Combining Machine Learning and Computational Chemistry for Predictive Insights Into Chemical Systems

A Unified View of Vibrational Spectroscopy Simulation through Kernel Density Estimations

To date, vibrational simulation results constitute more of an experimental support than a predictive tool, as the simulated vibrational modes are discrete due to quantization. This is different from what is obtained experimentally. Here, we propose a way to combine outputs such as the phonon density of states surrogate and peak intensities obtained from ab initio simulations to allow comparison with experimental data by using machine learning. This work is paving the way for using simulated vibrational spectra as a tool to identify materials with defined stoichiometry, enabling the separation of genuine vibrational features of pure phases from morphological and defect-induced signals.

SchNetPack 2.0: A neural network toolbox for atomistic machine learning

SchNetPack is a versatile neural network toolbox that addresses both the requirements of method development and the application of atomistic machine learning. Version 2.0 comes with an improved data pipeline, modules for equivariant neural networks, and a PyTorch implementation of molecular dynamics. An optional integration with PyTorch Lightning and the Hydra configuration framework powers a flexible command-line interface. This makes SchNetPack 2.0 easily extendable with a custom code and ready for complex training tasks, such as the generation of 3D molecular structures.

An Expedited Route to Optical and Electronic Properties at Finite Temperature via Unsupervised Learning

Electronic properties and absorption spectra are the grounds to investigate molecular electronic states and their interactions with the environment. Modeling and computations are required for the molecular understanding and design strategies of photo-active materials and sensors. However, the interpretation of such properties demands expensive computations and dealing with the interplay of electronic excited states with the conformational freedom of the chromophores in complex matrices (i.e., solvents, biomolecules, crystals) at finite temperature. Computational protocols combining time dependent density functional theory and ab initio molecular dynamics (MD) have become very powerful in this field, although they require still a large number of computations for a detailed reproduction of electronic properties, such as band shapes. Besides the ongoing research in more traditional computational chemistry fields, data analysis and machine learning methods have been increasingly employed as complementary approaches for efficient data exploration, prediction and model development, starting from the data resulting from MD simulations and electronic structure calculations. In this work, dataset reduction capabilities by unsupervised clustering techniques applied to MD trajectories are proposed and tested for the ab initio modeling of electronic absorption spectra of two challenging case studies: a non-covalent charge-transfer dimer and a ruthenium complex in solution at room temperature. The K-medoids clustering technique is applied and is proven to be able to reduce by ∼100 times the total cost of excited state calculations on an MD sampling with no loss in the accuracy and it also provides an easier understanding of the representative structures (medoids) to be analyzed on the molecular scale.

Machine-Learning-Based Prediction of the Glass Transition Temperature of Organic Compounds Using Experimental Data

Knowledge of the glass transition temperature of molecular compounds that occur in atmospheric aerosol particles is important for estimating their viscosity, as it directly influences the kinetics of chemical reactions and particle phase state. While there is a great diversity of organic compounds present in aerosol particles, for only a minor fraction of them experimental glass transition temperatures are known. Therefore, we have developed a machine learning model designed to predict the glass transition temperature of organic molecular compounds based on molecule-derived input variables. The extremely randomized trees (extra trees) procedure was chosen for this purpose. Two approaches using different sets of input variables were followed. The first one uses the number of selected functional groups present in the compound, while the second one generates descriptors from a SMILES (Simplified Molecular Input Line Entry System) string. Organic compounds containing carbon, hydrogen, oxygen, nitrogen, and halogen atoms are included. For improved results, both approaches can be combined with the melting temperature of the compound as an additional input variable. The results show that the predictions of both approaches show a similar mean absolute error of about 12-13 K, with the SMILES-based predictions performing slightly better. In general, the model shows good predictive power considering the diversity of the experimental input data. Furthermore, we also show that its performance exceeds that of previous parameterizations developed for this purpose and also performs better than existing machine learning models. In order to provide user-friendly versions of the model for applications, we have developed a web site where the model can be run by interested scientists via a web-based interface without prior technical knowledge. We also provide Python code of the model. Additionally, all experimental input data are provided in form of the Bielefeld Molecular Organic Glasses (BIMOG) database. We believe that this model is a powerful tool for many applications in atmospheric aerosol science and material science.

Machine Learning Interatomic Potentials and Long-Range Physics

Advances in machine learned interatomic potentials (MLIPs), such as those using neural networks, have resulted in short-range models that can infer interaction energies with near ab initio accuracy and orders of magnitude reduced computational cost. For many atom systems, including macromolecules, biomolecules, and condensed matter, model accuracy can become reliant on the description of short- and long-range physical interactions. The latter terms can be difficult to incorporate into an MLIP framework. Recent research has produced numerous models with considerations for nonlocal electrostatic and dispersion interactions, leading to a large range of applications that can be addressed using MLIPs. In light of this, we present a Perspective focused on key methodologies and models being used where the presence of nonlocal physics and chemistry are crucial for describing system properties. The strategies covered include MLIPs augmented with dispersion corrections, electrostatics calculated with charges predicted from atomic environment descriptors, the use of self-consistency and message passing iterations to propagated nonlocal system information, and charges obtained via equilibration schemes. We aim to provide a pointed discussion to support the development of machine learning-based interatomic potentials for systems where contributions from only nearsighted terms are deficient.

