Obtaining Robust Density Functional Tight-Binding Parameters for Solids across the Periodic Table.

The density functional tight-binding (DFTB) approach allows electronic structure-based simulations at length and time scales far beyond what is possible with first-principles methods. This is achieved by using minimal basis sets and empirical approximations. Unfortunately, the sparse availability of parameters across the periodic table is a significant barrier to the use of DFTB in many cases. We therefore propose a workflow that allows the robust and consistent parametrization of DFTB across the periodic table. Importantly, our approach requires no element-pairwise parameters so that the parameters can be used for all element combinations and are readily extendable. This is achieved by parametrizing all elements on a consistent set of artificial homoelemental crystals, spanning a wide range of coordination environments. The transferability of the resulting periodic table baseline parameters to multielement systems and unknown structures is explored and the model is extensively benchmarked against previous specialized and general DFTB parametrizations.

Neural graph distance embedding for molecular geometry generation.

This article introduces neural graph distance embedding (nGDE), a method for generating 3D molecular geometries. Leveraging a graph neural network trained on the OE62 dataset of molecular geometries, nGDE predicts interatomic distances based on molecular graphs. These distances are then used in multidimensional scaling to produce 3D geometries, subsequently refined with standard bioorganic forcefields. The machine learning-based graph distance introduced herein is found to be an improvement over the conventional shortest path distances used in graph drawing. Comparative analysis with a state-of-the-art distance geometry method demonstrates nGDE's competitive performance, particularly showcasing robustness in handling polycyclic molecules-a challenge for existing methods.

Operando Characterization and Molecular Simulations Reveal the Growth Kinetics of Graphene on Liquid Copper During Chemical Vapor Deposition.

In recent years, liquid metal catalysts have emerged as a compelling choice for the controllable, large-scale, and high-quality synthesis of two-dimensional materials. At present, there is little mechanistic understanding of the intricate catalytic process, though, of its governing factors or what renders it superior to growth at the corresponding solid catalysts. Here, we report on a combined experimental and computational study of the kinetics of graphene growth during chemical vapor deposition on a liquid copper catalyst. By monitoring the growing graphene flakes in real time using in situ radiation-mode optical microscopy, we explore the growth morphology and kinetics over a wide range of CH4-to-H2 pressure ratios and deposition temperatures. Constant growth rates of the flakes' radius indicate a growth mode limited by precursor attachment, whereas methane-flux-dependent flake shapes point to limited precursor availability. Large-scale free energy simulations enabled by an efficient machine-learning moment tensor potential trained to density functional theory data provide quantitative barriers for key atomic-scale growth processes. The wealth of experimental and theoretical data can be consistently combined into a microkinetic model that reveals mixed growth kinetics that, in contrast to the situation at solid Cu, is partly controlled by precursor attachment alongside precursor availability. Key mechanistic aspects that directly point toward the improved graphene quality are a largely suppressed carbon dimer attachment due to the facile incorporation of this precursor species into the liquid surface and a low-barrier ring-opening process that self-heals 5-membered rings resulting from remaining dimer attachments.

Discovering High Entropy Alloy Electrocatalysts in Vast Composition Spaces with Multiobjective Optimization.

High entropy alloys (HEAs) are a highly promising class of materials for electrocatalysis as their unique active site distributions break the scaling relations that limit the activity of conventional transition metal catalysts. Existing Bayesian optimization (BO)-based virtual screening approaches focus on catalytic activity as the sole objective and correspondingly tend to identify promising materials that are unlikely to be entropically stabilized. Here, we overcome this limitation with a multiobjective BO framework for HEAs that simultaneously targets activity, cost-effectiveness, and entropic stabilization. With diversity-guided batch selection further boosting its data efficiency, the framework readily identifies numerous promising candidates for the oxygen reduction reaction that strike the balance between all three objectives in hitherto unchartered HEA design spaces comprising up to 10 elements.

