High accuracy quantum-chemistry-based calculation and blind prediction of macroscopic pKa values in the context of the SAMPL6 challenge

POMSimulator: An open-source tool for predicting the aqueous speciation and self-assembly mechanisms of polyoxometalates

Elucidating the speciation (in terms of concentration versus pH) and understanding the formation mechanisms of polyoxometalates remains a significant challenge, both in experimental and computational domains. POMSimulator is a new methodology that tackles this problem from a purely computational perspective. The methodology uses results from quantum mechanics based methods to automatically set up the chemical reaction network, and to build speciation models. As a result, it becomes possible to predict speciation and phase diagrams, as well as to derive new insights into the formation mechanisms of large molecular clusters. In this work we present the main features of the first open-source version of the software. Since the first report [Chem. Sci. 2020, 11, 8448-8456], POMSimulator has undergone several improvements to keep up with the growing challenges that were tackled. After four years of research, we recognize that the source code is sufficiently stable to share a polished and user-friendly version. The Python code, manual, examples, and install instructions can be found at https://github.com/petrusen/pomsimulator.

QupKake: Integrating Machine Learning and Quantum Chemistry for Micro-pKa Predictions

Accurate prediction of micro-pKa values is crucial for understanding and modulating the acidity and basicity of organic molecules, with applications in drug discovery, materials science, and environmental chemistry. This work introduces QupKake, a novel method that combines graph neural network models with semiempirical quantum mechanical (QM) features to achieve exceptional accuracy and generalization in micro-pKa prediction. QupKake outperforms state-of-the-art models on a variety of benchmark data sets, with root-mean-square errors between 0.5 and 0.8 pKa units on five external test sets. Feature importance analysis reveals the crucial role of QM features in both the reaction site enumeration and micro-pKa prediction models. QupKake represents a significant advancement in micro-pKa prediction, offering a powerful tool for various applications in chemistry and beyond.

Recent Progress in the Endosomal Escape Mechanism and Chemical Structures of Polycations for Nucleic Acid Delivery

Nucleic acid-based therapies are seeing a spiralling surge. Stimuli-responsive polymers, especially pH-responsive ones, are gaining widespread attention because of their ability to efficiently deliver nucleic acids. These polymers can be synthesized and modified according to target requirements, such as delivery sites and the nature of nucleic acids. In this regard, the endosomal escape mechanism of polymer-nucleic acid complexes (polyplexes) remains a topic of considerable interest owing to various plausible escape mechanisms. This review describes current progress in the endosomal escape mechanism of polyplexes and state-of-the-art chemical designs for pH-responsive polymers. The importance is also discussed of the acid dissociation constant (i.e., pKa) in designing the new generation of pH-responsive polymers, along with assays to monitor and quantify the endosomal escape behavior. Further, the use of machine learning is addressed in pKa prediction and polymer design to find novel chemical structures for pH responsiveness. This review will facilitate the design of new pH-responsive polymers for advanced and efficient nucleic acid delivery.

CREST-A program for the exploration of low-energy molecular chemical space

Conformer-rotamer sampling tool (CREST) is an open-source program for the efficient and automated exploration of molecular chemical space. Originally developed in Pracht et al. [Phys. Chem. Chem. Phys. 22, 7169 (2020)] as an automated driver for calculations at the extended tight-binding level (xTB), it offers a variety of molecular- and metadynamics simulations, geometry optimization, and molecular structure analysis capabilities. Implemented algorithms include automated procedures for conformational sampling, explicit solvation studies, the calculation of absolute molecular entropy, and the identification of molecular protonation and deprotonation sites. Calculations are set up to run concurrently, providing efficient single-node parallelization. CREST is designed to require minimal user input and comes with an implementation of the GFNn-xTB Hamiltonians and the GFN-FF force-field. Furthermore, interfaces to any quantum chemistry and force-field software can easily be created. In this article, we present recent developments in the CREST code and show a selection of applications for the most important features of the program. An important novelty is the refactored calculation backend, which provides significant speed-up for sampling of small or medium-sized drug molecules and allows for more sophisticated setups, for example, quantum mechanics/molecular mechanics and minimum energy crossing point calculations.

Leveraging DFT and Molecular Fragmentation for Chemically Accurate pKa Prediction Using Machine Learning

We present a quantum mechanical/machine learning (ML) framework based on random forest to accurately predict the pKas of complex organic molecules using inexpensive density functional theory (DFT) calculations. By including physics-based features from low-level DFT calculations and structural features from our connectivity-based hierarchy (CBH) fragmentation protocol, we can correct the systematic error associated with DFT. The generalizability and performance of our model are evaluated on two benchmark sets (SAMPL6 and Novartis). We believe the carefully curated input of physics-based features lessens the model's data dependence and need for complex deep learning architectures, without compromising the accuracy of the test sets. As a point of novelty, our work extends the applicability of CBH, employing it for the generation of viable molecular descriptors for ML.

