Gaussian Process Regression for Materials and Molecules

Translational eigenstates of He@C60 from four-dimensional ab initio potential energy surfaces interpolated using Gaussian process regression

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two ab initio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

Electrostatics as a Guiding Principle in Understanding and Designing Enzymes

Enzyme design faces challenges related to the implementation of the basic principles that govern the catalytic activity in natural enzymes. In this work, we revisit basic electrostatic concepts that have been shown to explain the origin of enzymatic efficiency like preorganization and reorganization. Using magnitudes such as the electrostatic potential and the electric field generated by the protein, we explain how these concepts work in different enzymes and how they can be used to rationalize the consequences of point mutations. We also discuss examples of protein design in which electrostatic effects have been implemented. For the near future, molecular simulations, coupled with the use of machine learning methods, can be used to implement electrostatics as a guiding principle for enzyme designs.

Accelerating the prediction of inorganic surfaces with machine learning interatomic potentials

The surface properties of solid-state materials often dictate their functionality, especially for applications where nanoscale effects become important. The relevant surface(s) and their properties are determined, in large part, by the material's synthesis or operating conditions. These conditions dictate thermodynamic driving forces and kinetic rates responsible for yielding the observed surface structure and morphology. Computational surface science methods have long been applied to connect thermochemical conditions to surface phase stability, particularly in the heterogeneous catalysis and thin film growth communities. This review provides a brief introduction to first-principles approaches to compute surface phase diagrams before introducing emerging data-driven approaches. The remainder of the review focuses on the application of machine learning, predominantly in the form of learned interatomic potentials, to study complex surfaces. As machine learning algorithms and large datasets on which to train them become more commonplace in materials science, computational methods are poised to become even more predictive and powerful for modeling the complexities of inorganic surfaces at the nanoscale.

Gaussian Process Regression-Based Near-Infrared d-Luciferin Analogue Design Using Mutation-Controlled Graph-Based Genetic Algorithm

Molecular discovery is central to the field of chemical informatics. Although optimization approaches have been developed that target-specific molecular properties in combination with machine learning techniques, optimization using databases of limited size is challenging for efficient molecular design. We present a molecular design method with a Gaussian process regression model and a graph-based genetic algorithm (GB-GA) from a data set comprising a small number of compounds by introducing mutation probability control in the genetic algorithm to enhance the optimization capability and speed up the convergence to the optimal solution. In addition, we propose reducing the number of parameters in the conventional GB-GA focusing on efficient molecular design from a small database. We generated a target-specific database by combining active learning and iterative design in the evolutionary methodologies and chose Gaussian process regression as the prediction model for molecular properties. We show that the proposed scheme is more efficient for optimization toward the target properties from goal-directed benchmarks with several drug-like molecules compared to the conventional GB-GA method. Finally, we provide a demonstration whereby we designed D-luciferin analogues with near-infrared fluorescence for bioimaging, which is desirable for effective in vivo light sources, from a small-size data set.

Machine-learning accelerated structure search for ligand-protected clusters

Finding low-energy structures of ligand-protected clusters is challenging due to the enormous conformational space and the high computational cost of accurate quantum chemical methods for determining the structures and energies of conformers. Here, we adopted and utilized a kernel rigid regression based machine learning method to accelerate the search for low-energy structures of ligand-protected clusters. We chose the Au25(Cys)18 (Cys: cysteine) cluster as a model system to test and demonstrate our method. We found that the low-energy structures of the cluster are characterized by a specific hydrogen bond type in the cysteine. The different configurations of the ligand layer influence the structural and electronic properties of clusters.

Optimized Machine learning techniques Enable prediction of organic dyes photophysical Properties: Absorption Wavelengths, emission Wavelengths, and quantum yields

Applications of organic dyes, ranging from basic research to industry, are functions of their photophysical properties. Two important aspects- (1) knowledge of the photophysical properties of existing dyes long before real applications and (2) discovery of new organic dyes with desired photophysical properties for either upgradation of existing or development of new applications-are needed to be addressed. These two cases are coupled together with the common goal of estimating photophysical properties with high accuracy at the minimum cost of time and money long before the hard-core laboratory experiment. For this purpose, machine learning-based techniques are the most suitable approach. In this study, we used optimized machine-learning techniques to assess a dataset of 3066 organic dyes, which were evaluated using three evaluation parameters: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the coefficient of determination (R2). The Quadratic Support Vector Machine (QSVM) was the best predictive model for RMSE-16.614, MAE-10.837, and R2-0.961 for absorption wavelengths and RMSE-23.636, MAE-16.278, and R2-0.929 for emission wavelengths. These R2 values are 0.7% and 0.4% greater than the Gradient Boost Regression Tree (GBRT) model's recently reported values of 0.954 and 0.925 for absorption and emission wavelengths, respectively. Furthermore, we estimated the quantum yield and found that the Coarse Gaussian Support Vector Machine (CGSVM) outperformed all examined models. For more validation of these models, we compared the predicted results with the experimental results of selective dyes. The proposed automated approach can be used for predicting photophysical properties without much computer programming knowledge.

From Organic Fragments to Photoswitchable Catalysts: The OFF-ON Structural Repository for Transferable Kernel-Based Potentials

Structurally and conformationally diverse databases are needed to train accurate neural networks or kernel-based potentials capable of exploring the complex free energy landscape of flexible functional organic molecules. Curating such databases for species beyond "simple" drug-like compounds or molecules composed of well-defined building blocks (e.g., peptides) is challenging as it requires thorough chemical space mapping and evaluation of both chemical and conformational diversities. Here, we introduce the OFF-ON (organic fragments from organocatalysts that are non-modular) database, a repository of 7869 equilibrium and 67,457 nonequilibrium geometries of organic compounds and dimers aimed at describing conformationally flexible functional organic molecules, with an emphasis on photoswitchable organocatalysts. The relevance of this database is then demonstrated by training a local kernel regression model on a low-cost semiempirical baseline and comparing it with a PBE0-D3 reference for several known catalysts, notably the free energy surfaces of exemplary photoswitchable organocatalysts. Our results demonstrate that the OFF-ON data set offers reliable predictions for simulating the conformational behavior of virtually any (photoswitchable) organocatalyst or organic compound composed of H, C, N, O, F, and S atoms, thereby opening a computationally feasible route to explore complex free energy surfaces in order to rationalize and predict catalytic behavior.

