Designing in the Face of Uncertainty: Exploiting Electronic Structure and Machine Learning Models for Discovery in Inorganic Chemistry

Advancing Molecular-Scale Logic Devices through Multistage Switching in a Luminescent Bimetallic Ru(II)-Terpyridine Complex

Stimuli-responsive multistep switching phenomena of a luminescent bimetallic Ru(II) complex are employed herein to fabricate multiple configurable logic devices. The complex exhibits "off-on" and "on-off" emission switching upon alternative treatment with visible and UV light. Additionally, remarkable augmentation of the rate as well as quantum yield of photoisomerization was achieved via the use of a chemical oxidant (Ce4+) as well as a reductant (metallic sodium). Upon exploiting the emission spectral response of the complex, several advanced Boolean logic functions, including IMPLICATION as well as 2-input 2-output and 3-input 2-output complex combinational logic gates, are successfully implemented. Additionally, by utilizing the vast efficacy of Python, a novel "logic_circuit" model is devised that is capable of making accurate decisions under the influence of various input combinations. This model transcends traditional Boolean logic gates, offering flexibility and intuition to design logical functions tailored to specific chemical contexts. By integrating principles of logic circuits with chemical processes, this innovative approach enables structure determination of the chemical states based on input conditions, thereby unlocking avenues for exploring intricate interactions and reactions beyond conventional Boolean logic paradigms.

Using Machine Learning to Predict the Antibacterial Activity of Ruthenium Complexes

Rising antimicrobial resistance (AMR) and lack of innovation in the antibiotic pipeline necessitate novel approaches to discovering new drugs. Metal complexes have proven to be promising antimicrobial compounds, but the number of studied compounds is still low compared to the millions of organic molecules investigated so far. Lately, machine learning (ML) has emerged as a valuable tool for guiding the design of small organic molecules, potentially even in low-data scenarios. For the first time, we extend the application of ML to the discovery of metal-based medicines. Utilising 288 modularly synthesized ruthenium arene Schiff-base complexes and their antibacterial properties, a series of ML models were trained. The models perform well and are used to predict the activity of 54 new compounds. These displayed a 5.7x higher hit-rate (53.7 %) against methicillin-resistant Staphylococcus aureus (MRSA) compared to the original library (9.4 %), demonstrating that ML can be applied to improve the success-rates in the search of new metalloantibiotics. This work paves the way for more ambitious applications of ML in the field of metal-based drug discovery.

The prediction of single-molecule magnet properties via deep learning

This paper uses deep learning to present a proof-of-concept for data-driven chemistry in single-molecule magnets (SMMs). Previous discussions within SMM research have proposed links between molecular structures (crystal structures) and single-molecule magnetic properties; however, these have only interpreted the results. Therefore, this study introduces a data-driven approach to predict the properties of SMM structures using deep learning. The deep-learning model learns the structural features of the SMM molecules by extracting the single-molecule magnetic properties from the 3D coordinates presented in this paper. The model accurately determined whether a molecule was a single-molecule magnet, with an accuracy rate of approximately 70% in predicting the SMM properties. The deep-learning model found SMMs from 20 000 metal complexes extracted from the Cambridge Structural Database. Using deep-learning models for predicting SMM properties and guiding the design of novel molecules is promising.

Machine Learning Prediction of the Experimental Transition Temperature of Fe(II) Spin-Crossover Complexes

Spin-crossover (SCO) complexes are materials that exhibit changes in the spin state in response to external stimuli, with potential applications in molecular electronics. It is challenging to know a priori how to design ligands to achieve the delicate balance of entropic and enthalpic contributions needed to tailor a transition temperature close to room temperature. We leverage the SCO complexes from the previously curated SCO-95 data set [Vennelakanti et al. J. Chem. Phys. 159, 024120 (2023)] to train three machine learning (ML) models for transition temperature (T1/2) prediction using graph-based revised autocorrelations as features. We perform feature selection using random forest-ranked recursive feature addition (RF-RFA) to identify the features essential to model transferability. Of the ML models considered, the full feature set RF and recursive feature addition RF models perform best, achieving moderate correlation to experimental T1/2 values. We then compare ML T1/2 predictions to those from three previously identified best-performing density functional approximations (DFAs) which accurately predict SCO behavior across SCO-95, finding that the ML models predict T1/2 more accurately than the best-performing DFAs. In addition, we study ML model predictions for a set of 18 SCO complexes for which only estimated T1/2 values are available. Upon excluding outliers from this set, the RF-RFA RF model shows a strong correlation to estimated T1/2 values with a Pearson's r of 0.82. In contrast, DFA-predicted T1/2 values have large errors and show no correlation to estimated T1/2 values over the same set of complexes. Overall, our study demonstrates slightly superior performance of ML models in comparison with some of the best-performing DFAs, and we expect ML models to improve further as larger data sets of SCO complexes are curated and become available for model training.

