Machine learning for the structure-energy-property landscapes of molecular crystals

Global machine learning potentials for molecular crystals

Molecular crystals are difficult to model with accurate first-principles methods due to large unit cells. On the other hand, accurate modeling is required as polymorphs often differ by only 1 kJ/mol. Machine learning interatomic potentials promise to provide accuracy of the baseline first-principles methods with a cost lower by orders of magnitude. Using the existing databases of the density functional theory calculations for molecular crystals and molecules, we train global machine learning interatomic potentials, usable for any molecular crystal. We test the performance of the potentials on experimental benchmarks and show that they perform better than classical force fields and, in some cases, are comparable to the density functional theory calculations.

Polymorph Identification for Flexible Molecules: Linear Regression Analysis of Experimental and Calculated Solution- and Solid-State NMR Data

The Δδ regression approach of Blade et al. [ J. Phys. Chem. A 2020, 124(43), 8959-8977] for accurately discriminating between solid forms using a combination of experimental solution- and solid-state NMR data with density functional theory (DFT) calculation is here extended to molecules with multiple conformational degrees of freedom, using furosemide polymorphs as an exemplar. As before, the differences in measured 1H and 13C chemical shifts between solution-state NMR and solid-state magic-angle spinning (MAS) NMR (Δδexperimental) are compared to those determined by gauge-including projector augmented wave (GIPAW) calculations (Δδcalculated) by regression analysis and a t-test, allowing the correct furosemide polymorph to be precisely identified. Monte Carlo random sampling is used to calculate solution-state NMR chemical shifts, reducing computation times by avoiding the need to systematically sample the multidimensional conformational landscape that furosemide occupies in solution. The solvent conditions should be chosen to match the molecule's charge state between the solution and solid states. The Δδ regression approach indicates whether or not correlations between Δδexperimental and Δδcalculated are statistically significant; the approach is differently sensitive to the popular root mean squared error (RMSE) method, being shown to exhibit a much greater dynamic range. An alternative method for estimating solution-state NMR chemical shifts by approximating the measured solution-state dynamic 3D behavior with an ensemble of 54 furosemide crystal structures (polymorphs and cocrystals) from the Cambridge Structural Database (CSD) was also successful in this case, suggesting new avenues for this method that may overcome its current dependency on the prior determination of solution dynamic 3D structures.

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.

Two-Step Machine Learning Approach for Charge-Transfer Coupling with Structurally Diverse Data

Electronic coupling is important in determining charge-transfer rates and dynamics. Coupling strength is sensitive to both intermolecular, e.g., orientation or distance, and intramolecular degrees of freedom. Hence, it is challenging to build an accurate machine learning model to predict electronic coupling of molecular pairs, especially for those derived from the amorphous phase, for which intermolecular configurations are much more diverse than those derived from crystals. In this work, we devise a new prediction algorithm that employs two consecutive KRR models. The first model predicts molecular orbitals (MOs) from structural variation for each fragment, and coupling is further predicted by using the overlap integral included in a second model. With our two-step procedure, we achieved mean absolute errors of 0.27 meV for an ethylene dimer and 1.99 meV for a naphthalene pair, much improved accuracy amounting to 14-fold and 3-fold error reductions, respectively. In addition, MOs from the first model can also be the starting point to obtain other quantum chemical properties from atomistic structures. This approach is also compatible with a MO predictor with sufficient accuracy.

Accelerated Organic Crystal Structure Prediction with Genetic Algorithms and Machine Learning

We present a high-throughput, end-to-end pipeline for organic crystal structure prediction (CSP)─the problem of identifying the stable crystal structures that will form from a given molecule based only on its molecular composition. Our tool uses neural network potentials to allow for efficient screening and structural relaxation of generated crystal candidates. Our pipeline consists of two distinct stages: random search, whereby crystal candidates are randomly generated and screened, and optimization, where a genetic algorithm (GA) optimizes this screened population. We assess the performance of each stage of our pipeline on 21 molecules taken from the Cambridge Crystallographic Data Centre's CSP blind tests. We show that random search alone yields matches for ≈50% of targets. We then validate the potential of our full pipeline, making use of the GA to optimize the root-mean-square deviation between crystal candidates and the experimentally derived structure. With this approach, we are able to find matches for ≈80% of candidates with 10-100 times smaller initial population sizes than when using random search. Lastly, we run our full pipeline with an ANI model that is trained on a small data set of molecules extracted from crystal structures in the Cambridge Structural Database, generating ≈60% of targets. By leveraging machine learning models trained to predict energies at the density functional theory level, our pipeline has the potential to approach the accuracy of ab initio methods and the efficiency of empirical force fields.

Frontiers of molecular crystal structure prediction for pharmaceuticals and functional organic materials

The reliability of organic molecular crystal structure prediction has improved tremendously in recent years. Crystal structure predictions for small, mostly rigid molecules are quickly becoming routine. Structure predictions for larger, highly flexible molecules are more challenging, but their crystal structures can also now be predicted with increasing rates of success. These advances are ushering in a new era where crystal structure prediction drives the experimental discovery of new solid forms. After briefly discussing the computational methods that enable successful crystal structure prediction, this perspective presents case studies from the literature that demonstrate how state-of-the-art crystal structure prediction can transform how scientists approach problems involving the organic solid state. Applications to pharmaceuticals, porous organic materials, photomechanical crystals, organic semi-conductors, and nuclear magnetic resonance crystallography are included. Finally, efforts to improve our understanding of which predicted crystal structures can actually be produced experimentally and other outstanding challenges are discussed.