Local-environment-guided selection of atomic structures for the development of machine-learning potentials

Machine learning potentials (MLPs) have attracted significant attention in computational chemistry and materials science due to their high accuracy and computational efficiency. The proper selection of atomic structures is crucial for developing reliable MLPs. Insufficient or redundant atomic structures can impede the training process and potentially result in a poor quality MLP. Here, we propose a local-environment-guided screening algorithm for efficient dataset selection in MLP development. The algorithm utilizes a local environment bank to store unique local environments of atoms. The dissimilarity between a particular local environment and those stored in the bank is evaluated using the Euclidean distance. A new structure is selected only if its local environment is significantly different from those already present in the bank. Consequently, the bank is then updated with all the new local environments found in the selected structure. To demonstrate the effectiveness of our algorithm, we applied it to select structures for a Ge system and a Pd13H2 particle system. The algorithm reduced the training data size by around 80% for both without compromising the performance of the MLP models. We verified that the results were independent of the selection and ordering of the initial structures. We also compared the performance of our method with the farthest point sampling algorithm, and the results show that our algorithm is superior in both robustness and computational efficiency. Furthermore, the generated local environment bank can be continuously updated and can potentially serve as a growing database of feature local environments, aiding in efficient dataset maintenance for constructing accurate MLPs.

Mechanism of Charge Transport in Lithium Thiophosphate

Lithium ortho-thiophosphate (Li3PS4) has emerged as a promising candidate for solid-state electrolyte batteries, thanks to its highly conductive phases, cheap components, and large electrochemical stability range. Nonetheless, the microscopic mechanisms of Li-ion transport in Li3PS4 are far from being fully understood, the role of PS4 dynamics in charge transport still being controversial. In this work, we build machine learning potentials targeting state-of-the-art DFT references (PBEsol, r2SCAN, and PBE0) to tackle this problem in all known phases of Li3PS4 (α, β, and γ), for large system sizes and time scales. We discuss the physical origin of the observed superionic behavior of Li3PS4: the activation of PS4 flipping drives a structural transition to a highly conductive phase, characterized by an increase in Li-site availability and by a drastic reduction in the activation energy of Li-ion diffusion. We also rule out any paddle-wheel effects of PS4 tetrahedra in the superionic phases-previously claimed to enhance Li-ion diffusion-due to the orders-of-magnitude difference between the rate of PS4 flips and Li-ion hops at all temperatures below melting. We finally elucidate the role of interionic dynamical correlations in charge transport, by highlighting the failure of the Nernst-Einstein approximation to estimate the electrical conductivity. Our results show a strong dependence on the target DFT reference, with PBE0 yielding the best quantitative agreement with experimental measurements not only for the electronic band gap but also for the electrical conductivity of β- and α-Li3PS4.

Recalibrating the Experimentally Derived Structure of the Metastable Surface Oxide on Copper via Machine Learning-Accelerated In Silico Global Optimization

The oxidation of copper and its surface oxides are gaining increasing attention due to the enhanced CO2 reduction reaction (CO2RR) activity exhibited by partially oxidized copper among the copper-based catalysts. The "8" surface oxide on Cu(111) is seen as a promising structure for further study due to its resemblance to the highly active Cu2O(110) surface in the C-C coupling of the CO2RR, setting it apart from other O/Cu(111) surface oxides resembling Cu2O(111). However, recent X-ray photoelectron spectroscopy analysis challenges the currently accepted atomic structure of the "8" surface oxide, prompting a need for reevaluation. This study highlights the limitations of conventional methods when addressing such challenges, leading us to adopt global optimization search techniques. After a rigorous process to ensure robustness, the unbiased global minimum of the "8" surface oxide is identified. Interestingly, this configuration differs significantly from other surface oxides and also from previous "8" models while retaining similarities to the Cu2O(110) surface.

First-principles spectroscopy of aqueous interfaces using machine-learned electronic and quantum nuclear effects

Vibrational spectroscopy is a powerful approach to visualising interfacial phenomena. However, extracting structural and dynamical information from vibrational spectra is a challenge that requires first-principles simulations, including non-Condon and quantum nuclear effects. We address this challenge by developing a machine-learning enhanced first-principles framework to speed up predictive modelling of infrared, Raman, and sum-frequency generation spectra. Our approach uses machine learning potentials that encode quantum nuclear effects to generate quantum trajectories using simple molecular dynamics efficiently. In addition, we reformulate bulk and interfacial selection rules to express them unambiguously in terms of the derivatives of polarisation and polarisabilities of the whole system and predict these derivatives efficiently using fully-differentiable machine learning models of dielectric response tensors. We demonstrate our framework's performance by predicting the IR, Raman, and sum-frequency generation spectra of liquid water, ice and the water-air interface by achieving near quantitative agreement with experiments at nearly the same computational efficiency as pure classical methods. Finally, to aid the experimental discovery of new phases of nanoconfined water, we predict the temperature-dependent vibrational spectra of monolayer water across the solid-hexatic-liquid phases transition.

Machine Learning Potentials with the Iterative Boltzmann Inversion: Training to Experiment

Methodologies for training machine learning potentials (MLPs) with quantum-mechanical simulation data have recently seen tremendous progress. Experimental data have a very different character than simulated data, and most MLP training procedures cannot be easily adapted to incorporate both types of data into the training process. We investigate a training procedure based on iterative Boltzmann inversion that produces a pair potential correction to an existing MLP using equilibrium radial distribution function data. By applying these corrections to an MLP for pure aluminum based on density functional theory, we observe that the resulting model largely addresses previous overstructuring in the melt phase. Interestingly, the corrected MLP also exhibits improved performance in predicting experimental diffusion constants, which are not included in the training procedure. The presented method does not require autodifferentiating through a molecular dynamics solver and does not make assumptions about the MLP architecture. Our results suggest a practical framework for incorporating experimental data into machine learning models to improve the accuracy of molecular dynamics simulations.

