Systematic Comparison of Experimental Crystallographic Geometries and Gas-Phase Computed Conformers for Torsion Preferences.

We performed exhaustive torsion sampling on more than 3 million compounds using the GFN2-xTB method and performed a comparison of experimental crystallographic and gas-phase conformers. Many conformer sampling methods derive torsional angle distributions from experimental crystallographic data, limiting the torsion preferences to molecules that must be stable, synthetically accessible, and able to be crystallized. In this work, we evaluate the differences in torsional preferences of experimental crystallographic geometries and gas-phase computed conformers from a broad selection of compounds to determine whether torsional angle distributions obtained from semiempirical methods are suitable priors for conformer sampling. We find that differences in torsion preferences can be mostly attributed to a lack of available experimental crystallographic data with small deviations derived from gas-phase geometry differences. GFN2 demonstrates the ability to provide accurate and reliable torsional preferences that can provide a basis for new methods free from the limitations of experimental data collection. We provide Gaussian-based fits and sampling distributions suitable for torsion sampling and propose an alternative to the widely used "experimental torsion and knowledge distance geometry" (ETKDG) method using quantum torsion-derived distance geometry (QTDG) methods.

Conformer Generation for Structure-Based Drug Design: How Many and How Good?

Conformer generation, the assignment of realistic 3D coordinates to a small molecule, is fundamental to structure-based drug design. Conformational ensembles are required for rigid-body matching algorithms, such as shape-based or pharmacophore approaches, and even methods that treat the ligand flexibly, such as docking, are dependent on the quality of the provided conformations due to not sampling all degrees of freedom (e.g., only sampling torsions). Here, we empirically elucidate some general principles about the size, diversity, and quality of the conformational ensembles needed to get the best performance in common structure-based drug discovery tasks. In many cases, our findings may parallel "common knowledge" well-known to practitioners of the field. Nonetheless, we feel that it is valuable to quantify these conformational effects while reproducing and expanding upon previous studies. Specifically, we investigate the performance of a state-of-the-art generative deep learning approach versus a more classical geometry-based approach, the effect of energy minimization as a postprocessing step, the effect of ensemble size (maximum number of conformers), and construction (filtering by root-mean-square deviation for diversity) and how these choices influence the ability to recapitulate bioactive conformations and perform pharmacophore screening and molecular docking.

Using genetic algorithms to discover novel ground-state triplet conjugated polymers.

Stable ground-state triplet π-conjugated copolymers have many interesting electronic and optoelectronic properties. However, the large number of potential monomer combinations makes it impractical to synthesize or even just use density functional theory (DFT) to calculate their triplet ground-state stability. Here, we present a genetic algorithm implementation that uses the semi-empirical GFN2-xTB to find ground-state triplet polymer candidates. We find more than 1400 polymer candidates with a triplet ground-state stability of up to 4 eV versus the singlet. Additionally, we explore the properties of the monomers of those candidates in order to understand the design rules which promote the formation of a stable ground-state triplet in π-conjugated polymers.

Determining best practices for using genetic algorithms in molecular discovery.

Genetic algorithms (GAs) are a powerful tool to search large chemical spaces for inverse molecular design. However, GAs have multiple hyperparameters that have not been thoroughly investigated for chemical space searches. In this tutorial, we examine the general effects of a number of hyperparameters, such as population size, elitism rate, selection method, mutation rate, and convergence criteria, on key GA performance metrics. We show that using a self-termination method with a minimum Spearman's rank correlation coefficient of 0.8 between generations maintained for 50 consecutive generations along with a population size of 32, a 50% elitism rate, three-way tournament selection, and a 40% mutation rate provides the best balance of finding the overall champion, maintaining good coverage of elite targets, and improving relative speedup for general use in molecular design GAs.

Evaluating fast methods for static polarizabilities on extended conjugated oligomers.

