The central role of density functional theory in the AI age

Density functional theory (DFT) plays a pivotal role in chemical and materials science because of its relatively high predictive power, applicability, versatility, and computational efficiency. We review recent progress in machine learning (ML) model developments, which have relied heavily on DFT for synthetic data generation and for the design of model architectures. The general relevance of these developments is placed in a broader context for chemical and materials sciences. DFT-based ML models have reached high efficiency, accuracy, scalability, and transferability and pave the way to the routine use of successful experimental planning software within self-driving laboratories.

Machine learning-guided discovery of ionic polymer electrolytes for lithium metal batteries

As essential components of ionic polymer electrolytes (IPEs), ionic liquids (ILs) with high ionic conductivity and wide electrochemical window are promising candidates to enable safe and high-energy-density lithium metal batteries (LMBs). Here, we describe a machine learning workflow embedded with quantum calculation and graph convolutional neural network to discover potential ILs for IPEs. By selecting subsets of the recommended ILs, combining with a rigid-rod polyelectrolyte and a lithium salt, we develop a series of thin (~50 μm) and robust (>200 MPa) IPE membranes. The Li|IPEs|Li cells exhibit ultrahigh critical-current-density (6 mA cm^-2) at 80 °C. The Li|IPEs|LiFePO₄ (10.3 mg cm^-2) cells deliver outstanding capacity retention in 350 cycles (>96% at 0.5C; >80% at 2C), fast charge/discharge capability (146 mAh g^-1 at 3C) and excellent efficiency (>99.92%). This performance is rarely reported by other single-layer polymer electrolytes without any flammable organics for LMBs.

Relative energies without electronic perturbations via alchemical integral transform

We show that the energy of a perturbed system can be fully recovered from the unperturbed system’s electron density. We derive an alchemical integral transform by parametrizing space in terms of transmutations, the chain rule, and integration by parts. Within the radius of convergence, the zeroth order yields the energy expansion at all orders, restricting the textbook statement by Wigner that the p-th order wave function derivative is necessary to describe the (2 p + 1)-th energy derivative. Without the need for derivatives of the electron density, this allows us to cover entire chemical neighborhoods from just one quantum calculation instead of single systems one by one. Numerical evidence presented indicates that predictive accuracy is achieved in the range of mHa for the harmonic oscillator or the Morse potential and in the range of machine accuracy for hydrogen-like atoms. Considering isoelectronic nuclear charge variations by one proton in all multi-electron atoms from He to Ne, alchemical integral transform based estimates of the relative energy deviate by only few mHa from corresponding Hartree–Fock reference numbers.

Smart Materials Prediction: Applying Machine Learning to Lithium Solid-State Electrolyte

Traditionally, the discovery of new materials has often depended on scholars’ computational and experimental experience. The traditional trial-and-error methods require many resources and computing time. Due to new materials’ properties becoming more complex, it is difficult to predict and identify new materials only by general knowledge and experience. Material prediction tools based on machine learning (ML) have been successfully applied to various materials fields; they are beneficial for modeling and accelerating the prediction process for materials that cannot be accurately predicted. However, the obstacles of disciplinary span led to many scholars in materials not having complete knowledge of data-driven materials science methods. This paper provides an overview of the general process of ML applied to materials prediction and uses solid-state electrolytes (SSE) as an example. Recent approaches and specific applications to ML in the materials field and the requirements for building ML models for predicting lithium SSE are reviewed. Finally, some current obstacles to applying ML in materials prediction and prospects are described with the expectation that more materials scholars will be aware of the application of ML in materials prediction.

Ab Initio Machine Learning in Chemical Compound Space

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first-principles based virtual sampling of this space, for example, in search of novel molecules or materials which exhibit desirable properties, is therefore prohibitive for all but the smallest subsets and simplest properties. We review studies aimed at tackling this challenge using modern machine learning techniques based on (i) synthetic data, typically generated using quantum mechanics based methods, and (ii) model architectures inspired by quantum mechanics. Such Quantum mechanics based Machine Learning (QML) approaches combine the numerical efficiency of statistical surrogate models with an ab initio view on matter. They rigorously reflect the underlying physics in order to reach universality and transferability across CCS. While state-of-the-art approximations to quantum problems impose severe computational bottlenecks, recent QML based developments indicate the possibility of substantial acceleration without sacrificing the predictive power of quantum mechanics.