Perturbative Expansion in Reciprocal Space: Bridging Microscopic and Mesoscopic Descriptions of Molecular Interactions

Determining the Fourier representation of various molecular interactions is important for constructing density-based field theories from a microscopic point of view, enabling a multiscale bridge between microscopic and mesoscopic descriptions. However, due to the strongly repulsive nature of short-ranged interactions, interparticle interactions cannot be formally defined in Fourier space, which renders coarse-grained (CG) approaches in k-space somewhat ambiguous. In this paper, we address this issue by designing a perturbative expansion of pair interactions in reciprocal space. Our perturbation theory, starting from reciprocal space, elucidates the microscopic origins underlying zeroth-order (long-range attractions) and divergent repulsive interactions from higher order contributions. We propose a systematic framework for constructing a faithful Fourier-space representation of molecular interactions, capturing key structural correlations in various systems, including simple model systems and molecular CG models of liquids. Building upon the Ornstein-Zernike equation, our approach can be combined with appropriate closure relations, and to further improve the closure approximations, we develop a bottom-up parameterization strategy for inferring the bridge function from microscopic statistics. By incorporating the bridge function into the Fourier representation, our findings suggest a systematic, bottom-up approach to performing coarse-graining in reciprocal space, leading to the systematic construction of a bottom-up classical field theory of complex aqueous systems.

Prediction of Hydrogen Abstraction Rate Constants at the Allylic Site between Alkenes and OH with Multiple Machine Learning Models

Hydrogen abstraction reactions between hydrocarbons and hydroxyl radicals are important propagation steps in radical chain reactions, playing a crucial role in atmospheric and combustion chemistry. This study focuses on predicting the rate constants of the prototype of the reaction class of hydrogen abstractions, i.e., the primary allylic hydrogen abstraction from alkenes by the OH radical, via utilizing machine learning (ML) methods. Specifically, three distinct models, namely, feedforward neural network (FNN), support vector regression (SVR), and Gaussian process regression (GPR), have been employed to construct robust ML models for prediction. We proposed a novel strategy that seamlessly integrates descriptor preprocessing, a pairwise linear correlation analysis, and a model-specific Wrapper method to enhance the effectiveness of the feature selection procedure. The selected feature subset was then evaluated using two cross-validation techniques, i.e., leave-one-group-out (LOGO) and K-fold cross-validations, for each of the three ML models (FNN, SVR, and GPR) to assess their predictive and stability performance. The results demonstrate that the FNN model, trained with seven representative descriptors, achieves superior performance compared to the other two methods. For the FNN model, the average percentage deviation is 39.06% on the test set by performing LOGO cross-validation, while the repeated 10-fold cross-validation achieves a percentage prediction deviation of 19.1%. Two larger alkenes with 10 carbons were selected to test the prediction performance of the trained FNN model on primary allylic hydrogen abstraction. Results show that the kinetic predictions follow well the modified three-parameter Arrhenius equation, indicating the reliable performance of FNN in predicting hydrogen abstraction rate constants, especially for the primary allylic site. Hopefully, this work can shed useful light on the application of ML in generating chemical kinetic parameters of hydrocarbon combustion chemistry.

Accelerating Elastic Property Prediction in Fe-C Alloys through Coupling of Molecular Dynamics and Machine Learning

The scarcity of high-quality data presents a major challenge to the prediction of material properties using machine learning (ML) models. Obtaining material property data from experiments is economically cost-prohibitive, if not impossible. In this work, we address this challenge by generating an extensive material property dataset comprising thousands of data points pertaining to the elastic properties of Fe-C alloys. The data were generated using molecular dynamic (MD) calculations utilizing reference-free Modified embedded atom method (RF-MEAM) interatomic potential. This potential was developed by fitting atomic structure-dependent energies, forces, and stress tensors evaluated at ground state and finite temperatures using ab-initio. Various ML algorithms were subsequently trained and deployed to predict elastic properties. In addition to individual algorithms, super learner (SL), an ensemble ML technique, was incorporated to refine predictions further. The input parameters comprised the alloy's composition, crystal structure, interstitial sites, lattice parameters, and temperature. The target properties were the bulk modulus and shear modulus. Two distinct prediction approaches were undertaken: employing individual models for each property prediction and simultaneously predicting both properties using a single integrated model, enabling a comparative analysis. The efficiency of these models was assessed through rigorous evaluation using a range of accuracy metrics. This work showcases the synergistic power of MD simulations and ML techniques for accelerating the prediction of elastic properties in alloys.

Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension

Kernel methods such as kernel ridge regression and Gaussian process regression with Matern-type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials informatics. When the dimensionality of the feature space is high, these methods are used with necessarily sparse data. In this regime, the optimal length parameter of a Matern-type kernel may become so large that the method effectively degenerates into a low-order polynomial regression and, therefore, loses any advantage over such regression. This is demonstrated theoretically as well as numerically in the examples of six- and fifteen-dimensional molecular PES using squared exponential and simple exponential kernels. The results shed additional light on the success of polynomial approximations such as PIP for medium-size molecules and on the importance of orders-of-coupling-based models for preserving the advantages of kernel methods with Matern-type kernels of on the use of physically motivated (reproducing) kernels.

Distilling coarse-grained representations of molecular electronic structure with continuously gated message passing

Bottom-up methods for coarse-grained (CG) molecular modeling are critically needed to establish rigorous links between atomistic reference data and reduced molecular representations. For a target molecule, the ideal reduced CG representation is a function of both the conformational ensemble of the system and the target physical observable(s) to be reproduced at the CG resolution. However, there is an absence of algorithms for selecting CG representations of molecules from which complex properties, including molecular electronic structure, can be accurately modeled. We introduce continuously gated message passing (CGMP), a graph neural network (GNN) method for atomically decomposing molecular electronic structure sampled over conformational ensembles. CGMP integrates 3D-invariant GNNs and a novel gated message passing system to continuously reduce the atomic degrees of freedom accessible for electronic predictions, resulting in a one-shot importance ranking of atoms contributing to a target molecular property. Moreover, CGMP provides the first approach by which to quantify the degeneracy of "good" CG representations conditioned on specific prediction targets, facilitating the development of more transferable CG representations. We further show how CGMP can be used to highlight multiatom correlations, illuminating a path to developing CG electronic Hamiltonians in terms of interpretable collective variables for arbitrarily complex molecules.