Sustainability in Wood Products: A New Perspective for Handling Natural Diversity

Wood is a renewable resource with excellent qualities and the potential to become a key element of a future bioeconomy. The increasing environmental awareness and drive to achieve sustainability is leading to a resurgence of research on wood materials. Nevertheless, the global climate changes and associated consequences will soon challenge the wood-value chains in several regions (e.g., central Europe). To cope with these challenges, it is necessary to rethink the current practice of wood sourcing and transformation. The goal of this review is to address the intrinsic natural diversity of wood, from its origin to its technological consequences for the present and future manufacturing of wood products. So far, industrial processes have been optimized to repress the variability of wood properties, enabling more efficient processing and production of reliable products. However, the need to preserve biodiversity and the impact of climate change on forests call for new wood processing techniques and green chemistry protocols for wood modification as enabling factors necessary for managing a more diverse wood provision in the future. This article discusses the past developments that have resulted in the current wood value chains and provides a perspective about how natural variability could be turned into an asset for making truly sustainable wood products. After briefly introducing the chemical and structural complexity of wood, the methods conventionally adopted for industrial homogenization and modification of wood are discussed in relation to their evolution toward increased sustainability. Finally, a perspective is given on technological potentials of machine learning techniques and of novel functional wood materials. Here the main message is that through a combination of sustainable forestry, adherence to green chemistry principles and adapted processes based on machine learning, the wood industry could not only overcome current challenges but also thrive in the near future despite the awaiting challenges.

Uncertainty-driven dynamics for active learning of interatomic potentials

Machine learning (ML) models, if trained to data sets of high-fidelity quantum simulations, produce accurate and efficient interatomic potentials. Active learning (AL) is a powerful tool to iteratively generate diverse data sets. In this approach, the ML model provides an uncertainty estimate along with its prediction for each new atomic configuration. If the uncertainty estimate passes a certain threshold, then the configuration is included in the data set. Here we develop a strategy to more rapidly discover configurations that meaningfully augment the training data set. The approach, uncertainty-driven dynamics for active learning (UDD-AL), modifies the potential energy surface used in molecular dynamics simulations to favor regions of configuration space for which there is large model uncertainty. The performance of UDD-AL is demonstrated for two AL tasks: sampling the conformational space of glycine and sampling the promotion of proton transfer in acetylacetone. The method is shown to efficiently explore the chemically relevant configuration space, which may be inaccessible using regular dynamical sampling at target temperature conditions.

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Polarizabilities play significant roles in describing dispersive and inductive interactions of the atom and molecular systems. However, an accurate prediction of molecular polarizabilities from first principles is computationally prohibitive. Although physical models or statistical machine learning models have been proposed, either a lack of accurate description of local chemical environments or demanding a large number of samples for training has limited their practical applications. In this study, we combine a physically inspired dipole interaction model and an accurate neural network method for predicting the polarizability tensors of molecules. With the local chemical environment precisely described and the requirement of rotational covariance naturally fulfilled, this hybrid model is proven to give an accurate molecular polarizability prediction, essentially reducing the number of training samples. The atomic polarizabilities are physically interpretable and transferable to larger molecules unseen in the training set. This promising method may find its wide range of applications, such as spectroscopic simulations and the construction of polarizable force fields.

Data-Driven Machine Learning for Understanding Surface Structures of Heterogeneous Catalysts

The design of heterogeneous catalysts is necessarily surface-focused, generally achieved via optimization of adsorption energy and microkinetic modelling. A prerequisite is to ensure the adsorption energy is physically meaningful is the stable existence of the conceived active-site structure on the surface. The development of improved understanding of the catalyst surface, however, is challenging practically because of the complex nature of dynamic surface formation and evolution under in-situ reactions. We propose therefore data-driven machine-learning (ML) approaches as a solution. In this Minireview we summarize recent progress in using machine-learning to search and predict (meta)stable structures, assist operando simulation under reaction conditions and micro-environments, and critically analyze experimental characterization data. We conclude that ML will become the new norm to lower costs associated with discovery and design of optimal heterogeneous catalysts.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Collective Variables for Conformational Polymorphism in Molecular Crystals

Controlling polymorphism in molecular crystals is crucial in the pharmaceutical, dye, and pesticide industries. However, its theoretical description is extremely challenging, due to the associated long time scales (>1 μs). We present an efficient procedure for identifying collective variables that promote transitions between conformational polymorphs in molecular dynamics simulations. It involves applying a simple dimensionality reduction algorithm to data from short (∼ps) simulations of the isolated conformers that correspond to each polymorph. We demonstrate the utility of our method in the challenging case of the important energetic material, CL-20, which has three anhydrous conformational polymorphs at ambient pressure. Using these collective variables in Metadynamics simulations, we observe transitions between all solid polymorphs in the biased trajectories. We reconstruct the free energy surface and identify previously unknown defect and intermediate forms in the transition from one known polymorph to another. Our method provides insights into complex conformational polymorphic transitions of flexible molecular crystals.

