A big data approach to the ultra-fast prediction of DFT-calculated bond energies

Computational tools for the prediction of site- and regioselectivity of organic reactions

The regio- and site-selectivity of organic reactions is one of the most important aspects when it comes to synthesis planning. Due to that, massive research efforts were invested into computational models for regio- and site-selectivity prediction, and the introduction of machine learning to the chemical sciences within the past decade has added a whole new dimension to these endeavors. This review article walks through the currently available predictive tools for regio- and site-selectivity with a particular focus on machine learning models while being organized along the individual reaction classes of organic chemistry. Respective featurization techniques and model architectures are described and compared to each other; applications of the tools to critical real-world examples are highlighted. This paper aims to serve as an overview of the field's status quo for both the intended users of the tools, that is synthetic chemists, as well as for developers to find potential new research avenues.

SwissADME studies and Density Functional Theory (DFT) approaches of methyl substituted curcumin derivatives

Research suggests curcumin's safety and efficacy, prompting interest in its use for treating and preventing various human diseases. The current study aimed to predict drag ability of methyl substituted curcumin derivatives (BL1 to BL4) using SwissADME and Density Functional Theory (DFT) approaches. The curcumin derivatives investigated mostly adhere to Lipinski's rule of five, with molecular properties including MW, F. Csp3, nHBA, nHBD, and TPSA falling within acceptable limits. The compounds demonstrating high lipophilicity while poor water solubility. The pharmacokinetic evaluation revealed favorable gastrointestinal absorption and blood-brain barrier permeation while none were identified as substrates for P-glycoprotein, however, revealed inhibitory actions against various cytochrome P450 enzymes. Additionally, all derivatives exhibited a consistent bioavailability score of 0.55. Similarly, the DFT computations of the compounds of the curcumin derivatives were conducted at B3LYP/6-311 G** level to predict and then assess the key electronic characteristics underlying the bioactivity. Accordingly, the BL4 molecule (ΔEgap= 4.105 eV) would prefer to interact with the external molecular system more than the other molecules due to having the biggest energy gap. The ΔNmax (2.328 eV) and Δεback-donat. (-0.446 eV) scores implied that BL1 would have more charge transfer capability and the lowest stability via back donation among the compounds. In short, the derivative (BL1 to BL4) exhibited strong extrinsic therapeutic properties and therefore stand eligible for further in vitro and in vivo studies.

A combined solid state, solution and DFT study of a dimethyl-cyclen-Pd(II) complex

A new palladium(II) complex containing the previously synthesized 4,10-bis[(3-hydroxy-4-pyron-2-yl)methyl]-1,7-dimethyl-1,4,7,10-tetraazacyclododecane ligand maltonis was prepared and characterized both in solution and in the solid state. Hirshfeld surface and energy framework analyses were also performed. Because maltonis already showed antineoplastic activity, the complexation of Pd(II), chosen as an alternative to Pt(II), was investigated to study its possible biological activity. UV-vis and NMR studies confirmed the formation and stability of the complex in aqueous solution at physiological pH. X-ray diffraction data revealed a structure where the Pd(II) ion is lodged in the dimethyl-cyclen cavity, with maltol rings facing each other (closed shape) even if they are not involved in the coordination. DFT analysis was performed in order to understand the most stable shape of the complex. In view of evaluating its possible bioactive conformation, the DFT study suggested a slight energetic preference for the closed one. The resulting closed complex was stabilized in the X-ray structure by intermolecular interactions that replace the intramolecular interactions present in the optimized complex. According to the DFT calculated formation energies, notwithstanding its rarity, the Pd(II) complex of maltonis is the thermodynamically preferred one among analogous complexes containing different metal ions (Pt(II), Co(II), and Cu(II)). Finally, to study its possible biological activity, the interaction between the Pd(II) complex of maltonis and nucleosides was evaluated through NMR and DFT calculations, revealing a possible interaction with purines via the maltol moieties.