Estimating Free Energy Barriers for Heterogeneous Catalytic Reactions with Machine Learning Potentials and Umbrella Integration.

Predicting the rate constants of elementary reaction steps is key for the computational modeling of catalytic processes. Within transition state theory (TST), this requires an accurate estimation of the corresponding free energy barriers. While sophisticated methods for estimating free energy differences exist, these typically require extensive (biased) molecular dynamics simulations that are computationally prohibitive with the first-principles electronic structure methods that are typically used in catalysis research. In this contribution, we show that machine-learning (ML) interatomic potentials can be trained in an automated iterative workflow to perform such free energy calculations at a much reduced computational cost as compared to a direct density functional theory (DFT) based evaluation. For the decomposition of CHO on Rh(111), we find that thermal effects are substantial and lead to a decrease in the free energy barrier, which can be vanishingly small, depending on the DFT functional used. This is in stark contrast to previously reported estimates based on a harmonic TST approximation, which predicted an increase in the barrier at elevated temperatures. Since CHO is the reactant of the putative rate limiting reaction step in syngas conversion on Rh(111) and essential for the selectivity toward oxygenates containing multiple carbon atoms (C2+ oxygenates), our results call into question the reported mechanism established by microkinetic models.

q-pac: A Python package for machine learned charge equilibration models.

Many state-of-the art machine learning (ML) interatomic potentials are based on a local or semi-local (message-passing) representation of chemical environments. They, therefore, lack a description of long-range electrostatic interactions and non-local charge transfer. In this context, there has been much interest in developing ML-based charge equilibration models, which allow the rigorous calculation of long-range electrostatic interactions and the energetic response of molecules and materials to external fields. The recently reported kQEq method achieves this by predicting local atomic electronegativities using Kernel ML. This paper describes the q-pac Python package, which implements several algorithmic and methodological advances to kQEq and provides an extendable framework for the development of ML charge equilibration models.

Physics-inspired machine learning of localized intensive properties.

Machine learning (ML) has been widely applied to chemical property prediction, most prominently for the energies and forces in molecules and materials. The strong interest in predicting energies in particular has led to a 'local energy'-based paradigm for modern atomistic ML models, which ensures size-extensivity and a linear scaling of computational cost with system size. However, many electronic properties (such as excitation energies or ionization energies) do not necessarily scale linearly with system size and may even be spatially localized. Using size-extensive models in these cases can lead to large errors. In this work, we explore different strategies for learning intensive and localized properties, using HOMO energies in organic molecules as a representative test case. In particular, we analyze the pooling functions that atomistic neural networks use to predict molecular properties, and suggest an orbital weighted average (OWA) approach that enables the accurate prediction of orbital energies and locations.

Science-Driven Atomistic Machine Learning.

Machine learning (ML) algorithms are currently emerging as powerful tools in all areas of science. Conventionally, ML is understood as a fundamentally data-driven endeavour. Unfortunately, large well-curated databases are sparse in chemistry. In this contribution, I therefore review science-driven ML approaches which do not rely on "big data", focusing on the atomistic modelling of materials and molecules. In this context, the term science-driven refers to approaches that begin with a scientific question and then ask what training data and model design choices are appropriate. As key features of science-driven ML, the automated and purpose-driven collection of data and the use of chemical and physical priors to achieve high data-efficiency are discussed. Furthermore, the importance of appropriate model evaluation and error estimation is emphasized.

Green synthesis of propylene oxide directly from propane.

The chemical industry faces the challenge of bringing emissions of climate-damaging CO2 to zero. However, the synthesis of important intermediates, such as olefins or epoxides, is still associated with the release of large amounts of greenhouse gases. This is due to both a high energy input for many process steps and insufficient selectivity of the underlying catalyzed reactions. Surprisingly, we find that in the oxidation of propane at elevated temperature over apparently inert materials such as boron nitride and silicon dioxide not only propylene but also significant amounts of propylene oxide are formed, with unexpectedly small amounts of CO2. Process simulations reveal that the combined synthesis of these two important chemical building blocks is technologically feasible. Our discovery leads the ways towards an environmentally friendly production of propylene oxide and propylene in one step. We demonstrate that complex catalyst development is not necessary for this reaction.