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously unknown materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting "alchemical" enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for electronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively.

Comparative Ab Initio Calculations of ReO3, SrZrO3, BaZrO3, PbZrO3 and CaZrO3 (001) Surfaces

We performed, for first time, ab initio calculations for the ReO2-terminated ReO3 (001) surface and analyzed systematic trends in the ReO3, SrZrO3, BaZrO3, PbZrO3 and CaZrO3 (001) surfaces using first-principles calculations. According to the ab initio calculation results, all ReO3, SrZrO3, BaZrO3, PbZrO3 and CaZrO3 (001) surface upper-layer atoms relax inwards towards the crystal bulk, all second-layer atoms relax upwards and all third-layer atoms, again, relax inwards. The ReO2-terminated ReO3 and ZrO2-terminated SrZrO3, BaZrO3, PbZrO3 and CaZrO3 (001) surface band gaps at the Γ–Γ point are always reduced in comparison to their bulk band gap values. The Zr–O chemical bond populations in the SrZrO3, BaZrO3, PbZrO3 and CaZrO3 perovskite bulk are always smaller than those near the ZrO2-terminated (001) surfaces. In contrast, the Re–O chemical bond population in the ReO3 bulk (0.212e) is larger than that near the ReO2-terminated ReO3 (001) surface (0.170e). Nevertheless, the Re–O chemical bond population between the Re atom located on the ReO2-terminated ReO3 (001) surface upper layer and the O atom located on the ReO2-terminated ReO3 (001) surface second layer (0.262e) is the largest.

Data-Driven Materials Science: Status, Challenges, and Perspectives

Data-driven science is heralded as a new paradigm in materials science. In this field, data is the new resource, and knowledge is extracted from materials datasets that are too big or complex for traditional human reasoning-typically with the intent to discover new or improved materials or materials phenomena. Multiple factors, including the open science movement, national funding, and progress in information technology, have fueled its development. Such related tools as materials databases, machine learning, and high-throughput methods are now established as parts of the materials research toolset. However, there are a variety of challenges that impede progress in data-driven materials science: data veracity, integration of experimental and computational data, data longevity, standardization, and the gap between industrial interests and academic efforts. In this perspective article, the historical development and current state of data-driven materials science, building from the early evolution of open science to the rapid expansion of materials data infrastructures are discussed. Key successes and challenges so far are also reviewed, providing a perspective on the future development of the field.

Achievements, Challenges, and Prospects of Calcium Batteries

This Review flows from past attempts to develop a (rechargeable) battery technology based on Ca via crucial breakthroughs to arrive at a comprehensive discussion of the current challenges at hand. The realization of a rechargeable Ca battery technology primarily requires identification and development of suitable electrodes and electrolytes, which is why we here cover the progress starting from the fundamental electrode/electrolyte requirements, concepts, materials, and compositions employed and finally a critical analysis of the state-of-the-art, allowing us to conclude with the particular roadblocks still existing. As for crucial breakthroughs, reversible plating and stripping of calcium at the metal-anode interface was achieved only recently and for very specific electrolyte formulations. Therefore, while much of the current research aims at finding suitable cathodes to achieve proof-of-concept for a full Ca battery, the spectrum of electrolytes researched is also expanded. Compatibility of cell components is essential, and to ensure this, proper characterization is needed, which requires design of a multitude of reliable experimental setups and sometimes methodology development beyond that of other next generation battery technologies. Finally, we conclude with recommendations for future strategies to make best use of the current advances in materials science combined with computational design, electrochemistry, and battery engineering, all to propel the Ca battery technology to reality and ultimately reach its full potential for energy storage.