Density functional theory based computational investigations on the stability of highly active trimetallic PtPdCu nanoalloys for electrochemical oxygen reduction

Activity, cost, and durability are the trinity of catalysis research for the electrochemical oxygen reduction reaction (ORR). While studies towards increasing activity and reducing cost of ORR catalysts have been carried out extensively, much effort is needed in durability investigation of highly active ORR catalysts. In this work, we examined the stability of a trimetallic PtPdCu catalyst that has demonstrated high activity and incredible durability during ORR using density functional theory (DFT) based computations. Specifically, we studied the processes of dissolution/deposition and diffusion between the surface and inner layer of Cu species of Pt₂₀Pd₂₀Cu₆₀ catalysts at electrode potentials up to 1.2 V to understand their role towards stabilizing Pt₂₀Pd₂₀Cu₆₀ catalysts. The results show there is a dynamic Cu surface composition range that is dictated by the interplay of the four processes, dissolution, deposition, diffusion from the surface to inner layer, and diffusion from the inner layer to the surface of Cu species, in the stability and observed oscillation of lattice constants of Cu-rich PtPdCu nanoalloys.

Accurate global machine learning force fields for molecules with hundreds of atoms

Global machine learning force fields, with the capacity to capture collective interactions in molecular systems, now scale up to a few dozen atoms due to considerable growth of model complexity with system size. For larger molecules, locality assumptions are introduced, with the consequence that nonlocal interactions are not described. Here, we develop an exact iterative approach to train global symmetric gradient domain machine learning (sGDML) force fields (FFs) for several hundred atoms, without resorting to any potentially uncontrolled approximations. All atomic degrees of freedom remain correlated in the global sGDML FF, allowing the accurate description of complex molecules and materials that present phenomena with far-reaching characteristic correlation lengths. We assess the accuracy and efficiency of sGDML on a newly developed MD22 benchmark dataset containing molecules from 42 to 370 atoms. The robustness of our approach is demonstrated in nanosecond path-integral molecular dynamics simulations for supramolecular complexes in the MD22 dataset.

Multitask Deep Ensemble Prediction of Molecular Energetics in Solution: From Quantum Mechanics to Experimental Properties

The past few years have witnessed significant advances in developing machine learning methods for molecular energetics predictions, including calculated electronic energies with high-level quantum mechanical methods and experimental properties, such as solvation free energy and logP. Typically, task-specific machine learning models are developed for distinct prediction tasks. In this work, we present a multitask deep ensemble model, sPhysNet-MT-ens5, which can simultaneously and accurately predict electronic energies of molecules in gas, water, and octanol phases, as well as transfer free energies at both calculated and experimental levels. On the calculated data set Frag20-solv-678k, which is developed in this work and contains 678,916 molecular conformations, up to 20 heavy atoms, and their properties calculated at B3LYP/6-31G* level of theory with continuum solvent models, sPhysNet-MT-ens5 predicts density functional theory (DFT)-level electronic energies directly from force field-optimized geometry within chemical accuracy. On the experimental data sets, sPhysNet-MT-ens5 achieves state-of-the-art performances, which predict both experimental hydration free energy with a RMSE of 0.620 kcal/mol on the FreeSolv data set and experimental logP with a RMSE of 0.393 on the PHYSPROP data set. Furthermore, sPhysNet-MT-ens5 also provides a reasonable estimation of model uncertainty which shows correlations with prediction error. Finally, by analyzing the atomic contributions of its predictions, we find that the developed deep learning model is aware of the chemical environment of each atom by assigning reasonable atomic contributions consistent with our chemical knowledge.

Modeling, optimization and understanding of adsorption process for pollutant removal via machine learning: Recent progress and future perspectives

It is crucial to reduce the concentration of pollutants in water environment to below safe levels. Some cost-effective pollutant removal technologies have been developed, among which adsorption technology is considered as a promising solution. However, the batch experiments and adsorption isotherms widely employed at present are inefficient and time-consuming to some extent, which limits the development of adsorption technology. As a new research paradigm, machine learning (ML) is expected to innovate traditional adsorption models. This reviews summarized the general workflow of ML and commonly employed ML algorithms for pollutant adsorption. Then, the latest progress of ML for pollutant adsorption was reviewed from the perspective of all-round regulation of adsorption process, including adsorption efficiency, operating conditions and adsorption mechanism. General guidelines of ML for pollutant adsorption were presented. Finally, the existing problems and future perspectives of ML for pollutant adsorption were put forward. We highly expect that this review will promote the application of ML in pollutant adsorption and improve the interpretability of ML.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Machine Learning-Based Analytical Systems: Food Forensics

Despite a large amount of money being spent on both food analyses and control measures, various food-borne illnesses associated with pathogens, toxins, pesticides, adulterants, colorants, and other contaminants pose a serious threat to human health, and thus food safety draws considerable attention in the modern pace of the world. The presence of various biogenic amines in processed food have been frequently considered as the primary quality parameter in order to check food freshness and spoilage of protein-rich food. Various conventional detection methods for detecting hazardous analytes including microscopy, nucleic acid, and immunoassay-based techniques have been employed; however, recently, array-based sensing strategies are becoming popular for the development of a highly accurate and precise analytical method. Array-based sensing is majorly facilitated by the advancements in multivariate analytical techniques as well as machine learning-based approaches. These techniques allow one to solve the typical problem associated with the interpretation of the complex response patterns generated in array-based strategies. Consequently, the machine learning-based neural networks enable the fast, robust, and accurate detection of analytes using sensor arrays. Thus, for commercial applications, most of the focus has shifted toward the development of analytical methods based on electrical and chemical sensor arrays. Therefore, herein, we briefly highlight and review the recently reported array-based sensor systems supported by machine learning and multivariate analytics to monitor food safety and quality in the field of food forensics.

