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Two-dimensional (2D) materials, such as transition metal dichalcogenides (TMDCs) in the 2H or 1T crystal phases, are promising (electro)catalyst candidates due to their high surface to volume ratio and composition of low-cost, abundant elements. While the edges of elemental TMDC nanoparticles, such as MoS$_2$, can show significant catalytic activity, the basal plane of the pristine materials are notoriously inert, which limits their normalized activity. Here we show that high densities of catalytically active sites can be formed on the TMDC basal plane by alloying elements that prefer the 2H (1T) phase into a 1T (2H) structure. The global stability of the alloy, in particular whether it crystallizes in the 2H or 1T phase, can be controlled by ensuring a majority of elements preferring the target phase. We further show that the mixing entropy plays a decisive role for stabilizing the alloy implying that high-entropy alloying becomes essential. Our calculations point to a number of interesting non-precious hydrogen evolution catalysts, including (CrHfTaVZr)S$_2$ and (CrNbTiVZr)S$_2$ in the T-phase and (MoNbTaVTi)S$_2$ in the H-phase. Our work opens new directions for designing catalytic sites via high-entropy alloy stabilization of locally unstable structures.

The optimization of atomic structures plays a pivotal role in understanding and designing materials with desired properties. However, conventional computational methods often struggle with the formidable task of navigating the vast potential energy surface, especially in high-dimensional spaces with numerous local minima. Recent advancements in machine learning-driven surrogate models offer a promising avenue for alleviating this computational burden. In this study, we propose a novel approach that combines the strengths of universal machine learning potentials with a Bayesian approach using Gaussian processes. By using the machine learning potentials as priors for the Gaussian process, the Gaussian process has to learn only the difference between the machine learning potential and the target energy surface calculated for example by density functional theory. This turns out to improve the speed by which the global optimal structure is identified across diverse systems for a well-behaved machine learning potential. The approach is tested on periodic bulk materials, surface structures, and a cluster.

We review the GPAW open-source Python package for electronic structure calculations. GPAW is based on the projector-augmented wave method and can solve the self-consistent density functional theory (DFT) equations using three different wave-function representations, namely real-space grids, plane waves, and numerical atomic orbitals. The three representations are complementary and mutually independent and can be connected by transformations via the real-space grid. This multi-basis feature renders GPAW highly versatile and unique among similar codes. By virtue of its modular structure, the GPAW code constitutes an ideal platform for implementation of new features and methodologies. Moreover, it is well integrated with the Atomic Simulation Environment (ASE) providing a flexible and dynamic user interface. In addition to ground-state DFT calculations, GPAW supports many-body GW band structures, optical excitations from the Bethe-Salpeter Equation (BSE), variational calculations of excited states in molecules and solids via direct optimization, and real-time propagation of the Kohn-Sham equations within time-dependent DFT. A range of more advanced methods to describe magnetic excitations and non-collinear magnetism in solids are also now available. In addition, GPAW can calculate non-linear optical tensors of solids, charged crystal point defects, and much more. Recently, support of GPU acceleration has been achieved with minor modifications of the GPAW code thanks to the CuPy library. We end the review with an outlook describing some future plans for GPAW.

We introduce a method for global optimization of the structure of atomic systems that uses additional atoms with fractional existence. The method allows for movement of atoms over long distances bypassing energy barriers encountered in the conventional position space. The method is based on Gaussian processes, where the extrapolation to fractional existence is performed with a vectorial fingerprint. The method is applied to clusters and two-dimensional systems, where the fractional existence variables are optimized while keeping the atomic positions fixed on a lattice. Simultaneous optimization of atomic coordinates and existence variables is demonstrated on copper clusters of varying size. The existence variables are shown to speed up the global optimization of large and particularly difficult-to-optimize clusters., Comment: 6 pages, 5 figures, plus supplement

We introduce a computational method for global optimization of structure and ordering in atomic systems. The method relies on interpolation between chemical elements, which is incorporated in a machine learning structural fingerprint. The method is based on Bayesian optimization with Gaussian processes and is applied to the global optimization of Au-Cu bulk systems, Cu-Ni surfaces with CO adsorption, and Cu-Ni clusters. The method consistently identifies low-energy structures, which are likely to be the global minima of the energy. For the investigated systems with 23-66 atoms, the number of required energy and force calculations is in the range 3-75.

