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The accuracy of density-functional theory (DFT) is determined by the quality of the approximate functionals, such as exchange-correlation in electronic DFT and the excess functional in the classical DFT formalism of fluids. The exact functional is highly nonlocal for both electrons and fluids, yet most approximate functionals are semi-local or nonlocal in a limited weighted-density form. Machine-learned (ML) nonlocal density-functional approximations are promising in both electronic and classical DFT, but have so far employed disparate approaches with limited generality. Here, we formulate a universal approximation framework and training protocol for nonlocal ML functionals, combining features of equivariant convolutional neural networks and the weighted-density approximation. We prototype this approach for several 1D and quasi-1D problems and demonstrate that a functional with exactly the same hyperparameters achieves excellent accuracy for the hard-rod fluid, the inhomogeneous Ising model, the exact exchange functional for electrons, the electron kinetic energy functional for orbital-free DFT, as well as for liquid water with 1D inhomogeneities. These results lay the foundation for a universal ML approach to exact 3D functionals spanning electronic and classical DFT., Comment: 12 pages, 7 figures

We present BEAST DB, an open-source database comprised of ab initio electrochemical data computed using grand-canonical density functional theory in implicit solvent at consistent calculation parameters. The database contains over 20,000 surface calculations and covers a broad set of heterogeneous catalyst materials and electrochemical reactions. Calculations were performed at self-consistent fixed potential as well as constant charge to facilitate comparisons to the computational hydrogen electrode. This article presents common use cases of the database to rationalize trends in catalyst activity, screen catalyst material spaces, understand elementary mechanistic steps, analyze electronic structure, and train machine learning models to predict higher fidelity properties. Users can interact graphically with the database by querying for individual calculations to gain granular understanding of reaction steps or by querying for an entire reaction pathway on a given material using an interactive reaction pathway tool. BEAST DB will be periodically updated, with planned future updates to include advanced electronic structure data, surface speciation studies, and greater reaction coverage., Comment: 24 pages, 8 figures

Low dimensional hybrid organic-inorganic perovskites (HOIPs) represent a promising class of electronically active materials for both light absorption and emission. The design space of HOIPs is extremely large, since a diverse space of organic cations can be combined with different inorganic frameworks. This immense design space allows for tunable electronic and mechanical properties, but also necessitates the development of new tools for in silico high throughput analysis of candidate structures. In this work, we present an accurate, efficient, transferable and widely applicable machine learning interatomic potential (MLIP) for predicting the structure of new 2D HOIPs. Using the MACE architecture, an MLIP is trained on 86 diverse experimentally reported HOIP structures. The model is tested on 73 unseen perovskite compositions, and achieves chemical accuracy with respect to the reference electronic structure method. Our model is then combined with a simple random structure search algorithm to predict the structure of hypothetical HOIPs given only the proposed composition. Success is demonstrated by correctly and reliably recovering the crystal structure of a set of experimentally known 2D perovskites. Such a random structure search is impossible with ab initio methods due to the associated computational cost, but is relatively inexpensive with the MACE potential. Finally, the procedure is used to predict the structure formed by a new organic cation with no previously known corresponding perovskite. Laboratory synthesis of the new hybrid perovskite confirms the accuracy of our prediction. This capability, applied at scale, enables efficient screening of thousands of combinations of organic cations and inorganic layers., Comment: 14 pages and 9 figures in the main text. Supplementary included in pdf

We combine graph neural networks (GNN) with an inexpensive and reliable structure generation approach based on the bond-valence method (BVM) to train accurate machine learning models for screening 222,960 halide perovskites using statistical estimates of the DFT/PBE formation energy (Ef), and the PBE and HSE band gaps (Eg). The GNNs were fined tuned using domain adaptation (DA) from a source model, which yields a factor of 1.8 times improvement in Ef and 1.2 - 1.35 times improvement in HSE Eg compared to direct training (i.e., without DA). Using these two ML models, 48 compounds were identified out of 222,960 candidates as both stable and that have an HSE Eg that is relevant for photovoltaic applications. For this subset, only 8 have been reported to date, indicating that 40 compounds remain unexplored to the best of our knowledge and therefore offer opportunities for potential experimental examination.