Synergy of machine learning and density functional theory calculations for predicting experimental Lewis base affinity and Lewis polybase binding atoms

Investigation of Lewis acid-base interactions has been conducted by ab initio calculations and machine learning (ML) models. This study aims to resolve two critical tasks that have not been quantitatively investigated. First, ML models developed from density functional theory (DFT) calculations predict experimental BF3 affinity with Pearson correlation coefficients around 0.9 and mean absolute errors around 10 kJ mol-1. The ML models are trained by DFT-calculated BF3 affinity of more than 3000 adducts, with input features readily obtained by rdkit. Second, the ML models have the capability of predicting the relative strength of Lewis base binding atoms in Lewis polybases, which is either an extremely challenging task to conduct experimentally or a computationally expensive task for ab initio methods. The study demonstrates and solidifies the potential of combining DFT calculations and ML models to predict experimental properties, especially those that are scarce and impractical to empirically acquire.

Development and uniqueness test of highly selective atomic topological indices based on the number of attached hydrogen atoms

On the basis of the atomic graph-theoretical index - aEAID (atomic Extended Adjacency matrix IDentification) and molecular adjacent topological index - ATID (Adjacent Topological IDentification) suggested by one of the authors (Zhang Q), a highly selective atomic topological index - aATID (atomic Adjacent Topological IDentification) index was suggested to identify the equivalent atoms in this study. The aATID index of an atom was derived from the number of the attached hydrogen atoms of the atom but omitting bond types. In this case, the suggested index can be used to identify equivalent atoms in chemistry but perhaps not equivalent in the molecular graph. To test the uniqueness of aATID indices, the virtual atomic data sets were derived from alkanes containing 15-20 carbon atoms and the isomers of Octogen, as well as a real data set was derived from the NCI database. Only four pairs of atoms from alkanes containing 20 carbons can't be discriminated by aATID, that is, four pairs of degenerates were found for this data set. To solve this problem, the aATID index was modified by introducing distance factors between atoms, and the 2-aATID index was suggested. Its uniqueness was examined by 5,939,902 atoms derived from alkanes containing 20 carbons and further 16,166,984 atoms from alkanes of 21 carbons, and no degenerates were found. In addition, another large real data set of 16,650,688 atoms derived from the PubChem database was also used to test the uniqueness of both aATID and 2-aATID. As a result, each atom was successfully discriminated by any of the two indices. Finally, the suggested aATID index was applied to the identification of duplicate atoms as data pretreatment for QSPR (Quantitative Structure-Property Relationships) studies.

Exploring an accurate machine learning model to quickly estimate stability of diverse energetic materials

High energy and low sensitivity have been the focus of developing new energetic materials (EMs). However, there has been a lack of a quick and accurate method for evaluating the stability of diverse EMs. Here, we develop a machine learning prediction model with high accuracy for bond dissociation energy (BDE) of EMs. A reliable and representative BDE dataset of EMs is constructed by collecting 778 experimental energetic compounds and quantum mechanics calculation. To sufficiently characterize the BDE of EMs, a hybrid feature representation is proposed by coupling the local target bond into the global structure characteristics. To alleviate the limitation of the low dataset, pairwise difference regression is utilized as a data augmentation with the advantage of reducing systematic errors and improving diversity. Benefiting from these improvements, the XGBoost model achieves the best prediction accuracy with R2 of 0.98 and MAE of 8.8 kJ mol-1, significantly outperforming competitive models.

Toward Quantum-Informed Atom Pairs

In the following research, a new modification of traditional atom pairs is studied. The atom pairs are enriched with values originating from quantum chemistry calculations. A random forest machine learning algorithm is applied to model 10 different properties and biological activities based on different molecular representations, and it is evaluated via repeated cross-validation. The predictive power of modified atom pairs, quantum atom pairs, are compared to the predictive powers of traditional molecular representations known and widely applied in cheminformatics. The root mean squared error (RMSE), R2, area under the receiver operating characteristic curve (AUC) and balanced accuracy were used to evaluate the predictive power of the applied molecular representations. Research has shown that while performing regression tasks, quantum atom pairs provide better fits to the data than do their precursors.