Recent progress in theoretical and computational investigations of Li-ion battery materials and electrolytes

Advancements and progress in computational and theoretical investigations of Li-ion battery materials and electrolytes are reviewed and assessed.

Theoretical understanding and prediction of lithiated sodium hexatitanates

Sodium hexatitanates (Na(2)Ti(6)O(13)) with tunnelled structures have been experimentally proposed to be good candidates for anode materials of lithium ion batteries because of their low potential, small shape transformation, and good reversibility. The understanding of the properties of this lithiated titanate is significant for their development. To this end, the first-principle calculations were performed to investigate the interaction between Li ions and Na(2)Ti(6)O(13) at the atomic level. After structural optimization with various Li:Ti ratios, the Li ions are found to energetically prefer to stay at the small rhombic tunnels of Na(2)Ti(6)O(13), where the diffusion energy barrier of Li ions is also lower. Such preference is determined by the chemical environment around Li ions. Our theoretical intercalation potential and volume change on the basis of the optimized atomic structures agree with the experimental observations. The analysis of the electronic properties reveals the Burstein-Moss effect in lithiated Na(2)Ti(6)O(13) due to the heavy n-type doping. Such materials possess high conductivity, which can benefit their applications in photoelectrochemical or electrochemical areas.

Structure and properties of functional oxide thin films: insights from electronic-structure calculations

The confluence of state-of-the-art electronic-structure computations and modern synthetic materials growth techniques is proving indispensable in the search for and discovery of new functionalities in oxide thin films and heterostructures. Here, we review the recent contributions of electronic-structure calculations to predicting, understanding, and discovering new materials physics in thin-film perovskite oxides. We show that such calculations can accurately predict both structure and properties in advance of film synthesis, thereby guiding the search for materials combinations with specific targeted functionalities. In addition, because they can isolate and decouple the effects of various parameters which unavoidably occur simultaneously in an experiment-such as epitaxial strain, interfacial chemistry and defect profiles-they are able to provide new fundamental knowledge about the underlying physics. We conclude by outlining the limitations of current computational techniques, as well as some important open questions that we hope will motivate further methodological developments in the field.

Predicting crystal structure by merging data mining with quantum mechanics

Modern methods of quantum mechanics have proved to be effective tools to understand and even predict materials properties. An essential element of the materials design process, relevant to both new materials and the optimization of existing ones, is knowing which crystal structures will form in an alloy system. Crystal structure can only be predicted effectively with quantum mechanics if an algorithm to direct the search through the large space of possible structures is found. We present a new approach to the prediction of structure that rigorously mines correlations embodied within experimental data and uses them to direct quantum mechanical techniques efficiently towards the stable crystal structure of materials.

Ultra-fast evaluation of protein energies directly from sequence

The structure, function, stability, and many other properties of a protein in a fixed environment are fully specified by its sequence, but in a manner that is difficult to discern. We present a general approach for rapidly mapping sequences directly to their energies on a pre-specified rigid backbone, an important sub-problem in computational protein design and in some methods for protein structure prediction. The cluster expansion (CE) method that we employ can, in principle, be extended to model any computable or measurable protein property directly as a function of sequence. Here we show how CE can be applied to the problem of computational protein design, and use it to derive excellent approximations of physical potentials. The approach provides several attractive advantages. First, following a one-time derivation of a CE expansion, the amount of time necessary to evaluate the energy of a sequence adopting a specified backbone conformation is reduced by a factor of 10⁷ compared to standard full-atom methods for the same task. Second, the agreement between two full-atom methods that we tested and their CE sequence-based expressions is very high (root mean square deviation 1.1–4.7 kcal/mol, R² = 0.7–1.0). Third, the functional form of the CE energy expression is such that individual terms of the expansion have clear physical interpretations. We derived expressions for the energies of three classic protein design targets—a coiled coil, a zinc finger, and a WW domain—as functions of sequence, and examined the most significant terms. Single-residue and residue-pair interactions are sufficient to accurately capture the energetics of the dimeric coiled coil, whereas higher-order contributions are important for the two more globular folds. For the task of designing novel zinc-finger sequences, a CE-derived energy function provides significantly better solutions than a standard design protocol, in comparable computation time. Given these advantages, CE is likely to find many uses in computational structural modeling.