Impact of Static Distortion Waves on Superlubricity

Friction is a major source of energy loss in mechanical devices. This energy loss may be minimized by creating interfaces with extremely reduced friction, i.e., superlubricity. Conventional wisdom holds that incommensurate interface structures facilitate superlubricity. Accurately describing friction necessitates the precise modeling of the interface structure. This, in turn, requires the use of accurate first-principles electronic structure methods, especially when studying organic/metal interfaces, which are highly relevant due to their tunability and propensity to form incommensurate structures. However, the system size required to calculate incommensurate structures renders such calculations intractable. As a result, studies of incommensurate interfaces have been limited to very simple model systems or strongly simplified methodology. We overcome this limitation by developing a machine-learned interatomic potential that is able to determine energies and forces for structures containing thousands to tens of thousands of atoms with an accuracy comparable to conventional first-principles methods but at a fraction of the cost. Using this approach, we quantify the breakdown of superlubricity in incommensurate structures due to the formation of static distortion waves. Moreover, we extract design principles to engineer incommensurate interface systems where the formation of static distortion waves is suppressed, which facilitates low friction coefficients.

Conjugated Polymer Process Ontology and Experimental Data Repository for Organic Field-Effect Transistors

Polymer-based semiconductors and organic electronics encapsulate a significant research thrust for informatics-driven materials development. However, device measurements are described by a complex array of design and parameter choices, many of which are sparsely reported. For example, the mobility of a polymer-based organic field-effect transistor (OFET) may vary by several orders of magnitude for a given polymer as a plethora of parameters related to solution processing, interface design/surface treatment, thin-film deposition, postprocessing, and measurement settings have a profound effect on the value of the final measurement. Incomplete contextual, experimental details hamper the availability of reusable data applicable for data-driven optimization, modeling (e.g., machine learning), and analysis of new organic devices. To curate organic device databases that contain reproducible and findable, accessible, interoperable, and reusable (FAIR) experimental data records, data ontologies that fully describe sample provenance and process history are required. However, standards for generating such process ontologies are not widely adopted for experimental materials domains. In this work, we design and implement an object-relational database for storing experimental records of OFETs. A data structure is generated by drawing on an international standard for batch process control (ISA-88) to facilitate the design. We then mobilize these representative data records, curated from the literature and laboratory experiments, to enable data-driven learning of process-structure-property relationships. The work presented herein opens the door for the broader adoption of data management practices and design standards for both the organic electronics and the wider materials community.

Graph Comparison of Molecular Crystals in Band Gap Prediction Using Neural Networks

In material informatics, the representation of the material structure is fundamentally essential to obtaining better prediction results, and graph representation has attracted much attention in recent years. Molecular crystals can be graphically represented in molecular and crystal representations, but a comparison of which representation is more effective has not been examined. In this study, we compared the prediction accuracy between molecular and crystal graphs for band gap prediction. The results showed that the prediction accuracies using crystal graphs were better than those obtained using molecular graphs. While this result is not surprising, error analysis quantitatively evaluated that the error of the crystal graph was 0.4 times that of the molecular graph with moderate correlation. The novelty of this study lies in the comparison of molecular crystal representations and in the quantitative evaluation of the contribution of crystal structures to the band gap.

Reducing the Cost of Neural Network Potential Generation for Reactive Molecular Systems

Although machine learning potentials have recently had a substantial impact on molecular simulations, the construction of a robust training set can still become a limiting factor, especially due to the requirement of a reference ab initio simulation that covers all the relevant geometries of the system. Recognizing that this can be prohibitive for certain systems, we develop the method of transition tube sampling that mitigates the computational cost of training set and model generation. In this approach, we generate classical or quantum thermal geometries around a transition path describing a conformational change or a chemical reaction using only a sparse set of local normal mode expansions along this path and select from these geometries by an active learning protocol. This yields a training set with geometries that characterize the whole transition without the need for a costly reference trajectory. The performance of the method is evaluated on different molecular systems with the complexity of the potential energy landscape increasing from a single minimum to a double proton-transfer reaction with high barriers. Our results show that the method leads to training sets that give rise to models applicable in classical and path integral simulations alike that are on par with those based directly on ab initio calculations while providing the computational speedup we have come to expect from machine learning potentials.

Intermolecular 3D-MoRSE Descriptors for Fast and Accurate Prediction of Electronic Couplings in Organic Semiconductors

The theoretical rational design of organic semiconductors faces an obstacle in that the performance of organic semiconductors depends very much on their stacking and local morphology (for example, phase domains), which involves numerous molecules. Simulation becomes computationally expensive as intermolecular electronic couplings have to be calculated from density functional theory. Therefore, developing fast and accurate methods for intermolecular electronic coupling estimation is essential. In this work, by developing a series of new intermolecular 3D descriptors, we achieved fast and accurate prediction of electronic couplings in both crystalline and amorphous thin films. Three groups of developed descriptors could perform faster and higher accuracy prediction on electronic couplings than the most advanced state-of-the-art descriptors. This work paves the way for large-scale simulations, high-throughput calculations, and screening of organic semiconductors.

Quantum Chemistry-Machine Learning Approach for Predicting Properties of Lewis Acid-Lewis Base Adducts

Synthetic design allowing predictive control of charge transfer and other optoelectronic properties of Lewis acid adducts remains elusive. This challenge must be addressed through complementary methods combining experimental with computational insights from first principles. Ab initio calculations for optoelectronic properties can be computationally expensive and less straightforward than those sufficient for simple ground-state properties, especially for adducts of large conjugated molecules and Lewis acids. In this contribution, we show that machine learning (ML) can accurately predict density functional theory (DFT)-calculated charge transfer and even properties associated with excited states of adducts from readily obtained molecular descriptors. Seven ML models, built from a dataset of over 1000 adducts, show exceptional performance in predicting charge transfer and other optoelectronic properties with a Pearson correlation coefficient of up to 0.99. More importantly, the influence of each molecular descriptor on predicted properties can be quantitatively evaluated from ML models. This contributes to the optimization of a priori design of Lewis adducts for future applications, especially in organic electronics.