Barrier Height Prediction by Machine Learning Correction of Semiempirical Calculations

Different machine learning (ML) models are proposed in the present work to predict density functional theory-quality barrier heights (BHs) from semiempirical quantum mechanical (SQM) calculations. The ML models include a multitask deep neural network, gradient-boosted trees by means of the XGBoost interface, and Gaussian process regression. The obtained mean absolute errors are similar to those of previous models considering the same number of data points. The ML corrections proposed in this paper could be useful for rapid screening of the large reaction networks that appear in combustion chemistry or in astrochemistry. Finally, our results show that 70% of the features with the highest impact on model output are bespoke predictors. This custom-made set of predictors could be employed by future Δ-ML models to improve the quantitative prediction of other reaction properties.

Machine Learned Composite Methods for Electronic Structure Theory

Because of the prohibitive scaling of ab initio techniques for modeling chemical species with high accuracy, they are not generally tractable for large systems. It is therefore of considerable interest to develop high-accuracy computational models with low computational cost that can afford predictions of electronic structure and properties of macromolecular species. Composite methods, as first introduced by Pople [Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys.1989, 90, 5622.], are an intuitive solution to this problem as they seek to systematically increase accuracy in model chemistries by taking advantage of favorable error cancellation among reasonably low-cost models. By linearly combining a series of carefully chosen model chemistries, the result of a prohibitive-scaling correlated model chemistry with a large basis set may be approximated with relatively good fidelity. However, the full extent to which the choice of low-cost models dictates the predictive accuracy of composite methods is not known, and a full exploration of all model chemistries would be advantageous for the design and validation of a generalizable composite method for widespread application. Here, we show that remarkable accuracy can be generally achieved with composite methods that are more judiciously constructed, leading to increased accuracy with significantly reduced computational cost. By designing a systematic procedure for the automated generation and assessment of over 10 billion unique composite methods, we have extensively explored the space of modern model chemistries to elucidate important design principles in the construction of reliable composite procedures. We anticipate our work to be the starting point in the pursuit of creative approaches to modeling large chemical systems with high accuracy by using novel combinatorial modeling.

Machine Learning to Predict Homolytic Dissociation Energies of C-H Bonds: Calibration of DFT-based Models with Experimental Data

Random Forest (RF) QSPR models were developed with a data set of homolytic bond dissociation energies (BDE) previously calculated by B3LYP/6-311++G(d,p)//DFTB for 2263 sp3C-H covalent bonds. The best set of attributes consisted in 114 descriptors of the carbon atom (counts of atom types in 5 spheres around the kernel atom and ring descriptors). The optimized model predicted the DFT-calculated BDE of an independent test set of 224 bonds with MAE=2.86 kcal/mol. A new data set of 409 bonds from the iBonD database (http://ibond.nankai.edu.cn) was predicted by the RF with a modest MAE (5.36 kcal/mol) but a relatively high R2 (0.75) against experimental energies. A prediction scheme was explored that corrects the RF prediction with the average deviation observed for the k nearest neighbours (KNN) in an additional memory of experimental data. The corrected predictions achieved MAE=2.22 kcal/mol for an independent test set of 145 bonds and the corresponding experimental bond energies.

Facile and highly precise pH-value estimation using common pH paper based on machine learning techniques and supported mobile devices

Numerous scientific, health care, and industrial applications are showing increasing interest in developing optical pH sensors with low-cost, high precision that cover a wide pH range. Although serious efforts, the development of high accuracy and cost-effectiveness, remains challenging. In this perspective, we present the implementation of the machine learning technique on the common pH paper for precise pH-value estimation. Further, we develop a simple, flexible, and free precise mobile application based on a machine learning algorithm to predict the accurate pH value of a solution using an available commercial pH paper. The common light conditions were studied under different light intensities of 350, 200, and 20 Lux. The models were trained using 2689 experimental values without a special instrument control. The pH range of 1: 14 is covered by an interval of ~ 0.1 pH value. The results show a significant relationship between pH values and both the red color and green color, in contrast to the poor correlation by the blue color. The K Neighbors Regressor model improves linearity and shows a significant coefficient of determination of 0.995 combined with the lowest errors. The free, publicly accessible online and mobile application was developed and enables the highly precise estimation of the pH value as a function of the RGB color code of typical pH paper. Our findings could replace higher expensive pH instruments using handheld pH detection, and an intelligent smartphone system for everyone, even the chef in the kitchen, without the need for additional costly and time-consuming experimental work.