Given the importance of accurate polarizability calculations to many chemical applications, coupled with the need for efficiency when calculating the properties of sets of molecules or large oligomers, we present a benchmark study examining possible calculation methods for polarizable materials. We first investigate the accuracy of the additive model used in GFN2, a highly-efficient semi-empirical tight-binding method, and the D4 dispersion model, comparing its predicted additive polarizabilities to ωB97XD results for a subset of PubChemQC and a compiled benchmark set of molecules spanning polarizabilities from approximately 3 Å3 to 600 Å3, with some compounds in the range of approximately 1200-1400 Å3. Although we find additive GFN2 polarizabilities, and thus D4, to have large errors with polarizability calculations on large conjugated oligomers, it would appear an empirical quadratic correction can largely remedy this. We also compare the accuracy of DFT polarizability calculations run using basis sets of varying size and level of augmentation, determining that a non-augmented basis set may be used for large, highly polarizable species in conjunction with a linear correction factor to achieve accuracy extremely close to that of aug-cc-pVTZ.

Pareto Optimization of Oligomer Polarizability and Dipole Moment Using a Genetic Algorithm.

High-performance electronic components are highly sought after in order to produce increasingly smaller and cheaper electronic devices. Drawing inspiration from inorganic dielectric materials, in which both polarizability and polarization contribute, organic materials can also maximize both. For a large set of small molecules drawn from PubChem, a Pareto-like front appears between the polarizability and dipole moment, indicating the presence of an apparent trade-off between these two properties. We tested this balance in π-conjugated materials by searching for novel conjugated hexamers with simultaneously large polarizabilities and dipole moments with potential use for dielectric materials. Using a genetic algorithm (GA) screening technique in conjunction with an approximate density functional tight-binding method for property calculations, we were able to efficiently search chemical space for optimal hexamers. Given the scope of chemical space, using the GA technique saves considerable time and resources by speeding up molecular searches compared to a systematic search. We also explored the underlying structure-function relationships, including sequence and monomer properties, that characterize large polarizability and dipole moment regimes.

Computational evolution of high-performing unfused non-fullerene acceptors for organic solar cells.

Materials optimization for organic solar cells (OSCs) is a highly active field, with many approaches using empirical experimental synthesis, computational brute force to screen a subset of chemical space, or generative machine learning methods that often require significant training sets. While these methods may find high-performing materials, they can be inefficient and time-consuming. Genetic algorithms (GAs) are an alternative approach, allowing for the "virtual synthesis" of molecules and a prediction of their "fitness" for some property, with new candidates suggested based on good characteristics of previously generated molecules. In this work, a GA is used to discover high-performing unfused non-fullerene acceptors (NFAs) based on an empirical prediction of power conversion efficiency (PCE) and provides design rules for future work. The electron-withdrawing/donating strength, as well as the sequence and symmetry, of those units are examined. The utilization of a GA over a brute-force approach resulted in speedups up to 1.8 × 1012. New types of units, not frequently seen in OSCs, are suggested, and in total 5426 NFAs are discovered with the GA. Of these, 1087 NFAs are predicted to have a PCE greater than 18%, which is roughly the current record efficiency. While the symmetry of the sequence showed no correlation with PCE, analysis of the sequence arrangement revealed that higher performance can be achieved with a donor core and acceptor end groups. Future NFA designs should consider this strategy as an alternative to the current A-D-A'-D-A architecture.

Understanding Ring Puckering in Small Molecules and Cyclic Peptides.

The geometry of a molecule plays a significant role in determining its physical and chemical properties. Despite its importance, there are relatively few studies on ring puckering and conformations, often focused on small cycloalkanes, 5- and 6-membered carbohydrate rings, and specific macrocycle families. We lack a general understanding of the puckering preferences of medium-sized rings and macrocycles. To address this, we provide an extensive conformational analysis of a diverse set of rings. We used Cremer-Pople puckering coordinates to study the trends of the ring conformation across a set of 140 000 diverse small molecules, including small rings, macrocycles, and cyclic peptides. By standardizing using key atoms, we show that the ring conformations can be classified into relatively few conformational clusters, based on their canonical forms. The number of such canonical clusters increases slowly with ring size. Ring puckering motions, especially pseudo-rotations, are generally restricted and differ between clusters. More importantly, we propose models to map puckering preferences to torsion space, which allows us to understand the inter-related changes in torsion angles during pseudo-rotation and other puckering motions. Beyond ring puckers, our models also explain the change in substituent orientation upon puckering. We also present a novel knowledge-based sampling method using the puckering preferences and coupled substituent motion to generate ring conformations efficiently. In summary, this work provides an improved understanding of general ring puckering preferences, which will in turn accelerate the identification of low-energy ring conformations for applications from polymeric materials to drug binding.