Efficient Assessment of 'Instantaneous pK' Values from Molecular Dynamics Simulations

We present a molecular simulation approach to studying the role of local and momentary molecular environment for potential acid-base reactions. For this, we combine thermodynamic considerations on the pK of ionic species with rapid sampling of energy changes related to (de)protonation. Using dispersed carbonate ions in water as a reference, our approach aims at the fast assessment of the momentary protonation energy, and thus the 'instantaneous pK', of calcium-carbonate ion aggregates. The latter include transient complexes that are elusive to long sampling runs. This motivated the elaboration of approximate, yet particularly fast assessable sampling strategies. Along this line, we were able to characterize instantaneous pK values at a statistical accuracy of 0.4 pK units within sampling runs of only 10 ps duration, whereas statistical errors reduce to 0.1 pK units in 75 ps sampling runs, respectively. This readily enabled the required time resolution for the characterization of [Cax (CO3 )y ]2(x-y) aggregates with x=1,2 and y=1,2,3, respectively. In turn, the analysis of the pH-dependent nature of calcite-water interfaces and dynamically ordered liquid-like oxyanion polymers (dollop) domains is outlined at 10 ps resolution.

ConfSolv: Prediction of Solute Conformer-Free Energies across a Range of Solvents

Predicting Gibbs free energy of solution is key to understanding the solvent effects on thermodynamics and reaction rates for kinetic modeling. Accurately computing solution free energies requires the enumeration and evaluation of relevant solute conformers in solution. However, even after generation of relevant conformers, determining their free energy of solution requires an expensive workflow consisting of several ab initio computational chemistry calculations. To help address this challenge, we generate a large data set of solution free energies for nearly 44,000 solutes with almost 9 million conformers calculated in 41 different solvents using density functional theory and COSMO-RS and quantify the impact of solute conformers on the solution free energy. We then train a message passing neural network to predict the relative solution free energies of a set of solute conformers, enabling the identification of a small subset of thermodynamically relevant conformers. The model offers substantial computational time savings with predictions usually substantially within 1 kcal/mol of the free energy of the solution calculated by using computational chemical methods.

Accurate Computation of Aqueous pKas of Biologically Relevant Organic Acids: Overcoming the Challenges Posed by Multiple Conformers, Tautomeric Equilibria, and Disparate Functional Groups with the Fully Black-Box pK-Yay Method

The use of static electronic structure calculations to compute solution-phase pKas offers a great advantage in that a macroscopic bulk property could be computed via microscopic computations involving very few molecules. There are various sources of errors in the quantum chemical calculations though. Overcoming these errors to accurately compute pKas of a plethora of acids is an active area of research in physical chemistry pursued by both computational as well as experimental chemists. We recently developed the pK-Yay method in our attempt to accurately compute aqueous pKas of strong and weak acids. The method is fully black-box, computationally inexpensive, and is very easy for even a nonexpert to use. However, the method was thus far tested on very few molecules (only 16 in all). Herein, in order to assess the future applicability of pK-Yay, we study the effect of multiple conformers, the presence of tautomers under equilibrium, and the impact of a wide variety of functional groups (derivatives of acetic acid with substituents at various positions, dicarboxylic acids, aromatic carboxylic acids, amines and amides, phenols and thiols, and fluorine bearing organic acids). Starting with more than 1000 conformers and tautomers, this study establishes that overall errors of ∼ 1.0 pKa units are routinely obtained for a majority of the molecules. Larger errors are noted in cases where multiple charges, intramolecular hydrogen bonding, and several ionizable functional groups are simultaneously present. An important conclusion to emerge from this work is that, the computed pKas are insensitive (difference <0.5) to whether we consider multiple conformers/tautomers or only choose the most stable conformer/tautomer. Further, pK-Yay captures the stereoelectronic effects arising due to differing axial vs equatorial pattern, and is useful to predict the dominant acid-base equilibrium in a system featuring several equilibria. Overall, pK-Yay may be employed in several chemical applications featuring organic molecules and biomonomers.

Recent Studies of Artificial Intelligence on In Silico Drug Absorption

Absorption is an important area of research in pharmacochemistry and drug development, because the drug has to be absorbed before any drug effects can occur. Furthermore, the ADMET (Absorption, Distribution, Metabolism, Excretion, and Toxicity) profile of drugs can be directly and considerably altered by modulating factors affecting absorption. Many drugs in development fail because of poor absorption. The research and continuous efforts of researchers in recent years have brought many successes and promises in drug absorption property prediction, especially in silico, which helps to reduce the time and cost significantly for screening undesirable drug candidates. In this report, we explicitly provide an overview of recent in silico studies on predicting absorption properties, especially from 2019 to the present, using artificial intelligence. Additionally, we have collected and investigated public databases that support absorption prediction research. On those grounds, we also proposed the challenges and development directions of absorption prediction in the future. We hope this review can provide researchers with valuable guidelines on absorption prediction to facilitate the development of newer approaches in drug discovery.

