Machine learning for molecular and materials science.

Here we summarize recent progress in machine learning for the chemical sciences. We outline machine-learning techniques that are suitable for addressing research questions in this domain, as well as future directions for the field. We envisage a future in which the design, synthesis, characterization and application of molecules and materials is accelerated by artificial intelligence.

Origin of Ferroelectricity in Two Prototypical Hybrid Organic-Inorganic Perovskites.

Hybrid organic-inorganic perovskite (HOIP) ferroelectrics are attracting considerable interest because of their high performance, ease of synthesis, and lightweight. However, the intrinsic thermodynamic origins of their ferroelectric transitions remain insufficiently understood. Here, we identify the nature of the ferroelectric phase transitions in displacive [(CH3)2NH2][Mn(N3)3] and order-disorder type [(CH3)2NH2][Mn(HCOO)3] via spatially resolved structural analysis and ab initio lattice dynamics calculations. Our results demonstrate that the vibrational entropy change of the extended perovskite lattice drives the ferroelectric transition in the former and also contributes importantly to that of the latter along with the rotational entropy change of the A-site. This finding not only reveals the delicate atomic dynamics in ferroelectric HOIPs but also highlights that both the local and extended fluctuation of the hybrid perovskite lattice can be manipulated for creating ferroelectricity by taking advantages of their abundant atomic, electronic, and phononic degrees of freedom.

Linking in situ charge accumulation to electronic structure in doped SrTiO3 reveals design principles for hydrogen-evolving photocatalysts.

Recently, high solar-to-hydrogen efficiencies were demonstrated using La and Rh co-doped SrTiO3 (La,Rh:SrTiO3) incorporated into a low-cost and scalable Z-scheme device, known as a photocatalyst sheet. However, the unique properties that enable La,Rh:SrTiO3 to support this impressive performance are not fully understood. Combining in situ spectroelectrochemical measurements with density functional theory and photoelectron spectroscopy produces a depletion model of Rh:SrTiO3 and La,Rh:SrTiO3 photocatalyst sheets. This reveals remarkable properties, such as deep flatband potentials (+2 V versus the reversible hydrogen electrode) and a Rh oxidation state dependent reorganization of the electronic structure, involving the loss of a vacant Rh 4d mid-gap state. This reorganization enables Rh:SrTiO3 to be reduced by co-doping without compromising the p-type character. In situ time-resolved spectroscopies show that the electronic structure reorganization induced by Rh reduction controls the electron lifetime in photocatalyst sheets. In Rh:SrTiO3, enhanced lifetimes can only be obtained at negative applied potentials, where the complete Z-scheme operates inefficiently. La co-doping fixes Rh in the 3+ state, which results in long-lived photogenerated electrons even at very positive potentials (+1 V versus the reversible hydrogen electrode), in which both components of the complete device operate effectively. This understanding of the role of co-dopants provides a new insight into the design principles for water-splitting devices based on bandgap-engineered metal oxides.

Ultralow work function of the electride Sr3CrN3.

Electrides have valence electrons that occupy free space in the crystal structure, making them easier to extract. This feature can be used in catalysis for important reactions that usually require a high-temperature and high-pressure environments, such as ammonia synthesis. In this paper, we use density functional theory to investigate the behaviour of interstitial electrons of the 1-dimensional electride Sr3CrN3. We find that the bulk excess electron density persists on introduction of surface terminations, that the crystal termination perpendicular to the 1D free-electron channel is highly stable and we confirm an extremely low work function with hybrid functional methods. Our results indicate that Sr3CrN3 is a potentially important novel catalyst, with accessible, directional and extractable free electron density.

Entropy-based active learning of graph neural network surrogate models for materials properties.

Graph neural networks trained on experimental or calculated data are becoming an increasingly important tool in computational materials science. Networks once trained are able to make highly accurate predictions at a fraction of the cost of experiments or first-principles calculations of comparable accuracy. However, these networks typically rely on large databases of labeled experiments to train the model. In scenarios where data are scarce or expensive to obtain, this can be prohibitive. By building a neural network that provides confidence on the predicted properties, we are able to develop an active learning scheme that can reduce the amount of labeled data required by identifying the areas of chemical space where the model is most uncertain. We present a scheme for coupling a graph neural network with a Gaussian process to featurize solid-state materials and predict properties including a measure of confidence in the prediction. We then demonstrate that this scheme can be used in an active learning context to speed up the training of the model by selecting the optimal next experiment for obtaining a data label. Our active learning scheme can double the rate at which the performance of the model on a test dataset improves with additional data compared to choosing the next sample at random. This type of uncertainty quantification and active learning has the potential to open up new areas of materials science, where data are scarce and expensive to obtain, to the transformative power of graph neural networks.

Differentiating the role of organic additives to assemble open framework aluminosilicates using INS spectroscopy.

