Electron density learning of non-covalent systems

Efficient Sampling for Machine Learning Electron Density and Its Response in Real Space

Electron density is a fundamental quantity that can in principle determine all ground state electronic properties of a given system. Although machine learning (ML) models for electron density based on either an atom-centered basis or a real-space grid have been proposed, the demand for a number of high-order basis functions or grid points is enormous. In this work, we propose an efficient grid-point sampling strategy that combines targeted sampling favoring a large density and a screening of grid points associated with linearly independent atomic features. This new sampling strategy is integrated with a field-induced recursively embedded atom neural network model to develop a real-space grid-based ML model for the electron density and its response to an electric field. This approach is applied to a QM9 molecular data set, a H2O/Pt(111) interfacial system, an Au(100) electrode, and an Au nanoparticle under an electric field. The number of training points is found to be much smaller than previous models, while yielding comparably accurate predictions for the electron density of the entire grid. The resultant machine-learned electron density model enables us to properly partition partial charge onto each atom and analyze the charge variation upon proton transfer in the H2O/Pt(111) system. The machine-learning electronic response model allows us to predict charge transfer and the electrostatic potential change induced by an electric field applied to an Au(100) electrode or an Au nanoparticle.

Recent advances and various detection strategies of deep eutectic solvents for zinc air batteries

Sustainable technology in energy-related applications will be crucial in the coming decades. As a result, developing new materials for existing processes has presently arisen as a major research priority. Recently, Deep eutectic solvents (DESs) have been expected as low-cost task-specific solvents for zinc-air batteries (ZABs). Here in, initially the various preparation methods of DESs their detection strategies, and the fundamental characteristics of DESs are summarized. Then, the recent utilization of DESs on ZABs has been reviewed. After that, the chemical and physical characteristics of DESs including phase behavior, viscosity, density, ionic conductivity, refractive index, pH, surface tension and stability have been studied. Lastly, the challenges, limitations, and possible upcoming research fields of DESs for ZABs were discussed.

Spiers Memorial Lecture: How to do impactful research in artificial intelligence for chemistry and materials science

Machine learning has been pervasively touching many fields of science. Chemistry and materials science are no exception. While machine learning has been making a great impact, it is still not reaching its full potential or maturity. In this perspective, we first outline current applications across a diversity of problems in chemistry. Then, we discuss how machine learning researchers view and approach problems in the field. Finally, we provide our considerations for maximizing impact when researching machine learning for chemistry.

Generalizing deep learning electronic structure calculation to the plane-wave basis

Deep neural networks capable of representing the density functional theory (DFT) Hamiltonian as a function of material structure hold great promise for revolutionizing future electronic structure calculations. However, a notable limitation of previous neural networks is their compatibility solely with the atomic-orbital (AO) basis, excluding the widely used plane-wave (PW) basis. Here we overcome this critical limitation by proposing an accurate and efficient real-space reconstruction method for directly computing AO Hamiltonian matrices from PW DFT results. The reconstruction method is orders of magnitude faster than traditional projection-based methods to convert PW results to the AO basis, and the reconstructed Hamiltonian matrices can faithfully reproduce the PW electronic structure, thus bridging the longstanding gap between the AO basis deep learning electronic structure approach and PW DFT. Advantages of the PW methods, such as high accuracy, high flexibility and wide applicability, thus can be all integrated into deep learning electronic structure methods without sacrificing these methods' inherent benefits. This allows for the construction of large-scale and high-fidelity training datasets with the help of PW DFT results towards the development of precise and broadly applicable deep learning electronic structure models.

3DReact: Geometric Deep Learning for Chemical Reactions

Geometric deep learning models, which incorporate the relevant molecular symmetries within the neural network architecture, have considerably improved the accuracy and data efficiency of predictions of molecular properties. Building on this success, we introduce 3DReact, a geometric deep learning model to predict reaction properties from three-dimensional structures of reactants and products. We demonstrate that the invariant version of the model is sufficient for existing reaction data sets. We illustrate its competitive performance on the prediction of activation barriers on the GDB7-22-TS, Cyclo-23-TS, and Proparg-21-TS data sets in different atom-mapping regimes. We show that, compared to existing models for reaction property prediction, 3DReact offers a flexible framework that exploits atom-mapping information, if available, as well as geometries of reactants and products (in an invariant or equivariant fashion). Accordingly, it performs systematically well across different data sets, atom-mapping regimes, as well as both interpolation and extrapolation tasks.

Machine learning for accuracy in density functional approximations

Machine learning techniques have found their way into computational chemistry as indispensable tools to accelerate atomistic simulations and materials design. In addition, machine learning approaches hold the potential to boost the predictive power of computationally efficient electronic structure methods, such as density functional theory, to chemical accuracy and to correct for fundamental errors in density functional approaches. Here, recent progress in applying machine learning to improve the accuracy of density functional and related approximations is reviewed. Promises and challenges in devising machine learning models transferable between different chemistries and materials classes are discussed with the help of examples applying promising models to systems far outside their training sets.