Tackling Structural Complexity in Li2S-P2S5 Solid-State Electrolytes Using Machine Learning Potentials.

The lithium thiophosphate (LPS) material class provides promising candidates for solid-state electrolytes (SSEs) in lithium ion batteries due to high lithium ion conductivities, non-critical elements, and low material cost. LPS materials are characterized by complex thiophosphate microchemistry and structural disorder influencing the material performance. To overcome the length and time scale restrictions of ab initio calculations to industrially applicable LPS materials, we develop a near-universal machine-learning interatomic potential for the LPS material class. The trained Gaussian Approximation Potential (GAP) can likewise describe crystal and glassy materials and different P-S connectivities PmSn. We apply the GAP surrogate model to probe lithium ion conductivity and the influence of thiophosphate subunits on the latter. The materials studied are crystals (modifications of Li3PS4 and Li7P3S11), and glasses of the xLi2S-(100 - x)P2S5 type (x = 67, 70 and 75). The obtained material properties are well aligned with experimental findings and we underscore the role of anion dynamics on lithium ion conductivity in glassy LPS. The GAP surrogate approach allows for a variety of extensions and transferability to other SSEs.

A Hybrid Machine Learning Approach for Structure Stability Prediction in Molecular Co-crystal Screenings.

Co-crystals are a highly interesting material class as varying their components and stoichiometry in principle allows tuning supramolecular assemblies toward desired physical properties. The in silico prediction of co-crystal structures represents a daunting task, however, as they span a vast search space and usually feature large unit cells. This requires theoretical models that are accurate and fast to evaluate, a combination that can in principle be accomplished by modern machine-learned (ML) potentials trained on first-principles data. Crucially, these ML potentials need to account for the description of long-range interactions, which are essential for the stability and structure of molecular crystals. In this contribution, we present a strategy for developing Δ-ML potentials for co-crystals, which use a physical baseline model to describe long-range interactions. The applicability of this approach is demonstrated for co-crystals of variable composition consisting of an active pharmaceutical ingredient and various co-formers. We find that the Δ-ML approach offers a strong and consistent improvement over the density functional tight binding baseline. Importantly, this even holds true when extrapolating beyond the scope of the training set, for instance in molecular dynamics simulations under ambient conditions.

Regularized second-order correlation methods for extended systems.

Second-order Møller-Plesset perturbation theory (MP2) constitutes the simplest form of many-body wavefunction theory and often provides a good compromise between efficiency and accuracy. There are, however, well-known limitations to this approach. In particular, MP2 is known to fail or diverge for some prototypical condensed matter systems like the homogeneous electron gas (HEG) and to overestimate dispersion-driven interactions in strongly polarizable systems. In this paper, we explore how the issues of MP2 for metallic, polarizable, and strongly correlated periodic systems can be ameliorated through regularization. To this end, two regularized second-order methods (including a new, size-extensive Brillouin-Wigner approach) are applied to the HEG, the one-dimensional Hubbard model, and the graphene-water interaction. We find that regularization consistently leads to improvements over the MP2 baseline and that different regularizers are appropriate for the various systems.

CO2-Activation by size-selected tantalum cluster cations (Ta1-16+): thermalization governing reaction selectivity.

The reactions of tantalum cluster cations of different sizes toward carbon dioxide are studied in an ion trap under multi-collisional conditions. For all sizes studied, consecutive reactions with several CO2 molecules are observed. This reveals two different pathways, namely oxide formation and the pickup of an entire molecule. Supported by calculations of the thermochemistry of TanO+ formation upon reaction with CO2, changes in the branching ratios at a particular cluster size are related to heat effects due to the vibrational heat capacity of the clusters and the exothermicity of the reaction.