Heterogeneous catalysis mediated by light, electricity and enzyme via machine learning: Paradigms, applications and prospects

Energy crisis and environmental pollution have become the bottleneck of human sustainable development. Therefore, there is an urgent need to develop new catalysts for energy production and environmental remediation. Due to the high cost caused by blind screening and limited valuable computing resources, the traditional experimental methods and theoretical calculations are difficult to meet with the requirements. In the past decades, computer science has made great progress, especially in the field of machine learning (ML). As a new research paradigm, ML greatly accelerates the theoretical calculation methods represented by first principal calculation and molecular dynamics, and establish the physical picture of heterogeneous catalytic processes for energy and environment. This review firstly summarized the general research paradigms of ML in the discovery of catalysts. Then, the latest progresses of ML in light-, electricity- and enzyme-mediated heterogeneous catalysis were reviewed from the perspective of catalytic performance, operating conditions and reaction mechanism. The general guidelines of ML for heterogeneous catalysis were proposed. Finally, the existing problems and future development trend of ML in heterogeneous catalysis mediated by light, electricity and enzyme were summarized. We highly expect that this review will facilitate the interaction between ML and heterogeneous catalysis, and illuminate the development prospect of heterogeneous catalysis.

Uncertainty quantification for predictions of atomistic neural networks

The value of uncertainty quantification on predictions for trained neural networks (NNs) on quantum chemical reference data is quantitatively explored. For this, the architecture of the PhysNet NN was suitably modified and the resulting model (PhysNet-DER) was evaluated with different metrics to quantify its calibration, the quality of its predictions, and whether prediction error and the predicted uncertainty can be correlated. Training on the QM9 database and evaluating data in the test set within and outside the distribution indicate that error and uncertainty are not linearly related. However, the observed variance provides insight into the quality of the data used for training. Additionally, the influence of the chemical space covered by the training data set was studied by using a biased database. The results clarify that noise and redundancy complicate property prediction for molecules even in cases for which changes - such as double bond migration in two otherwise identical molecules - are small. The model was also applied to a real database of tautomerization reactions. Analysis of the distance between members in feature space in combination with other parameters shows that redundant information in the training dataset can lead to large variances and small errors whereas the presence of similar but unspecific information returns large errors but small variances. This was, e.g., observed for nitro-containing aliphatic chains for which predictions were difficult although the training set contained several examples for nitro groups bound to aromatic molecules. The finding underlines the importance of the composition of the training data and provides chemical insight into how this affects the prediction capabilities of a ML model. Finally, the presented method can be used for information-based improvement of chemical databases for target applications through active learning optimization.

The fourth-order expansion of the exchange hole and neural networks to construct exchange–correlation functionals

The curvature Q σ of spherically averaged exchange (X) holes ρX, σ(r, u) is one of the crucial variables for the construction of approximations to the exchange–correlation energy of Kohn–Sham theory, the most prominent example being the Becke–Roussel model [A. D. Becke and M. R. Roussel, Phys. Rev. A 39, 3761 (1989)]. Here, we consider the next higher nonzero derivative of the spherically averaged X hole, the fourth-order term T σ. This variable contains information about the nonlocality of the X hole and we employ it to approximate hybrid functionals, eliminating the sometimes demanding calculation of the exact X energy. The new functional is constructed using machine learning; having identified a physical correlation between T σ and the nonlocality of the X hole, we employ a neural network to express this relation. While we only modify the X functional of the Perdew–Burke–Ernzerhof functional [Perdew et al., Phys. Rev. Lett. 77, 3865 (1996)], a significant improvement over this method is achieved.

A New Theobromine-Based EGFRWT and EGFRT790M Inhibitor and Apoptosis Inducer: Design, Semi-Synthesis, Docking, DFT, MD Simulations, and In Vitro Studies

The essential pharmacophoric structural properties were applied to design a new derivative of theobromine as an antiangiogenic EGFR inhibitor. The designed candidate is a (para-nitrophenyl)acetamide derivative of the natural alkaloid, theobromine (T-2-PNPA). The potentialities of T-2-PNPA to inhibit the EGFR protein were studied computationally in an extensive way. Firstly, the molecular docking against EGFRWT and EGFRT790M demonstrated T-2-PNPA’s capabilities of binding with the targeted receptors. Then, the MD experiments (for 100 ns) illustrated through six different studies the changes that occurred in the energy as well as in the structure of EGFR–T-2-PNPA complex. Additionally, an MM-GBSA analysis determined the exact energy of binding and the essential residues. Furthermore, DFT calculations investigated the stability, reactivity, and electrostatic potential of T-2-PNPA. Finally, ADMET and toxicity studies confirmed both the safety as well as the general likeness of T-2-PNPA. Consequently, T-2-PNPA was prepared for the in vitro biological studies. T-2-PNPA inhibited EGFRWT and EGFRT790M with IC50 values of 7.05 and 126.20 nM, respectively, which is comparable with erlotinib activities (5.91 and 202.40, respectively). Interestingly, T-2-PNPA expressed cytotoxic potentialities against A549 and HCT-116 cells with IC50 values of 11.09 and 21.01 µM, respectively, which is again comparable with erlotinib activities (6.73 and 16.35, respectively). T-2-PNPA was much safer against WI-38 (IC50 = 48.06 µM) than erlotinib (IC50 = 31.17 µM). The calculated selectivity indices of T-2-PNPA against A549 and HCT-116 cells were 4.3 and 2.3, respectively. This manuscript presents a new lead anticancer compound (T-2-PNPA) that has been synthesized for the first time and exhibited promising in silico and in vitro anticancer potentialities.