Machine-learned force fields have transformed the atomistic modelling of materials by enabling simulations of ab initio quality on unprecedented time and length scales. However, they are currently limited by: (i) the significant computational and human effort that must go into development and validation of potentials for each particular system of interest; and (ii) a general lack of transferability from one chemical system to the next. Here, using the state-of-the-art MACE architecture we introduce a single general-purpose ML model, trained on a public database of 150k inorganic crystals, that is capable of running stable molecular dynamics on molecules and materials. We demonstrate the power of the MACE-MP-0 model - and its qualitative and at times quantitative accuracy - on a diverse set problems in the physical sciences, including the properties of solids, liquids, gases, chemical reactions, interfaces and even the dynamics of a small protein. The model can be applied out of the box and as a starting or "foundation model" for any atomistic system of interest and is thus a step towards democratising the revolution of ML force fields by lowering the barriers to entry., Comment: 119 pages, 63 figures, 37MB PDF

This study investigates the use of machine learning (ML) to correct the enthalpy of formation (Hf) from two separate DFT functionals, PBE and SCAN, to the experimental Hf across 1011 solid-state compounds. The ML model uses a set of 25 properties that characterize the electronic structure as calculated using PBE and SCAN. The ML model significantly decreases the error in PBE-calculated Hf values from an mean absolute error (MAE) of 195 meV/atom to an MAE = 80 meV/atom when compared to the experiment. For PBE, the PDP+GAM analysis shows compounds with a high ionicity (I), i.e., I>0.22, have errors in Hf that are twice as large as compounds having I < 0.22 (246 meV/atom compared to 113 meV/atom). Conversely, no analogous trend is observed for SCAN-calculated Hfs, which explains why the ML model for PBE can more easily correct the systematic error in calculated Hfs for PBE but not for SCAN. Although the literature suggests PBE is reliable for intermetallics but less so for oxides and halides, our analysis reveals intermetallics pose a challenge for PBE only when the charge transfer is significant (I >0.22). Meanwhile, oxides and halides may be described accurately by PBE for systems in which charge transfer is relatively low (I < 0.22).

Networks of atom-centered coordination octahedra commonly occur in inorganic and hybrid solid-state materials. Characterizing their spatial arrangements and characteristics is crucial for relating structures to properties for many materials families. The traditional method using case-by-case inspection becomes prohibitive for discovering trends and similarities in large datasets. Here, we operationalize chemical intuition to automate the geometric parsing, quantification, and classification of coordination octahedral networks. We find axis-resolved tilting trends in ABO$_{3}$ perovskite polymorphs, which assist in detecting oxidation state changes. Moreover, we develop a scale-invariant encoding scheme to represent these networks, which, combined with human-assisted unsupervised machine learning, allows us to taxonomize the inorganic framework polytypes in hybrid iodoplumbates (A$_x$Pb$_y$I$_z$). Consequently, we uncover a violation of Pauling's third rule and the design principles underpinning their topological diversity. Our results offer a glimpse into the vast design space of atomic octahedral networks and inform high-throughput, targeted screening of specific structure types., Comment: 56 pages

The atomic-scale response of inhomogeneous fluids at interfaces and surrounding solute particles plays a critical role in governing chemical, electrochemical and biological processes at such interfaces. Classical molecular dynamics simulations have been applied extensively to simulate the response of inhomogeneous fluids directly, and as inputs to classical density functional theory, but are limited by the accuracy of the underlying empirical force fields. Here, we deploy neural network potentials (NNPs) trained to \emph{ab initio} simulations to accurately predict the inhomogeneous response of two widely different fluids: liquid water and molten NaCl. Although the advantages of NNPs is that they can be readily trained to model complex systems, one limitation in modeling the inhomogeneous response of liquids is the need for including the correct configurations of the system in the training data. Therefore, first we establish protocols, based on molecular dynamics simulations in external atomic potentials, to sufficiently sample the correct configurations of inhomogeneous fluids. We show that NNPs trained to inhomogeneous fluid configurations can predict several properties such as the density response, surface tension and size-dependent cavitation free energies in water and molten NaCl corresponding to \emph{ab initio} interactions, more accurately than with empirical force fields. This work therefore provides a first demonstration and framework for extracting the response of inhomogeneous fluids from first principles for classical density-functional treatment of fluids free from empirical potentials.