Raman Spectra of Amino Acids and Peptides from Machine Learning Polarizabilities

Raman spectroscopy is an important tool in the study of vibrational properties and composition of molecules, peptides, and even proteins. Raman spectra can be simulated based on the change of the electronic polarizability with vibrations, which can nowadays be efficiently obtained via machine learning models trained on first-principles data. However, the transferability of the models trained on small molecules to larger structures is unclear, and direct training on large structures is prohibitively expensive. In this work, we first train two machine learning models to predict the polarizabilities of all 20 amino acids. Both models are carefully benchmarked and compared to density functional theory (DFT) calculations, with the neural network method being found to offer better transferability. By combination of machine learning models with classical force field molecular dynamics, Raman spectra of all amino acids are also obtained and investigated, showing good agreement with experiments. The models are further extended to small peptides. We find that adding structures containing peptide bonds to the training set greatly improves predictions, even for peptides not included in training sets.

Building an ab initio solvated DNA model using Euclidean neural networks

Accurately modeling large biomolecules such as DNA from first principles is fundamentally challenging due to the steep computational scaling of ab initio quantum chemistry methods. This limitation becomes even more prominent when modeling biomolecules in solution due to the need to include large numbers of solvent molecules. We present a machine-learned electron density model based on a Euclidean neural network framework that includes a built-in understanding of equivariance to model explicitly solvated double-stranded DNA. By training the machine learning model using molecular fragments that sample the key DNA and solvent interactions, we show that the model predicts electron densities of arbitrary systems of solvated DNA accurately, resolves polarization effects that are neglected by classical force fields, and captures the physics of the DNA-solvent interaction at the ab initio level.

SPAHM(a,b): Encoding the Density Information from Guess Hamiltonian in Quantum Machine Learning Representations

Recently, we introduced a class of molecular representations for kernel-based regression methods─the spectrum of approximated Hamiltonian matrices (SPAHM)─that takes advantage of lightweight one-electron Hamiltonians traditionally used as a self-consistent field initial guess. The original SPAHM variant is built from occupied-orbital energies (i.e., eigenvalues) and naturally contains all of the information about nuclear charges, atomic positions, and symmetry requirements. Its advantages were demonstrated on data sets featuring a wide variation of charge and spin, for which traditional structure-based representations commonly fail. SPAHM(a,b), as introduced here, expand the eigenvalue SPAHM into local and transferable representations. They rely upon one-electron density matrices to build fingerprints from atomic and bond density overlap contributions inspired from preceding state-of-the-art representations. The performance and efficiency of SPAHM(a,b) is assessed on the predictions for data sets of prototypical organic molecules (QM7) of different charges and azoheteroarene dyes in an excited state. Overall, both SPAHM(a) and SPAHM(b) outperform state-of-the-art representations on difficult prediction tasks such as the atomic properties of charged open-shell species and of π-conjugated systems.

Bioscreening specific peptide-expressing phage and its application in sensitive dual-mode immunoassay of SARS-CoV-2 spike antigen

Biorecognition components with high affinity and selectivity are vital in bioassay to diagnose and treat epidemic disease. Herein a phage display strategy of combining single-amplification-panning with non-amplification-panning was developed, by which a phage displaying cyclic heptapeptide ACLDWLFNSC (peptide J4) with good affinity and specificity to SARS-CoV-2 spike protein (SP) was identified. Molecular docking suggests that peptide J4 binds to S2 subunit by hydrogen bonding and hydrophobic interaction. Then the J4-phage was used as the capture antibody to establish phage-based chemiluminescence immunoassay (CLIA) and electrochemical impedance spectroscopy (EIS) analytical systems. The as-proposed dual-modal immunoassay platform exhibited good sensitivity and reliability in SARS-CoV-2 SP and pseudovirus assay. The limit of detection for SARS-CoV-2 SP by EIS immunoassay is 0.152 pg/mL, which is dramatically lower than that of 42 pg/mL for J4-phage based CLIA. Further, low to 40 transducing units (TU)/mL, 10 TU/mL SARS-CoV-2 pseudoviruses can be detected by the proposed J4-phage based CLIA and electrochemical immunosensor, respectively. Therefore, the as-developed dual mode immunoassays are potential methods to detect SARS-CoV-2. It is also expected to explore various phages with specific peptides to different targets for bioanalysis.