Gas-phase C60Hn+q (n = 0-4, q = 0,1) fullerenes and fulleranes: spectroscopic simulations shed light on cosmic molecular structures

The discovery of C60, C60+, and C70 in the interstellar medium has ignited a profound interest in the astrochemistry of fullerene and related systems. In particular, the presence of diffuse interstellar bands and their association with C60+ has led to the hypothesis that hydrogenated derivatives, known as fulleranes, may also exist in the interstellar medium and contribute to these bands. In this study, we systematically investigated the structural and spectroscopic properties of C60Hn+q (n = 0-4, q = 0,1) using an automated global minimum search and density functional theory calculations. Our results revealed novel global minimum structures for C60H2 and C60H4, distinct from previous reports. Notably, all hydrogenated fullerenes exhibited lower ionization potentials and higher proton affinities compared to C60. From an astrochemical perspective, our results exposed the challenges in establishing definitive spectroscopic criteria for detecting fulleranes using mid-infrared and UV-Vis spectroscopies. However, we successfully identified distinct electronic transitions in the near-infrared range that serve as distinctive signatures of cationic fulleranes. We strongly advocate for further high-resolution experimental studies to fully explore the potential of these transitions for the interstellar detection of fulleranes.

N-oxidation Regioselectivity and Risk Prediction Using DFT-ALIE Calculations

INTRODUCTION

The formation of N-oxide degradants is a major concern in development of new drugs due to potential effects on a compound's pharmacological activity. Such effects include but are not limited to solubility, stability, toxicity, and efficacy. In addition, these chemical transformations can impact physicochemical properties that affect drug manufacturability. Hence identification and control of N-oxide transformations is of critical importance in the development of new therapeutics.

OBJECTIVE

This study describes the development of an in-silico approach to identify N-oxide formation in APIs with respect to autoxidation.

METHODS

Average Local Ionization Energy (ALIE) calculations were carried out using molecular modeling techniques and application of Density Functional Theory (DFT) at the B3LYP/6-31G(d,p) level of theory. A total of 257 nitrogen atoms and 15 different oxidizable nitrogen types were used in developing this method.

RESULTS

The results show that ALIE could be reliably used to predict the most susceptible nitrogen for N-oxide formation. A risk scale was developed that rapidly categorizes nitrogen's oxidative vulnerabilities as small, medium, or high.

CONCLUSIONS

The developed process presents a powerful tool to identify structural susceptibilities for N-oxidation as well as enabling rapid structure elucidation in resolving potential experimental ambiguities.

Architector for high-throughput cross-periodic table 3D complex building

Rare-earth and actinide complexes are critical for a wealth of clean-energy applications. Three-dimensional (3D) structural generation and prediction for these organometallic systems remains a challenge, limiting opportunities for computational chemical discovery. Here, we introduce Architector, a high-throughput in-silico synthesis code for s-, p-, d-, and f-block mononuclear organometallic complexes capable of capturing nearly the full diversity of the known experimental chemical space. Beyond known chemical space, Architector performs in-silico design of new complexes including any chemically accessible metal-ligand combinations. Architector leverages metal-center symmetry, interatomic force fields, and tight binding methods to build many possible 3D conformers from minimal 2D inputs including metal oxidation and spin state. Over a set of more than 6,000 x-ray diffraction (XRD)-determined complexes spanning the periodic table, we demonstrate quantitative agreement between Architector-predicted and experimentally observed structures. Further, we demonstrate out-of-the box conformer generation and energetic rankings of non-minimum energy conformers produced from Architector, which are critical for exploring potential energy surfaces and training force fields. Overall, Architector represents a transformative step towards cross-periodic table computational design of metal complex chemistry.

Epik: pKa and Protonation State Prediction through Machine Learning

Epik version 7 is a software program that uses machine learning for predicting the pK_a values and protonation state distribution of complex, druglike molecules. Using an ensemble of atomic graph convolutional neural networks (GCNNs) trained on over 42,000 pK_a values across broad chemical space from both experimental and computed origins, the model predicts pK_a values with 0.42 and 0.72 pK_a unit median absolute and root mean square errors, respectively, across seven test sets. Epik version 7 also generates protonation states and recovers 95% of the most populated protonation states compared to previous versions. Requiring on average only 47 ms per ligand, Epik version 7 is rapid and accurate enough to evaluate protonation states for crucial molecules and prepare ultra-large libraries of compounds to explore vast regions of chemical space. The simplicity and time required for the training allow for the generation of highly accurate models customized to a program's specific chemistry.

