The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules

Nutmeg and SPICE: Models and Data for Biomolecular Machine Learning

We describe version 2 of the SPICE data set, a collection of quantum chemistry calculations for training machine learning potentials. It expands on the original data set by adding much more sampling of chemical space and more data on noncovalent interactions. We train a set of potential energy functions called Nutmeg on it. They are based on the TensorNet architecture. They use a novel mechanism to improve performance on charged and polar molecules, injecting precomputed partial charges into the model to provide a reference for the large-scale charge distribution. Evaluation of the new models shows that they do an excellent job of reproducing energy differences between conformations even on highly charged molecules or ones that are significantly larger than the molecules in the training set. They also produce stable molecular dynamics trajectories and are fast enough to be useful for routine simulation of small molecules.

Quantum-level machine learning calculations of Levodopa

Many drug molecules contain functional groups, resulting in a torsional barrier corresponding to rotation around the bond linking the fragments. In medicinal chemistry and pharmaceutical sciences, inclusive of drug design studies, the exact calculation of the potential energy surface (PES) of these molecular torsions is extremely important and precious. Machine learning (ML), including deep learning (DL), is currently one of the most rapidly evolving tools in computer-aided drug discovery and molecular simulations. In this work, we used ANI-1x neural network potential as a quantum-level ML to predict the PESs of the L-3,4-dihydroxyphenylalanine (Levodopa) antiparkinsonian drug molecule. The electronic energies and structural parameters calculated by density functional theory (DFT) using the wB97X method and all possible Pople's basis sets indicated the 6-31G(d) basis set, when used with the wB97X functional, exhibits behavior similar to that of the ANI-1x model. The vibrational frequencies investigation showed a linear correlation between DFT and ML data. All ANI-1x calculations were completed quickly in a very short computing time. From this perspective, we expect the ANI-1x dataset applied in this work to be appreciably efficient and effective in computational structure-based drug design studies.

Physics-Informed Active Learning for Accelerating Quantum Chemical Simulations

Quantum chemical simulations can be greatly accelerated by constructing machine learning potentials, which is often done using active learning (AL). The usefulness of the constructed potentials is often limited by the high effort required and their insufficient robustness in the simulations. Here, we introduce the end-to-end AL for constructing robust data-efficient potentials with affordable investment of time and resources and minimum human interference. Our AL protocol is based on the physics-informed sampling of training points, automatic selection of initial data, uncertainty quantification, and convergence monitoring. The versatility of this protocol is shown in our implementation of quasi-classical molecular dynamics for simulating vibrational spectra, conformer search of a key biochemical molecule, and time-resolved mechanism of the Diels-Alder reaction. These investigations took us days instead of weeks of pure quantum chemical calculations on a high-performance computing cluster.

E(n)-Equivariant cartesian tensor message passing interatomic potential

Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.

A physics-aware neural network for protein-ligand interactions with quantum chemical accuracy

Quantifying intermolecular interactions with quantum chemistry (QC) is useful for many chemical problems, including understanding the nature of protein-ligand interactions. Unfortunately, QC computations on protein-ligand systems are too computationally expensive for most use cases. The flourishing field of machine-learned (ML) potentials is a promising solution, but it is limited by an inability to easily capture long range, non-local interactions. In this work we develop an atomic-pairwise neural network (AP-Net) specialized for modeling intermolecular interactions. This model benefits from a number of physical constraints, including a two-component equivariant message passing neural network architecture that predicts interaction energies via an intermediate prediction of monomer electron densities. The AP-Net model is trained on a comprehensive dataset composed of paired ligand and protein fragments. This model accurately predicts QC-quality interaction energies of protein-ligand systems at a computational cost reduced by orders of magnitude. Applications of the AP-Net model to molecular crystal structure prediction are explored, as well as limitations in modeling highly polarizable systems.

Benchmarking Quantum Mechanical Levels of Theory for Valence Parametrization in Force Fields

A wide range of density functional methods and basis sets are available to derive the electronic structure and properties of molecules. Quantum mechanical calculations are too computationally intensive for routine simulation of molecules in the condensed phase, prompting the development of computationally efficient force fields based on quantum mechanical data. Parametrizing general force fields, which cover a vast chemical space, necessitates the generation of sizable quantum mechanical data sets with optimized geometries and torsion scans. To achieve this efficiently, choosing a quantum mechanical method that balances computational cost and accuracy is crucial. In this study, we seek to assess the accuracy of quantum mechanical theory for specific properties such as conformer energies and torsion energetics. To comprehensively evaluate various methods, we focus on a representative set of 59 diverse small molecules, comparing approximately 25 combinations of functional and basis sets against the reference level coupled cluster calculations at the complete basis set limit.

A Euclidean transformer for fast and stable machine learned force fields

Recent years have seen vast progress in the development of machine learned force fields (MLFFs) based on ab-initio reference calculations. Despite achieving low test errors, the reliability of MLFFs in molecular dynamics (MD) simulations is facing growing scrutiny due to concerns about instability over extended simulation timescales. Our findings suggest a potential connection between robustness to cumulative inaccuracies and the use of equivariant representations in MLFFs, but the computational cost associated with these representations can limit this advantage in practice. To address this, we propose a transformer architecture called SO3KRATES that combines sparse equivariant representations (Euclidean variables) with a self-attention mechanism that separates invariant and equivariant information, eliminating the need for expensive tensor products. SO3KRATES achieves a unique combination of accuracy, stability, and speed that enables insightful analysis of quantum properties of matter on extended time and system size scales. To showcase this capability, we generate stable MD trajectories for flexible peptides and supra-molecular structures with hundreds of atoms. Furthermore, we investigate the PES topology for medium-sized chainlike molecules (e.g., small peptides) by exploring thousands of minima. Remarkably, SO3KRATES demonstrates the ability to strike a balance between the conflicting demands of stability and the emergence of new minimum-energy conformations beyond the training data, which is crucial for realistic exploration tasks in the field of biochemistry.