MISPR: an open-source package for high-throughput multiscale molecular simulations

Computational tools provide a unique opportunity to study and design optimal materials by enhancing our ability to comprehend the connections between their atomistic structure and functional properties. However, designing materials with tailored functionalities is complicated due to the necessity to integrate various computational-chemistry software (not necessarily compatible with one another), the heterogeneous nature of the generated data, and the need to explore vast chemical and parameter spaces. The latter is especially important to avoid bias in scattered data points-based models and derive statistical trends only accessible by systematic datasets. Here, we introduce a robust high-throughput multi-scale computational infrastructure coined MISPR (Materials Informatics for Structure-Property Relationships) that seamlessly integrates classical molecular dynamics (MD) simulations with density functional theory (DFT). By enabling high-performance data analytics and coupling between different methods and scales, MISPR addresses critical challenges arising from the needs of automated workflow management and data provenance recording. The major features of MISPR include automated DFT and MD simulations, error handling, derivation of molecular and ensemble properties, and creation of output databases that organize results from individual calculations to enable reproducibility and transparency. In this work, we describe fully automated DFT workflows implemented in MISPR to compute various properties such as nuclear magnetic resonance chemical shift, binding energy, bond dissociation energy, and redox potential with support for multiple methods such as electron transfer and proton-coupled electron transfer reactions. The infrastructure also enables the characterization of large-scale ensemble properties by providing MD workflows that calculate a wide range of structural and dynamical properties in liquid solutions. MISPR employs the methodologies of materials informatics to facilitate understanding and prediction of phenomenological structure-property relationships, which are crucial to designing novel optimal materials for numerous scientific applications and engineering technologies.

Leveraging Regio- and Stereoselective C(sp3)-H Functionalization of Silyl Ethers to Train a Logistic Regression Classification Model for Predicting Site-Selectivity Bias

The C-H functionalization of silyl ethers via carbene-induced C-H insertion represents an efficient synthetic disconnection strategy. In this work, site- and stereoselective C(sp3)-H functionalization at α, γ, δ, and even more distal positions to the siloxy group has been achieved using donor/acceptor carbene intermediates. By exploiting the predilections of Rh2(R-TCPTAD)4 and Rh2(S-2-Cl-5-BrTPCP)4 catalysts to target either more electronically activated or more spatially accessible C-H sites, respectively, divergent desired products can be formed with good diastereocontrol and enantiocontrol. Notably, the reaction can also be extended to enable desymmetrization of meso silyl ethers. Leveraging the broad substrate scope examined in this study, we have trained a machine learning classification model using logistic regression to predict the major C-H functionalization site based on intrinsic substrate reactivity and catalyst propensity for overriding it. This model enables prediction of the major product when applying these C-H functionalization methods to a new substrate of interest. Applying this model broadly, we have demonstrated its utility for guiding late-stage functionalization in complex settings and developed an intuitive visualization tool to assist synthetic chemists in such endeavors.

Wani T, Batiha GES, Siddique F, Alqarni M, Akintola AA. Deep Learning and Structure-Based Virtual Screening for Drug Discovery against NEK7: A Novel Target for the Treatment of Cancer

NIMA-related kinase7 (NEK7) plays a multifunctional role in cell division and NLRP3 inflammasone activation. A typical expression or any mutation in the genetic makeup of NEK7 leads to the development of cancer malignancies and fatal inflammatory disease, i.e., breast cancer, non-small cell lung cancer, gout, rheumatoid arthritis, and liver cirrhosis. Therefore, NEK7 is a promising target for drug development against various cancer malignancies. The combination of drug repurposing and structure-based virtual screening of large libraries of compounds has dramatically improved the development of anticancer drugs. The current study focused on the virtual screening of 1200 benzene sulphonamide derivatives retrieved from the PubChem database by selecting and docking validation of the crystal structure of NEK7 protein (PDB ID: 2WQN). The compounds library was subjected to virtual screening using Auto Dock Vina. The binding energies of screened compounds were compared to standard Dabrafenib. In particular, compound 762 exhibited excellent binding energy of -42.67 kJ/mol, better than Dabrafenib (-33.89 kJ/mol). Selected drug candidates showed a reactive profile that was comparable to standard Dabrafenib. To characterize the stability of protein-ligand complexes, molecular dynamic simulations were performed, providing insight into the molecular interactions. The NEK7-Dabrafenib complex showed stability throughout the simulated trajectory. In addition, binding affinities, pIC50, and ADMET profiles of drug candidates were predicted using deep learning models. Deep learning models predicted the binding affinity of compound 762 best among all derivatives, which supports the findings of virtual screening. These findings suggest that top hits can serve as potential inhibitors of NEK7. Moreover, it is recommended to explore the inhibitory potential of identified hits compounds through in-vitro and in-vivo approaches.