Benchmarking quantum chemical methods for accurate gas-phase structure predictions of carbonyl compounds: the case of ethyl butyrate

High-resolution spectroscopy techniques play a pivotal role to validate and efficiently benchmark available methods from quantum chemistry. In this work, we analyzed the microwave spectrum of ethyl butyrate within the scope of a systematic investigation to benchmark state-of-the-art exchange-correlation functionals and ab initio methods, to accurately predict the lowest energy conformers of carbonyl compounds in their isolated state. Under experimental conditions, we observed two distinct conformers, one of C_s and one of C₁ symmetry. As reported earlier in the cases of some ethyl and methyl alkynoates, structural optimizations of the most abundant conformer that exhibits a C₁ symmetry proved extremely challenging for several quantum chemical levels. To probe the sensitivity of different methods and basis sets, we use the identified soft-degree of freedom in proximity to the carbonyl group as an order parameter. The results of our study provide useful insight for spectroscopists to select an adapted method for structure prediction of carbonyl compounds based on their available computational resources, suggesting a reasonable trade-off between accuracy and CPU cost. At the same time, our observations and the resulting sets of highly accurate experimental constants from high-resolution spectroscopy experiments give an appeal to theoretical groups to look further into this seemingly simple family of chemical compounds, which may prove useful for the further development and parametrization of theoretical methods in computational chemistry.

Machine learning methods for pKa prediction of small molecules: Advances and challenges

The acid-base dissociation constant (pK_a) is a fundamental property influencing many ADMET properties of small molecules. However, rapid and accurate pK_a prediction remains a great challenge. In this review, we outline the current advances in machine-learning-based QSAR models for pK_a prediction, including descriptor-based and graph-based approaches, and summarize their pros and cons. Moreover, we highlight the current challenges and future directions regarding experimental data, crucial factors influencing pK_a and in silico prediction tools. We hope that this review can provide a practical guidance for the follow-up studies.

MolGpka: A Web Server for Small Molecule pKa Prediction Using a Graph-Convolutional Neural Network

pK_a is an important property in the lead optimization process since the charge state of a molecule in physiologic pH plays a critical role in its biological activity, solubility, membrane permeability, metabolism, and toxicity. Accurate and fast estimation of small molecule pK_a is vital during the drug discovery process. We present MolGpKa, a web server for pK_a prediction using a graph-convolutional neural network model. The model works by learning pK_a related chemical patterns automatically and building reliable predictors with learned features. ACD/pK_a data for 1.6 million compounds from the ChEMBL database was used for model training. We found that the performance of the model is better than machine learning models built with human-engineered fingerprints. Detailed analysis shows that the substitution effect on pK_a is well learned by the model. MolGpKa is a handy tool for the rapid estimation of pK_a during the ligand design process. The MolGpKa server is freely available to researchers and can be accessed at https://xundrug.cn/molgpka.

SAMPL7 blind challenge: quantum-mechanical prediction of partition coefficients and acid dissociation constants for small drug-like molecules

The physicochemical properties of a drug molecule determine the therapeutic effectiveness of the drug. Thus, the development of fast and accurate theoretical approaches for the prediction of such properties is inevitable. The participation to the SAMPL7 challenge is based on the estimation of logP coefficients and pK_a values of small drug-like sulfonamide derivatives. Thereby, quantum mechanical calculations were carried out in order to calculate the free energy of solvation and the transfer energy of 22 drug-like compounds in different environments (water and n-octanol) by employing the SMD solvation model. For logP calculations, we studied eleven different methodologies to calculate the transfer free energies, the lowest RMSE value was obtained for the M06L/def2-TZVP//M06L/def2-SVP level of theory. On the other hand, we employed an isodesmic reaction scheme within the macro pK_a framework; this was based on selecting reference molecules similar to the SAMPL7 challenge molecules. Consequently, highly well correlated pK_a values were obtained with the M062X/6-311+G(2df,2p)//M052X/6-31+G(d,p) level of theory.

Evaluation of log P, pKa, and log D predictions from the SAMPL7 blind challenge

The Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) challenges focuses the computational modeling community on areas in need of improvement for rational drug design. The SAMPL7 physical property challenge dealt with prediction of octanol-water partition coefficients and pK_a for 22 compounds. The dataset was composed of a series of N-acylsulfonamides and related bioisosteres. 17 research groups participated in the log P challenge, submitting 33 blind submissions total. For the pK_a challenge, 7 different groups participated, submitting 9 blind submissions in total. Overall, the accuracy of octanol-water log P predictions in the SAMPL7 challenge was lower than octanol-water log P predictions in SAMPL6, likely due to a more diverse dataset. Compared to the SAMPL6 pK_a challenge, accuracy remains unchanged in SAMPL7. Interestingly, here, though macroscopic pK_a values were often predicted with reasonable accuracy, there was dramatically more disagreement among participants as to which microscopic transitions produced these values (with methods often disagreeing even as to the sign of the free energy change associated with certain transitions), indicating far more work needs to be done on pK_a prediction methods.