Algorithmic Differentiation for Automated Modeling of Machine Learned Force Fields

Reconstructing force fields (FFs) from atomistic simulation data is a challenge since accurate data can be highly expensive. Here, machine learning (ML) models can help to be data economic as they can be successfully constrained using the underlying symmetry and conservation laws of physics. However, so far, every descriptor newly proposed for an ML model has required a cumbersome and mathematically tedious remodeling. We therefore propose using modern techniques from algorithmic differentiation within the ML modeling process, effectively enabling the usage of novel descriptors or models fully automatically at an order of magnitude higher computational efficiency. This paradigmatic approach enables not only a versatile usage of novel representations and the efficient computation of larger systems─all of high value to the FF community─but also the simple inclusion of further physical knowledge, such as higher-order information (e.g., Hessians, more complex partial differential equations constraints etc.), even beyond the presented FF domain.

Obtaining Electronic Properties of Molecules through Combining Density Functional Tight Binding with Machine Learning

We have introduced a machine learning workflow that allows for optimizing electronic properties in the density functional tight binding method (DFTB). The workflow allows for the optimization of electronic properties by generating two-center integrals, either by training basis function parameters directly or by training a spline model for the diatomic integrals, which are then used to build the Hamiltonian and the overlap matrices. Using our workflow, we have managed to obtain improved electronic properties, such as charge distributions, dipole moments, and approximated polarizabilities. While both machine learning approaches enabled us to improve on the electronic properties of the molecules as compared with existing DFTB parametrizations, only by training on the basis function parameters we were able to obtain consistent Hamiltonians and overlap matrices in the physically reasonable ranges or to improve on multiple electronic properties simultaneously.

Higher-Order Explanations of Graph Neural Networks via Relevant Walks

Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent, GNNs have remained black-boxes for the user so far. In this paper, we show that GNNs can in fact be naturally explained using higher-order expansions, i.e., by identifying groups of edges that jointly contribute to the prediction. Practically, we find that such explanations can be extracted using a nested attribution scheme, where existing techniques such as layer-wise relevance propagation (LRP) can be applied at each step. The output is a collection of walks into the input graph that are relevant for the prediction. Our novel explanation method, which we denote by GNN-LRP, is applicable to a broad range of graph neural networks and lets us extract practically relevant insights on sentiment analysis of text data, structure-property relationships in quantum chemistry, and image classification.

Homogeneous Electrocatalytic Reduction of CO2 by a CrN3O Complex: Electronic Coupling with a Redox-Active Terpyridine Fragment Favors Selectivity for CO

Electrocatalyst design and optimization strategies continue to be an active area of research interest for the applied use of renewable energy resources. The electrocatalytic conversion of carbon dioxide (CO₂) is an attractive approach in this context because of the added potential benefit of addressing its rising atmospheric concentrations. In previous experimental and computational studies, we have described the mechanism of the first molecular Cr complex capable of electrocatalytically reducing CO₂ to carbon monoxide (CO) in the presence of an added proton donor, which contained a redox-active 2,2'-bipyridine (bpy) fragment, CrN₂O₂. The high selectivity for CO in the bpy-based system was dependent on a delocalized Cr^II(bpy^•-) active state. Subsequently, we became interested in exploring how expanding the polypyridyl ligand core would impact the selectivity and activity during electrocatalytic CO₂ reduction. Here, we report a new CrN₃O catalyst, Cr(tpy^tbupho)Cl₂ (1), where 2-(2,2':6',2″-terpyridin-6-yl)-4,6-di-tert-butylphenolate = [tpy^tbupho]^-, which reduces CO₂ to CO with almost quantitative selectivity via a different mechanism than our previously reported Cr(^tbudhbpy)Cl(H₂O) catalyst. Computational analyses indicate that, although the stoichiometry of both reactions is identical, changes in the observed rate law are the combined result of a decrease in the intrinsic ligand charge (L₃X vs L₂X₂) and an increase in the ligand redox activity, which result in increased electronic coupling between the doubly reduced tpy fragment of the ligand and the Cr^II center. The strong electronic coupling enhances the rate of protonation and subsequent C-OH bond cleavage, resulting in CO₂ binding becoming the rate-determining step, which is an uncommon mechanism during protic CO₂ reduction.

SELFIES and the future of molecular string representations

Artificial intelligence (AI) and machine learning (ML) are expanding in popularity for broad applications to challenging tasks in chemistry and materials science. Examples include the prediction of properties, the discovery of new reaction pathways, or the design of new molecules. The machine needs to read and write fluently in a chemical language for each of these tasks. Strings are a common tool to represent molecular graphs, and the most popular molecular string representation, Smiles, has powered cheminformatics since the late 1980s. However, in the context of AI and ML in chemistry, Smiles has several shortcomings-most pertinently, most combinations of symbols lead to invalid results with no valid chemical interpretation. To overcome this issue, a new language for molecules was introduced in 2020 that guarantees 100% robustness: SELF-referencing embedded string (Selfies). Selfies has since simplified and enabled numerous new applications in chemistry. In this perspective, we look to the future and discuss molecular string representations, along with their respective opportunities and challenges. We propose 16 concrete future projects for robust molecular representations. These involve the extension toward new chemical domains, exciting questions at the interface of AI and robust languages, and interpretability for both humans and machines. We hope that these proposals will inspire several follow-up works exploiting the full potential of molecular string representations for the future of AI in chemistry and materials science.