Energy-structure-property relationships in uranium metal-organic frameworks

Located at the foot of the periodic table, uranium is a relatively underexplored element possessing rich chemistry. In addition to its high relevance to nuclear power, uranium shows promise for small molecule activation and photocatalysis, among many other powerful functions. Researchers have used metal-organic frameworks (MOFs) to harness uranium's properties, and in their quest to do so, have discovered remarkable structures and unique properties unobserved in traditional transition metal MOFs. More recently, (e.g. the last 8-10 years), theoretical calculations of framework energetics have supplemented structure-property studies in uranium MOFs (U-MOFs). In this Perspective, we summarize how these budding energy-structure-property relationships in U-MOFs enable a deeper understanding of chemical phenomena, enlarge chemical space, and elevate the field to targeted, rather than exploratory, discovery. Importantly, this Perspective encourages interdisciplinary connections between experimentalists and theorists by demonstrating how these collaborations have elevated the entire U-MOF field.

A general force field by machine learning on experimental crystal structures. Calculations of intermolecular Gibbs energy with FlexCryst

Machine learning was employed on the experimental crystal structures of the Cambridge Structural Database (CSD) to derive an intermolecular force field for all available types of atoms (general force field). The obtained pairwise interatomic potentials of the general force field allow for the fast and accurate calculation of intermolecular Gibbs energy. The approach is based on three postulates regarding Gibbs energy: the lattice energy must be below zero, the crystal structure must be a local minimum, and, if available, the experimental and the calculated lattice energy must coincide. The parametrized general force field was then validated regarding these three conditions. First, the experimental lattice energy was compared with the calculated energies. The observed errors were found to be in the order of experimental errors. Second, Gibbs lattice energy was calculated for all structures available in the CSD. Their energy values were found to be below zero in 99.86% of the cases. Finally, 500 random structures were minimized, and the change in density and energy was examined. The mean error in the case of density was below 4.06%, and for energy it was below 5.7%. The obtained general force field calculated Gibbs lattice energies of 259 041 known crystal structures within a few hours. Since Gibbs energy defines the reaction energy, the calculated energy can be used to predict chemical-physical properties of crystals, for instance, the formation of co-crystals, polymorph stability and solubility.

A data-driven interpretation of the stability of organic molecular crystals

Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of different interactions enables the design of molecular crystals and fine-tuning of their stabilities. While this is usually performed based on the empirical observation of the most commonly encountered motifs in known crystal structures, we propose to apply a combination of supervised and unsupervised machine-learning techniques to automate the construction of an extensive library of molecular building blocks. We introduce a structural descriptor tailored to the prediction of the binding (lattice) energy and apply it to a curated dataset of organic crystals, exploiting its atom-centered nature to obtain a data-driven assessment of the contribution of different chemical groups to the lattice energy of the crystal. We then interpret this library using a low-dimensional representation of the structure-energy landscape and discuss selected examples of the insights into crystal engineering that can be extracted from this analysis, providing a complete database to guide the design of molecular materials.

XDM-corrected hybrid DFT with numerical atomic orbitals predicts molecular crystal lattice energies with unprecedented accuracy

Molecular crystals are important for many applications, including energetic materials, organic semiconductors, and the development and commercialization of pharmaceuticals. The exchange-hole dipole moment (XDM) dispersion model has shown good performance in the calculation of relative and absolute lattice energies of molecular crystals, although it has traditionally been applied in combination with plane-wave/pseudopotential approaches. This has limited XDM to use with semilocal functional approximations, which suffer from delocalization error and poor quality conformational energies, and to systems with a few hundreds of atoms at most due to unfavorable scaling. In this work, we combine XDM with numerical atomic orbitals, which enable the efficient use of XDM-corrected hybrid functionals for molecular crystals. We test the new XDM-corrected functionals for their ability to predict the lattice energies of molecular crystals for the X23 set and 13 ice phases, the latter being a particularly stringent test. A composite approach using a XDM-corrected, 25% hybrid functional based on B86bPBE achieves a mean absolute error of 0.48 kcal mol^-1 per molecule for the X23 set and 0.19 kcal mol^-1 for the total lattice energies of the ice phases, compared to recent diffusion Monte-Carlo data. These results make the new XDM-corrected hybrids not only far more computationally efficient than previous XDM implementations, but also the most accurate density-functional methods for molecular crystal lattice energies to date.

Spotting Local Environments in Self-Assembled Monolayer-Protected Gold Nanoparticles

Organic-inorganic (O-I) nanomaterials are versatile platforms for an incredible high number of applications, ranging from heterogeneous catalysis to molecular sensing, cell targeting, imaging, and cancer diagnosis and therapy, just to name a few. Much of their potential stems from the unique control of organic environments around inorganic sites within a single O-I nanomaterial, which allows for new properties that were inaccessible using purely organic or inorganic materials. Structural and mechanistic characterization plays a key role in understanding and rationally designing such hybrid nanoconstructs. Here, we introduce a general methodology to identify and classify local (supra)molecular environments in an archetypal class of O-I nanomaterials, i.e., self-assembled monolayer-protected gold nanoparticles (SAM-AuNPs). By using an atomistic machine-learning guided workflow based on the Smooth Overlap of Atomic Positions (SOAP) descriptor, we analyze a collection of chemically different SAM-AuNPs and detect and compare local environments in a way that is agnostic and automated, i.e., with no need of a priori information and minimal user intervention. In addition, the computational results coupled with experimental electron spin resonance measurements prove that is possible to have more than one local environment inside SAMs, being the thickness of the organic shell and solvation primary factors in the determining number and nature of multiple coexisting environments. These indications are extended to complex mixed hydrophilic-hydrophobic SAMs. This work demonstrates that it is possible to spot and compare local molecular environments in SAM-AuNPs exploiting atomistic machine-learning approaches, establishes ground rules to control them, and holds the potential for the rational design of O-I nanomaterials instructed from data.