Efficient Quantum-Chemical Calculations of Acid Dissociation Constants from Free-Energy Relationships

The calculation of acid dissociation constants (pK_a) is an important task in computational chemistry and chemoinformatics. Theoretically and with minimal empiricism, this is possible from computed acid dissociation free energies via so-called linear free-energy relationships. In this study some modifications are introduced to the latter, providing a straightforward, broadly applicable protocol with an adjustable degree of sophistication for quantum chemistry-based calculations of pK_a in water. It targets a wide pK_a range (∼70 units) and medium-sized, flexible molecules. Herein, a focus is set on the recently published r²SCAN-3c and related efficient composite density functionals and the semiempirical GFN2-xTB method, including a newly introduced energy correction for heterolytic dissociation, both in combination with implicit solvation models. The performance is evaluated in comparison with experimental data, showing mean errors often smaller than a targeted 1 pK_a unit accuracy. Larger deviations are observed only upon inclusion of challenging highly negative (<-5) or positive (>15) pK_a values. Among all those tested, it is found that B97-3c is the best performing functional, although rather independently of the density functional theory (DFT) method used; low root-mean-square errors of 0.8-1.0 pK_a units for typical drugs are obtained. For optimal performance, it is recommended to employ DFT functional specific free-energy relationship parameters. Additionally, a significant conformational dependence of the pK_a values is revealed and quantified for some nonrigid drug molecules.

COSMO-RS predictions of logP in the SAMPL7 blind challenge

We applied the COSMO-RS method to predict the partition coefficient logP between water and 1-octanol for 22 small drug like molecules within the framework of the SAMPL7 blind challenge. We carefully collected a set of thermodynamically meaningful microstates, including tautomeric forms of the neutral species, and calculated the logP using the current COSMOtherm implementation on the most accurate level. With this approach, COSMO-RS was ranked as the 6st most accurate method (Measured by the mean absolute error (MAE) of 0.57) over all 17 ranked submissions. We achieved a root mean square deviation (RMSD) of 0.78. The largest deviations from experimental values are exhibited by five SAMPL molecules (SM), which seem to be shifted in most SAMPL7 contributions. In context with previous SAMPL challenges, COSMO-RS demonstrates a wide range of applicability and one of the best in class reliability and accuracy among the physical methods.

Unlocking Phase Diagrams for Molybdenum and Tungsten Nanoclusters and Prediction of their Formation Constants

Understanding and controlling aqueous speciation of metal oxides are key for the discovery and development of novel materials, and challenge both experimental and computational approaches. Here we present a computational method, called POMSimulator, which is able to predict speciation phase diagrams (Conc. vs pH) for multispecies chemical equilibria in solution, and which we apply to molybdenum and tungsten isopolyoxoanions (IPAs). Starting from the MO₄ monomers, and considering dimers, trimers, and larger species, the chemical reaction networks involved in the formation of [H₃₂Mo₃₆O₁₂₈]^8- and [W₁₂O₄₂]^12- are sampled in an automatic manner. This information is used for setting up ∼10⁵ speciation models, and from there, we generate the speciation phase diagrams, which show an insightful picture of the behavior of IPAs in aqueous solution. Furthermore, we predict the values of 107 formation constants for a diversity of molybdenum and tungsten molecular oxides. Among these species, we could include several pentagonal-shaped species and very reactive tungsten intermediates as well. Last but not least, the calibration employed for correcting the density functional theory (DFT) Gibbs energies is remarkably similar for both metals, which suggests that a general rule might exist for correcting computed free energies for other metals.

Efficient Quantum Chemical Calculation of Structure Ensembles and Free Energies for Nonrigid Molecules

The application of quantum chemical, automatic multilevel modeling workflows for the determination of thermodynamic (e.g., conformation equilibria, partition coefficients, pK_a values) and spectroscopic properties of relatively large, nonrigid molecules in solution is described. Key points are the computation of rather complete structure (conformer) ensembles with extremely fast but still reasonable GFN2-xTB or GFN-FF semiempirical methods in the CREST searching approach and subsequent refinement at a recently developed, accurate r²SCAN-3c DFT composite level. Solvation effects are included in all steps by accurate continuum solvation models (ALPB, (D)COSMO-RS). Consistent inclusion of thermostatistical contributions in the framework of the modified rigid-rotor-harmonic-oscillator approximation (mRRHO) based on xTB/FF computed PES is also recommended.

Overview of the SAMPL6 pKa challenge: evaluating small molecule microscopic and macroscopic pKa predictions