Towards fully ab initio simulation of atmospheric aerosol nucleation

Atmospheric aerosol nucleation contributes to approximately half of the worldwide cloud condensation nuclei. Despite the importance of climate, detailed nucleation mechanisms are still poorly understood. Understanding aerosol nucleation dynamics is hindered by the nonreactivity of force fields (FFs) and high computational costs due to the rare event nature of aerosol nucleation. Developing reactive FFs for nucleation systems is even more challenging than developing covalently bonded materials because of the wide size range and high dimensional characteristics of noncovalent hydrogen bonding bridging clusters. Here, we propose a general workflow that is also applicable to other systems to train an accurate reactive FF based on a deep neural network (DNN) and further bridge DNN-FF-based molecular dynamics (MD) with a cluster kinetics model based on Poisson distributions of reactive events to overcome the high computational costs of direct MD. We found that previously reported acid-base formation rates tend to be significantly underestimated, especially in polluted environments, emphasizing that acid-base nucleation observed in multiple environments should be revisited.

Machine Learning for Efficient Prediction of Protein Redox Potential: The Flavoproteins Case

Determining the redox potentials of protein cofactors and how they are influenced by their molecular neighborhoods is essential for basic research and many biotechnological applications, from biosensors and biocatalysis to bioremediation and bioelectronics. The laborious determination of redox potential with current experimental technologies pushes forward the need for computational approaches that can reliably predict it. Although current computational approaches based on quantum and molecular mechanics are accurate, their large computational costs hinder their usage. In this work, we explored the possibility of using more efficient QSPR models based on machine learning (ML) for the prediction of protein redox potential, as an alternative to classical approaches. As a proof of concept, we focused on flavoproteins, one of the most important families of enzymes directly involved in redox processes. To train and test different ML models, we retrieved a dataset of flavoproteins with a known midpoint redox potential (Em) and 3D structure. The features of interest, accounting for both short- and long-range effects of the protein matrix on the flavin cofactor, have been automatically extracted from each protein PDB file. Our best ML model (XGB) has a performance error below 1 kcal/mol (∼36 mV), comparing favorably to more sophisticated computational approaches. We also provided indications on the features that mostly affect the Em value, and when possible, we rationalized them on the basis of previous studies.

Machine Learning Accelerated Discovery of Promising Thermal Energy Storage Materials with High Heat Capacity

Thermal energy storage offers numerous benefits by reducing energy consumption and promoting the use of renewable energy sources. Thermal energy storage materials have been investigated for many decades with the aim of improving the overall efficiency of energy systems. However, finding solid materials that meet the requirement of high heat capacity has been a grand challenge for material scientists. Herewith, by training various machine learning models on 3377 high-quality data from full density functional theory (DFT) calculations, we efficiently search for potential materials with high heat capacity. We build four traditional machine learning models and two graph neural network models. Cross-comparison of the prediction performance and model accuracy was conducted among different models. The deeperGATGNN model exhibits high prediction accuracy and is used for predicting the heat capacity of 32,026 structures screened from the open quantum material database. We gain deep insight into the correlation between heat capacity and structure descriptors such as space group, prototype, lattice volume, atomic weight, etc. Twenty-two structures were predicted to possess high heat capacity, and the results were further validated with DFT calculations. We also identified one special structure, namely, MnIn₂Se₄, with space group no. 227 (Fd3̅m), that exhibits extremely high heat capacity, even higher than that of the Dulong-Petit limit at room temperature. This study paves the way for accelerating the discovery of novel thermal energy storage materials by combining machine learning with minimal DFT inquiry.

Orbital Mixer: Using Atomic Orbital Features for Basis-Dependent Prediction of Molecular Wavefunctions

Leveraging ab initio data at scale has enabled the development of machine learning models capable of extremely accurate and fast molecular property prediction. A central paradigm of many previous studies focuses on generating predictions for only a fixed set of properties. Recent lines of research instead aim to explicitly learn the electronic structure via molecular wavefunctions, from which other quantum chemical properties can be directly derived. While previous methods generate predictions as a function of only the atomic configuration, in this work we present an alternate approach that directly purposes basis-dependent information to predict molecular electronic structure. Our model, Orbital Mixer, is composed entirely of multi-layer perceptrons (MLPs) using MLP-Mixer layers within a simple, intuitive, and scalable architecture that achieves competitive Hamiltonian and molecular orbital energy and coefficient prediction accuracies compared to the state-of-the-art.