Data-efficient machine learning for molecular crystal structure prediction.

The combination of modern machine learning (ML) approaches with high-quality data from quantum mechanical (QM) calculations can yield models with an unrivalled accuracy/cost ratio. However, such methods are ultimately limited by the computational effort required to produce the reference data. In particular, reference calculations for periodic systems with many atoms can become prohibitively expensive for higher levels of theory. This trade-off is critical in the context of organic crystal structure prediction (CSP). Here, a data-efficient ML approach would be highly desirable, since screening a huge space of possible polymorphs in a narrow energy range requires the assessment of a large number of trial structures with high accuracy. In this contribution, we present tailored Δ-ML models that allow screening a wide range of crystal candidates while adequately describing the subtle interplay between intermolecular interactions such as H-bonding and many-body dispersion effects. This is achieved by enhancing a physics-based description of long-range interactions at the density functional tight binding (DFTB) level-for which an efficient implementation is available-with a short-range ML model trained on high-quality first-principles reference data. The presented workflow is broadly applicable to different molecular materials, without the need for a single periodic calculation at the reference level of theory. We show that this even allows the use of wavefunction methods in CSP.

Active discovery of organic semiconductors.

The versatility of organic molecules generates a rich design space for organic semiconductors (OSCs) considered for electronics applications. Offering unparalleled promise for materials discovery, the vastness of this design space also dictates efficient search strategies. Here, we present an active machine learning (AML) approach that explores an unlimited search space through consecutive application of molecular morphing operations. Evaluating the suitability of OSC candidates on the basis of charge injection and mobility descriptors, the approach successively queries predictive-quality first-principles calculations to build a refining surrogate model. The AML approach is optimized in a truncated test space, providing deep methodological insight by visualizing it as a chemical space network. Significantly outperforming a conventional computational funnel, the optimized AML approach rapidly identifies well-known and hitherto unknown molecular OSC candidates with superior charge conduction properties. Most importantly, it constantly finds further candidates with highest efficiency while continuing its exploration of the endless design space.

Pure non-local machine-learned density functional theory for electron correlation.

Density-functional theory (DFT) is a rigorous and (in principle) exact framework for the description of the ground state properties of atoms, molecules and solids based on their electron density. While computationally efficient density-functional approximations (DFAs) have become essential tools in computational chemistry, their (semi-)local treatment of electron correlation has a number of well-known pathologies, e.g. related to electron self-interaction. Here, we present a type of machine-learning (ML) based DFA (termed Kernel Density Functional Approximation, KDFA) that is pure, non-local and transferable, and can be efficiently trained with fully quantitative reference methods. The functionals retain the mean-field computational cost of common DFAs and are shown to be applicable to non-covalent, ionic and covalent interactions, as well as across different system sizes. We demonstrate their remarkable possibilities by computing the free energy surface for the protonated water dimer at hitherto unfeasible gold-standard coupled cluster quality on a single commodity workstation.

Data-efficient iterative training of Gaussian approximation potentials: Application to surface structure determination of rutile IrO2 and RuO2.

Machine-learning interatomic potentials, such as Gaussian Approximation Potentials (GAPs), constitute a powerful class of surrogate models to computationally involved first-principles calculations. At a similar predictive quality but significantly reduced cost, they could leverage otherwise barely tractable extensive sampling as in global surface structure determination (SSD). This efficiency is jeopardized though, if an a priori unknown structural and chemical search space as in SSD requires an excessive number of first-principles data for the GAP training. To this end, we present a general and data-efficient iterative training protocol that blends the creation of new training data with the actual surface exploration process. Demonstrating this protocol with the SSD of low-index facets of rutile IrO2 and RuO2, the involved simulated annealing on the basis of the refining GAP identifies a number of unknown terminations even in the restricted sub-space of (1 × 1) surface unit cells. Particularly in an O-poor environment, some of these, then metal-rich terminations, are thermodynamically most stable and are reminiscent of complexions as discussed for complex ceramic materials.