The two-dimensional transition metal dichalcogenides (TMDs) have been proposed as candidates for the channel material in future field effect transistor designs. The heterophase design which utilizes the metallic T- or T' phase of the TMD as contacts to the semiconducting H phase channel has shown promising results in terms of bringing down the contact resistance of the device. In this work, we use ab-initio calculations to demonstrate how atomic-scale and quantum effects influence the ballistic transport properties in such heterophase transistors with channel lengths up to 20 nm. We investigate how the charge transfer depends on the carrier density both in T'-H MoTe$_2$ Schottky contacts and planar T'-H-T' MoTe$_2$ transistors. We find that the size of the Schottky barrier and the charge transfer is dominated by the local atomic arrangements at the interface and the doping level. Furthermore, two types of quantum states have a large influence on the charge transport; interface states and standing waves in the semiconductor due to quantum confinement. We find that the latter can be associated with rises in the current by more than an order of magnitude due to resonant tunneling. Our results demonstrate the quantum mechanical nature of these 2D transistors and highlight several challenges and possible solutions for achieving a competitive performance of such devices.

Determination of atomic structures is a key challenge in the fields of computational physics and materials science, as a large variety of mechanical, chemical, electronic, and optical properties depend sensitively on structure. Here, we present a global optimization scheme where energy and force information from density functional theory (DFT) calculations is transferred to a probabilistic surrogate model to estimate both the potential energy surface (PES) and the associated uncertainties. The local minima in the surrogate PES are then used to guide the search for the global minimum in the DFT potential. We find that adding the gradients in most cases improves the efficiency of the search significantly. The method is applied to global optimization of [Ta$_2$O$_5$]$_x$ clusters with $x=1,2,3$, and the surface structure of oxidized ZrN.

Local optimization of adsorption systems inherently involves different scales: within the substrate, within the molecule, and between molecule and substrate. In this work, we show how the explicit modeling of the different character of the bonds in these systems improves the performance of machine learning methods for optimization. We introduce an anisotropic kernel in the Gaussian process regression framework that guides the search for the local minimum, and we show its overall good performance across different types of atomic systems. The method shows a speed-up of up to a factor two compared with the fastest standard optimization methods on adsorption systems. Additionally, we show that a limited memory approach is not only beneficial in terms of overall computational resources, but can result in a further reduction of energy and force calculations.

The Schottky barrier of a metal-semiconductor junction is one of the key quantities affecting the charge transport in a transistor. The Schottky barrier height depends on several factors, such as work function difference, local atomic configuration in the interface, and impurity doping. We show that also the presence of interface states at 2D metal-semiconductor junctions can give rise to a large renormalization of the effective Schottky barrier determined from the temperature dependence of the current. We investigate the charge transport in n- and p-doped monolayer MoTe$_2$ 1T'-1H junctions using ab-initio quantum transport calculations. The Schottky barriers are extracted both from the projected density of states and the transmission spectrum, and by simulating the IT-characteristic and applying the thermionic emission model. We find interface states originating from the metallic 1T' phase rather than the semiconducting 1H phase in contrast to the phenomenon of Fermi level pinning. Furthermore, we find that these interface states mediate large tunneling currents which dominates the charge transport and can lower the effective barrier to a value of only 55 meV., Comment: 6 figures

Computational materials screening studies require fast calculation of the properties of thousands of materials. The calculations are often performed with Density Functional Theory (DFT), but the necessary computer time sets limitations for the investigated material space. Therefore, the development of machine learning models for prediction of DFT calculated properties are currently of interest. A particular challenge for \emph{new} materials is that the atomic positions are generally not known. We present a machine learning model for the prediction of DFT-calculated formation energies based on Voronoi quotient graphs and local symmetry classification without the need for detailed information about atomic positions. The model is implemented as a message passing neural network and tested on the Open Quantum Materials Database (OQMD) and the Materials Project database. The test mean absolute error is 20 meV on the OQMD database and 40 meV on Materials Project Database. The possibilities for prediction in a realistic computational screening setting is investigated on a dataset of 5976 ABSe$_3$ selenides with very limited overlap with the OQMD training set. Pretraining on OQMD and subsequent training on 100 selenides result in a mean absolute error below 0.1 eV for the formation energy of the selenides., Comment: 14 pages including references and 13 figures