Physics-Inspired Equivariant Descriptors of Nonbonded Interactions

One essential ingredient in many machine learning (ML) based methods for atomistic modeling of materials and molecules is the use of locality. While allowing better system-size scaling, this systematically neglects long-range (LR) effects such as electrostatic or dispersion interactions. We present an extension of the long distance equivariant (LODE) framework that can handle diverse LR interactions in a consistent way and seamlessly integrates with preexisting methods by building new sets of atom centered features. We provide a direct physical interpretation of these using the multipole expansion, which allows for simpler and more efficient implementations. The framework is applied to simple toy systems as proof of concept and a heterogeneous set of molecular dimers to push the method to its limits. By generalizing LODE to arbitrary asymptotic behaviors, we provide a coherent approach to treat arbitrary two- and many-body nonbonded interactions in the data-driven modeling of matter.

PepDRED: De Novo Peptide Design with Strong Binding Affinity for Target Protein

De novo design of peptides that bind specifically to functional proteins is beneficial for diagnostics and therapeutics. However, complex permutations and combinations of amino acids pose significant challenges to the rational design of peptides with desirable stability and affinity. Herein, we develop a computational-based evolution method, namely, peptidomimetics-driven recognition elements design (PepDRED), to derive hemoglobin-inspired peptidomimetics. PepDRED mimics the natural evolutionism pipeline to generate stable apovariant (AVs) structures for wild-type counterparts via automated point mutations and validates their efficiency through free binding energy analysis and per residue energy decomposition analysis. For application demonstration, we applied PepDRED to design de novo peptides to bind FhuA, a typical TonB-dependent transporter (TBDT). TBDTs are Gram-negative bacterial outer membrane proteins responsible for iron transport and vital for bacterial resistance. PepDRED generated a pool of AVs and proceeded to reach an optimized peptide, AV440, with a remarkable binding affinity of -21 kcal/mol. AV440 is ∼2.5-fold stronger than the existing FhuA inhibitor Microcin J25. Network energy analysis further unveils that incorporating methionine (M42) in the N-terminal region significantly enhances inter-residue contacts and binding affinity. PepDRED offers a prompt and efficient in silico approach to develop potent peptide candidates for target proteins.

Machine Learning Electron Density Prediction Using Weighted Smooth Overlap of Atomic Positions

Having access to accurate electron densities in chemical systems, especially for dynamical systems involving chemical reactions, ion transport, and other charge transfer processes, is crucial for numerous applications in materials chemistry. Traditional methods for computationally predicting electron density data for such systems include quantum mechanical (QM) techniques, such as density functional theory. However, poor scaling of these QM methods restricts their use to relatively small system sizes and short dynamic time scales. To overcome this limitation, we have developed a deep neural network machine learning formalism, which we call deep charge density prediction (DeepCDP), for predicting charge densities by only using atomic positions for molecules and condensed phase (periodic) systems. Our method uses the weighted smooth overlap of atomic positions to fingerprint environments on a grid-point basis and map it to electron density data generated from QM simulations. We trained models for bulk systems of copper, LiF, and silicon; for a molecular system, water; and for two-dimensional charged and uncharged systems, hydroxyl-functionalized graphane, with and without an added proton. We showed that DeepCDP achieves prediction R2 values greater than 0.99 and mean squared error values on the order of 10-5e2 Å-6 for most systems. DeepCDP scales linearly with system size, is highly parallelizable, and is capable of accurately predicting the excess charge in protonated hydroxyl-functionalized graphane. We demonstrate how DeepCDP can be used to accurately track the location of charges (protons) by computing electron densities at a few selected grid points in the materials, thus significantly reducing the computational cost. We also show that our models can be transferable, allowing prediction of electron densities for systems on which it has not been trained but that contain a subset of atomic species on which it has been trained. Our approach can be used to develop models that span different chemical systems and train them for the study of large-scale charge transport and chemical reactions.

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.

Proton Transport in Perfluorinated Ionomer Simulated by Machine-Learned Interatomic Potential

Polymers are a class of materials that are highly challenging to deal with using first-principles methods. Here, we present an application of machine-learned interatomic potentials to predict structural and dynamical properties of dry and hydrated perfluorinated ionomers. An improved active-learning algorithm using a small number of descriptors allows to efficiently construct an accurate and transferable model for this multielemental amorphous polymer. Molecular dynamics simulations accelerated by the machine-learned potentials accurately reproduce the heterogeneous hydrophilic and hydrophobic domains formed in this material as well as proton and water diffusion coefficients under a variety of humidity conditions. Our results reveal pronounced contributions of Grotthuss chains consisting of two to three water molecules to the high proton mobility under strongly humidified conditions.