Machine learning in chemical reaction space.

Chemical compound space refers to the vast set of all possible chemical compounds, estimated to contain 1060 molecules. While intractable as a whole, modern machine learning (ML) is increasingly capable of accurately predicting molecular properties in important subsets. Here, we therefore engage in the ML-driven study of even larger reaction space. Central to chemistry as a science of transformations, this space contains all possible chemical reactions. As an important basis for 'reactive' ML, we establish a first-principles database (Rad-6) containing closed and open-shell organic molecules, along with an associated database of chemical reaction energies (Rad-6-RE). We show that the special topology of reaction spaces, with central hub molecules involved in multiple reactions, requires a modification of existing compound space ML-concepts. Showcased by the application to methane combustion, we demonstrate that the learned reaction energies offer a non-empirical route to rationally extract reduced reaction networks for detailed microkinetic analyses.

Mapping Materials and Molecules.

The visualization of data is indispensable in scientific research, from the early stages when human insight forms to the final step of communicating results. In computational physics, chemistry and materials science, it can be as simple as making a scatter plot or as straightforward as looking through the snapshots of atomic positions manually. However, as a result of the "big data" revolution, these conventional approaches are often inadequate. The widespread adoption of high-throughput computation for materials discovery and the associated community-wide repositories have given rise to data sets that contain an enormous number of compounds and atomic configurations. A typical data set contains thousands to millions of atomic structures, along with a diverse range of properties such as formation energies, band gaps, or bioactivities.It would thus be desirable to have a data-driven and automated framework for visualizing and analyzing such structural data sets. The key idea is to construct a low-dimensional representation of the data, which facilitates navigation, reveals underlying patterns, and helps to identify data points with unusual attributes. Such data-intensive maps, often employing machine learning methods, are appearing more and more frequently in the literature. However, to the wider community, it is not always transparent how these maps are made and how they should be interpreted. Furthermore, while these maps undoubtedly serve a decorative purpose in academic publications, it is not always apparent what extra information can be garnered from reading or making them.This Account attempts to answer such questions. We start with a concise summary of the theory of representing chemical environments, followed by the introduction of a simple yet practical conceptual approach for generating structure maps in a generic and automated manner. Such analysis and mapping is made nearly effortless by employing the newly developed software tool ASAP. To showcase the applicability to a wide variety of systems in chemistry and materials science, we provide several illustrative examples, including crystalline and amorphous materials, interfaces, and organic molecules. In these examples, the maps not only help to sift through large data sets but also reveal hidden patterns that could be easily missed using conventional analyses.The explosion in the amount of computed information in chemistry and materials science has made visualization into a science in itself. Not only have we benefited from exploiting these visualization methods in previous works, we also believe that the automated mapping of data sets will in turn stimulate further creativity and exploration, as well as ultimately feed back into future advances in the respective fields.

Machine-Learning Coupled Cluster Properties through a Density Tensor Representation.

The introduction of machine-learning (ML) algorithms to quantum mechanics enables rapid evaluation of otherwise intractable expressions at the cost of prior training on appropriate benchmarks. Many computational bottlenecks in the evaluation of accurate electronic structure theory could potentially benefit from the application of such models, from reducing the complexity of the underlying wave function parameter space to circumventing the complications of solving the electronic Schrödinger equation entirely. Applications of ML to electronic structure have thus far been focused on learning molecular properties (mainly the energy) from geometric representations. While this line of study has been quite successful, highly accurate models typically require a "big data" approach with thousands of training data points. Herein, we propose a general, systematically improvable scheme for wave function-based ML of arbitrary molecular properties, inspired by the underlying equations that govern the canonical approach to computing the properties. To this end, we combine the established ML machinery of the t-amplitude tensor representation with a new reduced density matrix representation. The resulting model provides quantitative accuracy in both the electronic energy and dipoles of small molecules using only a few dozen training points per system.