Using density functional theory calculations and the Greens's function formalism, we report the existence of magnetic edge states with a non-collinear spin texture present on different edges of the 1T' phase of the three monolayer transition metal dichalcogenides (TMDs): MoS$_2$, MoTe$_2$ and WTe$_2$. The magnetic states are gapless and accompanied by a spontaneous breaking of the time-reversal symmetry. This may have an impact on the prospects of utilizing WTe$_2$ as a quantum spin Hall insulator. It has previously been suggested that the topologically protected edge states of the 1T' TMDs could be switched off by applying a perpendicular electric field. We confirm with fully self-consistent DFT calculations, that the topological edge states can be switched off. The investigated magnetic edge states are seen to be robust and remains gapless when applying a field., Comment: 7 pages, 7 figures

The last decade has seen intense research in materials with reduced dimensionality. The low dimensionality leads to interesting electronic behavior due to electronic confinement and reduced screening. The investigations have to a large extent focused on 2D materials both in their bulk form, as individual layers a few atoms thick, and through stacking of 2D layers into heterostructures. The identification of low-dimensional compounds is therefore of key interest. Here, we perform a geometric analysis of material structures, demonstrating a strong clustering of materials depending on their dimensionalities. Based on the geometric analysis, we propose a simple scoring parameter to identify materials of a particular dimension or of mixed dimensionality. The method identifies spatially connected components of the materials and gives a measure of the degree of "1D-ness," "2D-ness," etc., for each component. The scoring parameter is applied to the Inorganic Crystal Structure Database and the Crystallography Open Database ranking the materials according to their degree of dimensionality. In the case of 2D materials the scoring parameter is seen to clearly separate 2D from non-2D materials and the parameter correlates well with the bonding strength in the layered materials. About 3000 materials are identified as one-dimensional, while more than 9000 are mixed-dimensionality materials containing a molecular (0D) component. The charge states of the components in selected highly ranked materials are investigated using density functional theory and Bader analysis showing that the spatially separated components have either zero charge, corresponding to weak interactions, or integer charge, indicating ionic bonding.

Neural message passing on molecular graphs is one of the most promising methods for predicting formation energy and other properties of molecules and materials. In this work we extend the neural message passing model with an edge update network which allows the information exchanged between atoms to depend on the hidden state of the receiving atom. We benchmark the proposed model on three publicly available datasets (QM9, The Materials Project and OQMD) and show that the proposed model yields superior prediction of formation energies and other properties on all three datasets in comparison with the best published results. Furthermore we investigate different methods for constructing the graph used to represent crystalline structures and we find that using a graph based on K-nearest neighbors achieves better prediction accuracy than using maximum distance cutoff or the Voronoi tessellation graph.

We show that nanoparticles can have very rich ground state chemical order. This is illustrated by determining the chemical ordering of Ag-Au 309-atom Mackay icosahedral nanoparticles. The energy of the nanoparticles is described using a cluster expansion model, and a Mixed Integer Programming (MIP) approach is used to find the exact ground state configurations for all stoichiometries. The chemical ordering varies widely between the different stoichiometries, and display a rich zoo of structures with non-trivial ordering., Comment: Revised version. New figure added, discussion expanded, some material moved into supplementary file

We use density functional theory (DFT) to investigate the electronic structure and chemical properties of gold nanoparticles. Different structural families of clusters are compared. For up to 60 atoms we optimize structures using DFT-based simulated annealing. Cluster geometries are found to distort considerably, creating large band gaps at the Fermi level. For up to 200 atoms we consider structures generated with a simple EMT potential and clusters based on cuboctahedra and icosahedra. All types of cluster geometry exhibit jellium-like electronic shell structure. We calculate adsorption energies of several atoms on the cuboctahedral clusters. Adsorption energies are found to vary abruptly at magic numbers. Using a Newns-Anderson model we find that the effect of magic numbers on adsorption energy can be understood from the location of adsorbate-induced states with respect to the cluster Fermi level., Comment: 14 pages, 18 figures

We present an implementation of localized atomic orbital basis sets in the projector augmented wave (PAW) formalism within the density functional theory (DFT). The implementation in the real-space GPAW code provides a complementary basis set to the accurate but computationally more demanding grid representation. The possibility to switch seamlessly between the two representations implies that simulations employing the local basis can be fine tuned at the end of the calculation by switching to the grid, thereby combining the strength of the two representations for optimal performance. The implementation is tested by calculating atomization energies and equilibrium bulk properties of a variety of molecules and solids, comparing to the grid results. Finally, it is demonstrated how a grid-quality structure optimization can be performed with significantly reduced computational effort by switching between the grid and basis representations., Comment: 10 pages, 5 figures. http://prb.aps.org.globalproxy.cvt.dk/abstract/PRB/v80/i19/e195112