ReaLigands: A Ligand Library Cultivated from Experiment and Intended for Molecular Computational Catalyst Design

Computational catalyst design requires identification of a metal and ligand that together result in the desired reaction reactivity and/or selectivity. A major impediment to translating computational designs to experiments is evaluating ligands that are likely to be synthesized. Here, we provide a solution to this impediment with our ReaLigands library that contains >30,000 monodentate, bidentate (didentate), tridentate, and larger ligands cultivated by dismantling experimentally reported crystal structures. Individual ligands from mononuclear crystal structures were identified using a modified depth-first search algorithm and charge was assigned using a machine learning model based on quantum-chemical calculated features. In the library, ligands are sorted based on direct ligand-to-metal atomic connections and on denticity. Representative principal component analysis (PCA) and uniform manifold approximation and projection (UMAP) analyses were used to analyze several tridentate ligand categories, which revealed both the diversity of ligands and connections between ligand categories. We also demonstrated the utility of this library by implementing it with our building and optimization tools, which resulted in the very rapid generation of barriers for 750 bidentate ligands for Rh-hydride ethylene migratory insertion.

HiREX: High-Throughput Reactivity Exploration for Extended Databases of Transition-Metal Catalysts

A method is introduced for the automated analysis of reactivity exploration for extended in silico databases of transition-metal catalysts. The proposed workflow is designed to tackle two key challenges for bias-free mechanistic explorations on large databases of catalysts: (1) automated exploration of the chemical space around each catalyst with unique structural and chemical features and (2) automated analysis of the resulting large chemical data sets. To address these challenges, we have extended the application of our previously developed ReNeGate method for bias-free reactivity exploration and implemented an automated analysis procedure to identify the classes of reactivity patterns within specific catalyst groups. Our procedure applied to an extended series of representative Mn(I) pincer complexes revealed correlations between structural and reactive features, pointing to new channels for catalyst transformation under the reaction conditions. Such an automated high-throughput virtual screening of systematically generated hypothetical catalyst data sets opens new opportunities for the design of high-performance catalysts as well as an accelerated method for expert bias-free high-throughput in silico reactivity exploration.

Artificial Intelligence in Physical Sciences: Symbolic Regression Trends and Perspectives

Symbolic regression (SR) is a machine learning-based regression method based on genetic programming principles that integrates techniques and processes from heterogeneous scientific fields and is capable of providing analytical equations purely from data. This remarkable characteristic diminishes the need to incorporate prior knowledge about the investigated system. SR can spot profound and elucidate ambiguous relations that can be generalizable, applicable, explainable and span over most scientific, technological, economical, and social principles. In this review, current state of the art is documented, technical and physical characteristics of SR are presented, the available programming techniques are investigated, fields of application are explored, and future perspectives are discussed.

Supplementary Information

The online version contains supplementary material available at 10.1007/s11831-023-09922-z.

Insights into the deviation from piecewise linearity in transition metal complexes from supervised machine learning models

Virtual high-throughput screening (VHTS) and machine learning (ML) with density functional theory (DFT) suffer from inaccuracies from the underlying density functional approximation (DFA). Many of these inaccuracies can be traced to the lack of derivative discontinuity that leads to a curvature in the energy with electron addition or removal. Over a dataset of nearly one thousand transition metal complexes typical of VHTS applications, we computed and analyzed the average curvature (i.e., deviation from piecewise linearity) for 23 density functional approximations spanning multiple rungs of "Jacob's ladder". While we observe the expected dependence of the curvatures on Hartree-Fock exchange, we note limited correlation of curvature values between different rungs of "Jacob's ladder". We train ML models (i.e., artificial neural networks or ANNs) to predict the curvature and the associated frontier orbital energies for each of these 23 functionals and then interpret differences in curvature among the different DFAs through analysis of the ML models. Notably, we observe spin to play a much more important role in determining the curvature of range-separated and double hybrids in comparison to semi-local functionals, explaining why curvature values are weakly correlated between these and other families of functionals. Over a space of 187.2k hypothetical compounds, we use our ANNs to pinpoint DFAs for which representative transition metal complexes have near-zero curvature with low uncertainty, demonstrating an approach to accelerate screening of complexes with targeted optical gaps.

Molecular-orbital-based machine learning for open-shell and multi-reference systems with kernel addition Gaussian process regression

We introduce a novel machine learning strategy, kernel addition Gaussian process regression (KA-GPR), in molecular-orbital-based machine learning (MOB-ML) to learn the total correlation energies of general electronic structure theories for closed- and open-shell systems by introducing a machine learning strategy. The learning efficiency of MOB-ML(KA-GPR) is the same as the original MOB-ML method for the smallest criegee molecule, which is a closed-shell molecule with multi-reference characters. In addition, the prediction accuracies of different small free radicals could reach the chemical accuracy of 1 kcal/mol by training on one example structure. Accurate potential energy surfaces for the H₁₀ chain (closed-shell) and water OH bond dissociation (open-shell) could also be generated by MOB-ML(KA-GPR). To explore the breadth of chemical systems that KA-GPR can describe, we further apply MOB-ML to accurately predict the large benchmark datasets for closed- (QM9, QM7b-T, and GDB-13-T) and open-shell (QMSpin) molecules.

