Combining Machine Learning Potential and Structure Prediction for Accelerated Materials Design and Discovery

A Machine-Learning-Assisted Crystalline Structure Prediction Framework To Accelerate Materials Discovery

Modern crystal structure prediction methods based on structure generation algorithms and first-principles calculations play important roles in the design of new materials. However, the cost of these methods is very expensive because their success mostly relies on the efficient sampling of structures and the accurate evaluation of energies for those sampled structures. Herein, we develop a Machine-learning-Assisted CRYStalline Materials sAmpling sysTem (MAXMAT) aiming to accelerate the prediction of new crystal structures. For a given chemical composition, MAXMAT can generate efficient crystal structures with the help of a Python package for crystal structure generation (PyXtal) and can quickly evaluate the energies of these generated structures using a well-developed machine learning interaction potential model (M3GNET). We have used MAXMAT to perform crystal structure searches for three different chemical systems (TiO2, MgAl2O4, and BaBOF3) to test its accuracy and efficiency. Furthermore, we apply MAXMAT to predict new nonlinear optical materials, suggesting several thermodynamically synthesizable structures with high performance in LiZnGaS3 and CaBOF3 systems.

Machine-Learned Kohn-Sham Hamiltonian Mapping for Nonadiabatic Molecular Dynamics

In this work, we report a simple, efficient, and scalable machine-learning (ML) approach for mapping non-self-consistent Kohn-Sham Hamiltonians constructed with one kind of density functional to the nearly self-consistent Hamiltonians constructed with another kind of density functional. This approach is designed as a fast surrogate Hamiltonian calculator for use in long nonadiabatic dynamics simulations of large atomistic systems. In this approach, the input and output features are Hamiltonian matrices computed from different levels of theory. We demonstrate that the developed ML-based Hamiltonian mapping method (1) speeds up the calculations by several orders of magnitude, (2) is conceptually simpler than alternative ML approaches, (3) is applicable to different systems and sizes and can be used for mapping Hamiltonians constructed with arbitrary density functionals, (4) requires a modest training data, learns fast, and generates molecular orbitals and their energies with the accuracy nearly matching that of conventional calculations, and (5) when applied to nonadiabatic dynamics simulation of excitation energy relaxation in large systems yields the corresponding time scales within the margin of error of the conventional calculations. Using this approach, we explore the excitation energy relaxation in C60 fullerene and Si75H64 quantum dot structures and derive qualitative and quantitative insights into dynamics in these systems.

A kernel-based machine learning potential and quantum vibrational state analysis of the cationic Ar hydride (Ar2H+)

One of the most fascinating discoveries in recent years, in the cold and low pressure regions of the universe, was the detection of ArH+ and HeH+ species. The identification of such noble gas-containing molecules in space is the key to understanding noble gas chemistry. In the present work, we discuss the possibility of [Ar2H]+ existence as a potentially detectable molecule in the interstellar medium, providing new data on possible astronomical pathways and energetics of this compound. As a first step, a data-driven approach is proposed to construct a full 3D machine-learning potential energy surface (ML-PES) via the reproducing kernel Hilbert space (RKHS) method. The training and testing data sets are generated from CCSD(T)/CBS[56] computations, while a validation protocol is introduced to ensure the quality of the potential. In turn, the resulting ML-PES is employed to compute vibrational levels and molecular spectroscopic constants for the cation. In this way, the most common isotopologue in ISM, [36Ar2H]+, was characterized for the first time, while simultaneously, comparisons with previously reported values available for [40Ar2H]+ are discussed. Our present data could serve as a benchmark for future studies on this system, as well as on higher-order cationic Ar-hydrides of astrophysical interest.

Structure-Energy Relationship Prediction of the HZSM-5 Zeolite with Different Acid Site Distributions by the Neural Network Model

Zeolites are a very important family of catalysts. The catalytic activity of zeolites depends on the distribution of acid sites, which has been extensively studied. However, the relationship between the acid site distribution and catalytic efficiency remains unestablished. An onerous computational burden can be imposed when static calculations are applied to analyze the relationship between a catalyst structure and its energy. To resolve this issue, the current work uses neural network (NN) models to evaluate the relationship. By taking the typical HZSM-5 zeolite as an example, we applied the provided atomic coordinates to predict the energy. The network performances of the artificial neural network (ANN) and high-dimensional neural network (HDNN) are compared using the trained results from a dataset containing the identical number of acid sites. Furthermore, the importance of the feature is examined with the aid of a random forest model to identify the pivotal variables influencing the energy. In addition, the HDNN is employed to forecast the energy of an HZSM-5 system with varying numbers of acid sites. This study emphasizes that the energy of zeolites can be rapidly and accurately predicted through the NN, which can assist our understanding of the relationship between the structure and properties, thereby providing more accurate and efficient methods for the application of zeolite materials.