Electrocatalytic Biomass Upgrading of Furfural using Transition-Metal Borides via Density Functional Theory Investigation

Electrocatalytic biomass upgrading has proven to be an effective technique for generating value-added products. Herein, the design and development of furfural upgrading using transition-metal borides (MBenes) with simultaneous production of hydrogen are presented. Using density functional theory, the stabilities, selectivities, and activities of 13 MBene candidates are systematically evaluated for furfural upgrading. This research suggests that Fe₂ B₂ can serve as a promising electrocatalyst for the formation of furoic acid (FAC), with a limiting potential of -0.15 V, and 5-hydroxy-2(5H)-furanone (HFO), with a limiting potential of -0.93 V. Furthermore, Fe₂ B₂ and Mn₂ Fe₂ are shown to exhibit favorable limiting potentials of -1.35 and -1.36 V, respectively, for producing 6-hydroxy-2.3-dihydro-6H-pyrano-3-one (HDPO), indicating that they may also serve as electrocatalysts. Based on Sabatier's principle, a descriptor (φ) of material properties is developed for screening catalysts with high catalytic activity considering the electronegativities and d-electron number of metals. Additionally, surface redox potential, electronic properties, and charge-density differences are determined for Fe₂ B₂ , which is estimated to exhibit high catalytic activity for the oxidation of furfural to FAC and HFO.

Data-driven approach for benchmarking DFTB-approximate excited state methods

In this work we propose a chemically-informed data-driven approach to benchmark the approximate density-functional tight-binding (DFTB) excited state (ES) methods that are currently available within the DFTB+ suite. By taking advantage of the large volume of low-detail ES-data in the machine learning (ML) dataset, QM8, we were able to extract valuable insights regarding the limitations of the benchmarked methods in terms of the approximations made to the parent formalism, density-functional theory (DFT), while providing recommendations on how to overcome them. For this benchmark, we compared the first singlet-singlet vertical excitation energies (E₁) predicted by the DFTB-approximate methods with predictions of less approximate methods from the reference ML-dataset. For the nearly 21800 organic molecules in the GDB-8 chemical space, we were able to identify clear trends in the E₁ prediction error distributions, with respect to second-order approximate coupled cluster (CC2), showing a strong dependence on chemical identity.

Interheteromolecular Hyperconjugation Boosts (De)hydrogenation for Reversible H2 Storage

Interheteromolecular hyperconjugation is ubiquitous in organic systems, affecting bond length, dipole moments, conformations and so on, while its effect on (de)hydrogenation reactivity in a heterogeneous thermo-catalytic system has rarely been explored. Herein, the N-heterocycles containing a benzene ring and aliphatic chain [N-ethylcarbazole (NEC) and N-propylcarbazole (NPC)] were utilized to study the correlation between interheteromolecular hyperconjugation and catalytic (de)hydrogenation. Density functional theory calculations, variable-temperature ¹ H nuclear magnetic resonance spectroscopy, and catalytic experiments showed that the presented hyperconjugation between NEC and NPC weakened the electron cloud density of aromatic rings and thus facilitated the reactivity with hydrogen featuring unpaired electrons. Therefore, an extremely low temperature of 80 °C was enough for the hydrogenation. Moreover, this interheteromolecular hyperconjugation was general in other N-heterocycles (e. g., N-methyindole and NPC) and was also effective to (de)deuterate as revealed by isotope experiments. This work expands the application of interheteromolecular hyperconjugation to heterogeneous thermocatalysis for reversible H₂ storage.

Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multicentered atomic basis analogous to that routinely used in density fitting approximations. However, the nonorthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex data sets, obtaining very accurate predictions using a comparatively small training set. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark data set, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.

Predicting accurate ab initio DNA electron densities with equivariant neural networks

One of the fundamental limitations of accurately modeling biomolecules like DNA is the inability to perform quantum chemistry calculations on large molecular structures. We present a machine learning model based on an equivariant Euclidean neural network framework to obtain accurate ab initio electron densities for arbitrary DNA structures that are much too large for conventional quantum methods. The model is trained on representative B-DNA basepair steps that capture both base pairing and base stacking interactions. The model produces accurate electron densities for arbitrary B-DNA structures with typical errors of less than 1%. Crucially, the error does not increase with system size, which suggests that the model can extrapolate to large DNA structures with negligible loss of accuracy. The model also generalizes reasonably to other DNA structural motifs such as the A- and Z-DNA forms, despite being trained on only B-DNA configurations. The model is used to calculate electron densities of several large-scale DNA structures, and we show that the computational scaling for this model is essentially linear. We also show that this machine learning electron density model can be used to calculate accurate electrostatic potentials for DNA. These electrostatic potentials produce more accurate results compared with classical force fields and do not show the usual deficiencies at short range.