Machine learning prediction of UV-Vis spectra features of organic compounds related to photoreactive potential

Machine learning (ML) algorithms were explored for the classification of the UV-Vis absorption spectrum of organic molecules based on molecular descriptors and fingerprints generated from 2D chemical structures. Training and test data (~ 75 k molecules and associated UV-Vis data) were assembled from a database with lists of experimental absorption maxima. They were labeled with positive class (related to photoreactive potential) if an absorption maximum is reported in the range between 290 and 700 nm (UV/Vis) with molar extinction coefficient (MEC) above 1000 Lmol^-1 cm^-1, and as negative if no such a peak is in the list. Random forests were selected among several algorithms. The models were validated with two external test sets comprising 998 organic molecules, obtaining a global accuracy up to 0.89, sensitivity of 0.90 and specificity of 0.88. The ML output (UV-Vis spectrum class) was explored as a predictor of the 3T3 NRU phototoxicity in vitro assay for a set of 43 molecules. Comparable results were observed with the classification directly based on experimental UV-Vis data in the same format.

BSE49, a diverse, high-quality benchmark dataset of separation energies of chemical bonds

We present an extensive and diverse dataset of bond separation energies associated with the homolytic cleavage of covalently bonded molecules (A-B) into their corresponding radical fragments (A. and B.). Our dataset contains two different classifications of model structures referred to as "Existing" (molecules with associated experimental data) and "Hypothetical" (molecules with no associated experimental data). In total, the dataset consists of 4502 datapoints (1969 datapoints from the Existing and 2533 datapoints from the Hypothetical classes). The dataset covers 49 unique X-Y type single bonds (except H-H, H-F, and H-Cl), where X and Y are H, B, C, N, O, F, Si, P, S, and Cl atoms. All the reference data was calculated at the (RO)CBS-QB3 level of theory. The reference bond separation energies are non-relativistic ground-state energy differences and contain no zero-point energy corrections. This new dataset of bond separation energies (BSE49) is presented as a high-quality reference dataset for assessing and developing computational chemistry methods.

John PC, Kim S, Paton RS. Importance of Engineered and Learned Molecular Representations in Predicting Organic Reactivity, Selectivity, and Chemical Properties

Machine-readable chemical structure representations are foundational in all attempts to harness machine learning for the prediction of reactivities, selectivities, and chemical properties directly from molecular structure. The featurization of discrete chemical structures into a continuous vector space is a critical phase undertaken before model selection, and the development of new ways to quantitatively encode molecules is an active area of research. In this Account, we highlight the application and suitability of different representations, from expert-guided "engineered" descriptors to automatically "learned" features, in different prediction tasks relevant to organic and organometallic chemistry, where differing amounts of training data are available. These tasks include statistical models of stereo- and enantioselectivity, thermochemistry, and kinetics developed using experimental and quantum chemical data.The use of expert-guided molecular descriptors provides an opportunity to incorporate chemical knowledge, domain expertise, and physical constraints into statistical modeling. In applications to stereoselective organic and organometallic catalysis, where data sets may be relatively small and 3D-geometries and conformations play an important role, mechanistically informed features can be used successfully to obtain predictive statistical models that are also chemically interpretable. We provide an overview of several recent applications of this approach to obtain quantitative models for reactivity and selectivity, where topological descriptors, quantum mechanical calculations of electronic and steric properties, along with conformational ensembles, all feature as essential ingredients of the molecular representations used.Alternatively, more flexible, general-purpose molecular representations such as attributed molecular graphs can be used with machine learning approaches to learn the complex relationship between a structure and prediction target. This approach has the potential to out-perform more traditional representation methods such as "hand-crafted" molecular descriptors, particularly as data set sizes grow. One area where this is particularly relevant is in the use of large sets of quantum mechanical data to train quantitative structure-property relationships. A general approach toward curating useful data sets and training highly accurate graph neural network models is discussed in the context of organic bond dissociation enthalpies, where this strategy outperforms regression using precomputed descriptors.Finally, we describe how graph neural network predictions can be incorporated into mechanistically informed statistical models of chemical reactivity and selectivity. Once trained, this approach avoids the expensive computational overhead associated with quantum mechanical calculations, while maintaining chemical interpretability. We illustrate examples for which fast predictions of bond dissociation enthalpy and of the identities of radicals formed through cleavage of a molecule's weakest bond are used in simple physical models of site-selectivity and reactivity.