Neural Network with Optimal Neuron Activation Functions Based on Additive Gaussian Process Regression

Feed-forward neural networks (NNs) are a staple machine learning method widely used in many areas of science and technology, including physical chemistry, computational chemistry, and materials informatics. While even a single-hidden-layer NN is a universal approximator, its expressive power is limited by the use of simple neuron activation functions (such as sigmoid functions) that are typically the same for all neurons. More flexible neuron activation functions would allow the use of fewer neurons and layers and thereby save computational cost and improve expressive power. We show that additive Gaussian process regression (GPR) can be used to construct optimal neuron activation functions that are individual to each neuron. An approach is also introduced that avoids nonlinear fitting of neural network parameters by defining them with rules. The resulting method combines the advantage of robustness of a linear regression with the higher expressive power of an NN. We demonstrate the approach by fitting the potential energy surfaces of the water molecule and formaldehyde. Without requiring any nonlinear optimization, the additive-GPR-based approach outperforms a conventional NN in the high-accuracy regime, where a conventional NN suffers more from overfitting.

Deep Potential Molecular Dynamics Study of Chapman-Jouguet Detonation Events of Energetic Materials

Detonation of energetic materials (EMs) is of great importance for military applications, while the understanding of detailed events and mechanisms for the detonation process is scarce. In this study, the first deep neural network potential NNP_Shock for molecular dynamics (MD) simulation of shock-induced detonation of EMs was generated based on a deep potential model, providing DFT accuracy but 106 times the computational efficiency. On this basis, we employ our deep potential to perform MD simulations of shock-induced detonation of high-performance EM material 2,4,6,8,10,12-hexanitro-2,4,6,8,10,12-hexaazaisowurtzitane (CL-20, C6H6N12O12) and obtain the theoretical Chapman-Jouguet (C-J) detonation velocities and pressures directly by multiscale shock technique (MSST) for the first time, which are in good agreement with experiment. In addition, the Hugoniot curves and initial reaction mechanisms were successfully obtained. Therefore, the NNP_Shock potential is competent in research of the detonation performance and shock sensitivity of CL-20, and the method can also be transplanted to studies of other EMs.

MAGUS: machine learning and graph theory assisted universal structure searcher

Crystal structure predictions based on first-principles calculations have gained great success in materials science and solid state physics. However, the remaining challenges still limit their applications in systems with a large number of atoms, especially the complexity of conformational space and the cost of local optimizations for big systems. Here, we introduce a crystal structure prediction method, MAGUS, based on the evolutionary algorithm, which addresses the above challenges with machine learning and graph theory. Techniques used in the program are summarized in detail and benchmark tests are provided. With intensive tests, we demonstrate that on-the-fly machine-learning potentials can be used to significantly reduce the number of expensive first-principles calculations, and the crystal decomposition based on graph theory can efficiently decrease the required configurations in order to find the target structures. We also summarized the representative applications of this method on several research topics, including unexpected compounds in the interior of planets and their exotic states at high pressure and high temperature (superionic, plastic, partially diffusive state, etc.); new functional materials (superhard, high-energy-density, superconducting, photoelectric materials), etc. These successful applications demonstrated that MAGUS code can help to accelerate the discovery of interesting materials and phenomena, as well as the significant value of crystal structure predictions in general.

Accelerating the Discovery of Metastable IrO2 for the Oxygen Evolution Reaction by the Self-Learning-Input Graph Neural Network

The discovery of active and stable catalysts for the oxygen evolution reaction (OER) is vital to improve water electrolysis. To date, rutile iridium dioxide IrO₂ is the only known OER catalyst in the acidic solution, while its poor activity restricts its practical viability. Herein, we propose a universal graph neural network, namely, CrystalGNN, and introduce a dynamic embedding layer to self-update atomic inputs during the training process. Based on this framework, we train a model to accurately predict the formation energies of 10,500 IrO₂ configurations and discover 8 unreported metastable phases, among which C2/m-IrO₂ and P62-IrO₂ are identified as excellent electrocatalysts to reach the theoretical OER overpotential limit at their most stable surfaces. Our self-learning-input CrystalGNN framework exhibits reliable accuracy, generalization, and transferring ability and successfully accelerates the bottom-up catalyst design of novel metastable IrO₂ to boost the OER activity.