Machine learning, artificial intelligence, and chemistry: how smart algorithms are reshaping simulation and the laboratory

Machine learning and artificial intelligence are increasingly gaining in prominence through image analysis, language processing, and automation, to name a few applications. Machine learning is also making profound changes in chemistry. From revisiting decades-old analytical techniques for the purpose of creating better calibration curves, to assisting and accelerating traditional in silico simulations, to automating entire scientific workflows, to being used as an approach to deduce underlying physics of unexplained chemical phenomena, machine learning and artificial intelligence are reshaping chemistry, accelerating scientific discovery, and yielding new insights. This review provides an overview of machine learning and artificial intelligence from a chemist’s perspective and focuses on a number of examples of the use of these approaches in computational chemistry and in the laboratory.

Bi-LSTM-Augmented Deep Neural Network for Multi-Gbps VCSEL-Based Visible Light Communication Link

With the remarkable advances in vertical-cavity surface-emitting lasers (VCSELs) in recent decades, VCSELs have been considered promising light sources in the field of optical wireless communications. However, off-the-shelf VCSELs still have a limited modulation bandwidth to meet the multi-Gb/s data rate requirements imposed on the next-generation wireless communication system. Recently, employing machine learning (ML) techniques as a method to tackle such issues has been intriguing for researchers in wireless communication. In this work, through a systematic analysis, it is shown that the ML technique is also very effective in VCSEL-based visible light communication. Using a commercial VCSEL and bidirectional long short-term memory (Bi-LSTM)-based ML scheme, a high-speed visible light communication (VLC) link with a data rate of 13.5 Gbps is demonstrated, which is the fastest single channel result from a cost-effective, off-the-shelf VCSEL device, to the best of the authors' knowledge.

New Strategies for Direct Methane-to-Methanol Conversion from Active Learning Exploration of 16 Million Catalysts

Despite decades of effort, no earth-abundant homogeneous catalysts have been discovered that can selectively oxidize methane to methanol. We exploit active learning to simultaneously optimize methane activation and methanol release calculated with machine learning-accelerated density functional theory in a space of 16 M candidate catalysts including novel macrocycles. By constructing macrocycles from fragments inspired by synthesized compounds, we ensure synthetic realism in our computational search. Our large-scale search reveals that low-spin Fe(II) compounds paired with strong-field (e.g., P or S-coordinating) ligands have among the best energetic tradeoffs between hydrogen atom transfer (HAT) and methanol release. This observation contrasts with prior efforts that have focused on high-spin Fe(II) with weak-field ligands. By decoupling equatorial and axial ligand effects, we determine that negatively charged axial ligands are critical for more rapid release of methanol and that higher-valency metals [i.e., M(III) vs M(II)] are likely to be rate-limited by slow methanol release. With full characterization of barrier heights, we confirm that optimizing for HAT does not lead to large oxo formation barriers. Energetic span analysis reveals designs for an intermediate-spin Mn(II) catalyst and a low-spin Fe(II) catalyst that are predicted to have good turnover frequencies. Our active learning approach to optimize two distinct reaction energies with efficient global optimization is expected to be beneficial for the search of large catalyst spaces where no prior designs have been identified and where linear scaling relationships between reaction energies or barriers may be limited or unknown.

Machine Learning for the Discovery, Design, and Engineering of Materials

Machine learning (ML) has become a part of the fabric of high-throughput screening and computational discovery of materials. Despite its increasingly central role, challenges remain in fully realizing the promise of ML. This is especially true for the practical acceleration of the engineering of robust materials and the development of design strategies that surpass trial and error or high-throughput screening alone. Depending on the quantity being predicted and the experimental data available, ML can either outperform physics-based modes, be used to accelerate such models, or be integrated with them to improve their performance. We cover recent advances in algorithms and in their application that are starting to make inroads toward (a) the discovery of new materials through large-scale enumerative screening, (b) the design of materials through identification of rules and principles that govern materials properties, and (c) the engineering of practical materials by satisfying multiple objectives. We conclude with opportunities for further advancement to realize ML as a widespread tool for practical computational materials design. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

ChemSpaX: exploration of chemical space by automated functionalization of molecular scaffold

Exploration of the local chemical space of molecular scaffolds by post-functionalization (PF) is a promising route to discover novel molecules with desired structure and function. PF with rationally chosen substituents based on known electronic and steric properties is a commonly used experimental and computational strategy in screening, design and optimization of catalytic scaffolds. Automated generation of reasonably accurate geometric representations of post-functionalized molecular scaffolds is highly desirable for data-driven applications. However, automated PF of transition metal (TM) complexes remains challenging. In this work a Python-based workflow, ChemSpaX, that is aimed at automating the PF of a given molecular scaffold with special emphasis on TM complexes, is introduced. In three representative applications of ChemSpaX by comparing with DFT and DFT-B calculations, we show that the generated structures have a reasonable quality for use in computational screening applications. Furthermore, we show that ChemSpaX generated geometries can be used in machine learning applications to accurately predict DFT computed HOMO-LUMO gaps for transition metal complexes. ChemSpaX is open-source and aims to bolster and democratize the efforts of the scientific community towards data-driven chemical discovery.