Presently, there is little clarity concerning how organic additives control structure formation in the synthesis of zeolite catalysts. Such ambiguity is a major obstacle towards synthesis design of new bespoke zeolites with intended applications. Herein, we have applied inelastic neutron scattering (INS) spectroscopy to experimentally probe the nature of organic-framework interactions, which are crucial in understanding structure direction. With this technique we have studied the dynamics of 18-crown-6 ether, which can be used as an additive to direct the formation of four zeolites: Na-X, EMC-2, RHO and ZK-5. We observed significant softening of the 18-crown-6 ether molecule's dynamics upon occlusion within a zeolite host, with a strong influence on both the circular and radial vibrational modes. Furthermore, there is a strong correlation between the size/geometry of the zeolite framework cages and perturbations in the dynamics of the 18C6 oxyethylene chain. We propose that the approach used herein can be used to study other zeolites, and hence gain a more comprehensive view of organic-framework interactions.

Modeling the dielectric constants of crystals using machine learning.

The relative permittivity of a crystal is a fundamental property that links microscopic chemical bonding to macroscopic electromagnetic response. Multiple models, including analytical, numerical, and statistical descriptions, have been made to understand and predict dielectric behavior. Analytical models are often limited to a particular type of compound, whereas machine learning (ML) models often lack interpretability. Here, we combine supervised ML, density functional perturbation theory, and analysis based on game theory to predict and explain the physical trends in optical dielectric constants of crystals. Two ML models, support vector regression and deep neural networks, were trained on a dataset of 1364 dielectric constants. Analysis of Shapley additive explanations of the ML models reveals that they recover correlations described by textbook Clausius-Mossotti and Penn models, which gives confidence in their ability to describe physical behavior, while providing superior predictive power.

Tuning the Negative Thermal Expansion Behavior of the Metal-Organic Framework Cu3BTC2 by Retrofitting.

The modular building principle of metal-organic frameworks (MOFs) presents an excellent platform to explore and establish structure-property relations that tie microscopic to macroscopic properties. Negative thermal expansion (NTE) is a common phenomenon in MOFs and is often ascribed to collective motions that can move through the structure at sufficiently low energies. Here, we show that the introduction of additional linkages in a parent framework, retrofitting, is an effective approach to access lattice dynamics experimentally, in turn providing researchers with a tool to alter the NTE behavior in MOFs. By introducing TCNQ (7,7,8,8-tetracyanoquinodimethane) into the prototypical MOF Cu3BTC2 (BTC = 1,3,5-benzenetricarboxylate; HKUST-1), NTE can be tuned between αV = -15.3 × 10-6 K-1 (Cu3BTC2) and αV = -8.4 × 10-6 K-1 (1.0TCNQ@Cu3BTC2). We ascribe this phenomenon to a general stiffening of the framework as a function of TCNQ loading due to additional network connectivity, which is confirmed by computational modeling and far-infrared spectroscopy. Our findings imply that retrofitting is generally applicable to MOFs with open metal sites, opening yet another way to fine-tune properties in this versatile class of materials.

Subwavelength Spatially Resolved Coordination Chemistry of Metal-Organic Framework Glass Blends.

Microstructured metal-organic framework (MOF) glasses have been produced by combining two amorphous MOFs. However, the electronic structure of these materials has not been interrogated at the length scales of the chemical domains formed in these glasses. Here, we report a subwavelength spatially resolved physicochemical analysis of the electronic states at visible and UV energies in a blend of two zeolitic imidazolate frameworks (ZIFs), ZIF-4-Co and ZIF-62-Zn. By combining spectroscopy at visible and UV energies as well as at core ionization energies in electron energy loss spectroscopy in the scanning transmission electron microscope with density functional theory calculations, we show that domains less than 200 nm in size retain the electronic structure of the precursor crystalline ZIF phases. Prototypical signatures of coordination chemistry including d- d transitions in ZIF-4-Co are assigned and mapped with nanoscale precision.

Materials discovery by chemical analogy: role of oxidation states in structure prediction.

The likelihood of an element to adopt a specific oxidation state in a solid, given a certain set of neighbours, might often be obvious to a trained chemist. However, encoding this information for use in high-throughput searches presents a significant challenge. We carry out a statistical analysis of the occurrence of oxidation states in 16 735 ordered, inorganic compounds and show that a large number of cations are only likely to exhibit certain oxidation states in combination with particular anions. We use this data to build a model that ascribes probabilities to the formation of hypothetical compounds, given the proposed oxidation states of their constituent species. The model is then used as part of a high-throughput materials design process, which significantly narrows down the vast compositional search space for new ternary metal halide compounds. Finally, we employ a machine learning analysis of existing compounds to suggest likely structures for a small subset of the candidate compositions. We predict two new compounds, MnZnBr4 and YSnF7, that are thermodynamically stable according to density functional theory, as well as four compounds, MnCdBr4, MnRu2Br8, ScZnF5 and ZnCoBr4, which lie within the window of metastability.