BonDNet: a graph neural network for the prediction of bond dissociation energies for charged molecules

A broad collection of technologies, including e.g. drug metabolism, biofuel combustion, photochemical decontamination of water, and interfacial passivation in energy production/storage systems rely on chemical processes that involve bond-breaking molecular reactions. In this context, a fundamental thermodynamic property of interest is the bond dissociation energy (BDE) which measures the strength of a chemical bond. Fast and accurate prediction of BDEs for arbitrary molecules would lay the groundwork for data-driven projections of complex reaction cascades and hence a deeper understanding of these critical chemical processes and, ultimately, how to reverse design them. In this paper, we propose a chemically inspired graph neural network machine learning model, BonDNet, for the rapid and accurate prediction of BDEs. BonDNet maps the difference between the molecular representations of the reactants and products to the reaction BDE. Because of the use of this difference representation and the introduction of global features, including molecular charge, it is the first machine learning model capable of predicting both homolytic and heterolytic BDEs for molecules of any charge. To test the model, we have constructed a dataset of both homolytic and heterolytic BDEs for neutral and charged (-1 and +1) molecules. BonDNet achieves a mean absolute error (MAE) of 0.022 eV for unseen test data, significantly below chemical accuracy (0.043 eV). Besides the ability to handle complex bond dissociation reactions that no previous model could consider, BonDNet distinguishes itself even in only predicting homolytic BDEs for neutral molecules; it achieves an MAE of 0.020 eV on the PubChem BDE dataset, a 20% improvement over the previous best performing model. We gain additional insight into the model's predictions by analyzing the patterns in the features representing the molecules and the bond dissociation reactions, which are qualitatively consistent with chemical rules and intuition. BonDNet is just one application of our general approach to representing and learning chemical reactivity, and it could be easily extended to the prediction of other reaction properties in the future.

Prediction of organic homolytic bond dissociation enthalpies at near chemical accuracy with sub-second computational cost

Bond dissociation enthalpies (BDEs) of organic molecules play a fundamental role in determining chemical reactivity and selectivity. However, BDE computations at sufficiently high levels of quantum mechanical theory require substantial computing resources. In this paper, we develop a machine learning model capable of accurately predicting BDEs for organic molecules in a fraction of a second. We perform automated density functional theory (DFT) calculations at the M06-2X/def2-TZVP level of theory for 42,577 small organic molecules, resulting in 290,664 BDEs. A graph neural network trained on a subset of these results achieves a mean absolute error of 0.58 kcal mol^-1 (vs DFT) for BDEs of unseen molecules. We further demonstrate the model on two applications: first, we rapidly and accurately predict major sites of hydrogen abstraction in the metabolism of drug-like molecules, and second, we determine the dominant molecular fragmentation pathways during soot formation.

A Quantitative Model for Alkane Nucleophilicity Based on C-H Bond Structural/Topological Descriptors

A first quantitative model for calculating the nucleophilicity of alkanes is described. A statistical treatment was applied to the analysis of the reactivity of 29 different alkane C-H bonds towards in situ generated metal carbene electrophiles. The correlation of the recently reported experimental reactivity with two different sets of descriptors comprising a total of 86 parameters was studied, resulting in the quantitative descriptor-based alkane nucleophilicity (QDEAN) model. This model consists of an equation with only six structural/topological descriptors, and reproduces the relative reactivity of the alkane C-H bonds. This reactivity can be calculated from parameters emerging from the schematic drawing of the alkane and a simple set of sums.