Machine Learning for Harnessing Thermal Energy: From Materials Discovery to System Optimization

Recent advances in machine learning (ML) have impacted research communities based on statistical perspectives and uncovered invisibles from conventional standpoints. Though the field is still in the early stage, this progress has driven the thermal science and engineering communities to apply such cutting-edge toolsets for analyzing complex data, unraveling abstruse patterns, and discovering non-intuitive principles. In this work, we present a holistic overview of the applications and future opportunities of ML methods on crucial topics in thermal energy research, from bottom-up materials discovery to top-down system design across atomistic levels to multi-scales. In particular, we focus on a spectrum of impressive ML endeavors investigating the state-of-the-art thermal transport modeling (density functional theory, molecular dynamics, and Boltzmann transport equation), different families of materials (semiconductors, polymers, alloys, and composites), assorted aspects of thermal properties (conductivity, emissivity, stability, and thermoelectricity), and engineering prediction and optimization (devices and systems). We discuss the promises and challenges of current ML approaches and provide perspectives for future directions and new algorithms that could make further impacts on thermal energy research.

Metric Learning for Kernel Ridge Regression: Assessment of Molecular Similarity

Supervised and unsupervised kernel-based algorithms broadly used in physical sciences rely upon the notion of similarity. Their reliance on pre-defined distance metrics - e.g., the Euclidean or Manhattan distance - are problematic especially when used in combination with high-dimensional feature vectors for which the similarity measure does not well-reflect the differences in the target property. Metric learning is an elegant approach to surmount this shortcoming and find a property-informed transformation of the feature space. We propose a new algorithm for metric learning specifically adapted for Kernel Ridge Regression (Metric Learning for Kernel Ridge Regression or MLKRR), with applications in the physical sciences in mind. The MLKRR algorithm is built upon the Metric Learning for Kernel Regression (MLKR) framework based on the Nadaraya-Watson estimator, which we show to be inferior to the KRR estimator for typical physics-based machine learning tasks. Our MLKRR algorithm shows superior predictive performance on the benchmark regression task of atomisation energies of QM9 molecules, as well as generating more meaningful low-dimensional projections of the modified feature space.

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.

Informing geometric deep learning with electronic interactions to accelerate quantum chemistry

Predicting electronic energies, densities, and related chemical properties can facilitate the discovery of novel catalysts, medicines, and battery materials. However, existing machine learning techniques are challenged by the scarcity of training data when exploring unknown chemical spaces. We overcome this barrier by systematically incorporating knowledge of molecular electronic structure into deep learning. By developing a physics-inspired equivariant neural network, we introduce a method to learn molecular representations based on the electronic interactions among atomic orbitals. Our method, OrbNet-Equi, leverages efficient tight-binding simulations and learned mappings to recover high-fidelity physical quantities. OrbNet-Equi accurately models a wide spectrum of target properties while being several orders of magnitude faster than density functional theory. Despite only using training samples collected from readily available small-molecule libraries, OrbNet-Equi outperforms traditional semiempirical and machine learning-based methods on comprehensive downstream benchmarks that encompass diverse main-group chemical processes. Our method also describes interactions in challenging charge-transfer complexes and open-shell systems. We anticipate that the strategy presented here will help to expand opportunities for studies in chemistry and materials science, where the acquisition of experimental or reference training data is costly.

Accurate Molecular-Orbital-Based Machine Learning Energies via Unsupervised Clustering of Chemical Space

We introduce an unsupervised clustering algorithm to improve training efficiency and accuracy in predicting energies using molecular-orbital-based machine learning (MOB-ML). This work determines clusters via the Gaussian mixture model (GMM) in an entirely automatic manner and simplifies an earlier supervised clustering approach [ J. Chem. Theory Comput. 2019, 15, 6668] by eliminating both the necessity for user-specified parameters and the training of an additional classifier. Unsupervised clustering results from GMM have the advantages of accurately reproducing chemically intuitive groupings of frontier molecular orbitals and exhibiting improved performance with an increasing number of training examples. The resulting clusters from supervised or unsupervised clustering are further combined with scalable Gaussian process regression (GPR) or linear regression (LR) to learn molecular energies accurately by generating a local regression model in each cluster. Among all four combinations of regressors and clustering methods, GMM combined with scalable exact GPR (GMM/GPR) is the most efficient training protocol for MOB-ML. The numerical tests of molecular energy learning on thermalized data sets of drug-like molecules demonstrate the improved accuracy, transferability, and learning efficiency of GMM/GPR over other training protocols for MOB-ML, i.e., supervised regression clustering combined with GPR (RC/GPR) and GPR without clustering. GMM/GPR also provides the best molecular energy predictions compared with ones from the literature on the same benchmark data sets. With a lower scaling, GMM/GPR has a 10.4-fold speedup in wall-clock training time compared with scalable exact GPR with a training size of 6500 QM7b-T molecules.