Tackling Disorder in γ-Ga2 O3

Ga₂ O₃ and its polymorphs are attracting increasing attention. The rich structural space of polymorphic oxide systems such as Ga₂ O₃ offers potential for electronic structure engineering, which is of particular interest for a range of applications, such as power electronics. γ-Ga₂ O₃ presents a particular challenge across synthesis, characterization, and theory due to its inherent disorder and resulting complex structure-electronic-structure relationship. Here, density functional theory is used in combination with a machine-learning approach to screen nearly one million potential structures, thereby developing a robust atomistic model of the γ-phase. Theoretical results are compared with surface and bulk sensitive soft and hard X-ray photoelectron spectroscopy, X-ray absorption spectroscopy, spectroscopic ellipsometry, and photoluminescence excitation spectroscopy experiments representative of the occupied and unoccupied states of γ-Ga₂ O₃ . The first onset of strong absorption at room temperature is found at 5.1 eV from spectroscopic ellipsometry, which agrees well with the excitation maximum at 5.17 eV obtained by photoluminescence excitation spectroscopy, where the latter shifts to 5.33 eV at 5 K. This work presents a leap forward in the treatment of complex, disordered oxides and is a crucial step toward exploring how their electronic structure can be understood in terms of local coordination and overall structure.

Extending machine learning beyond interatomic potentials for predicting molecular properties

Machine learning (ML) is becoming a method of choice for modelling complex chemical processes and materials. ML provides a surrogate model trained on a reference dataset that can be used to establish a relationship between a molecular structure and its chemical properties. This Review highlights developments in the use of ML to evaluate chemical properties such as partial atomic charges, dipole moments, spin and electron densities, and chemical bonding, as well as to obtain a reduced quantum-mechanical description. We overview several modern neural network architectures, their predictive capabilities, generality and transferability, and illustrate their applicability to various chemical properties. We emphasize that learned molecular representations resemble quantum-mechanical analogues, demonstrating the ability of the models to capture the underlying physics. We also discuss how ML models can describe non-local quantum effects. Finally, we conclude by compiling a list of available ML toolboxes, summarizing the unresolved challenges and presenting an outlook for future development. The observed trends demonstrate that this field is evolving towards physics-based models augmented by ML, which is accompanied by the development of new methods and the rapid growth of user-friendly ML frameworks for chemistry.

Quantitatively Determining Surface-Adsorbate Properties from Vibrational Spectroscopy with Interpretable Machine Learning

Learning microscopic properties of a material from its macroscopic measurables is a grand and challenging goal in physical science. Conventional wisdom is to first identify material structures exploiting characterization tools, such as spectroscopy, and then to infer properties of interest, often with assistance of theory and simulations. This indirect approach has limitations due to the accumulation of errors from retrieving structures from spectral signals and the lack of quantitative structure-property relationship. A new pathway directly from spectral signals to microscopic properties is highly desirable, as it would offer valuable guidance toward materials evaluation and design via spectroscopic measurements. Herein, we exploit machine-learned vibrational spectroscopy to establish quantitative spectrum-property relationships. Key interaction properties of substrate-adsorbate systems, including adsorption energy and charge transfer, are quantitatively determined directly from Infrared and Raman spectroscopic signals of the adsorbates. The machine-learned spectrum-property relationships are presented as mathematical formulas, which are physically interpretable and therefore transferrable to a series of metal/alloy surfaces. The demonstrated ability of quantitative determination of hard-to-measure microscopic properties using machine-learned spectroscopy will significantly broaden the applicability of conventional spectroscopic techniques for materials design and high throughput screening under operando conditions.

Machine Learning for Electrocatalyst and Photocatalyst Design and Discovery

Electrocatalysts and photocatalysts are key to a sustainable future, generating clean fuels, reducing the impact of global warming, and providing solutions to environmental pollution. Improved processes for catalyst design and a better understanding of electro/photocatalytic processes are essential for improving catalyst effectiveness. Recent advances in data science and artificial intelligence have great potential to accelerate electrocatalysis and photocatalysis research, particularly the rapid exploration of large materials chemistry spaces through machine learning. Here a comprehensive introduction to, and critical review of, machine learning techniques used in electrocatalysis and photocatalysis research are provided. Sources of electro/photocatalyst data and current approaches to representing these materials by mathematical features are described, the most commonly used machine learning methods summarized, and the quality and utility of electro/photocatalyst models evaluated. Illustrations of how machine learning models are applied to novel electro/photocatalyst discovery and used to elucidate electrocatalytic or photocatalytic reaction mechanisms are provided. The review offers a guide for materials scientists on the selection of machine learning methods for electrocatalysis and photocatalysis research. The application of machine learning to catalysis science represents a paradigm shift in the way advanced, next-generation catalysts will be designed and synthesized.

Design, Synthesis, Docking, DFT, MD Simulation Studies of a New Nicotinamide-Based Derivative: In Vitro Anticancer and VEGFR-2 Inhibitory Effects