FeNNol: An efficient and flexible library for building force-field-enhanced neural network potentials

Neural network interatomic potentials (NNPs) have recently proven to be powerful tools to accurately model complex molecular systems while bypassing the high numerical cost of ab initio molecular dynamics simulations. In recent years, numerous advances in model architectures as well as the development of hybrid models combining machine-learning (ML) with more traditional, physically motivated, force-field interactions have considerably increased the design space of ML potentials. In this paper, we present FeNNol, a new library for building, training, and running force-field-enhanced neural network potentials. It provides a flexible and modular system for building hybrid models, allowing us to easily combine state-of-the-art embeddings with ML-parameterized physical interaction terms without the need for explicit programming. Furthermore, FeNNol leverages the automatic differentiation and just-in-time compilation features of the Jax Python library to enable fast evaluation of NNPs, shrinking the performance gap between ML potentials and standard force-fields. This is demonstrated with the popular ANI-2x model reaching simulation speeds nearly on par with the AMOEBA polarizable force-field on commodity GPUs (graphics processing units). We hope that FeNNol will facilitate the development and application of new hybrid NNP architectures for a wide range of molecular simulation problems.

OBIWAN: An Element-Wise Scalable Feed-Forward Neural Network Potential

Estimating the potential energy of a molecular system at a quantum level of theory is a task of paramount importance in computational chemistry. The often employed density functional theory approach allows one to accomplish this task, yet most often at significant computational costs. This prompted the community to develop so-called machine learning potentials to achieve near-quantum accuracy at molecular mechanics computational cost. In this paper, we introduce OBIWAN, a feed-forward neural network that bears some relevant structural properties that also led to the definition of a new kind of general-purpose neural network layer. Its featurization process scales efficiently with newly added atomic species. This allows one to seamlessly add new atom types without requiring to change the topology of the network. Also, this allows one to train on new data sets leveraging a previously trained OBIWAN, hence converging very quickly. This avoids training from scratch and renders the approach more compliant with a green computing perspective.

Developing a Differentiable Long-Range Force Field for Proteins with E(3) Neural Network-Predicted Asymptotic Parameters

Accurately describing long-range interactions is a significant challenge in molecular dynamics (MD) simulations of proteins. High-quality long-range potential is also an important component of the range-separated machine learning force field. This study introduces a comprehensive asymptotic parameter database encompassing atomic multipole moments, polarizabilities, and dispersion coefficients. Leveraging active learning, our database comprehensively represents protein fragments with up to 8 heavy atoms, capturing their conformational diversity with merely 78,000 data points. Additionally, the E(3) neural network (E3NN) is employed to predict the asymptotic parameters directly from the local geometry. The E3NN models demonstrate exceptional accuracy and transferability across all asymptotic parameters, achieving an R2 of 0.999 for both protein fragments and 20 amino acid dipeptide test sets. The long-range electrostatic and dispersion energies can be obtained using the E3NN-predicted parameters, with an error of 0.07 and 0.02 kcal/mol, respectively, when compared to symmetry-adapted perturbation theory (SAPT). Therefore, our force fields demonstrate the capability to accurately describe long-range interactions in proteins, paving the way for next-generation protein force fields.

Dataset for quantum-mechanical exploration of conformers and solvent effects in large drug-like molecules

We here introduce the Aquamarine (AQM) dataset, an extensive quantum-mechanical (QM) dataset that contains the structural and electronic information of 59,783 low-and high-energy conformers of 1,653 molecules with a total number of atoms ranging from 2 to 92 (mean: 50.9), and containing up to 54 (mean: 28.2) non-hydrogen atoms. To gain insights into the solvent effects as well as collective dispersion interactions for drug-like molecules, we have performed QM calculations supplemented with a treatment of many-body dispersion (MBD) interactions of structures and properties in the gas phase and implicit water. Thus, AQM contains over 40 global and local physicochemical properties (including ground-state and response properties) per conformer computed at the tightly converged PBE0+MBD level of theory for gas-phase molecules, whereas PBE0+MBD with the modified Poisson-Boltzmann (MPB) model of water was used for solvated molecules. By addressing both molecule-solvent and dispersion interactions, AQM dataset can serve as a challenging benchmark for state-of-the-art machine learning methods for property modeling and de novo generation of large (solvated) molecules with pharmaceutical and biological relevance.

Software Infrastructure for Next-Generation QM/MM-ΔMLP Force Fields

We present software infrastructure for the design and testing of new quantum mechanical/molecular mechanical and machine-learning potential (QM/MM-ΔMLP) force fields for a wide range of applications. The software integrates Amber's molecular dynamics simulation capabilities with fast, approximate quantum models in the xtb package and machine-learning potential corrections in DeePMD-kit. The xtb package implements the recently developed density-functional tight-binding QM models with multipolar electrostatics and density-dependent dispersion (GFN2-xTB), and the interface with Amber enables their use in periodic boundary QM/MM simulations with linear-scaling QM/MM particle-mesh Ewald electrostatics. The accuracy of the semiempirical models is enhanced by including machine-learning correction potentials (ΔMLPs) enabled through an interface with the DeePMD-kit software. The goal of this paper is to present and validate the implementation of this software infrastructure in molecular dynamics and free energy simulations. The utility of the new infrastructure is demonstrated in proof-of-concept example applications. The software elements presented here are open source and freely available. Their interface provides a powerful enabling technology for the design of new QM/MM-ΔMLP models for studying a wide range of problems, including biomolecular reactivity and protein-ligand binding.

Enhancing Molecular Energy Predictions with Physically Constrained Modifications to the Neural Network Potential

Exclusively prioritizing the precision of energy prediction frequently proves inadequate in satisfying multifaceted requirements. A heightened focus is warranted on assessing the rationality of potential energy curves predicted by machine learning-based force fields (MLFFs), alongside evaluating the pragmatic utility of these MLFFs. This study introduces SWANI, an optimized neural network potential stemming from the ANI framework. Through the incorporation of supplementary physical constraints, SWANI aligns more cohesively with chemical expectations, yielding rational potential energy profiles. It also exhibits superior predictive precision compared with that of the ANI model. Additionally, a comprehensive comparison is conducted between SWANI and a prominent graph neural network-based model. The findings indicate that SWANI outperforms the latter, particularly for molecules exceeding the dimensions of the training set. This outcome underscores SWANI's exceptional capacity for generalization and its proficiency in handling larger molecular systems.

TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for TensorNet models, with performance gains ranging from 2× to 10× over previous, nonoptimized, iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

Assessment of Embedding Schemes in a Hybrid Machine Learning/Classical Potentials (ML/MM) Approach

Machine learning (ML) methods have reached high accuracy levels for the prediction of in vacuo molecular properties. However, the simulation of large systems solely through ML methods (such as those based on neural network potentials) is still a challenge. In this context, one of the most promising frameworks for integrating ML schemes in the simulation of complex molecular systems are the so-called ML/MM methods. These multiscale approaches combine ML methods with classical force fields (MM), in the same spirit as the successful hybrid quantum mechanics-molecular mechanics methods (QM/MM). The key issue for such ML/MM methods is an adequate description of the coupling between the region of the system described by ML and the region described at the MM level. In the context of QM/MM schemes, the main ingredient of the interaction is electrostatic, and the state of the art is the so-called electrostatic-embedding. In this study, we analyze the quality of simpler mechanical embedding-based approaches, specifically focusing on their application within a ML/MM framework utilizing atomic partial charges derived in vacuo. Taking as reference electrostatic embedding calculations performed at a QM(DFT)/MM level, we explore different atomic charges schemes, as well as a polarization correction computed using atomic polarizabilites. Our benchmark data set comprises a set of about 80k small organic structures from the ANI-1x and ANI-2x databases, solvated in water. The results suggest that the minimal basis iterative stockholder (MBIS) atomic charges yield the best agreement with the reference coupling energy. Remarkable enhancements are achieved by including a simple polarization correction.

TorchMD-Net 2.0: Fast Neural Network Potentials for Molecular Simulations

Achieving a balance between computational speed, prediction accuracy, and universal applicability in molecular simulations has been a persistent challenge. This paper presents substantial advancements in the TorchMD-Net software, a pivotal step forward in the shift from conventional force fields to neural network-based potentials. The evolution of TorchMD-Net into a more comprehensive and versatile framework is highlighted, incorporating cutting-edge architectures such as TensorNet. This transformation is achieved through a modular design approach, encouraging customized applications within the scientific community. The most notable enhancement is a significant improvement in computational efficiency, achieving a very remarkable acceleration in the computation of energy and forces for Tensor-Net models, with performance gains ranging from 2x to 10x over previous, non-optimized, iterations. Other enhancements include highly optimized neighbor search algorithms that support periodic boundary conditions and smooth integration with existing molecular dynamics frameworks. Additionally, the updated version introduces the capability to integrate physical priors, further enriching its application spectrum and utility in research. The software is available at https://github.com/torchmd/torchmd-net.

Machine learning interatomic potential: Bridge the gap between small-scale models and realistic device-scale simulations

Machine learning interatomic potential (MLIP) overcomes the challenges of high computational costs in density-functional theory and the relatively low accuracy in classical large-scale molecular dynamics, facilitating more efficient and precise simulations in materials research and design. In this review, the current state of the four essential stages of MLIP is discussed, including data generation methods, material structure descriptors, six unique machine learning algorithms, and available software. Furthermore, the applications of MLIP in various fields are investigated, notably in phase-change memory materials, structure searching, material properties predicting, and the pre-trained universal models. Eventually, the future perspectives, consisting of standard datasets, transferability, generalization, and trade-off between accuracy and complexity in MLIPs, are reported.

Exploring the frontiers of condensed-phase chemistry with a general reactive machine learning potential

Atomistic simulation has a broad range of applications from drug design to materials discovery. Machine learning interatomic potentials (MLIPs) have become an efficient alternative to computationally expensive ab initio simulations. For this reason, chemistry and materials science would greatly benefit from a general reactive MLIP, that is, an MLIP that is applicable to a broad range of reactive chemistry without the need for refitting. Here we develop a general reactive MLIP (ANI-1xnr) through automated sampling of condensed-phase reactions. ANI-1xnr is then applied to study five distinct systems: carbon solid-phase nucleation, graphene ring formation from acetylene, biofuel additives, combustion of methane and the spontaneous formation of glycine from early earth small molecules. In all studies, ANI-1xnr closely matches experiment (when available) and/or previous studies using traditional model chemistry methods. As such, ANI-1xnr proves to be a highly general reactive MLIP for C, H, N and O elements in the condensed phase, enabling high-throughput in silico reactive chemistry experimentation.

Construction of High Accuracy Machine Learning Interatomic Potential for Surface/Interface of Nanomaterials-A Review

The inherent discontinuity and unique dimensional attributes of nanomaterial surfaces and interfaces bestow them with various exceptional properties. These properties, however, also introduce difficulties for both experimental and computational studies. The advent of machine learning interatomic potential (MLIP) addresses some of the limitations associated with empirical force fields, presenting a valuable avenue for accurate simulations of these surfaces/interfaces of nanomaterials. Central to this approach is the idea of capturing the relationship between system configuration and potential energy, leveraging the proficiency of machine learning (ML) to precisely approximate high-dimensional functions. This review offers an in-depth examination of MLIP principles and their execution and elaborates on their applications in the realm of nanomaterial surface and interface systems. The prevailing challenges faced by this potent methodology are also discussed.

The emergence of machine learning force fields in drug design

In the field of molecular simulation for drug design, traditional molecular mechanic force fields and quantum chemical theories have been instrumental but limited in terms of scalability and computational efficiency. To overcome these limitations, machine learning force fields (MLFFs) have emerged as a powerful tool capable of balancing accuracy with efficiency. MLFFs rely on the relationship between molecular structures and potential energy, bypassing the need for a preconceived notion of interaction representations. Their accuracy depends on the machine learning models used, and the quality and volume of training data sets. With recent advances in equivariant neural networks and high-quality datasets, MLFFs have significantly improved their performance. This review explores MLFFs, emphasizing their potential in drug design. It elucidates MLFF principles, provides development and validation guidelines, and highlights successful MLFF implementations. It also addresses potential challenges in developing and applying MLFFs. The review concludes by illuminating the path ahead for MLFFs, outlining the challenges to be overcome and the opportunities to be harnessed. This inspires researchers to embrace MLFFs in their investigations as a new tool to perform molecular simulations in drug design.

Tell Machine Learning Potentials What They Are Needed For: Simulation-Oriented Training Exemplified for Glycine

Machine learning potentials (MLPs) are widely applied as an efficient alternative way to represent potential energy surfaces (PESs) in many chemical simulations. The MLPs are often evaluated with the root-mean-square errors on the test set drawn from the same distribution as the training data. Here, we systematically investigate the relationship between such test errors and the simulation accuracy with MLPs on an example of a full-dimensional, global PES for the glycine amino acid. Our results show that the errors in the test set do not unambiguously reflect the MLP performance in different simulation tasks, such as relative conformer energies, barriers, vibrational levels, and zero-point vibrational energies. We also offer an easily accessible solution for improving the MLP quality in a simulation-oriented manner, yielding the most precise relative conformer energies and barriers. This solution also passed the stringent test by diffusion Monte Carlo simulations.