QMugs, quantum mechanical properties of drug-like molecules

Machine learning approaches in drug discovery, as well as in other areas of the chemical sciences, benefit from curated datasets of physical molecular properties. However, there currently is a lack of data collections featuring large bioactive molecules alongside first-principle quantum chemical information. The open-access QMugs (Quantum-Mechanical Properties of Drug-like Molecules) dataset fills this void. The QMugs collection comprises quantum mechanical properties of more than 665 k biologically and pharmacologically relevant molecules extracted from the ChEMBL database, totaling ~2 M conformers. QMugs contains optimized molecular geometries and thermodynamic data obtained via the semi-empirical method GFN2-xTB. Atomic and molecular properties are provided on both the GFN2-xTB and on the density-functional levels of theory (DFT, ωB97X-D/def2-SVP). QMugs features molecules of significantly larger size than previously-reported collections and comprises their respective quantum mechanical wave functions, including DFT density and orbital matrices. This dataset is intended to facilitate the development of models that learn from molecular data on different levels of theory while also providing insight into the corresponding relationships between molecular structure and biological activity.

Kernel charge equilibration: efficient and accurate prediction of molecular dipole moments with a machine-learning enhanced electron density model

State-of-the-art machine learning (ML) interatomic potentials use local representations of atomic environments to ensure linear scaling and size-extensivity. This implies a neglect of long-range interactions, most prominently related to electrostatics. To overcome this limitation, we herein present a ML framework for predicting charge distributions and their interactions termed kernel charge equilibration (kQEq). This model is based on classical charge equilibration (QEq) models expanded with an environment-dependent electronegativity. In contrast to previously reported neural network models with a similar concept, kQEq takes advantage of the linearity of both QEq and Kernel Ridge Regression to obtain a closed-form linear algebra expression for training the models. Furthermore, we avoid the ambiguity of charge partitioning schemes by using dipole moments as reference data. As a first application, we show that kQEq can be used to generate accurate and highly data-efficient models for molecular dipole moments.

Interactions of Co, Cu, and non-metal phthalocyanines with external structures of SARS-CoV-2 using docking and molecular dynamics

The new coronavirus, SARS-CoV-2, caused the COVID-19 pandemic, characterized by its high rate of contamination, propagation capacity, and lethality rate. In this work, we approach the use of phthalocyanines as an inhibitor of SARS-CoV-2, as they present several interactive properties of the phthalocyanines (Pc) of Cobalt (CoPc), Copper (CuPc) and without a metal group (NoPc) can interact with SARS-CoV-2, showing potential be used as filtering by adsorption on paints on walls, masks, clothes, and air conditioning filters. Molecular modeling techniques through Molecular Docking and Molecular Dynamics were used, where the target was the external structures of the virus, but specifically the envelope protein, main protease, and Spike glycoprotein proteases. Using the g_MM-GBSA module and with it, the molecular docking studies show that the ligands have interaction characteristics capable of adsorbing the structures. Molecular dynamics provided information on the root-mean-square deviation of the atomic positions provided values between 1 and 2.5. The generalized Born implicit solvation model, Gibbs free energy, and solvent accessible surface area approach were used. Among the results obtained through molecular dynamics, it was noticed that interactions occur since Pc could bind to residues of the active site of macromolecules, demonstrating good interactions; in particular with CoPc. Molecular couplings and free energy showed that S-gly active site residues interacted strongly with phthalocyanines with values ​​of - 182.443 kJ/mol (CoPc), 158.954 kJ/mol (CuPc), and - 129.963 kJ/mol (NoPc). The interactions of Pc's with SARS-CoV-2 may predict some promising candidates for antagonists to the virus, which if confirmed through experimental approaches, may contribute to resolving the global crisis of the COVID-19 pandemic.

Large scale dataset of real space electronic charge density of cubic inorganic materials from density functional theory (DFT) calculations

Driven by the big data science, material informatics has attracted enormous research interests recently along with many recognized achievements. To acquire knowledge of materials by previous experience, both feature descriptors and databases are essential for training machine learning (ML) models with high accuracy. In this regard, the electronic charge density ρ(r), which in principle determines the properties of materials at their ground state, can be considered as one of the most appropriate descriptors. However, the systematic electronic charge density ρ(r) database of inorganic materials is still in its infancy due to the difficulties in collecting raw data in experiment and the expensive first-principles based computational cost in theory. Herein, a real space electronic charge density ρ(r) database of 17,418 cubic inorganic materials is constructed by performing high-throughput density functional theory calculations. The displayed ρ(r) patterns show good agreements with those reported in previous studies, which validates our computations. Further statistical analysis reveals that it possesses abundant and diverse data, which could accelerate ρ(r) related machine learning studies. Moreover, the electronic charge density database will also assists chemical bonding identifications and promotes new crystal discovery in experiments.

Can second-order perturbation theory accurately predict electron density of open-shell molecules? The importance of self-consistency

Electron density plays an essential role in predicting molecular properties.

New venues in electron density analysis

We provide a comprehensive overview of the chemical information within the electron density: how to extract information, but also how to obtain and how to assess the quality of the...