Semiclassical Dynamics on Machine-Learned Coupled Multireference Potential Energy Surfaces: Application to the Photodissociation of the Simplest Criegee Intermediate

Determination of high-dimensional potential energy surfaces (PESs) and nonadiabatic couplings have always been quite challenging. To this end, machine learning (ML) models, trained with a finite set of ab initio data, allow accurate prediction of such properties. To express the PESs in terms of atomic contributions is the cornerstone of any ML based technique because it can be easily scaled to large systems. In this work, we have constructed high fidelity PESs and nonadiabatic coupling terms at the CASSCF level of ab initio data using a machine learning technique, namely, kernel-ridge regression. Additional MRCI-level calculations were carried out to assess the quality of the PESs. We use these machine-learned PESs and nonadiabatic couplings to simulate excited-state molecular dynamics based on Tully's fewest-switches surface hopping method (FSSH). FSSH is a semiclassical method in which nuclei move on the PESs due to the electrons according to the laws of classical mechanics. Nonadiabatic effects are taken into account in terms of transitions between PESs. We apply this scheme to study the O-O photodissociation of the simplest Criegee intermediate (CH₂OO). The FSSH trajectories were initiated on the lowest optically bright singlet excited state (S₂) and propagated along the three most important internal coordinates, namely, O-O and C-O bond distances and the COO bond angle. Some of the trajectories end up on energetically lower PESs as a result of radiationless transfer through conical intersections. All of the trajectories lead to the dissociation of the O-O bond due to the dissociative nature of the excited PESs through one of the two dissociative channels. The simulation reveals that there is about 88.4% probability of dissociation through the lower channel leading to the H₂CO (X¹A₁) and O (¹D) products, whereas there is only 11.6% probability of dissociation through the upper channel leading to H₂CO (a³A″) and O (³P) products.

Machine learning in computational chemistry: interplay between (non)linearity, basis sets, and dimensionality

Machine learning (ML) based methods and tools have now firmly established themselves in physical chemistry and in particular in theoretical and computational chemistry and in materials chemistry. The generality of popular ML techniques such as neural networks or kernel methods (Gaussian process and kernel ridge regression and their flavors) permitted their application to diverse problems from prediction of properties of functional materials (catalysts, solid state ionic conductors, etc.) from descriptors to the building of interatomic potentials (where ML is currently routinely used in applications) and electron density functionals. These ML techniques are assumed to have superior expressive power of nonlinear methods, and are often used "as is", with concepts such as "non-parametric" or "deep learning" used without a clear justification for their need or advantage over simpler and more robust alternatives. In this Perspective, we highlight some interrelations between popular ML techniques and traditional linear regressions and basis expansions and demonstrate that in certain regimes (such as a very high dimensionality) these approximations might collapse. We also discuss ways to recover the expressive power of a nonlinear approach and to help select hyperparameters with the help of high-dimensional model representation and to obtain elements of insight while preserving the generality of the method.

Machine learning accelerated random structure searching: Application to yttrium superhydrides

The search for new superhydrides, promising materials for both hydrogen storage and high temperature superconductivity, made great progress, thanks to atomistic simulations and Crystal Structure Prediction (CSP) algorithms. When they are combined with Density Functional Theory (DFT), these methods are highly reliable and often match a great part of the experimental results. However, systems of increasing complexity (number of atoms and chemical species) become rapidly challenging as the number of minima to explore grows exponentially with the number of degrees of freedom in the simulation cell. An efficient sampling strategy preserving a sustainable computational cost then remains to be found. We propose such a strategy based on an active-learning process where machine learning potentials and DFT simulations are jointly used, opening the way to the discovery of complex structures. As a proof of concept, this method is applied to the exploration of tin crystal structures under various pressures. We showed that the α phase, not included in the learning process, is correctly retrieved, despite its singular nature of bonding. Moreover, all the expected phases are correctly predicted under pressure (20 and 100 GPa), suggesting the high transferability of our approach. The method has then been applied to the search of yttrium superhydrides (YH x) crystal structures under pressure. The YH6 structure of space group Im-3m is successfully retrieved. However, the exploration of more complex systems leads to the appearance of a large number of structures. The selection of the relevant ones to be included in the active learning process is performed through the analysis of atomic environments and the clustering algorithm. Finally, a metric involving a distance based on x-ray spectra is introduced, which guides the structural search toward experimentally relevant structures. The global process (active-learning and new selection methods) is finally considered to explore more complex and unknown YH x phases, unreachable by former CSP algorithms. New complex phases are found, demonstrating the ability of our approach to push back the exponential wall of complexity related to CSP.

Machine Learning and Optoelectronic Materials Discovery: A Growing Synergy

Novel optoelectronic materials have the potential to revolutionize the ongoing green transition by both providing more efficient photovoltaic (PV) devices and lowering energy consumption of devices like LEDs and sensors. The lead candidate materials for these applications are both organic semiconductors and more recently perovskites. This Perspective illustrates how novel machine learning techniques can help explore these materials, from speeding up ab initio calculations toward experimental guidance. Furthermore, based on existing work, perspectives around machine-learned molecular dynamics potentials, physically informed neural networks, and generative methods are outlined.