John P, Gorai P. Predicting energy and stability of known and hypothetical crystals using graph neural network

The discovery of new inorganic materials in unexplored chemical spaces necessitates calculating total energy quickly and with sufficient accuracy. Machine learning models that provide such a capability for both ground-state (GS) and higher-energy structures would be instrumental in accelerated screening. Here, we demonstrate the importance of a balanced training dataset of GS and higher-energy structures to accurately predict total energies using a generic graph neural network architecture. Using ∼ 16,500 density functional theory calculations from the National Renewable Energy Laboratory (NREL) Materials Database and ∼ 11,000 calculations for hypothetical structures as our training database, we demonstrate that our model satisfactorily ranks the structures in the correct order of total energies for a given composition. Furthermore, we present a thorough error analysis to explain failure modes of the model, including both prediction outliers and occasional inconsistencies in the training data. By examining intermediate layers of the model, we analyze how the model represents learned structures and properties.

Solving the Schrödinger equation using program synthesis

We demonstrate that a program synthesis approach based on a linear code representation can be used to generate algorithms that approximate the ground-state solutions of one-dimensional time-independent Schrödinger equations constructed with bound polynomial potential energy surfaces (PESs). Here, an algorithm is constructed as a linear series of instructions operating on a set of input vectors, matrices, and constants that define the problem characteristics, such as the PES. Discrete optimization is performed using simulated annealing in order to identify sequences of code-lines, operating on the program inputs that can reproduce the expected ground-state wavefunctions ψ(x) for a set of target PESs. The outcome of this optimization is not simply a mathematical function approximating ψ(x) but is, instead, a complete algorithm that converts the input vectors describing the system into a ground-state solution of the Schrödinger equation. These initial results point the way toward an alternative route for developing novel algorithms for quantum chemistry applications.

Deciphering Cryptic Behavior in Bimetallic Transition-Metal Complexes with Machine Learning

We demonstrate an alternative, data-driven approach to uncovering structure-property relationships for the rational design of heterobimetallic transition-metal complexes that exhibit metal-metal bonding. We tailor graph-based representations of the metal-local environment for these complexes for use in multiple linear regression and kernel ridge regression (KRR) models. We curate a set of 28 experimentally characterized complexes to develop a multiple linear regression model for oxidation potentials. We achieve good accuracy (mean absolute error of 0.25 V) and preserve transferability to unseen experimental data with a new ligand structure. We also train a KRR model on a subset of 330 structurally characterized heterobimetallics to predict the degree of metal-metal bonding. This KRR model predicts relative metal-metal bond lengths in the test set to within 5%, and analysis of key features reveals the fundamental atomic contributions (e.g., the valence electron configuration) that most strongly influence the behavior of these complexes. Our work provides guidance for rational bimetallic design, suggesting that properties, including the formal shortness ratio, should be transferable from one period to another.

Machine learning to tame divergent density functional approximations: a new path to consensus materials design principles

Virtual high-throughput screening (VHTS) with density functional theory (DFT) and machine-learning (ML)-acceleration is essential in rapid materials discovery. By necessity, efficient DFT-based workflows are carried out with a single density functional approximation (DFA). Nevertheless, properties evaluated with different DFAs can be expected to disagree for cases with challenging electronic structure (e.g., open-shell transition-metal complexes, TMCs) for which rapid screening is most needed and accurate benchmarks are often unavailable. To quantify the effect of DFA bias, we introduce an approach to rapidly obtain property predictions from 23 representative DFAs spanning multiple families, “rungs” (e.g., semi-local to double hybrid) and basis sets on over 2000 TMCs. Although computed property values (e.g., spin state splitting and frontier orbital gap) differ by DFA, high linear correlations persist across all DFAs. We train independent ML models for each DFA and observe convergent trends in feature importance, providing DFA-invariant, universal design rules. We devise a strategy to train artificial neural network (ANN) models informed by all 23 DFAs and use them to predict properties (e.g., spin-splitting energy) of over 187k TMCs. By requiring consensus of the ANN-predicted DFA properties, we improve correspondence of computational lead compounds with literature-mined, experimental compounds over the typically employed single-DFA approach.

Machine learning (ML)-based feature analysis reveals universal design rules regardless of density functional choices. Using the consensus among multiple functionals, we identify robust lead complexes in ML-accelerated chemical discovery.

Computational Discovery of Transition-metal Complexes: From High-throughput Screening to Machine Learning

Transition-metal complexes are attractive targets for the design of catalysts and functional materials. The behavior of the metal-organic bond, while very tunable for achieving target properties, is challenging to predict and necessitates searching a wide and complex space to identify needles in haystacks for target applications. This review will focus on the techniques that make high-throughput search of transition-metal chemical space feasible for the discovery of complexes with desirable properties. The review will cover the development, promise, and limitations of "traditional" computational chemistry (i.e., force field, semiempirical, and density functional theory methods) as it pertains to data generation for inorganic molecular discovery. The review will also discuss the opportunities and limitations in leveraging experimental data sources. We will focus on how advances in statistical modeling, artificial intelligence, multiobjective optimization, and automation accelerate discovery of lead compounds and design rules. The overall objective of this review is to showcase how bringing together advances from diverse areas of computational chemistry and computer science have enabled the rapid uncovering of structure-property relationships in transition-metal chemistry. We aim to highlight how unique considerations in motifs of metal-organic bonding (e.g., variable spin and oxidation state, and bonding strength/nature) set them and their discovery apart from more commonly considered organic molecules. We will also highlight how uncertainty and relative data scarcity in transition-metal chemistry motivate specific developments in machine learning representations, model training, and in computational chemistry. Finally, we will conclude with an outlook of areas of opportunity for the accelerated discovery of transition-metal complexes.