Quantitative Structure-Reactivity Relationships for Synthesis Planning: The Benzhydrylium Case

Selective and feasible reactions are among the top targets in synthesis planning. Mayr's approach to quantifying chemical reactivity has greatly facilitated the planning process, but reactivity parameters for new compounds require time-consuming experiments. In the past decade, data-driven modeling has been gaining momentum in the field, as it shows promise in terms of efficient reactivity prediction. However, state-of-the-art models use quantum chemical data as input, which prevent access to real-time planning in organic synthesis. Here, we present a novel data-driven workflow for predicting reactivity parameters of molecules that takes only structural information as input, enabling de facto real-time reactivity predictions. We use the well-understood chemical space of benzhydrylium ions as an example to demonstrate the functionality of our approach and the performance of the resulting quantitative structure-reactivity relationships (QSRRs). Our results suggest that it is straightforward to build low-cost QSRR models that are accurate, interpretable, and transferable to unexplored systems within a given scope of application. Moreover, our QSRR approach suggests that Hammett σ parameters are only approximately additive.

Machine-learning-accelerated design of high-performance platinum intermetallic nanoparticle fuel cell catalysts

Carbon supported PtCo intermetallic alloys are known to be one of the most promising candidates as low-platinum oxygen reduction reaction electrocatalysts for proton-exchange-membrane fuel cells. Nevertheless, the intrinsic trade-off between particle size and ordering degree of PtCo makes it challenging to simultaneously achieve a high specific activity and a large active surface area. Here, by machine-learning-accelerated screenings from the immense configuration space, we are able to statistically quantify the impact of chemical ordering on thermodynamic stability. We find that introducing of Cu/Ni into PtCo can provide additional stabilization energy by inducing Co-Cu/Ni disorder, thus facilitating the ordering process and achieveing an improved tradeoff between specific activity and active surface area. Guided by the theoretical prediction, the small sized and highly ordered ternary Pt2CoCu and Pt2CoNi catalysts are experimentally prepared, showing a large electrochemically active surface area of ~90 m2 gPt‒1 and a high specific activity of ~3.5 mA cm‒2.

Transferable Machine Learning Interatomic Potential for Bond Dissociation Energy Prediction of Drug-like Molecules

We present a transferable MACE interatomic potential that is applicable to open- and closed-shell drug-like molecules containing hydrogen, carbon, and oxygen atoms. Including an accurate description of radical species extends the scope of possible applications to bond dissociation energy (BDE) prediction, for example, in the context of cytochrome P450 (CYP) metabolism. The transferability of the MACE potential was validated on the COMP6 data set, containing only closed-shell molecules, where it reaches better accuracy than the readily available general ANI-2x potential. MACE achieves similar accuracy on two CYP metabolism-specific data sets, which include open- and closed-shell structures. This model enables us to calculate the aliphatic C-H BDE, which allows us to compare reaction energies of hydrogen abstraction, which is the rate-limiting step of the aliphatic hydroxylation reaction catalyzed by CYPs. On the "CYP 3A4" data set, MACE achieves a BDE RMSE of 1.37 kcal/mol and better prediction of BDE ranks than alternatives: the semiempirical AM1 and GFN2-xTB methods and the ALFABET model that directly predicts bond dissociation enthalpies. Finally, we highlight the smoothness of the MACE potential over paths of sp3C-H bond elongation and show that a minimal extension is enough for the MACE model to start finding reasonable minimum energy paths of methoxy radical-mediated hydrogen abstraction. Altogether, this work lays the ground for further extensions of scope in terms of chemical elements, (CYP-mediated) reaction classes and modeling the full reaction paths, not only BDEs.

Dynamic Local Structure in Caesium Lead Iodide: Spatial Correlation and Transient Domains

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 behavior. In the higher temperature, higher symmetry phases of these materials, several complex structural features are observed. The local structure can differ greatly from the average structure and there is evidence that dynamic 2D 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 CsPbI3 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, it is revealed 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 the length and timescales of the motion are reported. Finally, the spatial arrangement of these features and their interactions are investigated and visualized, providing a comprehensive picture of local structure in the higher symmetry phases.

Low-Cost Vibrational Free Energies in Solid Solutions with Machine Learning Force Fields

The rational design of alloys and solid solutions relies on accurate computational predictions of phase diagrams. The cluster expansion method has proven to be a valuable tool for studying disordered crystals. However, the effects of vibrational entropy are commonly neglected due to the computational cost. Here, we devise a method for including the vibrational free energy in cluster expansions with a low computational cost by fitting a machine learning force field (MLFF) to the relaxation trajectories available from cluster expansion construction. We demonstrate our method for two (pseudo)binary systems, Na1-xKxCl and Ag1-xPdx, for which accurate phonon dispersions and vibrational free energies are derived from the MLFF. For both systems, the inclusion of vibrational effects results in significantly better agreement with miscibility gaps in experimental phase diagrams. This methodology can allow routine inclusion of vibrational effects in calculated phase diagrams and thus more accurate predictions of properties and stability for mixtures of materials.

Machine learning of kinetic energy densities with target and feature smoothing: Better results with fewer training data

Machine learning (ML) of kinetic energy functionals (KEFs), in particular kinetic energy density (KED) functionals, is a promising way to construct KEFs for orbital-free density functional theory (DFT). Neural networks and kernel methods including Gaussian process regression (GPR) have been used to learn Kohn-Sham (KS) KED from density-based descriptors derived from KS DFT calculations. The descriptors are typically expressed as functions of different powers and derivatives of the electron density. This can generate large and extremely unevenly distributed datasets, which complicates effective application of ML techniques. Very uneven data distributions require many training datapoints, can cause overfitting, and can ultimately lower the quality of an ML KED model. We show that one can produce more accurate ML models from fewer data by working with smoothed density-dependent variables and KED. Smoothing palliates the issue of very uneven data distributions and associated difficulties of sampling while retaining enough spatial structure necessary for working within the paradigm of KEDF. We use GPR as a function of smoothed terms of the fourth order gradient expansion and KS effective potential and obtain accurate and stable (with respect to different random choices of training points) kinetic energy models for Al, Mg, and Si simultaneously from as few as 2000 samples (about 0.3% of the total KS DFT data). In particular, accuracies on the order of 1% in a measure of the quality of energy-volume dependence B'=EV0-ΔV-2EV0+E(V0+ΔV)ΔV/V02 (where V0 is the equilibrium volume and ΔV is a deviation from it) are obtained simultaneously for all three materials.