The 2021 room-temperature superconductivity roadmap

Designing materials with advanced functionalities is the main focus of contemporary solid-state physics and chemistry. Research efforts worldwide are funneled into a few high-end goals, one of the oldest, and most fascinating of which is the search for an ambient temperature superconductor (A-SC). The reason is clear: superconductivity at ambient conditions implies being able to handle, measure and access a single, coherent, macroscopic quantum mechanical state without the limitations associated with cryogenics and pressurization. This would not only open exciting avenues for fundamental research, but also pave the road for a wide range of technological applications, affecting strategic areas such as energy conservation and climate change. In this roadmap we have collected contributions from many of the main actors working on superconductivity, and asked them to share their personal viewpoint on the field. The hope is that this article will serve not only as an instantaneous picture of the status of research, but also as a true roadmap defining the main long-term theoretical and experimental challenges that lie ahead. Interestingly, although the current research in superconductor design is dominated by conventional (phonon-mediated) superconductors, there seems to be a widespread consensus that achieving A-SC may require different pairing mechanisms.In memoriam, to Neil Ashcroft, who inspired us all.

Materials by design at high pressures

Pressure, a fundamental thermodynamic variable, can generate two essential effects on materials. First, pressure can create new high-pressure phases via modification of the potential energy surface. Second, pressure can produce new compounds with unconventional stoichiometries via modification of the compositional landscape. These new phases or compounds often exhibit exotic physical and chemical properties that are inaccessible at ambient pressure. Recent studies have established a broad scope for developing materials with specific desired properties under high pressure. Crystal structure prediction methods and first-principles calculations can be used to design materials and thus guide subsequent synthesis plans prior to any experimental work. A key example is the recent theory-initiated discovery of the record-breaking high-temperature superhydride superconductors H3S and LaH10 with critical temperatures of 200 K and 260 K, respectively. This work summarizes and discusses recent progress in the theory-oriented discovery of new materials under high pressure, including hydrogen-rich superconductors, high-energy-density materials, inorganic electrides, and noble gas compounds. The discovery of the considered compounds involved substantial theoretical contributions. We address future challenges facing the design of materials at high pressure and provide perspectives on research directions with significant potential for future discoveries.

Choosing the right molecular machine learning potential

Quantum-chemistry simulations based on potential energy surfaces of molecules provide invaluable insight into the physicochemical processes at the atomistic level and yield such important observables as reaction rates and spectra. Machine learning potentials promise to significantly reduce the computational cost and hence enable otherwise unfeasible simulations. However, the surging number of such potentials begs the question of which one to choose or whether we still need to develop yet another one. Here, we address this question by evaluating the performance of popular machine learning potentials in terms of accuracy and computational cost. In addition, we deliver structured information for non-specialists in machine learning to guide them through the maze of acronyms, recognize each potential's main features, and judge what they could expect from each one.

Dilute Element Compounds: A Route to Enriching Inorganic Functional Materials

The development of functional materials calls for ever-enriching the inorganic material database. Doping is an effective way of achieving this purpose. Herein, we propose the concept of dilute element compounds (DECs), which contain a small amount of a dopant element distributed in a host crystal structure in an ordered manner. Different from dilute alloys or solid solutions, the DECs could be more resistant to segregation and are ideal for dispersing functional elements for applications such as single-atom catalysts. It is also expected that the DECs will serve as a route to discovering new inorganic functional materials by controlling phase transitions and tuning intrinsic properties of the host materials with applications including, but not limited to, thermoelectrics and solid-state electrolytes for secondary batteries. As an initial work, we quantify the diluteness of DECs and find the limits of diluteness in existing DECs. We further provide a classification scheme for the DECs to guide future discoveries.

Gaussian Process Regression for Materials and Molecules

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Interpolating Nonadiabatic Molecular Dynamics Hamiltonian with Artificial Neural Networks

Nonadiabatic (NA) molecular dynamics (MD) allows one to study far-from-equilibrium processes involving excited electronic states coupled to atomic motions. While NAMD involves expensive calculations of excitation energies and NA couplings (NACs), ground-state properties require much less effort and can be obtained with machine learning (ML) at a fraction of the ab initio cost. Application of ML to excited states and NACs is more challenging, due to costly reference methods, many states, and complex geometry dependence. We developed a NAMD methodology that avoids time extrapolation of excitation energies and NACs. Instead, under the classical path approximation that employs a precomputed ground-state trajectory, we use a small fraction (2%) of the geometries to train neural networks and obtain excited-state energies and NACs for the remaining 98% of the geometries by interpolation. Demonstrated with metal halide perovskites that exhibit complex MD, the method provides nearly two orders of computational savings while generating accurate NAMD results.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.