic steps on (1x1)-TiO2(110). Specifically, the two most stable <001> and <1-11> step edges are considered. Employing an automated genetic algorithm that samples a large number of candidates for each step edge, more stable, reconstructed structures were found for the <1-11> step edge, while the bulk… ▽ More We present a detailed investigation of the structure and activity of extended defects namely monoatomic steps on (1x1)-TiO2(110). Specifically, the two most stable <001> and <1-11> step edges are considered. Employing an automated genetic algorithm that samples a large number of candidates for each step edge, more stable, reconstructed structures were found for the <1-11> step edge, while the bulk truncated structures were recovered for the <001> step edge. We demonstrate how oxygen vacancies along these defects have lower formation energies than on flat terraces and how water and methanol molecules adsorb dissociatively on reduced <1-11> step edges. Our findings are in agreement with earlier experimental results and indicate an important contribution from step edges to the reactivity of the TiO2(110) surface. △ Less

Submitted 2 November, 2011; originally announced November 2011.

Journal ref: Phys. Rev. B 84, 205434 (2011)

Structure and stability of small H clusters on graphene

Authors: Zeljko Sljivancanin, Mie Andersen, Liv Hornekaer, Bjork Hammer

Abstract: The structure and stability of small hydrogen clusters adsorbed on graphene is studied by means of Density Functional Theory (DFT) calculations. Clusters containing up to six H atoms are investigated systematically -- the clusters having either all H atoms on one side of the graphene sheet (\textit{cis}-clusters) or having the H atoms on both sides in an alternating manner (\textit{trans}-cluster)… ▽ More The structure and stability of small hydrogen clusters adsorbed on graphene is studied by means of Density Functional Theory (DFT) calculations. Clusters containing up to six H atoms are investigated systematically -- the clusters having either all H atoms on one side of the graphene sheet (\textit{cis}-clusters) or having the H atoms on both sides in an alternating manner (\textit{trans}-cluster). The most stable cis-clusters found have H atoms in ortho- and para-positions with respect to each other (two H's on neighboring or diagonally opposite carbon positions within one carbon hexagon) while the most stable trans-clusters found have H atoms in ortho-trans-positions with respect to each other (two H's on neighboring carbon positions, but on opposite sides of the graphene). Very stable trans-clusters with 13-22 H atoms were identified by optimizing the number of H atoms in ortho-trans-positions and thereby the number of closed, H-covered carbon hexagons. For the cis-clusters, the associative H$_2$ desorption was investigated. Generally, the desorption with the lowest activation energy proceeds via para-cis-dimer states, i.e.\ involving somewhere in the H clusters two H atoms that are positioned on opposite sites within one carbon hexagon. H$_2$ desorption from clusters lacking such H pairs is calculated to occur via hydrogen diffusion causing the formation of para-cis-dimer states. Studying the diffusion events showed a strong dependence of the diffusion energy barriers on the reaction energies and a general odd-even dependence on the number of H atoms in the cis-clusters. △ Less

Submitted 28 February, 2011; v1 submitted 24 February, 2011; originally announced February 2011.

Comments: 11 pages, 11 figures, to appear in Phys. Rev. B

A direct pathway for sticking/desorption of H$_2$ on Si(100)

Authors: P. Kratzer, B. Hammer, J. K. Norskov

Abstract: The energetics of H$_2$ interacting with the Si(100) surface is studied by means of {\em ab initio} total energy calculations within the framework of density functional theory. We find a direct desorption pathway from the mono-hydride phase which is compatible with experimental activation energies and demonstrate the importance of substrate relaxation for this process. Both the transition state… ▽ More The energetics of H$_2$ interacting with the Si(100) surface is studied by means of {\em ab initio} total energy calculations within the framework of density functional theory. We find a direct desorption pathway from the mono-hydride phase which is compatible with experimental activation energies and demonstrate the importance of substrate relaxation for this process. Both the transition state configuration and barrier height depend crucially on the degree of buckling of the Si dimers on the Si(100) surface. The adsorption barrier height on the clean surface is governed by the buckling via its influence on the surface electronic structure. We discuss the consequences of this coupling for adsorption experiments and the relation between adsorption and desorption. △ Less

Submitted 29 March, 1995; v1 submitted 27 March, 1995; originally announced March 1995.

Comments: 18 pages + 8 figures

High-dimensional quantum dynamics of adsorption and desorption of H$_2$ at Cu(111)

Authors: A. Gross, B. Hammer, M. Scheffler, W. Brenig

Abstract: We performed high-dimensional quantum dynamical calculations of the dissociative adsorption and associative desorption of hydrogen on Cu(111). The potential energy surface (PES) is obtained from density functional theory calculations. Two regimes of dynamics are found, at low energies sticking is determined by the minimum energy barrier, at high energies by the distribution of barrier heights. E… ▽ More We performed high-dimensional quantum dynamical calculations of the dissociative adsorption and associative desorption of hydrogen on Cu(111). The potential energy surface (PES) is obtained from density functional theory calculations. Two regimes of dynamics are found, at low energies sticking is determined by the minimum energy barrier, at high energies by the distribution of barrier heights. Experimental results are well-reproduced qualitatively, but some quantitative discrepancies are identified as well. △ Less

Submitted 22 November, 1994; originally announced November 1994.

Comments: 4 two column pages, revtex, 4 figures, to appear in Phys. Rev. Lett