The prediction of acid dissociation constants (pKa) is a prerequisite for predicting many other properties of a small molecule, such as its protein-ligand binding affinity, distribution coefficient (log D), membrane permeability, and solubility. The prediction of each of these properties requires knowledge of the relevant protonation states and solution free energy penalties of each state. The SAMPL6 pKa Challenge was the first time that a separate challenge was conducted for evaluating pKa predictions as part of the Statistical Assessment of Modeling of Proteins and Ligands (SAMPL) exercises. This challenge was motivated by significant inaccuracies observed in prior physical property prediction challenges, such as the SAMPL5 log D Challenge, caused by protonation state and pKa prediction issues. The goal of the pKa challenge was to assess the performance of contemporary pKa prediction methods for drug-like molecules. The challenge set was composed of 24 small molecules that resembled fragments of kinase inhibitors, a number of which were multiprotic. Eleven research groups contributed blind predictions for a total of 37 pKa distinct prediction methods. In addition to blinded submissions, four widely used pKa prediction methods were included in the analysis as reference methods. Collecting both microscopic and macroscopic pKa predictions allowed in-depth evaluation of pKa prediction performance. This article highlights deficiencies of typical pKa prediction evaluation approaches when the distinction between microscopic and macroscopic pKas is ignored; in particular, we suggest more stringent evaluation criteria for microscopic and macroscopic pKa predictions guided by the available experimental data. Top-performing submissions for macroscopic pKa predictions achieved RMSE of 0.7-1.0 pKa units and included both quantum chemical and empirical approaches, where the total number of extra or missing macroscopic pKas predicted by these submissions were fewer than 8 for 24 molecules. A large number of submissions had RMSE spanning 1-3 pKa units. Molecules with sulfur-containing heterocycles or iodo and bromo groups were less accurately predicted on average considering all methods evaluated. For a subset of molecules, we utilized experimentally-determined microstates based on NMR to evaluate the dominant tautomer predictions for each macroscopic state. Prediction of dominant tautomers was a major source of error for microscopic pKa predictions, especially errors in charged tautomers. The degree of inaccuracy in pKa predictions observed in this challenge is detrimental to the protein-ligand binding affinity predictions due to errors in dominant protonation state predictions and the calculation of free energy corrections for multiple protonation states. Underestimation of ligand pKa by 1 unit can lead to errors in binding free energy errors up to 1.2 kcal/mol. The SAMPL6 pKa Challenge demonstrated the need for improving pKa prediction methods for drug-like molecules, especially for challenging moieties and multiprotic molecules.

Theoretical study on conformational energies of transition metal complexes

Conformational energies are an important chemical property for which a performance assessment of theoretical methods is mandatory. Existing benchmark sets are often limited to biochemical or main group element containing molecules, while organometallic systems are generally less studied. A key problem herein is to routinely generate conformers for these molecules due to their complexity and manifold of possible coordination patterns. In this study we used our recently published CREST protocol [Pracht et al., Phys. Chem. Chem. Phys., 2020, 22, 7169-7192] to generate conformer ensembles for a variety of 40 challenging transition metal containing molecules, which were then used to form a comprehensive conformational energy benchmark set termed TMCONF40. Several low-cost semiempirical, density functional theory (DFT) and force-field methods were compared to high level DLPNO-CCSD(T1) and double-hybrid DFT reference values. Close attention was paid to the energetic ordering of the conformers in the statistical evaluation. With respect to the double-hybrid references, both tested low-cost composite DFT methods produce high Pearson correlation coefficients of rp,mean,B97-3c//B97-3c = 0.922 and rp,mean,PBEh-3c//B97-3c = 0.890, with mean absolute deviations close to or below 1 kcal mol-1. This good performance also holds for a comparison to DLPNO-CCSD(T1) reference energies for a smaller subset termed TMCONF5. Based on DFT geometries, the GFNn-xTB methods yield reasonable Pearson correlation coefficients of rp,mean,GFN1-xTB//B97-3c = 0.617 (MADmean = 2.15 kcal mol-1) and rp,mean,GFN2-xTB//B97-3c = 0.567 (MADmean = 2.68 kcal mol-1), outperforming the widely used PMx methods on the TMCONF40 test set. Employing the low-cost composite DFT method B97-3c on GFN2-xTB geometries yields an slightly improved correlation of rp,mean,B97-3c//GFN2-xTB = 0.632. Furthermore, for 68% of the investigated complexes at least one low-energy conformer was found that is more stable than the respective crystal structure conformation, which signals the importance of conformational studies. General recommendations for the application of the CREST protocol and DFT methods for transition metal conformational energies are given.

Accurate and rapid prediction of pKa of transition metal complexes: semiempirical quantum chemistry with a data-augmented approach

Data-augmented high-throughput QM approach to compute pK_a of transition metal hydride complexes with hDFT accuracy and low cost.

ReSCoSS: a flexible quantum chemistry workflow identifying relevant solution conformers of drug-like molecules

Conformational equilibria are at the heart of drug design, yet their energetic description is often hampered by the insufficient accuracy of low-cost methods. Here we present a flexible and semi-automatic workflow based on quantum chemistry, ReSCoSS, designed to identify relevant conformers and predict their equilibria across different solvent environments in the Conductor-like Screening Model for Real Solvents (COSMO-RS) framework. We demonstrate the utility and accuracy of the workflow through conformational case studies on several drug-like molecules from literature where relevant conformations are known. We further show that including ReSCoSS conformers significantly improves COSMO-RS based predictions of physicochemical properties over single-conformation approaches. ReSCoSS has found broad adoption in the in-house drug discovery and development work streams and has contributed to establishing quantum-chemistry methods as a strategic pillar in ligand discovery.