Metal halide perovskites are multifunctional semiconductors with tunable structures and properties. They are highly dynamic crystals with complex octahedral tilting patterns and strongly anharmonic atomic behaviour. In the higher temperature, higher symmetry phases of these materials, several complex structural features have been observed. The local structure can differ greatly from the average structure and there is evidence that dynamic two-dimensional structures of correlated octahedral motion form. An understanding of the underlying complex atomistic dynamics is, however, still lacking. In this work, the local structure of the inorganic perovskite CsPbI$_3$ is investigated using a new machine learning force field based on the atomic cluster expansion framework. Through analysis of the temporal and spatial correlation observed during large-scale simulations, we reveal that the low frequency motion of octahedral tilts implies a double-well effective potential landscape, even well into the cubic phase. Moreover, dynamic local regions of lower symmetry are present within both higher symmetry phases. These regions are planar and we report the length and timescales of the motion. Finally, we investigate and visualise the spatial arrangement of these features and their interactions, providing a comprehensive picture of local structure in the higher symmetry phases.

Machine learning (ML) is increasingly used in the field of materials science, where statistical estimates of computed properties are employed to rapidly examine the chemical space for new compounds. However, a systematic comparison of several ML models for this domain has been hindered by the scarcity of appropriate datasets of materials properties, as well as the lack of thorough benchmarking studies. To address this, a public data-analytics competition was organized by the Novel Materials Discovery (NOMAD) Centre of Excellence and hosted by the on-line platform Kaggle using a dataset of $3\,000$ (Al$_x$ Ga$_y$ In$_z$)$_2$ O$_3$ compounds (with $x+y+z = 1$). The aim of this challenge was to identify the best ML model for the prediction of two key physical properties that are relevant for optoelectronic applications: the electronic band gap energy and the crystalline formation energy. In this contribution, we present a summary of the top three ML approaches of the competition including the 1st place solution based on a crystal graph representation that is new for ML of the properties of materials. The 2nd place model combined many candidate descriptors from a set of compositional, atomic environment-based, and average structural properties with the light gradient-boosting machine regression model. The 3rd place model employed the smooth overlap of atomic positions representation with a neural network. To gain insight into whether the representation or the regression model determines the overall model performance, nine ML models obtained by combining the representations and regression models of the top three approaches were compared by looking at the correlations among prediction errors. At fixed representation, the largest correlation is observed in predictions made with kernel ridge regression and neural network, reflecting a similar performance on the same test set samples.

Predicting the stability of the perovskite structure remains a longstanding challenge for the discovery of new functional materials for many applications including photovoltaics and electrocatalysts. We developed an accurate, physically interpretable, and one-dimensional tolerance factor, {\tau}, that correctly predicts 92% of compounds as perovskite or nonperovskite for an experimental dataset of 576 $ABX_3$ materials ($\textit{X} =$ $O^{2-}$, $F^-$, $Cl^-$, $Br^-$, $I^-$) using a novel data analytics approach based on SISSO (sure independence screening and sparsifying operator). {\tau} is shown to generalize outside the training set for 1,034 experimentally realized single and double perovskites (91% accuracy) and is applied to identify 23,314 new double perovskites ($A_2$$\textit{BB'}$$X_6$) ranked by their probability of being stable as perovskite. This work guides experimentalists and theorists towards which perovskites are most likely to be successfully synthesized and demonstrates an approach to descriptor identification that can be extended to arbitrary applications beyond perovskite stability predictions.

We present a code to calculate effective masses from energy dispersion relation using finite difference method on a five-point stencil. We validate our code against inorganic (GaAs and InP) and organic (pentacene and rubrene) crystals., Comment: This paper has been withdrawn by the author due to mistakes