AI in computational chemistry through the lens of a decade-long journey

This article gives a perspective on the progress of AI tools in computational chemistry through the lens of the author's decade-long contributions put in the wider context of the trends in this rapidly expanding field. This progress over the last decade is tremendous: while a decade ago we had a glimpse of what was to come through many proof-of-concept studies, now we witness the emergence of many AI-based computational chemistry tools that are mature enough to make faster and more accurate simulations increasingly routine. Such simulations in turn allow us to validate and even revise experimental results, deepen our understanding of the physicochemical processes in nature, and design better materials, devices, and drugs. The rapid introduction of powerful AI tools gives rise to unique challenges and opportunities that are discussed in this article too.

Incorporating Neural Networks into the AMOEBA Polarizable Force Field

Neural network potentials (NNPs) offer significant promise to bridge the gap between the accuracy of quantum mechanics and the efficiency of molecular mechanics in molecular simulation. Most NNPs rely on the locality assumption that ensures the model's transferability and scalability and thus lack the treatment of long-range interactions, which are essential for molecular systems in the condensed phase. Here we present an integrated hybrid model, AMOEBA+NN, which combines the AMOEBA potential for the short- and long-range noncovalent atomic interactions and an NNP to capture the remaining local covalent contributions. The AMOEBA+NN model was trained on the conformational energy of the ANI-1x data set and tested on several external data sets ranging from small molecules to tetrapeptides. The hybrid model demonstrated substantial improvements over the baseline models in term of accuracy as the molecule size increased, suggesting its potential as a next-generation approach for chemically accurate molecular simulations.

Transfer learning with graph neural networks for improved molecular property prediction in the multi-fidelity setting

We investigate the potential of graph neural networks for transfer learning and improving molecular property prediction on sparse and expensive to acquire high-fidelity data by leveraging low-fidelity measurements as an inexpensive proxy for a targeted property of interest. This problem arises in discovery processes that rely on screening funnels for trading off the overall costs against throughput and accuracy. Typically, individual stages in these processes are loosely connected and each one generates data at different scale and fidelity. We consider this setup holistically and demonstrate empirically that existing transfer learning techniques for graph neural networks are generally unable to harness the information from multi-fidelity cascades. Here, we propose several effective transfer learning strategies and study them in transductive and inductive settings. Our analysis involves a collection of more than 28 million unique experimental protein-ligand interactions across 37 targets from drug discovery by high-throughput screening and 12 quantum properties from the dataset QMugs. The results indicate that transfer learning can improve the performance on sparse tasks by up to eight times while using an order of magnitude less high-fidelity training data. Moreover, the proposed methods consistently outperform existing transfer learning strategies for graph-structured data on drug discovery and quantum mechanics datasets.

TrIP─Transformer Interatomic Potential Predicts Realistic Energy Surface Using Physical Bias

Accurate interatomic energies and forces enable high-quality molecular dynamics simulations, torsion scans, potential energy surface mappings, and geometry optimizations. Machine learning algorithms have enabled rapid estimates of the energies and forces with high accuracy. Further development of machine learning algorithms holds promise for producing universal potentials that support many different atomic species. We present the Transformer Interatomic Potential (TrIP): a chemically sound potential based on the SE(3)-Transformer. TrIP's species-agnostic architecture, which uses continuous atomic representation and homogeneous graph convolutions, encourages parameter sharing between atomic species for more general representations of chemical environments, maintains a reasonable number of parameters, serves as a form of regularization, and is a step toward accurate universal interatomic potentials. TrIP achieves state-of-the-art accuracies on the COMP6 benchmark with an energy prediction of just 1.02 kcal/mol MAE. We introduce physical bias in the form of Ziegler-Biersack-Littmark-screened nuclear repulsion and constrained atomization energies. An energy scan of a water molecule demonstrates that these changes improve long- and near-range interactions compared to other neural network potentials. TrIP also demonstrates stability in molecular dynamics simulations, demonstrating reasonable exploration of Ramachandran space.

Transferable Machine Learning Interatomic Potential for Bond Dissociation Energy Prediction of Drug-like Molecules

We present a transferable MACE interatomic potential that is applicable to open- and closed-shell drug-like molecules containing hydrogen, carbon, and oxygen atoms. Including an accurate description of radical species extends the scope of possible applications to bond dissociation energy (BDE) prediction, for example, in the context of cytochrome P450 (CYP) metabolism. The transferability of the MACE potential was validated on the COMP6 data set, containing only closed-shell molecules, where it reaches better accuracy than the readily available general ANI-2x potential. MACE achieves similar accuracy on two CYP metabolism-specific data sets, which include open- and closed-shell structures. This model enables us to calculate the aliphatic C-H BDE, which allows us to compare reaction energies of hydrogen abstraction, which is the rate-limiting step of the aliphatic hydroxylation reaction catalyzed by CYPs. On the "CYP 3A4" data set, MACE achieves a BDE RMSE of 1.37 kcal/mol and better prediction of BDE ranks than alternatives: the semiempirical AM1 and GFN2-xTB methods and the ALFABET model that directly predicts bond dissociation enthalpies. Finally, we highlight the smoothness of the MACE potential over paths of sp3C-H bond elongation and show that a minimal extension is enough for the MACE model to start finding reasonable minimum energy paths of methoxy radical-mediated hydrogen abstraction. Altogether, this work lays the ground for further extensions of scope in terms of chemical elements, (CYP-mediated) reaction classes and modeling the full reaction paths, not only BDEs.

Minimal Peptoid Dynamics Inform Self-Assembly Propensity

Peptoids are structural isomers of natural peptides, with side chain attachment at the amide nitrogen, conferring this class of compounds with the ability to access both cis and trans ω torsions as well as an increased diversity of ψ/φ states with respect to peptides. Sampling within these dimensions is controlled through side chain selection, and an expansive set of viable peptoid residues exists. It has been shown recently that "minimal" di- and tripeptoids with aromatic side chains can self-assemble into highly ordered structures, with size and morphological definition varying as a function of sequence pattern (e.g., XFF and FXF, where X = a nonaromatic peptoid monomer). Aromatic groups, such as phenylalanine, are regularly used in the design of minimal peptide assemblers. In recognition of this, and to draw parallels between these compounds classes, we have developed a series of descriptors for intramolecular dynamics of aromatic side chains to discern whether these dynamics, in a preassembly condition, can be related to experimentally observed nanoscale assemblies. To do this, we have built on the atomistic peptoid force field reported by Weiser and Santiso (CGenFF-WS) through the rigorous fitting of partial charges and the collation of Charmm General Force Field (CGenFF) parameters relevant to these systems. Our study finds that the intramolecular dynamics of side chains, for a given sequence, is dependent on the specific combination of backbone ω torsions and that homogeneity of sampling across these states correlates well with the experimentally observed ability to assemble into nanomorphologies with long-range order. Sequence patterning is also shown to affect sampling, in a manner consistent for both tripeptoids and tripeptides. Additionally, sampling similarities between the nanofiber forming tripeptoid, Nf-Nke-Nf in the cc state, and the nanotube forming dipeptide FF, highlight a structural motif which may be relevant to the emergence of extended linear assemblies. To assess these properties, a variety of computational approaches have been employed.