Heterogeneous catalytic hydrogenation of CO2 by metal oxides: defect engineering - perfecting imperfection.

Metal oxides with their myriad compositions, structures and bonding exhibit an incredibly diverse range of properties. It is however the defects in metal oxides that endow them with a variety of functions and it is the ability to chemically tailor the type, population and distribution of defects on the surface and in the bulk of metal oxides that delivers utility in different applications. In this Tutorial Review, we discuss how metal oxides with designed defects can be synthesized and engineered, to enable heterogeneous catalytic hydrogenation of gaseous carbon dioxide to chemicals and fuels. If this approach to utilization and valorization of carbon dioxide could be developed at industrially significant rates, efficiencies and scales and made economically competitive with fossil-based chemicals and fuels, then carbon dioxide refineries envisioned in the future would be able to contribute to the reduction of greenhouse gas emissions, ameliorate climate changes, provide energy security and enable protection of the environment. This would bring the vision of a sustainable future closer to reality.

An Unusual Phase Transition Driven by Vibrational Entropy Changes in a Hybrid Organic-Inorganic Perovskite.

The driving forces for the phase transitions of ABX3 hybrid organic-inorganic perovskites have been limited to the octahedral tilting, order-disorder, and displacement. Now, a complex structural phase transition has been explored in a HOIP, [CH3 NH3 ][Mn(N3 )3 ], based on structural characterizations and ab initio lattice dynamics calculations. This unusual first-order phase transition between two ordered phases at about 265 K is primarily driven by changes in the collective atomic vibrations of the whole lattice, along with concurrent molecular displacements and an unusual octahedral tilting. A significant entropy difference (4.35 J K-1 mol-1 ) is observed between the low- and high-temperature structures induced by such atomic vibrations, which plays a main role in driving the transition. This finding offers an alternative pathway for designing new ferroic phase transitions and related physical properties in HOIPs and other hybrid crystals.

Designing porous electronic thin-film devices: band offsets and heteroepitaxy.

Increasing numbers of electrically active porous framework materials are being reported, with conductivities that make them attractive for technological applications. As design strategies for efficient carrier transport emerge, the next challenge is to incorporate the materials into a functioning device. In thin-film devices interface effects are of critical importance to overall function. In this article we present a method to identify compatible materials combinations to achieve mechanically robust, electronically optimal pairings. The computational screening is based on a two-step procedure: (i) matching of lattice constants to ensure interfaces with minimal epitaxial strain and therefore maximal mechanical and chemical stability; (ii) matching of absolute electron energies to construct energy-band-alignment diagrams, which can be used to screen for particular electronic applications. We apply the methodology to search for zeolitic imidazolate framework (ZIF) type materials that are compatible with native metal electrodes. The procedure allows us to predict simple routes for electrochemical deposition of ZIFs for application as conductive porous electrodes.

Computational materials design of crystalline solids.

The modelling of materials properties and processes from first principles is becoming sufficiently accurate as to facilitate the design and testing of new systems in silico. Computational materials science is both valuable and increasingly necessary for developing novel functional materials and composites that meet the requirements of next-generation technology. A range of simulation techniques are being developed and applied to problems related to materials for energy generation, storage and conversion including solar cells, nuclear reactors, batteries, fuel cells, and catalytic systems. Such techniques may combine crystal-structure prediction (global optimisation), data mining (materials informatics) and high-throughput screening with elements of machine learning. We explore the development process associated with computational materials design, from setting the requirements and descriptors to the development and testing of new materials. As a case study, we critically review progress in the fields of thermoelectrics and photovoltaics, including the simulation of lattice thermal conductivity and the search for Pb-free hybrid halide perovskites. Finally, a number of universal chemical-design principles are advanced.

Magnetic coupling in a hybrid Mn(ii) acetylene dicarboxylate.

The design of ligands that mediate through-bond long range super-exchange in metal-organic hybrid materials would expand chemical space beyond the commonly observed short range, low temperature magnetic ordering. Here we examine acetylene dicarboxylate as a potential ligand that could install long range magnetic ordering due to its spatially continuous frontier orbitals. Using a known Mn(ii)-containing coordination polymer we compute and measure the electronic structure and magnetic ordering. In this case, the latter is weak owing to the sub-optimal ligand coordination geometry, with a critical temperature of 2.5 K.

Absorbate-induced piezochromism in a porous molecular crystal.