Navigating the Expansive Landscapes of Soft Materials: A User Guide for High-Throughput Workflows

Synthetic polymers are highly customizable with tailored structures and functionality, yet this versatility generates challenges in the design of advanced materials due to the size and complexity of the design space. Thus, exploration and optimization of polymer properties using combinatorial libraries has become increasingly common, which requires careful selection of synthetic strategies, characterization techniques, and rapid processing workflows to obtain fundamental principles from these large data sets. Herein, we provide guidelines for strategic design of macromolecule libraries and workflows to efficiently navigate these high-dimensional design spaces. We describe synthetic methods for multiple library sizes and structures as well as characterization methods to rapidly generate data sets, including tools that can be adapted from biological workflows. We further highlight relevant insights from statistics and machine learning to aid in data featurization, representation, and analysis. This Perspective acts as a "user guide" for researchers interested in leveraging high-throughput screening toward the design of multifunctional polymers and predictive modeling of structure-property relationships in soft materials.

Force Field Analysis Software and Tools (FFAST): Assessing Machine Learning Force Fields under the Microscope

As the sophistication of machine learning force fields (MLFF) increases to match the complexity of extended molecules and materials, so does the need for tools to properly analyze and assess the practical performance of MLFFs. To go beyond average error metrics and into a complete picture of a model's applicability and limitations, we developed FFAST (force field analysis software and tools): a cross-platform software package designed to gain detailed insights into a model's performance and limitations, complete with an easy-to-use graphical user interface. The software allows the user to gauge the performance of any molecular force field,─such as popular state-of-the-art MLFF models, ─ on various popular data set types, providing general prediction error overviews, outlier detection mechanisms, atom-projected errors, and more. It has a 3D visualizer to find and picture problematic configurations, atoms, or clusters in a large data set. In this paper, the example of the MACE and NequIP models is used on two data sets of interest [stachyose and docosahexaenoic acid (DHA)]─to illustrate the use cases of the software. With this, it was found that carbons and oxygens involved in or near glycosidic bonds inside the stachyose molecule present increased prediction errors. In addition, prediction errors on DHA rise as the molecule folds, especially for the carboxylic group at the edge of the molecule. We emphasize the need for a systematic assessment of MLFF models for ensuring their successful application to the study of dynamics of molecules and materials.

A controlled study of the effect of deviations from symmetry of the potential energy surface (PES) on the accuracy of the vibrational spectrum computed with collocation

Symmetry, in particular permutational symmetry, of a potential energy surface (PES) is a useful property in quantum chemical calculations. It facilitates, in particular, state labelling and identification of degenerate states. In many practically important applications, however, these issues are unimportant. The imposition of exact symmetry and the perception that it is necessary create additional methodological requirements narrowing or complicating algorithmic choices that are thereby biased against methods and codes that by default do not incorporate symmetry, including most off-the-shelf machine learning methods that cannot be directly used if exact symmetry is demanded. By introducing symmetric and unsymmetric errors into the PES of H2CO in a controlled way and computing the vibrational spectrum with collocation using symmetric and nonsymmetric collocation point sets, we show that when the deviations from an ideal PES are random, imposition of exact symmetry does not bring any practical advantages. Moreover, a calculation ignoring symmetry may be more accurate. We also compare machine-learned PESs with and without symmetrization and demonstrate that there is no advantage of imposing exact symmetry for the accuracy of the vibrational spectrum.

Exploring torsional conformer space with physical prior mean function-driven meta-Gaussian processes

We present a novel approach for systematically exploring the conformational space of small molecules with multiple internal torsions. Identifying unique conformers through a systematic conformational search is important for obtaining accurate thermodynamic functions (e.g., free energy), encompassing contributions from the ensemble of all local minima. Traditional geometry optimizers focus on one structure at a time, lacking transferability from the local potential-energy surface (PES) around a specific minimum to optimize other conformers. In this work, we introduce a physics-driven meta-Gaussian processes (meta-GPs) method that not only enables efficient exploration of target PES for locating local minima but, critically, incorporates physical surrogates that can be applied universally across the optimization of all conformers of the same molecule. Meta-GPs construct surrogate PESs based on the optimization history of prior conformers, dynamically selecting the most suitable prior mean function (representing prior knowledge in Bayesian learning) as a function of the optimization progress. We systematically benchmarked the performance of multiple GP variants for brute-force conformational search of amino acids. Our findings highlight the superior performance of meta-GPs in terms of efficiency, comprehensiveness of conformer discovery, and the distribution of conformers compared to conventional non-surrogate optimizers and other non-meta-GPs. Furthermore, we demonstrate that by concurrently optimizing, training GPs on the fly, and learning PESs, meta-GPs exhibit the capacity to generate high-quality PESs in the torsional space without extensive training data. This represents a promising avenue for physics-based transfer learning via meta-GPs with adaptive priors in exploring torsional conformer space.

Machine Learning Driven Channel Thickness Optimization in Dual-Layer Oxide Thin-Film Transistors for Advanced Electrical Performance

Machine learning (ML) provides temporal advantage and performance improvement in practical electronic device design by adaptive learning. Herein, Bayesian optimization (BO) is successfully applied to the design of optimal dual-layer oxide semiconductor thin film transistors (OS TFTs). This approach effectively manages the complex correlation and interdependency between two oxide semiconductor layers, resulting in the efficient design of experiment (DoE) and reducing the trial-and-error. Considering field effect mobility (𝜇) and threshold voltage (Vth ) simultaneously, the dual-layer structure designed by the BO model allows to produce OS TFTs with remarkable electrical performance while significantly saving an amount of experimental trial (only 15 data sets are required). The optimized dual-layer OS TFTs achieve the enhanced field effect mobility of 36.1 cm2  V-1  s-1 and show good stability under bias stress with negligible difference in its threshold voltage compared to conventional IGZO TFTs. Moreover, the BO algorithm is successfully customized to the individual preferences by applying the weight factors assigned to both field effect mobility (𝜇) and threshold voltage (Vth ).