Trends in computational molecular catalyst design

Computational methods have emerged as a powerful tool to augment traditional experimental molecular catalyst design by providing useful predictions of catalyst performance and decreasing the time needed for catalyst screening. In this perspective, we discuss three approaches for computational molecular catalyst design: (i) the reaction mechanism-based approach that calculates all relevant elementary steps, finds the rate and selectivity determining steps, and ultimately makes predictions on catalyst performance based on kinetic analysis, (ii) the descriptor-based approach where physical/chemical considerations are used to find molecular properties as predictors of catalyst performance, and (iii) the data-driven approach where statistical analysis as well as machine learning (ML) methods are used to obtain relationships between available data/features and catalyst performance. Following an introduction to these approaches, we cover their strengths and weaknesses and highlight some recent key applications. Furthermore, we present an outlook on how the currently applied approaches may evolve in the near future by addressing how recent developments in building automated computational workflows and implementing advanced ML models hold promise for reducing human workload, eliminating human bias, and speeding up computational catalyst design at the same time. Finally, we provide our viewpoint on how some of the challenges associated with the up-and-coming approaches driven by automation and ML may be resolved.

Putting Density Functional Theory to the Test in Machine-Learning-Accelerated Materials Discovery

Accelerated discovery with machine learning (ML) has begun to provide the advances in efficiency needed to overcome the combinatorial challenge of computational materials design. Nevertheless, ML-accelerated discovery both inherits the biases of training data derived from density functional theory (DFT) and leads to many attempted calculations that are doomed to fail. Many compelling functional materials and catalytic processes involve strained chemical bonds, open-shell radicals and diradicals, or metal-organic bonds to open-shell transition-metal centers. Although promising targets, these materials present unique challenges for electronic structure methods and combinatorial challenges for their discovery. In this Perspective, we describe the advances needed in accuracy, efficiency, and approach beyond what is typical in conventional DFT-based ML workflows. These challenges have begun to be addressed through ML models trained to predict the results of multiple methods or the differences between them, enabling quantitative sensitivity analysis. For DFT to be trusted for a given data point in a high-throughput screen, it must pass a series of tests. ML models that predict the likelihood of calculation success and detect the presence of strong correlation will enable rapid diagnoses and adaptation strategies. These "decision engines" represent the first steps toward autonomous workflows that avoid the need for expert determination of the robustness of DFT-based materials discoveries.

Machine Learning-Aided Crystal Facet Rational Design with Ionic Liquid Controllable Synthesis

Crystallographic facets in a crystal carry interior properties and proffer rich functionalities in a wide range of application areas. However, rational prediction, on-demand customization, and accurate synthesis of facets and facet junctions of a crystal are enormously desirable but still challenging. Herein, a framework of machine learning (ML)-aided crystal facet design with ionic liquid controllable synthesis is developed and then demonstrated with the star-material anatase TiO₂ . Aided by employing ML to acquire surface energies from facet junction datasource, the relationships between surface energy and growth conditions based on the Langmuir adsorption isotherm are unveiled, enabling to develop controllable facet synthetic strategies. These strategies are successfully verified after applied for synthesizing TiO₂ crystals with custom crystal facets and facet junctions under tuning ionic liquid [bmim][BF₄ ] experimental conditions. Therefore, this innovative framework integrates data-intensive rational design and experimental controllable synthesis to develop and customize crystallographic facets and facet junctions. This proves the feasibility of an intelligent chemistry future to accelerate the discovery of facet-governed functional material candidates.

The Cascade Reactions of Indigo with Propargyl Substrates for Heterocyclic and Photophysical Diversity

The synthesis of structurally diverse heterocycles for chemical space exploration was achieved via the cascade reactions of indigo with propargylic electrophiles. New pyrazinodiindolodione, naphthyridinedione, azepinodiindolone, oxazinoindolone and pyrrolodione products were prepared in one pot reactions by varying the leaving group (-Cl, -Br, -OMs, -OTs) or propargyl terminal functionality (-H, -Me, -Ph, -Ar). Mechanistic and density functional theory studies revealed that the unsaturated propargyl moiety can behave as an electrophile when aromatic terminal substitutions are made, and therefore competes with leaving group substitution for new outcomes. Selected products from the cascade reactions were investigated for their absorption and fluorescence properties, including transient absorption spectroscopy. This revealed polarity dependent excited state relaxation pathways, fluorescence, and triplet formation, thus highlighting these reactions as a means to access diverse functional materials rapidly.