Evaluation of Thermochemical Machine Learning for Potential Energy Curves and Geometry Optimization.

While many machine learning (ML) methods, particularly deep neural networks, have been trained for density functional and quantum chemical energies and properties, the vast majority of these methods focus on single-point energies. In principle, such ML methods, once trained, offer thermochemical accuracy on par with density functional and wave function methods but at speeds comparable to traditional force fields or approximate semiempirical methods. So far, most efforts have focused on optimized equilibrium single-point energies and properties. In this work, we evaluate the accuracy of several leading ML methods across a range of bond potential energy curves and torsional potentials. The methods were trained on the existing ANI-1 training set, calculated using the ωB97X/6-31G(d) single points at nonequilibrium geometries. We find that across a range of small molecules, several methods offer both qualitative accuracy (e.g., correct minima, both repulsive and attractive bond regions, anharmonic shape, and single minima) and quantitative accuracy in terms of the mean absolute percent error near the minima. At the moment, ANI-2x, FCHL, and a new libmolgrid-based convolutional neural net, the Colorful CNN, show good performance.

Deep Learning Coordinate-Free Quantum Chemistry.

Computing quantum chemical properties of small molecules and polymers can provide insights valuable into physicists, chemists, and biologists when designing new materials, catalysts, biological probes, and drugs. Deep learning can compute quantum chemical properties accurately in a fraction of time required by commonly used methods such as density functional theory. Most current approaches to deep learning in quantum chemistry begin with geometric information from experimentally derived molecular structures or pre-calculated atom coordinates. These approaches have many useful applications, but they can be costly in time and computational resources. In this study, we demonstrate that accurate quantum chemical computations can be performed without geometric information by operating in the coordinate-free domain using deep learning on graph encodings. Coordinate-free methods rely only on molecular graphs, the connectivity of atoms and bonds, without atom coordinates or bond distances. We also find that the choice of graph-encoding architecture substantially affects the performance of these methods. The structures of these graph-encoding architectures provide an opportunity to probe an important, outstanding question in quantum mechanics: what types of quantum chemical properties can be represented by local variable models? We find that Wave, a local variable model, accurately calculates the quantum chemical properties, while graph convolutional architectures require global variables. Furthermore, local variable Wave models outperform global variable graph convolution models on complex molecules with large, correlated systems.

Machine learning to accelerate screening for Marcus reorganization energies.

Understanding and predicting the charge transport properties of π-conjugated materials is an important challenge for designing new organic electronic devices, such as solar cells, plastic transistors, light-emitting devices, and chemical sensors. A key component of the hopping mechanism of charge transfer in these materials is the Marcus reorganization energy which serves as an activation barrier to hole or electron transfer. While modern density functional methods have proven to accurately predict trends in intramolecular reorganization energy, such calculations are computationally expensive. In this work, we outline active machine learning methods to predict computed intramolecular reorganization energies of a wide range of polythiophenes and their use toward screening new compounds with low internal reorganization energies. Our models have an overall root mean square error (RMSE) of ±0.113 eV, but a much smaller RMSE of only ±0.036 eV on the new screening set. Since the larger error derives from high-reorganization energy compounds, the new method is highly effective to screen for compounds with potentially efficient charge transport parameters.

BOKEI: Bayesian optimization using knowledge of correlated torsions and expected improvement for conformer generation.