Target-Based Identification and Optimization of 5-Indazol-5-yl Pyridones as Toll-like Receptor 7 and 8 Antagonists Using a Biochemical TLR8 Antagonist Competition Assay

Inappropriate activation of endosomal TLR7 and TLR8 occurs in several autoimmune diseases, in particular systemic lupus erythematosus (SLE). Herein, the development of a TLR8 antagonist competition assay and its application for hit generation of dual TLR7/8 antagonists are reported. The structure-guided optimization of the pyridone hit 3 using this biochemical assay in combination with cellular and TLR8 cocrystal structural data resulted in the identification of a highly potent and selective TLR7/8 antagonist (27) with in vivo efficacy. The two key steps for optimization were (i) a core morph guided by a TLR7 sequence alignment to achieve a dual TLR7/8 antagonism profile and (ii) introduction of a fluorine in the piperidine ring to reduce its basicity, resulting in attractive oral pharmacokinetic (PK) properties and improved TLR8 binding affinity.

Predicting pKa Using a Combination of Semi-Empirical Quantum Mechanics and Radial Basis Function Methods

The acid dissociation constant (pK_a) has an important influence on molecular properties crucial to compound development in synthesis, formulation, and optimization of absorption, distribution, metabolism, and excretion properties. We will present a method that combines quantum mechanical calculations, at a semi-empirical level of theory, with machine learning to accurately predict pK_a for a diverse range of mono- and polyprotic compounds. The resulting model has been tested on two external data sets, one specifically used to test pK_a prediction methods (SAMPL6) and the second covering known drugs containing basic functionalities. Both sets were predicted with excellent accuracy (root-mean-square errors of 0.7-1.0 log units), comparable to other methodologies using a much higher level of theory and computational cost.

A deep learning approach for the blind logP prediction in SAMPL6 challenge

Water octanol partition coefficient serves as a measure for the lipophilicity of a molecule and is important in the field of drug discovery. A novel method for computational prediction of logarithm of partition coefficient (logP) has been developed using molecular fingerprints and a deep neural network. The machine learning model was trained on a dataset of 12,000 molecules and tested on 2000 molecules. In this article, we present our results for the blind prediction of logP for the SAMPL6 challenge. While the best submission achieved a RMSE of 0.41 logP units, our submission had a RMSE of 0.61 logP units. Overall, we ranked in the top quarter out of the 92 submissions that were made. Our results show that the deep learning model can be used as a fast, accurate and robust method for high throughput prediction of logP of small molecules.

Automated exploration of the low-energy chemical space with fast quantum chemical methods

We propose and discuss an efficient scheme for the in silico sampling for parts of the molecular chemical space by semiempirical tight-binding methods combined with a meta-dynamics driven search algorithm. The focus of this work is set on the generation of proper thermodynamic ensembles at a quantum chemical level for conformers, but similar procedures for protonation states, tautomerism and non-covalent complex geometries are also discussed. The conformational ensembles consisting of all significantly populated minimum energy structures normally form the basis of further, mostly DFT computational work, such as the calculation of spectra or macroscopic properties. By using basic quantum chemical methods, electronic effects or possible bond breaking/formation are accounted for and a very reasonable initial energetic ranking of the candidate structures is obtained. Due to the huge computational speedup gained by the fast low-cost quantum chemical methods, overall short computation times even for systems with hundreds of atoms (typically drug-sized molecules) are achieved. Furthermore, specialized applications, such as sampling with implicit solvation models or constrained conformational sampling for transition-states, metal-, surface-, or noncovalently bound complexes are discussed, opening many possible applications in modern computational chemistry and drug discovery. The procedures have been implemented in a freely available computer code called CREST, that makes use of the fast and reliable GFNn-xTB methods.

Standard state free energies, not pKas, are ideal for describing small molecule protonation and tautomeric states

The pK_a is the standard measure used to describe the aqueous proton affinity of a compound, indicating the proton concentration (pH) at which two protonation states (e.g. A^- and AH) have equal free energy. However, compounds can have additional protonation states (e.g. AH₂⁺), and may assume multiple tautomeric forms, with the protons in different positions (microstates). Macroscopic pK_as give the pH where the molecule changes its total number of protons, while microscopic pK_as identify the tautomeric states involved. As tautomers have the same number of protons, the free energy difference between them and their relative probability is pH independent so there is no pK_a connecting them. The question arises: What is the best way to describe protonation equilibria of a complex molecule in any pH range? Knowing the number of protons and the relative free energy of all microstates at a single pH, ∆G°, provides all the information needed to determine the free energy, and thus the probability of each microstate at each pH. Microstate probabilities as a function of pH generate titration curves that highlight the low energy, observable microstates, which can then be compared with experiment. A network description connecting microstates as nodes makes it straightforward to test thermodynamic consistency of microstate free energies. The utility of this analysis is illustrated by a description of one molecule from the SAMPL6 Blind pK_a Prediction Challenge. Analysis of microstate ∆G°s also makes a more compact way to archive and compare the pH dependent behavior of compounds with multiple protonatable sites.