Navigating Transition-Metal Chemical Space: Artificial Intelligence for First-Principles Design

The variability of chemical bonding in open-shell transition-metal complexes not only motivates their study as functional materials and catalysts but also challenges conventional computational modeling tools. Here, tailoring ligand chemistry can alter preferred spin or oxidation states as well as electronic structure properties and reactivity, creating vast regions of chemical space to explore when designing new materials atom by atom. Although first-principles density functional theory (DFT) remains the workhorse of computational chemistry in mechanism deduction and property prediction, it is of limited use here. DFT is both far too computationally costly for widespread exploration of transition-metal chemical space and also prone to inaccuracies that limit its predictive performance for localized d electrons in transition-metal complexes. These challenges starkly contrast with the well-trodden regions of small-organic-molecule chemical space, where the analytical forms of molecular mechanics force fields and semiempirical theories have for decades accelerated the discovery of new molecules, accurate DFT functional performance has been demonstrated, and gold-standard methods from correlated wavefunction theory can predict experimental results to chemical accuracy.The combined promise of transition-metal chemical space exploration and lack of established tools has mandated a distinct approach. In this Account, we outline the path we charted in exploration of transition-metal chemical space starting from the first machine learning (ML) models (i.e., artificial neural network and kernel ridge regression) and representations for the prediction of open-shell transition-metal complex properties. The distinct importance of the immediate coordination environment of the metal center as well as the lack of low-level methods to accurately predict structural properties in this coordination environment first motivated and then benefited from these ML models and representations. Once developed, the recipe for prediction of geometric, spin state, and redox potential properties was straightforwardly extended to a diverse range of other properties, including in catalysis, computational "feasibility", and the gas separation properties of periodic metal-organic frameworks. Interpretation of selected features most important for model prediction revealed new ways to encapsulate design rules and confirmed that models were robustly mapping essential structure-property relationships. Encountering the special challenge of ensuring that good model performance could generalize to new discovery targets motivated investigation of how to best carry out model uncertainty quantification. Distance-based approaches, whether in model latent space or in carefully engineered feature space, provided intuitive measures of the domain of applicability. With all of these pieces together, ML can be harnessed as an engine to tackle the large-scale exploration of transition-metal chemical space needed to satisfy multiple objectives using efficient global optimization methods. In practical terms, bringing these artificial intelligence tools to bear on the problems of transition-metal chemical space exploration has resulted in ML-model assessments of large, multimillion compound spaces in minutes and validated new design leads in weeks instead of decades.

Machine Learning in Computational Surface Science and Catalysis: Case Studies on Water and Metal-Oxide Interfaces

The goal of many computational physicists and chemists is the ability to bridge the gap between atomistic length scales of about a few multiples of an Ångström (Å), i. e., 10⁻¹⁰ m, and meso- or macroscopic length scales by virtue of simulations. The same applies to timescales. Machine learning techniques appear to bring this goal into reach. This work applies the recently published on-the-fly machine-learned force field techniques using a variant of the Gaussian approximation potentials combined with Bayesian regression and molecular dynamics as efficiently implemented in the Vienna ab initio simulation package, VASP. The generation of these force fields follows active-learning schemes. We apply these force fields to simple oxides such as MgO and more complex reducible oxides such as iron oxide, examine their generalizability, and further increase complexity by studying water adsorption on these metal oxide surfaces. We successfully examined surface properties of pristine and reconstructed MgO and Fe₃O₄ surfaces. However, the accurate description of water–oxide interfaces by machine-learned force fields, especially for iron oxides, remains a field offering plenty of research opportunities.

tmQM Dataset-Quantum Geometries and Properties of 86k Transition Metal Complexes

We report the transition metal quantum mechanics (tmQM) data set, which contains the geometries and properties of a large transition metal-organic compound space. tmQM comprises 86,665 mononuclear complexes extracted from the Cambridge Structural Database, including Werner, bioinorganic, and organometallic complexes based on a large variety of organic ligands and 30 transition metals (the 3d, 4d, and 5d from groups 3 to 12). All complexes are closed-shell, with a formal charge in the range {+1, 0, -1}e. The tmQM data set provides the Cartesian coordinates of all metal complexes optimized at the GFN2-xTB level, and their molecular size, stoichiometry, and metal node degree. The quantum properties were computed at the DFT(TPSSh-D3BJ/def2-SVP) level and include the electronic and dispersion energies, highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies, HOMO/LUMO gap, dipole moment, and natural charge of the metal center; GFN2-xTB polarizabilities are also provided. Pairwise representations showed the low correlation between these properties, providing nearly continuous maps with unusual regions of the chemical space, for example, complexes combining large polarizabilities with wide HOMO/LUMO gaps and complexes combining low-energy HOMO orbitals with electron-rich metal centers. The tmQM data set can be exploited in the data-driven discovery of new metal complexes, including predictive models based on machine learning. These models may have a strong impact on the fields in which transition metal chemistry plays a key role, for example, catalysis, organic synthesis, and materials science. tmQM is an open data set that can be downloaded free of charge from https://github.com/bbskjelstad/tmqm.

The Role of Machine Learning in the Understanding and Design of Materials

Developing algorithmic approaches for the rational design and discovery of materials can enable us to systematically find novel materials, which can have huge technological and social impact. However, such rational design requires a holistic perspective over the full multistage design process, which involves exploring immense materials spaces, their properties, and process design and engineering as well as a techno-economic assessment. The complexity of exploring all of these options using conventional scientific approaches seems intractable. Instead, novel tools from the field of machine learning can potentially solve some of our challenges on the way to rational materials design. Here we review some of the chief advancements of these methods and their applications in rational materials design, followed by a discussion on some of the main challenges and opportunities we currently face together with our perspective on the future of rational materials design and discovery.