A key challenge in conformer sampling is finding low-energy conformations with a small number of energy evaluations. We recently demonstrated the Bayesian Optimization Algorithm (BOA) is an effective method for finding the lowest energy conformation of a small molecule. Our approach balances between exploitation and exploration, and is more efficient than exhaustive or random search methods. Here, we extend strategies used on proteins and oligopeptides (e.g. Ramachandran plots of secondary structure) and study correlated torsions in small molecules. We use bivariate von Mises distributions to capture correlations, and use them to constrain the search space. We validate the performance of our new method, Bayesian Optimization with Knowledge-based Expected Improvement (BOKEI), on a dataset consisting of 533 diverse small molecules, using (i) a force field (MMFF94); and (ii) a semi-empirical method (GFN2), as the objective function. We compare the search performance of BOKEI, BOA with Expected Improvement (BOA-EI), and a genetic algorithm (GA), using a fixed number of energy evaluations. In more than 60% of the cases examined, BOKEI finds lower energy conformations than global optimization with BOA-EI or GA. More importantly, we find correlated torsions in up to 15% of small molecules in larger data sets, up to 8 times more often than previously reported. The BOKEI patterns not only describe steric clashes, but also reflect favorable intramolecular interactions such as hydrogen bonds and π-π stacking. Increasing our understanding of the conformational preferences of molecules will help improve our ability to find low energy conformers efficiently, which will have impact in a wide range of computational modeling applications.

Sequence Effects in Conjugated Donor-Acceptor Trimers and Polymers.

To investigate the sequence effect on donor-acceptor conjugated oligomers and polymers, the trimeric isomers PBP and BPP, comprising dialkoxy phenylene vinylene (P), benzothiadiazole vinylene (B), and alkyl endgroups with terminal olefins, are synthesized. Sequence effects are evident in the optical/electrochemical properties and thermal properties. Absorption maxima for PBP and BPP differ by 41 nm and the electrochemical band gaps by 0.1 V. The molar emission intensity is five times greater in PBP than BPP. Both trimers are crystalline and the melting points differ by 17 °C. The PBP and BPP trimers are used as macromonomers in an acyclic diene metathesis polymerization to give PolyPBP and PolyBPP. The optical and electrochemical properties are similar to those of their trimer precursors-sequence effects are still evident. These results suggest that sequence is a tunable variable for electronic materials and that the polymerization of oligomeric sequences is a useful approach to introducing sequence into polymers.

Piezoelectric hydrogen bonding: computational screening for a design rationale.

Organic piezoelectric materials are promising targets in applications such as energy harvesting or mechanical sensors and actuators. In a recent paper (Werling, K. A.; et al. J. Phys. Chem. Lett. 2013, 4, 1365-1370), we have shown that hydrogen bonding gives rise to a significant piezoelectric response. In this article, we aim to find organic hydrogen bonded systems with increased piezo-response by investigating different hydrogen bonding motifs and by tailoring the hydrogen bond strength via functionalization. The largest piezo-coefficient of 23 pm/V is found for the nitrobenzene-aniline dimer. We develop a simple, yet surprisingly accurate rationale to predict piezo-coefficients based on the zero-field compliance matrix and dipole derivatives. This rationale increases the speed of first-principles piezo-coefficient calculations by an order of magnitude. At the same time, it suggests how to understand and further increase the piezo-response. Our rationale also explains the remarkably large piezo-response of 150 pm/V and more for another class of systems, the "molecular springs" (Marvin, C.; et al. J. Phys. Chem. C 2013, 117, 16783-16790.).

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.

Electronic coupling between two amine redox sites through the 5,5'-positions of metal-chelating 2,2'-bipyridines.

Electron delocalization of new mixed-valent (MV) systems with the aid of lateral metal chelation is reported. 2,2'-Bipyridine (bpy) derivatives with one or two appended di-p-anisylamino groups on the 5,5'-positions and a coordinated [Ru(bpy)(2)] (bpy = 2,2'-bipyridine), [Re(CO)(3)Cl], or [Ir(ppy)(2)] (ppy = 2-phenylpyridine) component were prepared. The single-crystal molecular structure of the bis-amine ligand without metal chelation is presented. The electronic properties of these complexes were studied and compared by electrochemical and spectroscopic techniques and DFT/TDDFT calculations. Compounds with two di-p-anisylamino groups were oxidized by a chemical or electrochemical method and monitored by near-infrared (NIR) absorption spectral changes. Marcus-Hush analysis of the resulting intervalence charge-transfer transitions indicated that electron coupling of these mixed-valent systems is enhanced by metal chelation and that the iridium complex has the largest coupling. TDDFT calculations were employed to interpret the NIR transitions of these MV systems.