Force Field Analysis Software and Tools (FFAST): Assessing Machine Learning Force Fields under the Microscope

As the sophistication of machine learning force fields (MLFF) increases to match the complexity of extended molecules and materials, so does the need for tools to properly analyze and assess the practical performance of MLFFs. To go beyond average error metrics and into a complete picture of a model's applicability and limitations, we developed FFAST (force field analysis software and tools): a cross-platform software package designed to gain detailed insights into a model's performance and limitations, complete with an easy-to-use graphical user interface. The software allows the user to gauge the performance of any molecular force field,─such as popular state-of-the-art MLFF models, ─ on various popular data set types, providing general prediction error overviews, outlier detection mechanisms, atom-projected errors, and more. It has a 3D visualizer to find and picture problematic configurations, atoms, or clusters in a large data set. In this paper, the example of the MACE and NequIP models is used on two data sets of interest [stachyose and docosahexaenoic acid (DHA)]─to illustrate the use cases of the software. With this, it was found that carbons and oxygens involved in or near glycosidic bonds inside the stachyose molecule present increased prediction errors. In addition, prediction errors on DHA rise as the molecule folds, especially for the carboxylic group at the edge of the molecule. We emphasize the need for a systematic assessment of MLFF models for ensuring their successful application to the study of dynamics of molecules and materials.

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.

"Freedom of design" in chemical compound space: towards rational in silico design of molecules with targeted quantum-mechanical properties

The rational design of molecules with targeted quantum-mechanical (QM) properties requires an advanced understanding of the structure-property/property-property relationships (SPR/PPR) that exist across chemical compound space (CCS). In this work, we analyze these fundamental relationships in the sector of CCS spanned by small (primarily organic) molecules using the recently developed QM7-X dataset, a systematic, extensive, and tightly converged collection of 42 QM properties corresponding to ≈4.2M equilibrium and non-equilibrium molecular structures containing up to seven heavy/non-hydrogen atoms (including C, N, O, S, and Cl). By characterizing and enumerating progressively more complex manifolds of molecular property space-the corresponding high-dimensional space defined by the properties of each molecule in this sector of CCS-our analysis reveals that one has a substantial degree of flexibility or "freedom of design" when searching for a single molecule with a desired pair of properties or a set of distinct molecules sharing an array of properties. To explore how this intrinsic flexibility manifests in the molecular design process, we used multi-objective optimization to search for molecules with simultaneously large polarizabilities and HOMO-LUMO gaps; analysis of the resulting Pareto fronts identified non-trivial paths through CCS consisting of sequential structural and/or compositional changes that yield molecules with optimal combinations of these properties.

Treating Semiempirical Hamiltonians as Flexible Machine Learning Models Yields Accurate and Interpretable Results

Quantum chemistry provides chemists with invaluable information, but the high computational cost limits the size and type of systems that can be studied. Machine learning (ML) has emerged as a means to dramatically lower the cost while maintaining high accuracy. However, ML models often sacrifice interpretability by using components such as the artificial neural networks of deep learning that function as black boxes. These components impart the flexibility needed to learn from large volumes of data but make it difficult to gain insight into the physical or chemical basis for the predictions. Here, we demonstrate that semiempirical quantum chemical (SEQC) models can learn from large volumes of data without sacrificing interpretability. The SEQC model is that of density-functional-based tight binding (DFTB) with fixed atomic orbital energies and interactions that are one-dimensional functions of the interatomic distance. This model is trained to ab initio data in a manner that is analogous to that used to train deep learning models. Using benchmarks that reflect the accuracy of the training data, we show that the resulting model maintains a physically reasonable functional form while achieving an accuracy, relative to coupled cluster energies with a complete basis set extrapolation (CCSD(T)*/CBS), that is comparable to that of density functional theory (DFT). This suggests that trained SEQC models can achieve a low computational cost and high accuracy without sacrificing interpretability. Use of a physically motivated model form also substantially reduces the amount of ab initio data needed to train the model compared to that required for deep learning models.

PubChemQC B3LYP/6-31G*//PM6 Data Set: The Electronic Structures of 86 Million Molecules Using B3LYP/6-31G* Calculations

The presented "PubChemQC B3LYP/6-31G*//PM6" data set is composed of the electronic properties of 85,938,443 molecules, encompassing a broad spectrum of molecules from essential compounds to biomolecules with a molecular weight up to 1000. These molecules account for 94.0% of the original PubChem Compound catalog as of August 29, 2016. The electronic properties, including orbitals, orbital energies, total energies, dipole moments, and other pertinent properties, were computed by using the B3LYP/6-31G* and PM6 methods. The data set, available in three formats, namely, GAMESS quantum chemistry program files, selected JSON output files, and a PostgreSQL database, provides researchers with the ability to query molecular properties. It is further subdivided into five subdata sets for more specific data. The first two subsets encompass molecules with carbon, hydrogen, oxygen, and nitrogen with molecular weights under 300 and 500, respectively. The third and fourth subsets incorporate molecules with carbon, hydrogen, nitrogen, oxygen, phosphorus, sulfur, fluorine, and chlorine, with molecular weights under 300 and 500, respectively. The fifth subset comprises molecules with carbon, hydrogen, nitrogen, oxygen, phosphorus, sulfur, fluorine, chlorine, sodium, potassium, magnesium, and calcium, with a molecular weight of under 500. The coefficients of determination for the highest occupied molecular orbital-lowest unoccupied molecular orbital energy gap range from 0.892 (for CHON500) to 0.803 (for the whole data set). These comprehensive results pave the way for applications in drug discovery and materials science, among others. The data sets can be accessed under the Creative Commons Attribution 4.0 International license at the following web address: https://nakatamaho.riken.jp/pubchemqc.riken.jp/b3lyp_pm6_datasets.html.