Learning Electron Densities in the Condensed Phase

We introduce a local machine-learning method for predicting the electron densities of periodic systems. The framework is based on a numerical, atom-centered auxiliary basis, which enables an accurate expansion of the all-electron density in a form suitable for learning isolated and periodic systems alike. We show that, using this formulation, the electron densities of metals, semiconductors, and molecular crystals can all be accurately predicted using symmetry-adapted Gaussian process regression models, properly adjusted for the nonorthogonal nature of the basis. These predicted densities enable the efficient calculation of electronic properties, which present errors on the order of tens of meV/atom when compared to ab initio density-functional calculations. We demonstrate the key power of this approach by using a model trained on ice unit cells containing only 4 water molecules to predict the electron densities of cells containing up to 512 molecules and see no increase in the magnitude of the errors of derived electronic properties when increasing the system size. Indeed, we find that these extrapolated derived energies are more accurate than those predicted using a direct machine-learning model. Finally, on heterogeneous data sets SALTED can predict electron densities with errors below 4%.

Artificial Neural Networks as Propagators in Quantum Dynamics

The utilization of artificial neural networks (ANNs) provides strategies for accelerating molecular simulations. Herein, ANNs are implemented as propagators of the time-dependent Schrödinger equation to simulate the quantum dynamics of systems with time-dependent potentials. These ANN propagators are trained to map nonstationary wavepackets from a given time to a future time within the discrete variable representation. Each propagator is trained for a specified time step, and iterative application of the propagator enables the propagation of wavepackets over long time scales. Such ANN propagators are developed and applied to one- and two-dimensional proton transfer systems, which exhibit nuclear quantum effects such as hydrogen tunneling. These ANN propagators are trained for either a specific time-independent potential or general potentials that can be time-dependent. Hierarchical, multiple time step algorithms enable parallelization, and the extension to higher dimensions is straightforward. This strategy is applicable to quantum dynamical simulations of diverse chemical and biological processes.

Gaussian Process Regression for Materials and Molecules

We provide an introduction to Gaussian process regression (GPR) machine-learning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine Learning for Electronically Excited States of Molecules

Electronically excited states of molecules are at the heart of photochemistry, photophysics, as well as photobiology and also play a role in material science. Their theoretical description requires highly accurate quantum chemical calculations, which are computationally expensive. In this review, we focus on not only how machine learning is employed to speed up such excited-state simulations but also how this branch of artificial intelligence can be used to advance this exciting research field in all its aspects. Discussed applications of machine learning for excited states include excited-state dynamics simulations, static calculations of absorption spectra, as well as many others. In order to put these studies into context, we discuss the promises and pitfalls of the involved machine learning techniques. Since the latter are mostly based on quantum chemistry calculations, we also provide a short introduction into excited-state electronic structure methods and approaches for nonadiabatic dynamics simulations and describe tricks and problems when using them in machine learning for excited states of molecules.

Machine-Learned Energy Functionals for Multiconfigurational Wave Functions

We introduce multiconfiguration data-driven functional methods (MC-DDFMs), a group of methods which aim to correct the total or classical energy of a qualitatively accurate multiconfigurational wave function using a machine-learned functional of some featurization of the wave function such as its density, on-top density, or both. On a data set of carbene singlet-triplet energy splittings, we show that MC-DDFMs are able to achieve near-benchmark performance on systems not used for training with a robust degree of active-space independence. Beyond demonstrating that the density and on-top density hold the information necessary to correct the singlet-triplet energy splittings of multiconfigurational wave functions, this approach shows great promise for the development of functionals for MC-PDFT because corrections to the classical energy appear to be more transferable to types of molecules not included in the training data than corrections to total energies such as those yielded by CASSCF or NEVPT2.

Eutectics: formation, properties, and applications

Various eutectic systems have been proposed and studied over the past few decades. Most of the studies have focused on three typical types of eutectics: eutectic metals, eutectic salts, and deep eutectic solvents. On the one hand, they are all eutectic systems, and their eutectic principle is the same. On the other hand, they are representative of metals, inorganic salts, and organic substances, respectively. They have applications in almost all fields related to chemistry. Their different but overlapping applications stem from their very different properties. In addition, the proposal of new eutectic systems has greatly boosted the development of cross-field research involving chemistry, materials, engineering, and energy. The goal of this review is to provide a comprehensive overview of these typical eutectics and describe task-specific strategies to address growing demands.

Physics-Inspired Structural Representations for Molecules and Materials

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

A Multitask Approach to Learn Molecular Properties

The endeavors to pursue a robust multitask model to resolve intertask correlations have lasted for many years. A multitask deep neural network, as the most widely used multitask framework, however, experiences several issues such as inconsistent performance improvement over the independent model benchmark. The research aims to introduce an alternative framework by using the problem transformation methods. We build our multitask models essentially based on the stacking of a base regressor and classifier, where the multitarget predictions are realized from an additional training stage on the expanded molecular feature space. The model architecture is implemented on the QM9, Alchemy, and Tox21 datasets, by using a variety of baseline machine learning techniques. The resultant multitask performance shows 1 to 10% enhancement of forecasting precision, with the task prediction accuracy being consistently improved over the independent single-target models. The proposed method demonstrates a notable superiority in tackling the intertarget dependence and, moreover, a great potential to simulate a wide range of molecular properties under the transformation framework.