Global analysis of the energy landscapes of molecular crystal structures by applying the threshold algorithm

Polymorphism in molecular crystals has important consequences for the control of materials properties and our understanding of crystallization. Computational methods, including crystal structure prediction, have provided important insight into polymorphism, but have usually been limited to assessing the relative energies of structures. We describe the implementation of the Monte Carlo threshold algorithm as a method to provide an estimate of the energy barriers separating crystal structures. By sampling the local energy minima accessible from multiple starting structures, the simulations yield a global picture of the crystal energy landscapes and provide valuable information on the depth of the energy minima associated with crystal structures. We present results from applying the threshold algorithm to four polymorphic organic molecular crystals, examine the influence of applying space group symmetry constraints during the simulations, and discuss the relationship between the structure of the energy landscape and the intermolecular interactions present in the crystals.

Applications of Artificial Intelligence and Machine Learning Algorithms to Crystallization

Artificial intelligence and specifically machine learning applications are nowadays used in a variety of scientific applications and cutting-edge technologies, where they have a transformative impact. Such an assembly of statistical and linear algebra methods making use of large data sets is becoming more and more integrated into chemistry and crystallization research workflows. This review aims to present, for the first time, a holistic overview of machine learning and cheminformatics applications as a novel, powerful means to accelerate the discovery of new crystal structures, predict key properties of organic crystalline materials, simulate, understand, and control the dynamics of complex crystallization process systems, as well as contribute to high throughput automation of chemical process development involving crystalline materials. We critically review the advances in these new, rapidly emerging research areas, raising awareness in issues such as the bridging of machine learning models with first-principles mechanistic models, data set size, structure, and quality, as well as the selection of appropriate descriptors. At the same time, we propose future research at the interface of applied mathematics, chemistry, and crystallography. Overall, this review aims to increase the adoption of such methods and tools by chemists and scientists across industry and academia.

Beyond Woodward-Fieser Rules: Design Principles of Property-Oriented Chromophores Based on Explainable Deep Learning Optical Spectroscopy

An adequate understanding of molecular structure-property relationships is important for developing new molecules with desired properties. Although deep learning optical spectroscopy (DLOS) has been successfully applied to predict the optical and photophysical properties of organic chromophores, how specific functional groups and solvents affect the optical properties is not clearly understood. Here, we employed an explainable DLOS method by applying the integrated gradients method to DLOS. The integrated gradients method allows us to obtain attributions, indicating how much the functional group contributes to the optical properties including the absorption wavelength and bandwidth, extinction coefficients, emission wavelength and bandwidth, photoluminescence quantum yield, and lifetime. The attributions of 54 functional groups and 9 solvent molecules to seven optical properties are quantified and can be used to estimate the optical properties of chromophores as in the Woodward-Fieser rule. Unlike the Woodward-Fieser rule for only the absorption wavelength, the attributions obtained in this work can be applied to estimate all seven optical properties, which makes a significant extension of the Woodward-Fieser rules. In addition, we demonstrated a strategy for utilizing the attributions in the design of molecules and in tuning the optical properties of the molecules. The design of molecular structures using attributions can revolutionize the development of optimal molecules.

The interplay of intra- and intermolecular errors in modeling conformational polymorphs

Conformational polymorphs of organic molecular crystals represent a challenging test for quantum chemistry because they require careful balancing of the intra- and intermolecular interactions. This study examines 54 molecular conformations from 20 sets of conformational polymorphs, along with the relative lattice energies and 173 dimer interactions taken from six of the polymorph sets. These systems are studied with a variety of van der Waals-inclusive density functionals theory models; dispersion-corrected spin-component-scaled second-order Møller–Plesset perturbation theory (SCS-MP2D); and domain local pair natural orbital coupled cluster singles, doubles, and perturbative triples [DLPNO-CCSD(T)]. We investigate how delocalization error in conventional density functionals impacts monomer conformational energies, systematic errors in the intermolecular interactions, and the nature of error cancellation that occurs in the overall crystal. The density functionals B86bPBE-XDM, PBE-D4, PBE-MBD, PBE0-D4, and PBE0-MBD are found to exhibit sizable one-body and two-body errors vs DLPNO-CCSD(T) benchmarks, and the level of success in predicting the relative polymorph energies relies heavily on error cancellation between different types of intermolecular interactions or between intra- and intermolecular interactions. The SCS-MP2D and, to a lesser extent, ωB97M-V models exhibit smaller errors and rely less on error cancellation. Implications for crystal structure prediction of flexible compounds are discussed. Finally, the one-body and two-body DLPNO-CCSD(T) energies taken from these conformational polymorphs establish the CP1b and CP2b benchmark datasets that could be useful for testing quantum chemistry models in challenging real-world systems with complex interplay between intra- and intermolecular interactions, a number of which are significantly impacted by delocalization error.