Synergy of semiempirical models and machine learning in computational chemistry

Catalyzed by enormous success in the industrial sector, many research programs have been exploring data-driven, machine learning approaches. Performance can be poor when the model is extrapolated to new regions of chemical space, e.g., new bonding types, new many-body interactions. Another important limitation is the spatial locality assumption in model architecture, and this limitation cannot be overcome with larger or more diverse datasets. The outlined challenges are primarily associated with the lack of electronic structure information in surrogate models such as interatomic potentials. Given the fast development of machine learning and computational chemistry methods, we expect some limitations of surrogate models to be addressed in the near future; nevertheless spatial locality assumption will likely remain a limiting factor for their transferability. Here, we suggest focusing on an equally important effort-design of physics-informed models that leverage the domain knowledge and employ machine learning only as a corrective tool. In the context of material science, we will focus on semi-empirical quantum mechanics, using machine learning to predict corrections to the reduced-order Hamiltonian model parameters. The resulting models are broadly applicable, retain the speed of semiempirical chemistry, and frequently achieve accuracy on par with much more expensive ab initio calculations. These early results indicate that future work, in which machine learning and quantum chemistry methods are developed jointly, may provide the best of all worlds for chemistry applications that demand both high accuracy and high numerical efficiency.

Neural network atomistic potentials for global energy minima search in carbon clusters

The global energy optimization problem is an acute and important problem in chemistry. It is crucial to know the geometry of the lowest energy isomer (global minimum, GM) of a given compound for the evaluation of its chemical and physical properties. This problem is especially relevant for atomic clusters. Due to the exponential growth of the number of local minima geometries with the increase of the number of atoms in the cluster, it is important to find a computationally efficient and reliable method to navigate the energy landscape and locate a true global minima structure. Newly developed neural network (NN) atomistic potentials offer a numerically efficient and relatively accurate approach for molecular structure optimization. An important question that needs to be answered is "Can NN potentials, trained on a given set, represent the potential energy surface (PES) of a neighboring domain?". In this work, we tested the applicability of ANI-1ccx and ANI-nr NN atomistic potentials for the global minima optimization of carbon clusters Cn (n = 3-10). We showed that with the introduction of the cluster connectivity restriction and consequent DFT or ab initio calculations, ANI-1ccx and ANI-nr can be considered as robust PES pre-samplers that can capture the GM structure even for large clusters such as C20.

Denoise Pretraining on Nonequilibrium Molecules for Accurate and Transferable Neural Potentials

Recent advances in equivariant graph neural networks (GNNs) have made deep learning amenable to developing fast surrogate models to expensive ab initio quantum mechanics (QM) approaches for molecular potential predictions. However, building accurate and transferable potential models using GNNs remains challenging, as the data are greatly limited by the expensive computational costs and level of theory of QM methods, especially for large and complex molecular systems. In this work, we propose denoise pretraining on nonequilibrium molecular conformations to achieve more accurate and transferable GNN potential predictions. Specifically, atomic coordinates of sampled nonequilibrium conformations are perturbed by random noises, and GNNs are pretrained to denoise the perturbed molecular conformations which recovers the original coordinates. Rigorous experiments on multiple benchmarks reveal that pretraining significantly improves the accuracy of neural potentials. Furthermore, we show that the proposed pretraining approach is model-agnostic, as it improves the performance of different invariant and equivariant GNNs. Notably, our models pretrained on small molecules demonstrate remarkable transferability, improving performance when fine-tuned on diverse molecular systems, including different elements, charged molecules, biomolecules, and larger systems. These results highlight the potential for leveraging denoise pretraining approaches to build more generalizable neural potentials for complex molecular systems.

Evaluation of the MACE force field architecture: From medicinal chemistry to materials science

The MACE architecture represents the state of the art in the field of machine learning force fields for a variety of in-domain, extrapolation, and low-data regime tasks. In this paper, we further evaluate MACE by fitting models for published benchmark datasets. We show that MACE generally outperforms alternatives for a wide range of systems, from amorphous carbon, universal materials modeling, and general small molecule organic chemistry to large molecules and liquid water. We demonstrate the capabilities of the model on tasks ranging from constrained geometry optimization to molecular dynamics simulations and find excellent performance across all tested domains. We show that MACE is very data efficient and can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations. We further demonstrate that the strictly local atom-centered model is sufficient for such tasks even in the case of large molecules and weakly interacting molecular assemblies.

Clusterome: A Comprehensive Data Set of Atmospheric Molecular Clusters for Machine Learning Applications

Formation and growth of atmospheric molecular clusters into aerosol particles impact the global climate and contribute to the high uncertainty in modern climate models. Cluster formation is usually studied using quantum chemical methods, which quickly becomes computationally expensive when system sizes grow. In this work, we present a large database of ∼250k atmospheric relevant cluster structures, which can be applied for developing machine learning (ML) models. The database is used to train the ML model kernel ridge regression (KRR) with the FCHL19 representation. We test the ability of the model to extrapolate from smaller clusters to larger clusters, between different molecules, between equilibrium structures and out-of-equilibrium structures, and the transferability onto systems with new interactions. We show that KRR models can extrapolate to larger sizes and transfer acid and base interactions with mean absolute errors below 1 kcal/mol. We suggest introducing an iterative ML step in configurational sampling processes, which can reduce the computational expense. Such an approach would allow us to study significantly more cluster systems at higher accuracy than previously possible and thereby allow us to cover a much larger part of relevant atmospheric compounds.

Machine Learning for Bridging the Gap between Density Functional Theory and Coupled Cluster Energies

Accurate electronic energies and properties are crucial for successful reaction design and mechanistic investigations. Computing energies and properties of molecular structures has proven extremely useful, and, with increasing computational power, the limits of high-level approaches (such as coupled cluster theory) are expanding to ever larger systems. However, because scaling is highly unfavorable, these methods are still not universally applicable to larger systems. To address the need for fast and accurate electronic energies of larger systems, we created a database of around 8000 small organic monomers (2000 dimers) optimized at the B3LYP-D3(BJ)/cc-pVTZ level of theory. This database also includes single-point energies computed at various levels of theory, including PBE1PBE, ωΒ97Χ, M06-2X, revTPSS, B3LYP, and BP86, for density functional theory as well as DLPNO-CCSD(T) and CCSD(T) for coupled cluster theory, all in conjunction with a cc-pVTZ basis. We used this database to train machine learning models based on graph neural networks using two different graph representations. Our models are able to make energy predictions from B3LYP-D3(BJ)/cc-pVTZ inputs to CCSD(T)/cc-pVTZ outputs with a mean absolute error of 0.78 and to DLPNO-CCSD(T)/cc-pVTZ with an mean absolute error of 0.50 and 0.18 kcal mol^-1 for monomers and dimers, respectively. The model for dimers was further validated on the S22 database, and the monomer model was tested on challenging systems, including those with highly conjugated or functionally complex molecules.