Impact of quantum-chemical metrics on the machine learning prediction of electron density

Machine learning (ML) algorithms have undergone an explosive development impacting every aspect of computational chemistry. To obtain reliable predictions, one needs to maintain a proper balance between the black-box nature of ML frameworks and the physics of the target properties. One of the most appealing quantum-chemical properties for regression models is the electron density, and some of us recently proposed a transferable and scalable model based on the decomposition of the density onto an atom-centered basis set. The decomposition, as well as the training of the model, is at its core a minimization of some loss function, which can be arbitrarily chosen and may lead to results of different quality. Well-studied in the context of density fitting (DF), the impact of the metric on the performance of ML models has not been analyzed yet. In this work, we compare predictions obtained using the overlap and the Coulomb-repulsion metrics for both decomposition and training. As expected, the Coulomb metric used as both the DF and ML loss functions leads to the best results for the electrostatic potential and dipole moments. The origin of this difference lies in the fact that the model is not constrained to predict densities that integrate to the exact number of electrons N. Since an a posteriori correction for the number of electrons decreases the errors, we proposed a modification of the model, where N is included directly into the kernel function, which allowed lowering of the errors on the test and out-of-sample sets.

Learning the Exciton Properties of Azo-dyes

The ab initio determination of electronic excited state (ES) properties is the cornerstone of theoretical photochemistry. Yet, traditional ES methods become impractical when applied to fairly large molecules, or when used on thousands of systems. Machine learning (ML) techniques have demonstrated their accuracy at retrieving ES properties of large molecular databases at a reduced computational cost. For these applications, nonlinear algorithms tend to be specialized in targeting individual properties. Learning fundamental quantum objects potentially represents a more efficient, yet complex, alternative as a variety of molecular properties could be extracted through postprocessing. Herein, we report a general framework able to learn three fundamental objects: the hole and particle densities, as well as the transition density. We demonstrate the advantages of targeting those outputs and apply our predictions to obtain properties, including the state character and the exciton topological descriptors, for the two bands (nπ* and ππ*) of 3427 azoheteroarene photoswitches.

Perspective on integrating machine learning into computational chemistry and materials science

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

Machine Learning of Analytical Electron Density in Large Molecules Through Message-Passing

Machine learning milestones in computational chemistry are overshadowed by their unaccountability and the overwhelming zoo of tools for each specific task. A promising path to tackle these problems is using machine learning to reproduce physical magnitudes as a basis to derive many other properties. By using a model of the electron density consisting of an analytical expansion on a linear set of isotropic and anisotropic functions, we implemented in this work a message-passing neural network able to reproduce electron density in molecules with just a 2.5% absolute error in complex cases. We also adapted our methodology to describe electron density in large biomolecules (proteins) and to obtain atomic charges, interaction energies, and DFT energies. We show that electron density learning is a new promising avenue with a variety of forthcoming applications.

Machine Learning in QM/MM Molecular Dynamics Simulations of Condensed-Phase Systems

Quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulations have been developed to simulate molecular systems, where an explicit description of changes in the electronic structure is necessary. However, QM/MM MD simulations are computationally expensive compared to fully classical simulations as all valence electrons are treated explicitly and a self-consistent field (SCF) procedure is required. Recently, approaches have been proposed to replace the QM description with machine-learned (ML) models. However, condensed-phase systems pose a challenge for these approaches due to long-range interactions. Here, we establish a workflow, which incorporates the MM environment as an element type in a high-dimensional neural network potential (HDNNP). The fitted HDNNP describes the potential-energy surface of the QM particles with an electrostatic embedding scheme. Thus, the MM particles feel a force from the polarized QM particles. To achieve chemical accuracy, we find that even simple systems require models with a strong gradient regularization, a large number of data points, and a substantial number of parameters. To address this issue, we extend our approach to a Δ-learning scheme, where the ML model learns the difference between a reference method (density functional theory (DFT)) and a cheaper semiempirical method (density functional tight binding (DFTB)). We show that such a scheme reaches the accuracy of the DFT reference method while requiring significantly less parameters. Furthermore, the Δ-learning scheme is capable of correctly incorporating long-range interactions within a cutoff of 1.4 nm. It is validated by performing MD simulations of retinoic acid in water and the interaction between S-adenoslymethioniat and cytosine in water. The presented results indicate that Δ-learning is a promising approach for (QM)ML/MM MD simulations of condensed-phase systems.