Influence of Electronic Structure Modeling and Junction Structure on First-Principles Chiral Induced Spin Selectivity

We have carried out a comprehensive study of the influence of electronic structure modeling and junction structure description on the first-principles calculation of the spin polarization in molecular junctions caused by the chiral induced spin selectivity (CISS) effect. We explore the limits and the sensitivity to modeling decisions of a Landauer/Green's function/two-component density functional theory approach to CISS. We find that although the CISS effect is entirely attributed in the literature to molecular spin filtering, spin-orbit coupling being partially inherited from the metal electrodes plays an important role in our calculations on ideal carbon helices, even though this effect cannot explain the experimental conductance results. Its magnitude depends considerably on the shape, size, and material of the metal clusters modeling the electrodes. Also, a pronounced dependence on the specific description of exchange interaction and spin-orbit coupling is manifest in our approach. This is important because the interplay between exchange effects and spin-orbit coupling may play an important role in the description of the junction magnetic response. Our calculations are relevant for the whole field of spin-polarized electron transport and electron transfer, because there is still an open discussion in the literature about the detailed underlying mechanism and the magnitude of physical parameters that need to be included to achieve a consistent description of the CISS effect: seemingly good quantitative agreement between simulation and the experiment can be caused by error compensation, because spin polarization as contained in a Landauer/Green's function/two-component density functional theory approach depends strongly on computational and structural parameters.

Rapid Detection of Strong Correlation with Machine Learning for Transition-Metal Complex High-Throughput Screening

Despite its widespread use in chemical discovery, approximate density functional theory (DFT) is poorly suited to many targets, such as those containing open-shell, 3d transition metals that can be expected to have strong multireference (MR) character. For discovery workflows to be predictive, we need automated, low-cost methods that can distinguish the regions of chemical space where DFT should be applied from those where it should not. We curate more than 4800 open-shell transition-metal complexes up to hundreds of atoms in size from prior high-throughput DFT studies and evaluate affordable, finite-temperature DFT fractional occupation number (FON)-based MR diagnostics. We show that intuitive measures of strong correlation (i.e., the HOMO-LUMO gap) are not predictive of MR character as judged by FON-based diagnostics. Analysis of independently trained machine learning (ML) models to predict HOMO-LUMO gaps and FON-based diagnostics reveals differences in the metal and ligand sensitivity of the two quantities. We use our trained ML models to rapidly evaluate MR character over a space of ∼187000 theoretical complexes, identifying large-scale trends in spin-state-dependent MR character and finding small HOMO-LUMO gap complexes while ensuring low MR character.

Understanding the diversity of the metal-organic framework ecosystem

Millions of distinct metal-organic frameworks (MOFs) can be made by combining metal nodes and organic linkers. At present, over 90,000 MOFs have been synthesized and over 500,000 predicted. This raises the question whether a new experimental or predicted structure adds new information. For MOF chemists, the chemical design space is a combination of pore geometry, metal nodes, organic linkers, and functional groups, but at present we do not have a formalism to quantify optimal coverage of chemical design space. In this work, we develop a machine learning method to quantify similarities of MOFs to analyse their chemical diversity. This diversity analysis identifies biases in the databases, and we show that such bias can lead to incorrect conclusions. The developed formalism in this study provides a simple and practical guideline to see whether new structures will have the potential for new insights, or constitute a relatively small variation of existing structures.

Electronic Structure Modeling of Metal-Organic Frameworks

Owing to their molecular building blocks, yet highly crystalline nature, metal-organic frameworks (MOFs) sit at the interface between molecule and material. Their diverse structures and compositions enable them to be useful materials as catalysts in heterogeneous reactions, electrical conductors in energy storage and transfer applications, chromophores in photoenabled chemical transformations, and beyond. In all cases, density functional theory (DFT) and higher-level methods for electronic structure determination provide valuable quantitative information about the electronic properties that underpin the functions of these frameworks. However, there are only two general modeling approaches in conventional electronic structure software packages: those that treat materials as extended, periodic solids, and those that treat materials as discrete molecules. Each approach has features and benefits; both have been widely employed to understand the emergent chemistry that arises from the formation of the metal-organic interface. This Review canvases these approaches to date, with emphasis placed on the application of electronic structure theory to explore reactivity and electron transfer using periodic, molecular, and embedded models. This includes (i) computational chemistry considerations such as how functional, k-grid, and other model variables are selected to enable insights into MOF properties, (ii) extended solid models that treat MOFs as materials rather than molecules, (iii) the mechanics of cluster extraction and subsequent chemistry enabled by these molecular models, (iv) catalytic studies using both solids and clusters thereof, and (v) embedded, mixed-method approaches, which simulate a fraction of the material using one level of theory and the remainder of the material using another dissimilar theoretical implementation.