Current and future machine learning approaches for modeling atmospheric cluster formation

The formation of strongly bound atmospheric molecular clusters is the first step towards forming new aerosol particles. Recent advances in the application of machine learning models open an enormous opportunity for complementing expensive quantum chemical calculations with efficient machine learning predictions. In this Perspective, we present how data-driven approaches can be applied to accelerate cluster configurational sampling, thereby greatly increasing the number of chemically relevant systems that can be covered.

Scalable hybrid deep neural networks/polarizable potentials biomolecular simulations including long-range effects

Deep-HP is a scalable extension of the Tinker-HP multi-GPU molecular dynamics (MD) package enabling the use of Pytorch/TensorFlow Deep Neural Network (DNN) models. Deep-HP increases DNNs' MD capabilities by orders of magnitude offering access to ns simulations for 100k-atom biosystems while offering the possibility of coupling DNNs to any classical (FFs) and many-body polarizable (PFFs) force fields. It allows therefore the introduction of the ANI-2X/AMOEBA hybrid polarizable potential designed for ligand binding studies where solvent-solvent and solvent-solute interactions are computed with the AMOEBA PFF while solute-solute ones are computed by the ANI-2X DNN. ANI-2X/AMOEBA explicitly includes AMOEBA's physical long-range interactions via an efficient Particle Mesh Ewald implementation while preserving ANI-2X's solute short-range quantum mechanical accuracy. The DNN/PFF partition can be user-defined allowing for hybrid simulations to include key ingredients of biosimulation such as polarizable solvents, polarizable counter ions, etc.… ANI-2X/AMOEBA is accelerated using a multiple-timestep strategy focusing on the model's contributions to low-frequency modes of nuclear forces. It primarily evaluates AMOEBA forces while including ANI-2X ones only via correction-steps resulting in an order of magnitude acceleration over standard Velocity Verlet integration. Simulating more than 10 μs, we compute charged/uncharged ligand solvation free energies in 4 solvents, and absolute binding free energies of host-guest complexes from SAMPL challenges. ANI-2X/AMOEBA average errors are discussed in terms of statistical uncertainty and appear in the range of chemical accuracy compared to experiment. The availability of the Deep-HP computational platform opens the path towards large-scale hybrid DNN simulations, at force-field cost, in biophysics and drug discovery.

Lightweight and effective tensor sensitivity for atomistic neural networks

Atomistic machine learning focuses on the creation of models that obey fundamental symmetries of atomistic configurations, such as permutation, translation, and rotation invariances. In many of these schemes, translation and rotation invariance are achieved by building on scalar invariants, e.g., distances between atom pairs. There is growing interest in molecular representations that work internally with higher rank rotational tensors, e.g., vector displacements between atoms, and tensor products thereof. Here, we present a framework for extending the Hierarchically Interacting Particle Neural Network (HIP-NN) with Tensor Sensitivity information (HIP-NN-TS) from each local atomic environment. Crucially, the method employs a weight tying strategy that allows direct incorporation of many-body information while adding very few model parameters. We show that HIP-NN-TS is more accurate than HIP-NN, with negligible increase in parameter count, for several datasets and network sizes. As the dataset becomes more complex, tensor sensitivities provide greater improvements to model accuracy. In particular, HIP-NN-TS achieves a record mean absolute error of 0.927 kcalmol for conformational energy variation on the challenging COMP6 benchmark, which includes a broad set of organic molecules. We also compare the computational performance of HIP-NN-TS to HIP-NN and other models in the literature.

MF-PCBA: Multifidelity High-Throughput Screening Benchmarks for Drug Discovery and Machine Learning

High-throughput screening (HTS), as one of the key techniques in drug discovery, is frequently used to identify promising drug candidates in a largely automated and cost-effective way. One of the necessary conditions for successful HTS campaigns is a large and diverse compound library, enabling hundreds of thousands of activity measurements per project. Such collections of data hold great promise for computational and experimental drug discovery efforts, especially when leveraged in combination with modern deep learning techniques, and can potentially lead to improved drug activity predictions and cheaper and more effective experimental design. However, existing collections of machine-learning-ready public datasets do not exploit the multiple data modalities present in real-world HTS projects. Thus, the largest fraction of experimental measurements, corresponding to hundreds of thousands of "noisy" activity values from primary screening, are effectively ignored in the majority of machine learning models of HTS data. To address these limitations, we introduce Multifidelity PubChem BioAssay (MF-PCBA), a curated collection of 60 datasets that includes two data modalities for each dataset, corresponding to primary and confirmatory screening, an aspect that we call multifidelity. Multifidelity data accurately reflect real-world HTS conventions and present a new, challenging task for machine learning: the integration of low- and high-fidelity measurements through molecular representation learning, taking into account the orders-of-magnitude difference in size between the primary and confirmatory screens. Here we detail the steps taken to assemble MF-PCBA in terms of data acquisition from PubChem and the filtering steps required to curate the raw data. We also provide an evaluation of a recent deep-learning-based method for multifidelity integration across the introduced datasets, demonstrating the benefit of leveraging all HTS modalities, and a discussion in terms of the roughness of the molecular activity landscape. In total, MF-PCBA contains over 16.6 million unique molecule-protein interactions. The datasets can be easily assembled by using the source code available at https://github.com/davidbuterez/mf-pcba.