A nicotinamide-based derivative was designed as an antiproliferative VEGFR-2 inhibitor with the key pharmacophoric features needed to interact with the VEGFR-2 catalytic pocket. The ability of the designed congener ((E)-N-(4-(1-(2-(4-benzamidobenzoyl)hydrazono)ethyl)phenyl)nicotinamide), compound 10, to bind with the VEGFR-2 enzyme was demonstrated by molecular docking studies. Furthermore, six various MD simulations studies established the excellent binding of compound 10 with VEGFR-2 over 100 ns, exhibiting optimum dynamics. MM-GBSA confirmed the proper binding with a total exact binding energy of −38.36 Kcal/Mol. MM-GBSA studies also revealed the crucial amino acids in the binding through the free binding energy decomposition and declared the interactions variation of compound 10 inside VEGFR-2 via the Protein–Ligand Interaction Profiler (PLIP). Being new, its molecular structure was optimized by DFT. The DFT studies also confirmed the binding mode of compound 10 with the VEGFR-2. ADMET (in silico) profiling indicated the examined compound’s acceptable range of drug-likeness. The designed compound was synthesized through the condensation of N-(4-(hydrazinecarbonyl)phenyl)benzamide with N-(4-acetylphenyl)nicotinamide, where the carbonyl group has been replaced by an imine group. The in-vitro studies were consonant with the obtained in silico results as compound 10 prohibited VEGFR-2 with an IC₅₀ value of 51 nM. Compound 10 also showed antiproliferative effects against MCF-7 and HCT 116 cancer cell lines with IC₅₀ values of 8.25 and 6.48 μM, revealing magnificent selectivity indexes of 12.89 and 16.41, respectively.

Ab initio machine learning of phase space averages

Equilibrium structures determine material properties and biochemical functions. We here propose to machine learn phase space averages, conventionally obtained by ab initio or force-field-based molecular dynamics (MD) or Monte Carlo (MC) simulations. In analogy to ab initio MD, our ab initio machine learning (AIML) model does not require bond topologies and, therefore, enables a general machine learning pathway to obtain ensemble properties throughout the chemical compound space. We demonstrate AIML for predicting Boltzmann averaged structures after training on hundreds of MD trajectories. The AIML output is subsequently used to train machine learning models of free energies of solvation using experimental data and to reach competitive prediction errors (mean absolute error ∼ 0.8 kcal/mol) for out-of-sample molecules-within milliseconds. As such, AIML effectively bypasses the need for MD or MC-based phase space sampling, enabling exploration campaigns of Boltzmann averages throughout the chemical compound space at a much accelerated pace. We contextualize our findings by comparison to state-of-the-art methods resulting in a Pareto plot for the free energy of solvation predictions in terms of accuracy and time.

Exploiting Ligand Additivity for Transferable Machine Learning of Multireference Character across Known Transition Metal Complex Ligands

Accurate virtual high-throughput screening (VHTS) of transition metal complexes (TMCs) remains challenging due to the possibility of high multireference (MR) character that complicates property evaluation. We compute MR diagnostics for over 5,000 ligands present in previously synthesized octahedral mononuclear transition metal complexes in the Cambridge Structural Database (CSD). To accomplish this task, we introduce an iterative approach for consistent ligand charge assignment for ligands in the CSD. Across this set, we observe that the MR character correlates linearly with the inverse value of the averaged bond order over all bonds in the molecule. We then demonstrate that ligand additivity of the MR character holds in TMCs, which suggests that the TMC MR character can be inferred from the sum of the MR character of the ligands. Encouraged by this observation, we leverage ligand additivity and develop a ligand-derived machine learning representation to train neural networks to predict the MR character of TMCs from properties of the constituent ligands. This approach yields models with excellent performance and superior transferability to unseen ligand chemistry and compositions.

Heterogeneous catalyst design by generative adversarial network and first-principles based microkinetics

Microkinetic analysis based on density functional theory (DFT) was combined with a generative adversarial network (GAN) to enable the artificial proposal of heterogeneous catalysts based on the DFT-calculated dataset. The approach was applied to the NH₃ formation reaction on Rh−Ru alloy surfaces as an example. The NH₃ formation turnover frequency (TOF) was calculated by DFT-based microkinetics. Six elementary reactions, namely, N₂ dissociation, H₂ dissociation, NH_x (x = 1–3) formation, and NH₃ desorption, were explicitly considered, and their reaction energies were evaluated by DFT calculations. Based on the TOF values and atomic compositions, new alloy surfaces were generated using the GAN. This approach successfully generated the surfaces that were not included in the initial dataset but exhibited higher TOF values. The N₂ dissociation reaction was more exothermic for the generated surfaces, leading to higher TOF. The present study demonstrates that the automatic improvement of catalyst materials is possible using DFT calculations and GAN sample generation.

BIGDML-Towards accurate quantum machine learning force fields for materials

Machine-learning force fields (MLFF) should be accurate, computationally and data efficient, and applicable to molecules, materials, and interfaces thereof. Currently, MLFFs often introduce tradeoffs that restrict their practical applicability to small subsets of chemical space or require exhaustive datasets for training. Here, we introduce the Bravais-Inspired Gradient-Domain Machine Learning (BIGDML) approach and demonstrate its ability to construct reliable force fields using a training set with just 10-200 geometries for materials including pristine and defect-containing 2D and 3D semiconductors and metals, as well as chemisorbed and physisorbed atomic and molecular adsorbates on surfaces. The BIGDML model employs the full relevant symmetry group for a given material, does not assume artificial atom types or localization of atomic interactions and exhibits high data efficiency and state-of-the-art energy accuracies (errors substantially below 1 meV per atom) for an extended set of materials. Extensive path-integral molecular dynamics carried out with BIGDML models demonstrate the counterintuitive localization of benzene-graphene dynamics induced by nuclear quantum effects and their strong contributions to the hydrogen diffusion coefficient in a Pd crystal for a wide range of temperatures.

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.