COSMO-RS based predictions for the SAMPL6 logP challenge

Within the framework of the 6th physical property blind challenge (SAMPL6) the authors have participated in predicting the octanol-water partition coefficients (logP) for several small drug like molecules. Those logP values where experimentally known by the organizers but only revealed after the submissions of the predictions. Two different sets of predictions were submitted by the authors, both based on the COSMOtherm implementation of COSMO-RS theory. COSMOtherm predictions using the FINE parametrization level (hmz0n) obtained the highest accuracy among all submissions as measured by the root mean squared error. COSMOquick predictions using a fast algorithm to estimate σ-profiles and an a posterio machine learning correction on top of the COSMOtherm results (3vqbi) scored 3rd out of 91 submissions. Both results underline the high quality of COSMO-RS derived molecular free energies in solution.

Structure Optimisation of Large Transition-Metal Complexes with Extended Tight-Binding Methods

Large transition-metal complexes are used in numerous areas of chemistry. Computer-aided theoretical investigations of such complexes are limited by the sheer size of real systems often consisting of hundreds to thousands of atoms. Accordingly, the development and thorough evaluation of fast semi-empirical quantum chemistry methods that are universally applicable to a large part of the periodic table is indispensable. Herein, we report on the capability of the recently developed GFNn-xTB method family for full quantum-mechanical geometry optimisation of medium to very large transition-metal complexes and organometallic supramolecular structures. The results for a specially compiled benchmark set of 145 diverse closed-shell transition-metal complex structures for all metals up to Hg are presented. Further the GFNn-xTB methods are tested on three established benchmark sets regarding reaction energies and barrier heights of organometallic reactions.

pKa calculations for tautomerizable and conformationally flexible molecules: partition function vs. state transition approach

Calculations of acidities of molecules with multiple tautomeric and/or conformational states require adequate treatment of the relative energetics of accessible states accompanied by a statistical-mechanical formulation of their contribution to the macroscopic pK_a value. Here, we demonstrate rigorously the formal equivalence of two such approaches: a partition function treatment and statistics over transitions between molecular tautomeric and conformational states in the limit of a theory that does not require adjustment by empirical parameters correcting energetic values. However, for a frequently employed correction scheme, linear scaling of (free) energies and regression with respect to reference data taking an additive constant into account, this equivalence breaks down if more than one acid or base state is involved. The consequences of the resulting inconsistency are discussed on our datasets developed for aqueous pK_a predictions during the recent SAMPL6 challenge, where molecular state energetics were computed based on the "embedded cluster reference interaction site model" (EC-RISM). This method couples integral equation theory as a solvation model to quantum-chemical calculations and yielded a test set root mean square error of 1.1 pK units from a partition function ansatz. For all practical purposes, the present results indicate that a state transition approach yields comparable accuracy despite the formal theoretical inconsistency, and that an additive regression intercept, which is strictly constant in the limit of large compound mass only, is a valid approximation. Graphical abstract Embedded cluster reference interaction site model-derived vs. experimental pK_a for the test set calculated with either the partition function (blue) or the state transition approach (red), using m as a free parameter.

Exploration of Chemical Compound, Conformer, and Reaction Space with Meta-Dynamics Simulations Based on Tight-Binding Quantum Chemical Calculations

The semiempirical tight-binding based quantum chemistry method GFN2-xTB is used in the framework of meta-dynamics (MTD) to globally explore chemical compound, conformer, and reaction space. The biasing potential given as a sum of Gaussian functions is expressed with the root-mean-square-deviation (RMSD) in Cartesian space as a metric for the collective variables. This choice makes the approach robust and generally applicable to three common problems (i.e., conformer search, chemical reaction space exploration in a virtual nanoreactor, and for guessing reaction paths). Because of the inherent locality of the atomic RMSD, functional group or fragment selective treatments are possible facilitating the investigation of catalytic processes where, for example, only the substrate is thermally activated. Due to the approximate character of the GFN2-xTB method, the resulting structure ensembles require further refinement with more sophisticated, for example, density functional or wave function theory methods. However, the approach is extremely efficient running routinely on common laptop computers in minutes to hours of computation time even for realistically sized molecules with a few hundred atoms. Furthermore, the underlying potential energy surface for molecules containing almost all elements ( Z = 1-86) is globally consistent including the covalent dissociation process and electronically complicated situations in, for example, transition metal systems. As examples, thermal decomposition, ethyne oligomerization, the oxidation of hydrocarbons (by oxygen and a P450 enzyme model), a Miller-Urey model system, a thermally forbidden dimerization, and a multistep intramolecular cyclization reaction are shown. For typical conformational search problems of organic drug molecules, the new MTD(RMSD) algorithm yields lower energy structures and more complete conformer ensembles at reduced computational effort compared with its already well performing predecessor.