Machine learning models for hydrogen bond donor and acceptor strengths using large and diverse training data generated by first-principles interaction free energies

We present machine learning (ML) models for hydrogen bond acceptor (HBA) and hydrogen bond donor (HBD) strengths. Quantum chemical (QC) free energies in solution for 1:1 hydrogen-bonded complex formation to the reference molecules 4-fluorophenol and acetone serve as our target values. Our acceptor and donor databases are the largest on record with 4426 and 1036 data points, respectively. After scanning over radial atomic descriptors and ML methods, our final trained HBA and HBD ML models achieve RMSEs of 3.8 kJ mol-1 (acceptors), and 2.3 kJ mol-1 (donors) on experimental test sets, respectively. This performance is comparable with previous models that are trained on experimental hydrogen bonding free energies, indicating that molecular QC data can serve as substitute for experiment. The potential ramifications thereof could lead to a full replacement of wetlab chemistry for HBA/HBD strength determination by QC. As a possible chemical application of our ML models, we highlight our predicted HBA and HBD strengths as possible descriptors in two case studies on trends in intramolecular hydrogen bonding.

The maximum occupancy condition for the localized property-optimized orbitals

It is shown analytically that the Chemist's Localized Property-optimized Orbitals (CLPOs), which are the localized orbitals obtainable from the results of ab initio calculations by the open-source program JANPA (http://janpa.sourceforge.net/) according to the recently proposed optimal property partitioning condition, form the Lewis structure with nearly maximum possible total electron occupancy. The conditions required for this additional optimality to hold are discussed. In particular, when a single-determinant wavefunction is used to describe the molecular system without a noticeable electron delocalization, CLPOs derived from this wavefunction approximately optimize the same target quantity as the Natural Bond Orbitals (NBOs), establishing in this way the link between the two sets of localized orbitals. The performance of CLPO and NBO methods is compared by using a dataset containing 7101 small molecules, and the relevant methodological features of both methods are discussed.

A Density Functional Tight Binding Layer for Deep Learning of Chemical Hamiltonians

Current neural networks for predictions of molecular properties use quantum chemistry only as a source of training data. This paper explores models that use quantum chemistry as an integral part of the prediction process. This is done by implementing self-consistent-charge Density-Functional-Tight-Binding (DFTB) theory as a layer for use in deep learning models. The DFTB layer takes, as input, Hamiltonian matrix elements generated from earlier layers and produces, as output, electronic properties from self-consistent field solutions of the corresponding DFTB Hamiltonian. Backpropagation enables efficient training of the model to target electronic properties. Two types of input to the DFTB layer are explored, splines and feed-forward neural networks. Because overfitting can cause models trained on smaller molecules to perform poorly on larger molecules, regularizations are applied that penalize nonmonotonic behavior and deviation of the Hamiltonian matrix elements from those of the published DFTB model used to initialize the model. The approach is evaluated on 15 700 hydrocarbons by comparing the root-mean-square error in energy and dipole moment, on test molecules with eight heavy atoms, to the error from the initial DFTB model. When trained on molecules with up to seven heavy atoms, the spline model reduces the test error in energy by 60% and in dipole moments by 42%. The neural network model performs somewhat better, with error reductions of 67% and 59%, respectively. Training on molecules with up to four heavy atoms reduces performance, with both the spline and neural net models reducing the test error in energy by about 53% and in dipole by about 25%.

Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics

Classical Hamiltonian trajectories are initiated at random points in phase space on a fixed energy shell of a model two degrees of freedom potential, consisting of two interacting minima in an otherwise flat energy plane of infinite extent. Below the energy of the plane, the dynamics are demonstrably chaotic. However, most of the work in this paper involves trajectories at a fixed energy that is 1% above that of the plane, in which regime the dynamics exhibit behavior characteristic of chaotic scattering. The trajectories are analyzed without reference to the potential, as if they had been generated in a typical direct molecular dynamics simulation. The questions addressed are whether one can recover useful information about the structures controlling the dynamics in phase space from the trajectory data alone, and whether, despite the at least partially chaotic nature of the dynamics, one can make statistically meaningful predictions of trajectory outcomes from initial conditions. It is found that key unstable periodic orbits, which can be identified on the analytical potential, appear by simple classification of the trajectories, and that the specific roles of these periodic orbits in controlling the dynamics are also readily discerned from the trajectory data alone. Two different approaches to predicting trajectory outcomes from initial conditions are evaluated, and it is shown that the more successful of them has ∼90% success. The results are compared with those from a simple neural network, which has higher predictive success (97%) but requires the information obtained from the "by-hand" analysis to achieve that level. Finally, the dynamics, which occur partly on the very flat region of the potential, show characteristics of the much-studied phenomenon called "roaming." On this potential, it is found that roaming trajectories are effectively "failed" periodic orbits and that angular momentum can be identified as a key controlling factor, despite the fact that it is not a strictly conserved quantity. It is also noteworthy that roaming on this potential occurs in the absence of a "roaming saddle," which has previously been hypothesized to be a necessary feature for roaming to occur.

Intrinsic Bond Energies from a Bonds-in-Molecules Neural Network

Neural networks are being used to make new types of empirical chemical models as inexpensive as force fields, but with accuracy similar to the ab initio methods used to build them. In this work, we present a neural network that predicts the energies of molecules as a sum of intrinsic bond energies. The network learns the total energies of the popular GDB9 database to a competitive MAE of 0.94 kcal/mol on molecules outside of its training set, is naturally linearly scaling, and applicable to molecules consisting of thousands of bonds. More importantly, it gives chemical insight into the relative strengths of bonds as a function of their molecular environment, despite only being trained on total energy information. We show that the network makes predictions of relative bond strengths in good agreement with measured trends and human predictions. A Bonds-in-Molecules Neural Network (BIM-NN) learns heuristic relative bond strengths like expert synthetic chemists, and compares well with ab initio bond order measures such as NBO analysis.

Machine Learning Methods to Predict Density Functional Theory B3LYP Energies of HOMO and LUMO Orbitals

Machine learning algorithms were explored for the fast estimation of HOMO and LUMO orbital energies calculated by DFT B3LYP, on the basis of molecular descriptors exclusively based on connectivity. The whole project involved the retrieval and generation of molecular structures, quantum chemical calculations for a database with >111 000 structures, development of new molecular descriptors, and training/validation of machine learning models. Several machine learning algorithms were screened, and an applicability domain was defined based on Euclidean distances to the training set. Random forest models predicted an external test set of 9989 compounds achieving mean absolute error (MAE) up to 0.15 and 0.16 eV for the HOMO and LUMO orbitals, respectively. The impact of the quantum chemical calculation protocol was assessed with a subset of compounds. Inclusion of the orbital energy calculated by PM7 as an additional descriptor significantly improved the quality of estimations (reducing the MAE in >30%).

Chemoinformatics: Achievements and Challenges, a Personal View

Chemoinformatics provides computer methods for learning from chemical data and for modeling tasks a chemist is facing. The field has evolved in the past 50 years and has substantially shaped how chemical research is performed by providing access to chemical information on a scale unattainable by traditional methods. Many physical, chemical and biological data have been predicted from structural data. For the early phases of drug design, methods have been developed that are used in all major pharmaceutical companies. However, all domains of chemistry can benefit from chemoinformatics methods; many areas that are not yet well developed, but could substantially gain from the use of chemoinformatics methods. The quality of data is of crucial importance for successful results. Computer-assisted structure elucidation and computer-assisted synthesis design have been attempted in the early years of chemoinformatics. Because of the importance of these fields to the chemist, new approaches should be made with better hardware and software techniques. Society's concern about the impact of chemicals on human health and the environment could be met by the development of methods for toxicity prediction and risk assessment. In conjunction with bioinformatics, our understanding of the events in living organisms could be deepened and, thus, novel strategies for curing diseases developed. With so many challenging tasks awaiting solutions, the future is bright for chemoinformatics.