Perfecting Liquid-State Theories with Machine Intelligence

Recent years have seen a significant increase in the use of machine intelligence for predicting the electronic structure, molecular force fields, and physicochemical properties of various condensed systems. However, substantial challenges remain in developing a comprehensive framework capable of handling a wide range of atomic compositions and thermodynamic conditions. This perspective discusses potential future developments in liquid-state theories leveraging recent advancements in functional machine learning. By harnessing the strengths of theoretical analysis and machine learning techniques including surrogate models, dimension reduction, and uncertainty quantification, we envision that liquid-state theories will gain significant improvements in accuracy, scalability, and computational efficiency, enabling their broader applications across diverse materials and chemical systems.

Robustness of Local Predictions in Atomistic Machine Learning Models

Machine learning (ML) models for molecules and materials commonly rely on a decomposition of the global target quantity into local, atom-centered contributions. This approach is convenient from a computational perspective, enabling large-scale ML-driven simulations with a linear-scaling cost and also allows for the identification and posthoc interpretation of contributions from individual chemical environments and motifs to complicated macroscopic properties. However, even though practical justifications exist for the local decomposition, only the global quantity is rigorously defined. Thus, when the atom-centered contributions are used, their sensitivity to the training strategy or the model architecture should be carefully considered. To this end, we introduce a quantitative metric, which we call the local prediction rigidity (LPR), that allows one to assess how robust the locally decomposed predictions of ML models are. We investigate the dependence of the LPR on the aspects of model training, particularly the composition of training data set, for a range of different problems from simple toy models to real chemical systems. We present strategies to systematically enhance the LPR, which can be used to improve the robustness, interpretability, and transferability of atomistic ML models.

Applications and Advances in Machine Learning Force Fields

Force fields (FFs) form the basis of molecular simulations and have significant implications in diverse fields such as materials science, chemistry, physics, and biology. A suitable FF is required to accurately describe system properties. However, an off-the-shelf FF may not be suitable for certain specialized systems, and researchers often need to tailor the FF that fits specific requirements. Before applying machine learning (ML) techniques to construct FFs, the mainstream FFs were primarily based on first-principles force fields (FPFF) and empirical FFs. However, the drawbacks of FPFF and empirical FFs are high cost and low accuracy, respectively, so there is a growing interest in using ML as an effective and precise tool for reconciling this trade-off in developing FFs. In this review, we introduce the fundamental principles of ML and FFs in the context of machine learning force fields (MLFF). We also discuss the advantages and applications of MLFF compared to traditional FFs, as well as the MLFF toolkits widely employed in numerous applications.

Bayesian Optimization-guided Discovery of High-performance Methane Combustion Catalysts based on Multi-component PtPd@CeZrOx Core-Shell Nanospheres

Formula regulation of multi-component catalysts by manual search is undoubtedly a time-consuming task, which has severely impeded the development efficiency of high-performance catalysts. In this work, PtPd@CeZrOx core-shell nanospheres, as a successful case study, is explicitly demonstrated how Bayesian optimization (BO) accelerates the discovery of methane combustion catalysts with the optimal formula ratio (the Pt/Pd mole ratio ranges from 1/2.33-1/9.09, and Ce/Zr from 1/0.22-1/0.35), which directly results in a lower conversion temperature (T50 approaching to 330 °C) than ones reported hitherto. Consequently, the best sample obtained could be efficiently developed after two rounds of iterations, containing only 18 experiments in all that is far less than the common human workload via the traditional trial-and-error search for optimal compositions. Further, this BO-based machine learning strategy can be straightforward extended to serve the autonomous discovery in multi-component material systems, for other desired properties, showing promising opportunities to practical applications in future.

Zeolite encapsulated organometallic complexes as model catalysts

Heterogeneities in the structure of active centers in metal-containing porous materials are unavoidable and complicate the description of chemical events occurring along reaction coordinates at the atomic level. Metal containing zeolites include sites of varied local coordination and secondary confining environments, requiring careful titration protocols to quantify the predominant active sites. Hybrid organometallic-zeolite catalysts are useful well-defined platform materials for spectroscopic, kinetic, and computational studies of heterogeneous catalysis that avoid the complications of conventional metal-containing porous materials. Such materials have been synthesized and studied previously, but catalytic applications were mostly limited to liquid-phase oxidation and electrochemical reactions. The hydrothermal stability, time-on-stream stability, and utility of these materials in gas-phase oxidation reactions are under-studied. The potential applications for single-site heterogeneous catalysts in fundamental research are abundant and motivate future synthetic, spectroscopic, kinetic, and computational studies.

Global Neural Network Potential with Explicit Many-Body Functions for Improved Descriptions of Complex Potential Energy Surface

The high dimensional machine learning potential (MLP) that has developed rapidly in the past decade represents a giant step forward in large-scale atomic simulation for complex systems. The long-range interaction and the poor description of chemical reactions are typical problems of high dimensional MLP, which are mainly caused by the poor structure discrimination of the atom-centered ML model. Herein, we propose a low-cost neural-network-based MLP architecture for fitting global potential energy surface data, namely, G-MBNN, that can offer improved energy and force resolution on a complex potential energy surface. In G-MBNN, a set of many-body energy terms based on the local atomic environment are explicitly included in computing the total energy─the total energy of the system is written as the sum of atomic energy and many-body energy contributions. These extra many-body energy terms are computationally low-cost and, importantly, can provide easy access to delicate energy terms in complex systems such as very short repulsion, long-range attractions, and sensitive angular-dependent covalent interactions. We implement G-MBNN in the LASP code and demonstrate the improved accuracy of the new framework in representative systems, including ternary-element energy materials LiCoOx, TiO2 with defects, and a series of organic reactions.