Molecular Forcefield Methods for Describing Energetic Molecular Crystals: A Review

Energetic molecular crystals are widely applied for military and civilian purposes, and molecular forcefields (FF) are indispensable for treating the microscopic issues therein. This article reviews the three types of molecular FFs that are applied widely for describing energetic crystals—classic FFs, consistent FFs, and reactive FFs (ReaxFF). The basic principle of each type of FF is briefed and compared, with the application introduced, predicting polymorph, morphology, thermodynamics, vibration spectra, thermal property, mechanics, and reactivity. Finally, the advantages and disadvantages of these FFs are summarized, and some directions of future development are suggested.

Intermolecular interactions in the solid-state structures of isoflavones: the relationship between supramolecular structure, torsion angle, and macroscopic properties

The different macroscopic properties of closely related isoflavones were associated with the occurrence of intermolecular interactions and different torsion angles in the solid-state.

Charge-Transfer Landscape Manifesting the Structure-Rate Relationship in the Condensed Phase Via Machine Learning

In this work, we develop a machine learning (ML) strategy to map the molecular structure to condensed phase charge-transfer (CT) properties including CT rate constants, energy levels, electronic couplings, energy gaps, reorganization energies, and reaction free energies which are called CT fingerprints. The CT fingerprints of selected landmark structures covering the conformation space of an organic photovoltaic molecule dissolved in an explicit solvent are computed and used to train ML models using kernel ridge regression. The ML models show high predictive power with R² > 0.97 and both mean absolute error and root-mean-square error within chemical accuracy. The CT landscape for millions of molecular dynamics sampled structures is thus constructed, which allows for instant prediction of CT rate properties, given any conformation of the molecule. We demonstrate some immediate utilities of the CT landscape such as calculating the ensemble-averaged CT rate constant and interpreting the effects of molecular structural features on the CT rate. The unprecedented CT landscape will be useful for investigating real-time CT dynamics in nanoscale- and mesoscale-condensed phase systems and for the optimal fabrication design for homogeneous and heterogeneous optoelectronic devices.

Visualization and Quantification of Geometric Diversity in Metal-Organic Frameworks

With ever-growing numbers of metal-organic framework (MOF) materials being reported, new computational approaches are required for a quantitative understanding of structure-property correlations in MOFs. Here, we show how structural coarse-graining and embedding ("unsupervised learning") schemes can together give new insights into the geometric diversity of MOF structures. Based on a curated data set of 1262 reported experimental structures, we automatically generate coarse-grained and rescaled representations which we couple to a kernel-based similarity metric and to widely used embedding schemes. This approach allows us to visualize the breadth of geometric diversity within individual topologies and to quantify the distributions of local and global similarities across the structural space of MOFs. The methodology is implemented in an openly available Python package and is expected to be useful in future high-throughput studies.

Machine learning potentials for complex aqueous systems made simple

Understanding complex materials, in particular those with solid–liquid interfaces, such as water on surfaces or under confinement, is a key challenge for technological and scientific progress. Although established simulation approaches have been able to provide important atomistic insight, ab initio techniques struggle with the required time and length scales, while force field methods can often be limited in terms of their accuracy. Here we show how these limitations can be overcome in a simple and automated machine learning procedure to provide accurate models of interactions at the ab initio level, as illustrated for a variety of complex aqueous systems. These developments open up the prospect of the straightforward exploration of many technologically relevant systems by molecular simulations.

Simulation techniques based on accurate and efficient representations of potential energy surfaces are urgently needed for the understanding of complex systems such as solid–liquid interfaces. Here we present a machine learning framework that enables the efficient development and validation of models for complex aqueous systems. Instead of trying to deliver a globally optimal machine learning potential, we propose to develop models applicable to specific thermodynamic state points in a simple and user-friendly process. After an initial ab initio simulation, a machine learning potential is constructed with minimum human effort through a data-driven active learning protocol. Such models can afterward be applied in exhaustive simulations to provide reliable answers for the scientific question at hand or to systematically explore the thermal performance of ab initio methods. We showcase this methodology on a diverse set of aqueous systems comprising bulk water with different ions in solution, water on a titanium dioxide surface, and water confined in nanotubes and between molybdenum disulfide sheets. Highlighting the accuracy of our approach with respect to the underlying ab initio reference, the resulting models are evaluated in detail with an automated validation protocol that includes structural and dynamical properties and the precision of the force prediction of the models. Finally, we demonstrate the capabilities of our approach for the description of water on the rutile titanium dioxide (110) surface to analyze the structure and mobility of water on this surface. Such machine learning models provide a straightforward and uncomplicated but accurate extension of simulation time and length scales for complex systems.

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.

Unsupervised Learning Methods for Molecular Simulation Data

Unsupervised learning is becoming an essential tool to analyze the increasingly large amounts of data produced by atomistic and molecular simulations, in material science, solid state physics, biophysics, and biochemistry. In this Review, we provide a comprehensive overview of the methods of unsupervised learning that have been most commonly used to investigate simulation data and indicate likely directions for further developments in the field. In particular, we discuss feature representation of molecular systems and present state-of-the-art algorithms of dimensionality reduction, density estimation, and clustering, and kinetic models. We divide our discussion into self-contained sections, each discussing a specific method. In each section, we briefly touch upon the mathematical and algorithmic foundations of the method, highlight its strengths and limitations, and describe the specific ways in which it has been used-or can be used-to analyze molecular simulation data.