Many applications in computational structural biology involve evaluating the energy of a protein adopting a specific structure. A variety of functions are used for this purpose. Statistical potentials are fast to evaluate but do not have a clear biophysical basis, whereas physics-based functions consist of well-defined terms that can be costly to compute. This paper describes how the theory of cluster expansion, originally developed to describe the energies of alloys, can be applied to generate a physical potential for proteins that is extremely fast to evaluate. Cluster expansion is a way of representing a property of a system as a discrete function of its degrees of freedom. In this paper, it is used for the problem of protein design, where the energy is determined by the identities and conformations of amino acids at different sites on a fixed protein backbone. Application of cluster expansion to three small protein folds—the α-helical coiled coil, the zinc finger, and the WW domain—shows that protein sequence can be mapped directly to energy using a surprisingly simple function that maintains high accuracy. Promising results on these small systems suggest that the theory may have utility for macromolecular modeling more generally.

Electronic and local structural changes in Li2+xTi3O7ramsdellite compounds upon electrochemical Li-ion insertion reactions by X-ray absorption spectroscopy

Electronic and local structural changes in ramsdellite-type Li(2+x)Ti3O7 compound were investigated by X-ray absorption spectroscopy (XAS) measurements. Upon electrochemical Li-ion insertions, the host lattice with ramsdellite structure is retained, indicated by X-ray powder diffraction. Ti K-edge extended X-ray absorption fine structure (EXAFS) analysis shows, however, slight local structural distortions around Ti ions. The energy shifts and the changes in the peak intensity of Ti K-edge and Ti L-edge XAS reveal the reducing oxidation states of Ti ions as the amount of electrochemically-inserted Li-ion increases. Equally important, oxide ions have a significant effect on the electronic transfer process, suggested by O K-edge XAS. These results on electronic structural changes were interpreted using the Zaanen-Sawatzky-Allen scheme.

Changes in Electronic Structure upon Lithium Insertion into the A-Site Deficient Perovskite Type Oxides (Li,La)TiO3

Investigation on variation of the electronic structure accompanying the electrochemical lithium insertion into the perovskite type oxide, (Li,La)TiO3, has been carried out by X-ray absorption spectroscopy (XAS). During the electrochemical lithium insertion, titanium ion reduced its oxidation state from Ti4+ to Ti3+, while La3+ does not contribute to the reduction reaction resulting from Ti K-edge and La L3-edge XAS, respectively. Furthermore, O K-edge XAS showed marked spectral changes with electrochemical lithium insertion, indicating the electronic structure around oxide ion affected by lithium insertion reaction. From the XAS measurement, we have concluded the variation observed in O K-edge XAS was related to the strong interaction with inserted Li ion. To confirm this, first-principles band calculations were performed for the perovskite structure before and after electrochemical lithium insertion. The calculated results showed that the electron originated from inserted Li transferred to neighboring oxide ion locally as well as to Ti ion. This may be due to local neutralization effect of Li to reduce the electrostatic interaction in the crystal.

Experimental and Computational Study of the Electronic Structural Changes in LiTi2O4Spinel Compounds upon Electrochemical Li Insertion Reactions

Electronic structural changes in LiTi(2)O(4) spinel compounds upon electrochemical lithium insertions were investigated by X-ray absorption spectroscopy (XAS) measurements and first principles calculations based on spin-polarized density functional theory. Ti K-edge, O K-edge XAS spectra and theoretical calculations indicate that oxide ions as well as titanium ions are involved in electronic structural changes caused by electrochemical lithium ion insertions. The considerable effect of the oxide ions in the early 3d transition metal (titanium) oxide system is discussed in this article.