Does a Machine-Learned Potential Perform Better Than an Optimally Tuned Traditional Force Field? A Case Study on Fluorohydrins

We present a comparative study that evaluates the performance of a machine learning potential (ANI-2x), a conventional force field (GAFF), and an optimally tuned GAFF-like force field in the modeling of a set of 10 γ-fluorohydrins that exhibit a complex interplay between intra- and intermolecular interactions in determining conformer stability. To benchmark the performance of each molecular model, we evaluated their energetic, geometric, and sampling accuracies relative to quantum-mechanical data. This benchmark involved conformational analysis both in the gas phase and chloroform solution. We also assessed the performance of the aforementioned molecular models in estimating nuclear spin-spin coupling constants by comparing their predictions to experimental data available in chloroform. The results and discussion presented in this study demonstrate that ANI-2x tends to predict stronger-than-expected hydrogen bonding and overstabilize global minima and shows problems related to inadequate description of dispersion interactions. Furthermore, while ANI-2x is a viable model for modeling in the gas phase, conventional force fields still play an important role, especially for condensed-phase simulations. Overall, this study highlights the strengths and weaknesses of each model, providing guidelines for the use and future development of force fields and machine learning potentials.

Enhancing the accuracy of density functional tight binding models through ChIMES many-body interaction potentials

Semi-empirical quantum models such as Density Functional Tight Binding (DFTB) are attractive methods for obtaining quantum simulation data at longer time and length scales than possible with standard approaches. However, application of these models can require lengthy effort due to the lack of a systematic approach for their development. In this work, we discuss the use of the Chebyshev Interaction Model for Efficient Simulation (ChIMES) to create rapidly parameterized DFTB models, which exhibit strong transferability due to the inclusion of many-body interactions that might otherwise be inaccurate. We apply our modeling approach to silicon polymorphs and review previous work on titanium hydride. We also review the creation of a general purpose DFTB/ChIMES model for organic molecules and compounds that approaches hybrid functional and coupled cluster accuracy with two orders of magnitude fewer parameters than similar neural network approaches. In all cases, DFTB/ChIMES yields similar accuracy to the underlying quantum method with orders of magnitude improvement in computational cost. Our developments provide a way to create computationally efficient and highly accurate simulations over varying extreme thermodynamic conditions, where physical and chemical properties can be difficult to interrogate directly, and there is historically a significant reliance on theoretical approaches for interpretation and validation of experimental results.

Machine Learning and Informatics Based Elucidation of Reaction Pathways for Upcycling Model Polyolefin to Aromatics

Catalytic upcycling of plastics results in a complex network of potentially thousands of reactions and intermediates. Manual analysis of such a network using ab initio methods to identify plausible reaction pathways and rate-controlling steps is intractable. Here, we combine informatics-based reaction network generation and machine learning based thermochemistry calculation to identify plausible (nonelementary step) pathways involved in dehydroaromatization of a model polyolefin, n-decane, to form aromatic products. All 78 aromatic molecules found involve a sequence comprising dehydrogenation, β-scission, and cyclization steps (in slightly different order). The plausible flux-carrying pathway depends on the family of reactions that is rate-controlling while the thermodynamic bottleneck is the first dehydrogenation step of n-decane. The adopted workflow is system agnostic and can be applied to understand the overall thermochemistry of other upcycling systems.

Machine Learning Interatomic Potentials and Long-Range Physics

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

MolTaut: A Tool for the Rapid Generation of Favorable Tautomer in Aqueous Solution

Fast and proper treatment of the tautomeric states for drug-like molecules is critical in computer-aided drug discovery since the major tautomer of a molecule determines its pharmacophore features and physical properties. We present MolTaut, a tool for the rapid generation of favorable states of drug-like molecules in water. MolTaut works by enumerating possible tautomeric states with tautomeric transformation rules, ranking tautomers with their relative internal energies and solvation energies calculated by AI-based models, and generating preferred ionization states according to predicted microscopic pK_a. Our test shows that the ranking ability of the AI-based tautomer scoring approach is comparable to the DFT method (wB97X/6-31G*//M062X/6-31G*/SMD) from which the AI models try to learn. We find that the substitution effect on tautomeric equilibrium is well predicted by MolTaut, which is helpful in computer-aided ligand design. The source code of MolTaut is freely available to researchers and can be accessed at https://github.com/xundrug/moltaut. To facilitate the usage of MolTaut by medicinal chemists, we made a free web server, which is available at http://moltaut.xundrug.cn. MolTaut is a handy tool for investigating the tautomerization issue in drug discovery.

Uncertainty-driven dynamics for active learning of interatomic potentials

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

QDπ: A Quantum Deep Potential Interaction Model for Drug Discovery

We report QDπ-v1.0 for modeling the internal energy of drug molecules containing H, C, N, and O atoms. The QDπ model is in the form of a quantum mechanical/machine learning potential correction (QM/Δ-MLP) that uses a fast third-order self-consistent density-functional tight-binding (DFTB3/3OB) model that is corrected to a quantitatively high-level of accuracy through a deep-learning potential (DeepPot-SE). The model has the advantage that it is able to properly treat electrostatic interactions and handle changes in charge/protonation states. The model is trained against reference data computed at the ωB97X/6-31G* level (as in the ANI-1x data set) and compared to several other approximate semiempirical and machine learning potentials (ANI-1x, ANI-2x, DFTB3, MNDO/d, AM1, PM6, GFN1-xTB, and GFN2-xTB). The QDπ model is demonstrated to be accurate for a wide range of intra- and intermolecular interactions (despite its intended use as an internal energy model) and has shown to perform exceptionally well for relative protonation/deprotonation energies and tautomers. An example application to model reactions involved in RNA strand cleavage catalyzed by protein and nucleic acid enzymes illustrates QDπ has average errors less than 0.5 kcal/mol, whereas the other models compared have errors over an order of magnitude greater. Taken together, this makes QDπ highly attractive as a potential force field model for drug discovery.

WS22 database, Wigner Sampling and geometry interpolation for configurationally diverse molecular datasets

Multidimensional surfaces of quantum chemical properties, such as potential energies and dipole moments, are common targets for machine learning, requiring the development of robust and diverse databases extensively exploring molecular configurational spaces. Here we composed the WS22 database covering several quantum mechanical (QM) properties (including potential energies, forces, dipole moments, polarizabilities, HOMO, and LUMO energies) for ten flexible organic molecules of increasing complexity and with up to 22 atoms. This database consists of 1.18 million equilibrium and non-equilibrium geometries carefully sampled from Wigner distributions centered at different equilibrium conformations (either at the ground or excited electronic states) and further augmented with interpolated structures. The diversity of our datasets is demonstrated by visualizing the geometries distribution with dimensionality reduction as well as via comparison of statistical features of the QM properties with those available in existing datasets. Our sampling targets broader quantum mechanical distribution of the configurational space than provided by commonly used sampling through classical molecular dynamics, upping the challenge for machine learning models.