Ab initio structural dynamics of pure and nitrogen-containing amorphous carbon

Amorphous carbon (a-C) has attracted considerable interest due to its desirable properties, which are strongly dependent on its structure, density and impurities. Using ab initio molecular dynamics simulations we show that the sp2/sp3 content and underlying structural order of a-C produced via liquid quenching evolve at high temperatures and pressures on sub-nanosecond timescales. Graphite-like densities ([Formula: see text] 2.7 g/cc) favor the formation of layered arrangements characterized by sp2 disordered bonding resembling recently synthesized monolayer amorphous carbon (MAC), while at diamond-like densities ([Formula: see text] 3.3 g/cc) the resulting structures are dominated by disordered tetrahedral sp3 hybridization typical of diamond-like amorphous carbon (DLC). At intermediate densities the system is a highly compressible mixture of coexisting sp2 and sp3 regions that continue to segregate over 10's of picoseconds. The addition of nitrogen (20.3%) (a-CN) generates major system features similar with those of a-C, but has the unexpected effect of reinforcing the thermodynamically disfavored carbon structural motifs at low and high densities, while inhibiting phase separation in the intermediate region. At the same time, no nitrogen elimination from the carbon framework is observed above [Formula: see text] 2.8 g/cc, suggesting that nitrogen impurities are likely to remain embedded in the carbon structures during fast temperature quenches at high pressures.

Gaussian approximation potentials: Theory, software implementation and application examples

Gaussian Approximation Potentials (GAPs) are a class of Machine Learned Interatomic Potentials routinely used to model materials and molecular systems on the atomic scale. The software implementation provides the means for both fitting models using ab initio data and using the resulting potentials in atomic simulations. Details of the GAP theory, algorithms and software are presented, together with detailed usage examples to help new and existing users. We review some recent developments to the GAP framework, including Message Passing Interface parallelisation of the fitting code enabling its use on thousands of central processing unit cores and compression of descriptors to eliminate the poor scaling with the number of different chemical elements.

ACEpotentials.jl: A Julia implementation of the atomic cluster expansion

We introduce ACEpotentials.jl, a Julia-language software package that constructs interatomic potentials from quantum mechanical reference data using the Atomic Cluster Expansion [R. Drautz, Phys. Rev. B 99, 014104 (2019)]. As the latter provides a complete description of atomic environments, including invariance to overall translation and rotation as well as permutation of like atoms, the resulting potentials are systematically improvable and data efficient. Furthermore, the descriptor's expressiveness enables use of a linear model, facilitating rapid evaluation and straightforward application of Bayesian techniques for active learning. We summarize the capabilities of ACEpotentials.jl and demonstrate its strengths (simplicity, interpretability, robustness, performance) on a selection of prototypical atomistic modelling workflows.

Recent advances in computational design of structural multi-principal element alloys

Multi-principal element alloys (MPEAs) have gained extensive interest for structural applications owing to their excellent strength, fracture toughness, wear resistance, creep resistance, and fatigue resistance. In this review, recent progress in the computational design of MPEAs for structural applications is outlined. This includes the scientific advancements achieved through computational methods in the field of structural MPEAs, how new methodologies have emerged due to the needs of complex alloy systems, and adaptations to the existing tools to address emerging problems in the field. We discuss advances in atomistic simulation methods, including structure generation algorithms, element-resolved local lattice distortion, chemical short-range order, local slip resistance, and radiation tolerance, along with experimental comparisons. A detailed discussion on interatomic potentials is included, with a focus on various machine learning-based fitting methods. The application of data science and machine learning for identifying and discovering MPEAs with desirable mechanical performance is summarized and presented.

Universal machine learning for the response of atomistic systems to external fields

Machine learned interatomic interaction potentials have enabled efficient and accurate molecular simulations of closed systems. However, external fields, which can greatly change the chemical structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into atomic descriptors to represent system-field interactions with rigorous rotational equivariance. This "all-in-one" approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in molecular and periodic systems in the presence of electric fields. Especially for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training atomic forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.

"Freedom of design" in chemical compound space: towards rational in silico design of molecules with targeted quantum-mechanical properties

The rational design of molecules with targeted quantum-mechanical (QM) properties requires an advanced understanding of the structure-property/property-property relationships (SPR/PPR) that exist across chemical compound space (CCS). In this work, we analyze these fundamental relationships in the sector of CCS spanned by small (primarily organic) molecules using the recently developed QM7-X dataset, a systematic, extensive, and tightly converged collection of 42 QM properties corresponding to ≈4.2M equilibrium and non-equilibrium molecular structures containing up to seven heavy/non-hydrogen atoms (including C, N, O, S, and Cl). By characterizing and enumerating progressively more complex manifolds of molecular property space-the corresponding high-dimensional space defined by the properties of each molecule in this sector of CCS-our analysis reveals that one has a substantial degree of flexibility or "freedom of design" when searching for a single molecule with a desired pair of properties or a set of distinct molecules sharing an array of properties. To explore how this intrinsic flexibility manifests in the molecular design process, we used multi-objective optimization to search for molecules with simultaneously large polarizabilities and HOMO-LUMO gaps; analysis of the resulting Pareto fronts identified non-trivial paths through CCS consisting of sequential structural and/or compositional changes that yield molecules with optimal combinations of these properties.

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.

Ab initio quantum chemistry with neural-network wavefunctions

Deep learning methods outperform human capabilities in pattern recognition and data processing problems and now have an increasingly important role in scientific discovery. A key application of machine learning in molecular science is to learn potential energy surfaces or force fields from ab initio solutions of the electronic Schrödinger equation using data sets obtained with density functional theory, coupled cluster or other quantum chemistry (QC) methods. In this Review, we discuss a complementary approach using machine learning to aid the direct solution of QC problems from first principles. Specifically, we focus on quantum Monte Carlo methods that use neural-network ansatzes to solve the electronic Schrödinger equation, in first and second quantization, computing ground and excited states and generalizing over multiple nuclear configurations. Although still at their infancy, these methods can already generate virtually exact solutions of the electronic Schrödinger equation for small systems and rival advanced conventional QC methods for systems with up to a few dozen electrons.