An adaptive design approach for defects distribution modeling in materials from first-principle calculations

Designing and understanding the mechanism of non-stoichiometric materials with enhanced properties is challenging, both experimentally and even computationally, due to the large number of chemical spaces and their distributions through the material. In the current work, it is proposed a Machine Learning approach coupled with the Efficient Global Optimization (EGO) method-an Adaptive Design (AD)-to model local defects in materials from first-principle calculations. Our method takes into account the smallest sample set as possible, envisioning the material defect structure relationship with target properties for new insights. As an example, the AD framework allows us to study the stability and the structure of the modified goethite (Fe_0.875Al_0.125OOH) by considering a proper defect distribution, from first-principle calculations. The chemical space search for the modified goethite was evaluated by starting from different sizes and configurations of the samples as well as different surrogate models (ANN and Gaussian Process; GP), acquisition functions, and descriptors. Our results show that the same local solution of several defect arrangements in Fe_0.875Al_0.125OOH is found regardless of the initial sample and regression model. This indicates the efficiency of our search method. We also discuss the role of the descriptors in the accelerated global search for defects in material modeling. We conclude that the AD method applied in material defects is a successful approach in automating the search within huge chemical spaces from first-principle calculations by considering small samples. This method can be applied to mechanistic elucidation of non-stoichiometric materials, solid solutions, alloys, and Schottky and Frenkel defects, essential for material design and discovery. Graphical abstract.

Autonomous Discovery in the Chemical Sciences Part II: Outlook

This two-part Review examines how automation has contributed to different aspects of discovery in the chemical sciences. In this second part, we reflect on a selection of exemplary studies. It is increasingly important to articulate what the role of automation and computation has been in the scientific process and how that has or has not accelerated discovery. One can argue that even the best automated systems have yet to "discover" despite being incredibly useful as laboratory assistants. We must carefully consider how they have been and can be applied to future problems of chemical discovery in order to effectively design and interact with future autonomous platforms. The majority of this Review defines a large set of open research directions, including improving our ability to work with complex data, build empirical models, automate both physical and computational experiments for validation, select experiments, and evaluate whether we are making progress towards the ultimate goal of autonomous discovery. Addressing these practical and methodological challenges will greatly advance the extent to which autonomous systems can make meaningful discoveries.

Machine learning dihydrogen activation in the chemical space surrounding Vaska's complex

Homogeneous catalysis using transition metal complexes is ubiquitously used for organic synthesis, as well as technologically relevant in applications such as water splitting and CO2 reduction. The key steps underlying homogeneous catalysis require a specific combination of electronic and steric effects from the ligands bound to the metal center. Finding the optimal combination of ligands is a challenging task due to the exceedingly large number of possibilities and the non-trivial ligand-ligand interactions. The classic example of Vaska's complex, trans-[Ir(PPh3)2(CO)(Cl)], illustrates this scenario. The ligands of this species activate iridium for the oxidative addition of hydrogen, yielding the dihydride cis-[Ir(H)2(PPh3)2(CO)(Cl)] complex. Despite the simplicity of this system, thousands of derivatives can be formulated for the activation of H2, with a limited number of ligands belonging to the same general categories found in the original complex. In this work, we show how DFT and machine learning (ML) methods can be combined to enable the prediction of reactivity within large chemical spaces containing thousands of complexes. In a space of 2574 species derived from Vaska's complex, data from DFT calculations are used to train and test ML models that predict the H2-activation barrier. In contrast to experiments and calculations requiring several days to be completed, the ML models were trained and used on a laptop on a time-scale of minutes. As a first approach, we combined Bayesian-optimized artificial neural networks (ANN) with features derived from autocorrelation and deltametric functions. The resulting ANNs achieved high accuracies, with mean absolute errors (MAE) between 1 and 2 kcal mol-1, depending on the size of the training set. By using a Gaussian process (GP) model trained with a set of selected features, including fingerprints, accuracy was further enhanced. Remarkably, this GP model minimized the MAE below 1 kcal mol-1, by using only 20% or less of the data available for training. The gradient boosting (GB) method was also used to assess the relevance of the features, which was used for both feature selection and model interpretation purposes. Features accounting for chemical composition, atom size and electronegativity were found to be the most determinant in the predictions. Further, the ligand fragments with the strongest influence on the H2-activation barrier were identified.

Accurate Multiobjective Design in a Space of Millions of Transition Metal Complexes with Neural-Network-Driven Efficient Global Optimization

The accelerated discovery of materials for real world applications requires the achievement of multiple design objectives. The multidimensional nature of the search necessitates exploration of multimillion compound libraries over which even density functional theory (DFT) screening is intractable. Machine learning (e.g., artificial neural network, ANN, or Gaussian process, GP) models for this task are limited by training data availability and predictive uncertainty quantification (UQ). We overcome such limitations by using efficient global optimization (EGO) with the multidimensional expected improvement (EI) criterion. EGO balances exploitation of a trained model with acquisition of new DFT data at the Pareto front, the region of chemical space that contains the optimal trade-off between multiple design criteria. We demonstrate this approach for the simultaneous optimization of redox potential and solubility in candidate M(II)/M(III) redox couples for redox flow batteries from a space of 2.8 M transition metal complexes designed for stability in practical redox flow battery (RFB) applications. We show that a multitask ANN with latent-distance-based UQ surpasses the generalization performance of a GP in this space. With this approach, ANN prediction and EI scoring of the full space are achieved in minutes. Starting from ca. 100 representative points, EGO improves both properties by over 3 standard deviations in only five generations. Analysis of lookahead errors confirms rapid ANN model improvement during the EGO process, achieving suitable accuracy for predictive design in the space of transition metal complexes. The ANN-driven EI approach achieves at least 500-fold acceleration over random search, identifying a Pareto-optimal design in around 5 weeks instead of 50 years.