Organic Photovoltaic Efficiency Predictor: Data-Driven Models for Non-Fullerene Acceptor Organic Solar Cells.

In the design of organic solar cells, there has been a need for materials with high power conversion efficiencies. Scharber's model is commonly used to predict efficiency; however, it exhibits poor performance with new non-fullerene acceptor (NFA) devices, since it was designed for fullerene-based devices. In this work, an empirical model is proposed that can be a more accurate alternative for NFA organic solar cells. Additionally, many screening studies use computationally expensive methods. A model based on using semiempirical simplified time-dependent density functional theory (sTD-DFT) as an alternative method can accelerate the calculations and yield a similar accuracy. The models presented in this paper, termed organic photovoltaic efficiency predictor (OPEP) models, have shown significantly lower errors than previous models, with OPEP/B3LYP yielding errors of 1.53% and OPEP/sTD-DFT of 1.55%. The proposed computational models can be used for the fast and accurate screening of new high-efficiency NFAs/donor pairs.

Strategies for Computer-Aided Discovery of Novel Open-Shell Polymers.

Organic π-conjugated polymers with a triplet ground state have been the focus of recent research for their interesting and unique electronic properties, arising from the presence of the two unpaired electrons. These compounds are usually built from alternating electron-donating and electron-accepting monomer pairs which lower the HOMO-LUMO gap and yield a triplet state instead of the typical singlet ground state. In this paper, we use density functional theory calculations to explore the design rules that govern the creation of a ground-state triplet conjugated polymer and find that a small HOMO-LUMO gap in the singlet state is the best predictor for the existence of a triplet ground state, compared to previous use of a pro-quinoidal bonding character. This work can accelerate the discovery of new stable triplet materials by reducing the computational resources needed for electronic-state calculations and the number of potential candidates for synthesis.

Understanding Conformational Entropy in Small Molecules.

The calculation of the entropy of flexible molecules can be challenging, since the number of possible conformers can grow exponentially with molecule size and many low-energy conformers may be thermally accessible. Different methods have been proposed to approximate the contribution of conformational entropy to the molecular standard entropy, including performing thermochemistry calculations with all possible stable conformations and developing empirical corrections from experimental data. We have performed conformer sampling on over 120,000 small molecules generating some 12 million conformers, to develop models to predict conformational entropy across a wide range of molecules. Using insight into the nature of conformational disorder, our cross-validated physically motivated statistical model gives a mean absolute error of ∼4.8 J/mol·K or under 0.4 kcal/mol at 300 K. Beyond predicting molecular entropies and free energies, the model implies a high degree of correlation between torsions in most molecules, often assumed to be independent. While individual dihedral rotations may have low energetic barriers, the shape and chemical functionality of most molecules necessarily correlate their torsional degrees of freedom and hence restrict the number of low-energy conformations immensely. Our simple models capture these correlations and advance our understanding of small molecule conformational entropy.

Intrinsically Polar Piezoelectric Self-Assembled Oligopeptide Monolayers.

Flexible, biocompatible piezoelectric materials are of considerable research interest for a variety of applications, but many suffer from low response or high cost to manufacture. Herein, novel piezoelectric force and touch sensors based on self-assembled monolayers of oligopeptides are presented, which produce large piezoelectric voltage response and are easily manufactured without the need for electrical poling. While the devices generate modest piezoelectric charge constants (d33 ) of up to 9.8 pC N-1 , they exhibit immense piezoelectric voltage constants (g33 ) up to 2 V m N-1 . Furthermore, a flexible device prototype is demonstrated that produces open-circuit voltages of nearly 6 V under gentle bending motion. Improvements in peptide selection and device construction promise to further improve the already outstanding voltage response and open the door to numerous practical applications.