Influence of the choice of precursors on the synthesis of two-dimensional transition metal dichalcogenides

The interest in transition metal dichalcogenides (TMDCs; MEy/2; M = transition metal; E = chalcogenide, y = valence of the metal) has grown exponentially across various science and engineering disciplines due to their unique structural chemistry manifested in a two-dimensional lattice that results in extraordinary electronic and transport properties desired for applications in sensors, energy storage and optoelectronic devices. Since the properties of TMDCs can be tailored by changing the stacking sequence of 2D monolayers with similar or dis-similar materials, a number of synthetic routes essentially based on the disintegration of bulk (e.g., chemical exfoliation) or the integration of atomic constituents (e.g., vapor phase growth) have been explored. Despite a large body of data available on the chemical synthesis of TMDCs, experimental strategies with high repeatability of control over film thickness, phase and compositional purity remain elusive, which calls for innovative synthetic concepts offering, for instance, self-limited growth in the z-direction and homogeneous lateral topography. This review summarizes the recent conceptual advancements in the growth of layered van der Waals TMDCs from both mixtures of metal and chalcogen sources (multi-source precursors; MSPs) and from molecular compounds containing metals and chalcogens in one starting material (single-source precursor; SSPs). The critical evaluation of the strengths, limitations and opportunities of MSP and SSP approaches is provided as a guideline for the fabrication of TMDCs from commercial and customized molecular precursors. For example, alternative synthetic pathways using tailored molecular precursors circumvent the challenges of differential nucleation and crystal growth kinetics that are invariably associated with conventional gas phase chemical vapor transport (CVT) and chemical vapor deposition (CVD) of a mixture of components. The aspects of achieving high compositional purity and alternatives to minimize competing reactions or side products are discussed in the context of efficient chemical synthesis of TMDCs. Moreover, a critical analysis of the potential opportunities and existing bottlenecks in the synthesis of TMDCs and their intrinsic properties is provided.

Physics-Inspired Structural Representations for Molecules and Materials

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

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.

Combined Use of Structure Analysis, Studies of Molecular Association in Solution, and Molecular Modelling to Understand the Different Propensities of Dihydroxybenzoic Acids to Form Solid Phases

The arrangement of hydroxyl groups in the benzene ring has a significant effect on the propensity of dihydroxybenzoic acids (diOHBAs) to form different solid phases when crystallized from solution. All six diOHBAs were categorized into distinctive groups according to the solid phases obtained when crystallized from selected solvents. A combined study using crystal structure and molecule electrostatic potential surface analysis, as well as an exploration of molecular association in solution using spectroscopic methods and molecular dynamics simulations were used to determine the possible mechanism of how the location of the phenolic hydroxyl groups affect the diversity of solid phases formed by the diOHBAs. The crystal structure analysis showed that classical carboxylic acid homodimers and ring-like hydrogen bond motifs consisting of six diOHBA molecules are prominently present in almost all analyzed crystal structures. Both experimental spectroscopic investigations and molecular dynamics simulations indicated that the extent of intramolecular bonding between carboxyl and hydroxyl groups in solution has the most significant impact on the solid phases formed by the diOHBAs. Additionally, the extent of hydrogen bonding with solvent molecules and the mean lifetime of solute-solvent associates formed by diOHBAs and 2-propanol were also investigated.

Deep Learning Optical Spectroscopy Based on Experimental Database: Potential Applications to Molecular Design

Accurate and reliable prediction of the optical and photophysical properties of organic compounds is important in various research fields. Here, we developed deep learning (DL) optical spectroscopy using a DL model and experimental database to predict seven optical and photophysical properties of organic compounds, namely, the absorption peak position and bandwidth, extinction coefficient, emission peak position and bandwidth, photoluminescence quantum yield (PLQY), and emission lifetime. Our DL model included the chromophore-solvent interaction to account for the effect of local environments on the optical and photophysical properties of organic compounds and was trained using an experimental database of 30 094 chromophore/solvent combinations. Our DL optical spectroscopy made it possible to reliably and quickly predict the aforementioned properties of organic compounds in solution, gas phase, film, and powder with the root mean squared errors of 26.6 and 28.0 nm for absorption and emission peak positions, 603 and 532 cm-1 for absorption and emission bandwidths, and 0.209, 0.371, and 0.262 for the logarithm of the extinction coefficient, PLQY, and emission lifetime, respectively. Finally, we demonstrated how a blue emitter with desired optical and photophysical properties could be efficiently virtually screened and developed by DL optical spectroscopy. DL optical spectroscopy can be efficiently used for developing chromophores and fluorophores in various research areas.

Roughness evolution in strongly interacting donor:acceptor mixtures of molecular semiconductors. An in situ, real-time growth study using x-ray reflectivity

The evolution of surface roughness in binary mixtures of the two molecular organic semiconductors (OSCs) diindenoperylene (DIP) as electron-donor and 1, 3, 4, 5, 7, 8-hexafluoro-tetracyano naphthoquinodimethane (F6TCNNQ) as electron-acceptor is studied. We co-deposit DIP and F6TCNNQ in vacuum with varying relative molar content while keeping a molar excess of DIP in order to produce phase-heterogeneous mixtures. The excess DIP phase segregates in pristine crystallites, whereas the remaining mixed phase is constituted by DIP:F6TCNNQ co-crystallites. We calculate the surface roughness as function of film thickness by modelling x-ray reflectivity data acquired in situ and in real-time during film growth. To model the experimental data, two distinct approaches, namely the kinematic approximation and the Parratt formalism, are applied. A comparative study of surface roughness evolution as function of DIP:F6TCNNQ mixing ratio is carried out implementing the Trofimov growth model within the kinematic approximation. Depending on the thickness regime, mixing ratio-specific trends are identified and discussed. To explain them, a growth mechanism for binary heterogeneous mixtures of strongly interacting OSCs is proposed.