Atmospherically stable porous frameworks and materials are interesting for heterogeneous solid-gas applications. One motivation is the direct and selective uptake of pollutant/hazardous gases, where the material produces a measurable response in the presence of the analyte. In this report, we present a combined experimental and theoretical rationalization for the piezochromic response of a robust and porous molecular crystal built from an extensively fluorinated trispyrazole. The electronic response of the material is directly determined by analyte uptake, which provokes a subtle lattice contraction and an observable bathochromic shift in the optical absorption onset. Selectivity for fluorinated absorbates is demonstrated, and toluene is also found to crystallize within the pore. Furthermore, we demonstrate the application of electronic structure calculations to predict a physicochemical response, providing the foundations for the design of electronically tunable porous solids with the chemical properties required for development of novel gas-uptake media.

Prediction of electron energies in metal oxides.

The ability to predict energy levels in metal oxides is paramount to developinguseful materials, such as in the development of water photolysis catalysts and efficient photovoltaic cells. The binding energy of electrons in materials encompasses a wealth of information concerning their physicochemistry. The energies control the optical and electrical properties, dictating for which kinds of chemistry and physics a particular material is useful. Scientists have developed theories and models for electron energies in a variety of chemical systems over the past century. However, the prediction of quantitative energy levels in new materials remains a major challenge. This issue is of particular importance in metal oxide research, where novel chemistries have opened the possibility of a wide range of tailored systems with applications in important fields including light-emitting diodes, energy efficient glasses, and solar cells. In this Account, we discuss the application of atomistic modeling techniques, covering the spectrum from classical to quantum descriptions, to explore the alignment of electron energies between materials. We present a number of paradigmatic examples, including a series of oxides (ZnO, In2O3, and Cu2O). Such calculations allow the determination of a "band alignment diagram" between different materials and can facilitate the prediction of the optimal chemical composition of an oxide for use in a given application. Throughout this Account, we consider direct computational solutions in the context of heuristic models, which are used to relate the fundamental theory to experimental observations. We review a number of techniques that have been commonly applied in the study of electron energies in solids. These models have arisen from different answers to the same basic question, coming from solid-state chemistry and physics perspectives. We highlight common factors, as well as providing a critical appraisal of the strengths and weaknesses of each, emphasizing the difficulties in translating concepts from molecular to solid-state systems. Finally, we stress the need for a universal description of the alignment of band energies for materials design from first-principles. By demonstrating the applicability and challenges of using theory to calculate the relevant quantities, as well as impressing the necessity of a clarification and unification of the descriptions, we hope to provide a stimulus for the continued development of this field.

Crystal structure optimisation using an auxiliary equation of state.

Standard procedures for local crystal-structure optimisation involve numerous energy and force calculations. It is common to calculate an energy-volume curve, fitting an equation of state around the equilibrium cell volume. This is a computationally intensive process, in particular, for low-symmetry crystal structures where each isochoric optimisation involves energy minimisation over many degrees of freedom. Such procedures can be prohibitive for non-local exchange-correlation functionals or other "beyond" density functional theory electronic structure techniques, particularly where analytical gradients are not available. We present a simple approach for efficient optimisation of crystal structures based on a known equation of state. The equilibrium volume can be predicted from one single-point calculation and refined with successive calculations if required. The approach is validated for PbS, PbTe, ZnS, and ZnTe using nine density functionals and applied to the quaternary semiconductor Cu2ZnSnS4 and the magnetic metal-organic framework HKUST-1.

Atomistic origins of high-performance in hybrid halide perovskite solar cells.

The performance of organometallic perovskite solar cells has rapidly surpassed that of both conventional dye-sensitized and organic photovoltaics. High-power conversion efficiency can be realized in both mesoporous and thin-film device architectures. We address the origin of this success in the context of the materials chemistry and physics of the bulk perovskite as described by electronic structure calculations. In addition to the basic optoelectronic properties essential for an efficient photovoltaic device (spectrally suitable band gap, high optical absorption, low carrier effective masses), the materials are structurally and compositionally flexible. As we show, hybrid perovskites exhibit spontaneous electric polarization; we also suggest ways in which this can be tuned through judicious choice of the organic cation. The presence of ferroelectric domains will result in internal junctions that may aid separation of photoexcited electron and hole pairs, and reduction of recombination through segregation of charge carriers. The combination of high dielectric constant and low effective mass promotes both Wannier-Mott exciton separation and effective ionization of donor and acceptor defects. The photoferroic effect could be exploited in nanostructured films to generate a higher open circuit voltage and may contribute to the current-voltage hysteresis observed in perovskite solar cells.

Electronic chemical potentials of porous metal-organic frameworks.

The binding energy of an electron in a material is a fundamental characteristic, which determines a wealth of important chemical and physical properties. For metal-organic frameworks this quantity is hitherto unknown. We present a general approach for determining the vacuum level of porous metal-organic frameworks and apply it to obtain the first ionization energy for six prototype materials including zeolitic, covalent, and ionic frameworks. This approach for valence band alignment can explain observations relating to the electrochemical, optical, and electrical properties of porous frameworks.