Thermodynamics and kinetic analysis of membrane: Challenges and perspectives

The ultimate structure of the membrane is determined using two important effects: (i) thermodynamic effect and (ii) kinetic effect. Controlling the mechanism of kinetic and thermodynamic processes in phase separation is essential for enhancing membrane performance. However, the relationship between system parameters and the ultimate membrane morphology is still largely empirical. This review focuses on the fundamental ideas behind thermally induced phase separation (TIPS) and nonsolvent-induced phase separation (NIPS) methods, including both kinetic and thermodynamic elements. The thermodynamic approach to understanding phase separation and the effect of different interaction parameters on membrane morphology has been discussed in detail. Furthermore, this review explores the capabilities and limitations of different macroscopic transport models used for the last four decades to explore the phase inversion process. The application of molecular simulations and phase field to understand phase separation has also been briefly examined. Finally, it discusses the thermodynamic approach to understanding phase separation and the consequence of different interaction parameters on membrane morphology, as well as possible directions for artificial intelligence to fill the gaps in the literature. This review aims to provide comprehensive knowledge and motivation for future modeling work for membrane fabrication via new techniques such as nonsolvent-TIPS, complex-TIPS, non-solvent assisted TIPS, combined NIPS-TIPS method, and mixed solvent phase separation.

Structural Dynamics Descriptors for Metal Halide Perovskites

Metal halide perovskites have shown extraordinary performance in solar energy conversion technologies. They have been classified as "soft semiconductors" due to their flexible corner-sharing octahedral networks and polymorphous nature. Understanding the local and average structures continues to be challenging for both modeling and experiments. Here, we report the quantitative analysis of structural dynamics in time and space from molecular dynamics simulations of perovskite crystals. The compact descriptors provided cover a wide variety of structural properties, including octahedral tilting and distortion, local lattice parameters, molecular orientations, as well as their spatial correlation. To validate our methods, we have trained a machine learning force field (MLFF) for methylammonium lead bromide (CH3NH3PbBr3) using an on-the-fly training approach with Gaussian process regression. The known stable phases are reproduced, and we find an additional symmetry-breaking effect in the cubic and tetragonal phases close to the phase-transition temperature. To test the implementation for large trajectories, we also apply it to 69,120 atom simulations for CsPbI3 based on an MLFF developed using the atomic cluster expansion formalism. The structural dynamics descriptors and Python toolkit are general to perovskites and readily transferable to more complex compositions.

Toward Self-Healing Concrete Infrastructure: Review of Experiments and Simulations across Scales

Cement and concrete are vital materials used to construct durable habitats and infrastructure that withstand natural and human-caused disasters. Still, concrete cracking imposes enormous repair costs on societies, and excessive cement consumption for repairs contributes to climate change. Therefore, the need for more durable cementitious materials, such as those with self-healing capabilities, has become more urgent. In this review, we present the functioning mechanisms of five different strategies for implementing self-healing capability into cement based materials: (1) autogenous self-healing from ordinary portland cement and supplementary cementitious materials and geopolymers in which defects and cracks are repaired through intrinsic carbonation and crystallization; (2) autonomous self-healing by (a) biomineralization wherein bacteria within the cement produce carbonates, silicates, or phosphates to heal damage, (b) polymer-cement composites in which autonomous self-healing occurs both within the polymer and at the polymer-cement interface, and (c) fibers that inhibit crack propagation, thus allowing autogenous healing mechanisms to be more effective. In all cases, we discuss the self-healing agent and synthesize the state of knowledge on the self-healing mechanism(s). In this review article, the state of computational modeling across nano- to macroscales developed based on experimental data is presented for each self-healing approach. We conclude the review by noting that, although autogenous reactions help repair small cracks, the most fruitful opportunities lay within design strategies for additional components that can migrate into cracks and initiate chemistries that retard crack propagation and generate repair of the cement matrix.

Coarse-grained versus fully atomistic machine learning for zeolitic imidazolate frameworks

Zeolitic imidazolate frameworks are widely thought of as being analogous to inorganic AB2 phases. We test the validity of this assumption by comparing simplified and fully atomistic machine-learning models for local environments in ZIFs. Our work addresses the central question to what extent chemical information can be "coarse-grained" in hybrid framework materials.

scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science

Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domainspecific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.

scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science

Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domainspecific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.

Accelerating First Principles Calculation of Multi-Component Alloy Steady-State Structure and Elastic Properties in Full Component Space

The FeNiCrAlCoCuTi alloy system has great advantages in mechanical properties such as high hardness and toughness. It has high performance potential and research value and the key in research is designing alloy compositions with target properties. The traditional method, experimental analysis, is highly inefficient to properly exploit the intrinsic relationship between material characteristics and properties for multi-component alloys, especially in investigating the whole composition space. In this work, we present a research way that uses first principles calculation to obtain the properties of multi-component alloys and uses machine learning to accelerate the research. The FeNiCrAlCoCuTi alloy system with its elastic properties is used as an example to demonstrate this process. We specifically design models for each output, all of which have RMSE values of less than 1.1, and confirm their effectiveness through experimental data in the literature, showing that the relative error is below 5%. Additionally, we perform an interpretable analysis on the models, exposing the underlying relationship between input features and output. By means of spatial transformation, we achieve the prediction of the full-component spatial performance from binary to multiple components. Taking the FeNiCrAlM (M = Co, Cu, Ti) quinary alloy system as an example, we design a single-phase BCC structure composed of an Fe0.23Cr0.23Al0.23Ni0.03Cu0.28 alloy with a Young's modulus of 273.10 GPa, as well as a single-phase BCC structure composed of an Fe0.01Cr0.01Al0.01Ni0.44Co0.53 alloy with a shear modulus of 103.6 GPa. Through this research way, we use machine learning to accelerate the calculation, which greatly shortens research time and costs. This work overcomes the drawbacks of traditional experiments and directly obtains element compositions and composition intervals with excellent performance.

Fully First-Principles Surface Spectroscopy with Machine Learning

Our current understanding of the structure and dynamics of aqueous interfaces at the molecular level has grown substantially due to the continuous development of surface-specific spectroscopies, such as vibrational sum-frequency generation (VSFG). As in other vibrational spectroscopies, we must turn to atomistic simulations to extract all of the information encoded in the VSFG spectra. The high computational cost associated with existing methods means that they have limitations in representing systems with complex electronic structure or in achieving statistical convergence. In this work, we combine high-dimensional neural network interatomic potentials and symmetry-adapted Gaussian process regression to overcome these constraints. We show that it is possible to model VSFG signals with fully ab initio accuracy using machine learning and illustrate the versatility of our approach on the water/air interface. Our strategy allows us to identify the main sources of theoretical inaccuracy and establish a clear pathway toward the modeling of surface-sensitive spectroscopy of complex interfaces.