Integrating a Low-Cost Electronic Nose and Machine Learning Modelling to Assess Coffee Aroma Profile and Intensity

Aroma is one of the main attributes that consumers consider when appreciating and selecting a coffee; hence it is considered an important quality trait. However, the most common methods to assess aroma are based on expensive equipment or human senses through sensory evaluation, which is time-consuming and requires highly trained assessors to avoid subjectivity. Therefore, this study aimed to estimate the coffee intensity and aromas using a low-cost and portable electronic nose (e-nose) and machine learning modeling. For this purpose, triplicates of nine commercial coffee samples with different intensity levels were used for this study. Two machine learning models were developed based on artificial neural networks using the data from the e-nose as inputs to (i) classify the samples into low, medium, and high-intensity (Model 1) and (ii) to predict the relative abundance of 45 different aromas (Model 2). Results showed that it is possible to estimate the intensity of coffees with high accuracy (98%; Model 1), as well as to predict the specific aromas obtaining a high correlation coefficient (R = 0.99), and no under- or over-fitting of the models were detected. The proposed contactless, nondestructive, rapid, reliable, and low-cost method showed to be effective in evaluating volatile compounds in coffee, which is a potential technique to be applied within all stages of the production process to detect any undesirable characteristics on–time and ensure high-quality products.

A non-empirical intermolecular force-field for trinitrobenzene and its application in crystal structure prediction

An anisotropic atom-atom distributed intermolecular force-field (DIFF) for rigid trinitrobenzene (TNB) is developed using distributed multipole moments, dipolar polarizabilities, and dispersion coefficients derived from the charge density of the isolated molecule. The short-range parameters of the force-field are fitted to first- and second-order symmetry-adapted perturbation theory dimer interaction energy calculations using the distributed density-overlap model to guide the parameterization of the short-range anisotropy. The second-order calculations are used for fitting the damping coefficients of the long-range dispersion and polarization and also for relaxing the isotropic short-range coefficients in the final model, DIFF-srL2(rel). We assess the accuracy of the unrelaxed model, DIFF-srL2(norel), and its equivalent without short-range anisotropy, DIFF-srL0(norel), as these models are easier to derive. The model potentials are contrasted with empirical models for the repulsion-dispersion fitted to organic crystal structures with multipoles of iterated stockholder atoms (ISAs), FIT(ISA,L4), and with Gaussian Distributed Analysis (GDMA) multipoles, FIT(GDMA,L4), commonly used in modeling organic crystals. The potentials are tested for their ability to model the solid state of TNB. The non-empirical models provide more reasonable relative lattice energies of the three polymorphs of TNB and propose more sensible hypothetical structures than the empirical force-field (FIT). The DIFF-srL2(rel) model successfully has the most stable structure as one of the many structures that match the coordination sphere of form III. The neglect of the conformational flexibility of the nitro-groups is a significant approximation. This methodology provides a step toward force-fields capable of representing all phases of a molecule in molecular dynamics simulations.

Digital navigation of energy-structure-function maps for hydrogen-bonded porous molecular crystals

Energy-structure-function (ESF) maps can aid the targeted discovery of porous molecular crystals by predicting the stable crystalline arrangements along with their functions of interest. Here, we compute ESF maps for a series of rigid molecules that comprise either a triptycene or a spiro-biphenyl core, functionalized with six different hydrogen-bonding moieties. We show that the positioning of the hydrogen-bonding sites, as well as their number, has a profound influence on the shape of the resulting ESF maps, revealing promising structure-function spaces for future experiments. We also demonstrate a simple and general approach to representing and inspecting the high-dimensional data of an ESF map, enabling an efficient navigation of the ESF data to identify 'landmark' structures that are energetically favourable or functionally interesting. This is a step toward the automated analysis of ESF maps, an important goal for closed-loop, autonomous searches for molecular crystals with useful functions.

Stability and NMR Chemical Shift of Amorphous Precursors of Methane Hydrate: Insights from Dispersion-Corrected Density Functional Theory Calculations Combined with Machine Learning

Clathrate hydrates of natural gases are important backup energy sources. It is thus of great significance to explore the nucleation process of hydrates. Hydrate clusters are building blocks of crystalline hydrates and represent the initial stage of hydrate nucleation. Using dispersion-corrected density functional theory (DFT-D) combined with machine learning, herein, we systematically investigate the evolution of stabilities and nuclear magnetic resonance (NMR) chemical shifts of amorphous precursors from monocage clusters CH₄(H₂O)_n (n = 16-24) to decacage clusters (CH₄)₁₀(H₂O)_n (n = 121-125). Compared with planelike configurations, the close-packed structures formed by the water-cage clusters are energetically favorable. The 5¹² cages are dominant, and the emerging amorphous precursors may be part of sII hydrates at the initial stage of nucleation. Based on our data set, the possible initial fusion pathways for water-cage clusters are proposed. In addition, the ¹³C NMR chemical shifts for encapsulated methane molecules also showed regular changes during the fusion of water-cage clusters. Machine learning can reproduce the DFT-D results well, providing a structure-energy-property landscape that could be used to predict the energy and NMR chemical shifts of such multicages with more water molecules. These theoretical results present vital insights into the hydrate nucleation from a unique perspective.

Transfer learning with graph neural networks for optoelectronic properties of conjugated oligomers

Despite the remarkable progress of machine learning (ML) techniques in chemistry, modeling the optoelectronic properties of long conjugated oligomers and polymers with ML remains challenging due to the difficulty in obtaining sufficient training data. Here, we use transfer learning to address the data scarcity issue by pre-training graph neural networks using data from short oligomers. With only a few hundred training data, we are able to achieve an average error of about 0.1 eV for the excited-state energy of oligothiophenes against time-dependent density functional theory (TDDFT) calculations. We show that the success of our transfer learning approach relies on the relative locality of low-lying electronic excitations in long conjugated oligomers. Finally, we demonstrate the transferability of our approach by modeling the lowest-lying excited-state energies of poly(3-hexylthiophene) in its single-crystal and solution phases using the transfer learning models trained with the data of gas-phase oligothiophenes. The transfer learning predicted excited-state energy distributions agree quantitatively with TDDFT calculations and capture some important qualitative features observed in experimental absorption spectra.

Crystal structure prediction of energetic materials and a twisted arene with Genarris and GAtor

A molecular crystal structure prediction workflow, based on the random structure generator, Genarris, and the genetic algorithm (GA), GAtor, is successfully applied to two energetic materials and a chiral arene.

Structure prediction of crystals, surfaces and nanoparticles

We review the current techniques used in the prediction of crystal structures and their surfaces and of the structures of nanoparticles. The main classes of search algorithm and energy function are summarized, and we discuss the growing role of methods based on machine learning. We illustrate the current status of the field with examples taken from metallic, inorganic and organic systems. This article is part of a discussion meeting issue 'Dynamic in situ microscopy relating structure and function'.

Mean-field density matrix decompositions

We introduce new and robust decompositions of mean-field Hartree-Fock and Kohn-Sham density functional theory relying on the use of localized molecular orbitals and physically sound charge population protocols. The new lossless property decompositions, which allow for partitioning one-electron reduced density matrices into either bond-wise or atomic contributions, are compared to alternatives from the literature with regard to both molecular energies and dipole moments. Besides commenting on possible applications as an interpretative tool in the rationalization of certain electronic phenomena, we demonstrate how decomposed mean-field theory makes it possible to expose and amplify compositional features in the context of machine-learned quantum chemistry. This is made possible by improving upon the granularity of the underlying data. On the basis of our preliminary proof-of-concept results, we conjecture that many of the structure-property inferences in existence today may be further refined by efficiently leveraging an increase in dataset complexity and richness.

Artificial neural networks for predicting charge transfer coupling

Quantum chemistry calculations have been very useful in providing many key detailed properties and enhancing our understanding of molecular systems. However, such calculation, especially with ab initio models, can be time-consuming. For example, in the prediction of charge-transfer properties, it is often necessary to work with an ensemble of different thermally populated structures. A possible alternative to such calculations is to use a machine-learning based approach. In this work, we show that the general prediction of electronic coupling, a property that is very sensitive to intermolecular degrees of freedom, can be obtained with artificial neural networks, with improved performance as compared to the popular kernel ridge regression method. We propose strategies for optimizing the learning rate and batch size, improving model performance, and further evaluating models to ensure that the physical signatures of charge-transfer coupling are well reproduced. We also address the effect of feature representation as well as statistical insights obtained from the loss function and the data structure. Our results pave the way for designing a general strategy for training such neural-network models for accurate prediction.

Understanding the geometric diversity of inorganic and hybrid frameworks through structural coarse-graining

Much of our understanding of complex structures is based on simplification: for example, metal-organic frameworks are often discussed in the context of "nodes" and "linkers", allowing for a qualitative comparison with simpler inorganic structures. Here we show how such an understanding can be obtained in a systematic and quantitative framework, combining atom-density based similarity (kernel) functions and unsupervised machine learning with the long-standing idea of "coarse-graining" atomic structure. We demonstrate how the latter enables a comparison of vastly different chemical systems, and we use it to create a unified, two-dimensional structure map of experimentally known tetrahedral AB2 networks - including clathrate hydrates, zeolitic imidazolate frameworks (ZIFs), and diverse inorganic phases. The structural relationships that emerge can then be linked to microscopic properties of interest, which we exemplify for structural heterogeneity and tetrahedral density.

Multifidelity Statistical Machine Learning for Molecular Crystal Structure Prediction

The prediction of crystal structures from first-principles requires highly accurate energies for large numbers of putative crystal structures. High accuracy of solid state density functional theory (DFT) calculations is often required, but hundreds or more structures can be present in the low energy region of interest, so that the associated computational costs are prohibitive. Here, we apply statistical machine learning to predict expensive hybrid functional DFT (PBE0) calculations using a multifidelity approach to re-evaluate the energies of crystal structures predicted with an inexpensive force field. The method uses an autoregressive Gaussian process, making use of less expensive GGA DFT (PBE) calculations to bridge the gap between the force field and PBE0 energies. The method is benchmarked on the crystal structure landscapes of three small, hydrogen-bonded organic molecules and shown to produce accurate predictions of energies and crystal structure ranking using small numbers of the most expensive calculations; the PBE0 energies can be predicted with errors of less than 1 kJ mol^-1 with between 4.2 and 6.8% of the cost of the full calculations. As the model that we have developed is probabilistic, we discuss how the uncertainties in predicted energies impact the assessment of the energetic ranking of crystal structures.

Evaluation-oriented exploration of photo energy conversion systems: from fundamental optoelectronics and material screening to the combination with data science

Light is a form of energy that can be converted to electric and chemical energies. Thus, organic photovoltaics (OPVs), perovskite solar cells (PSCs), photocatalysts, and photodetectors have evolved as scientific and commercial enterprises. However, the complex photochemical reactions and multicomponent materials involved in these systems have hampered rapid progress in their fundamental understanding and material design. This review showcases the evaluation-oriented exploration of photo energy conversion materials by using electrodeless time-resolved microwave conductivity (TRMC) and materials informatics (MI). TRMC with its unique options (excitation sources, environmental control, frequency modulation, etc.) provides not only accelerated experimental screening of OPV and PSC materials but also a versatile route toward shedding light on their charge carrier dynamics. Furthermore, MI powered by machine learning is shown to allow extremely high-throughput exploration in the large molecular space, which is compatible with experimental screening and combinatorial synthesis.