Explainable chemical artificial intelligence from accurate machine learning of real-space chemical descriptors.

Machine-learned computational chemistry has led to a paradoxical situation in which molecular properties can be accurately predicted, but they are difficult to interpret. Explainable AI (XAI) tools can be used to analyze complex models, but they are highly dependent on the AI technique and the origin of the reference data. Alternatively, interpretable real-space tools can be employed directly, but they are often expensive to compute. To address this dilemma between explainability and accuracy, we developed SchNet4AIM, a SchNet-based architecture capable of dealing with local one-body (atomic) and two-body (interatomic) descriptors. The performance of SchNet4AIM is tested by predicting a wide collection of real-space quantities ranging from atomic charges and delocalization indices to pairwise interaction energies. The accuracy and speed of SchNet4AIM breaks the bottleneck that has prevented the use of real-space chemical descriptors in complex systems. We show that the group delocalization indices, arising from our physically rigorous atomistic predictions, provide reliable indicators of supramolecular binding events, thus contributing to the development of Explainable Chemical Artificial Intelligence (XCAI) models.

Biomolecular dynamics with machine-learned quantum-mechanical force fields trained on diverse chemical fragments.

The GEMS method enables molecular dynamics simulations of large heterogeneous systems at ab initio quality.

Quantum Drude oscillators coupled with Coulomb potential as an efficient model for bonded and non-covalent interactions in atomic dimers.

The quantum Drude oscillator (QDO) model has been widely used as an efficient surrogate to describe the electric response properties of matter as well as long-range interactions in molecules and materials. Most commonly, QDOs are coupled within the dipole approximation so that the Hamiltonian can be exactly diagonalized, which forms the basis for the many-body dispersion method [Phys. Rev. Lett. 108, 236402 (2012)]. The dipole coupling is efficient and allows us to study non-covalent many-body effects in systems with thousands of atoms. However, there are two limitations: (i) the need to regularize the interaction at short distances with empirical damping functions and (ii) the lack of multipolar effects in the coupling potential. In this work, we convincingly address both limitations of the dipole-coupled QDO model by presenting a numerically exact solution of the Coulomb-coupled QDO model by means of quantum Monte Carlo methods. We calculate the potential-energy surfaces of homogeneous QDO dimers, analyzing their properties as a function of the three tunable parameters: frequency, reduced mass, and charge. We study the coupled-QDO model behavior at short distances and show how to parameterize this model to enable an effective description of chemical bonds, such as the covalent bond in the H2 molecule.

Affinity of Telluronium Chalcogen Bond Donors for Lewis Bases in Solution: A Critical Experimental-Theoretical Joint Study.

Telluronium salts [Ar2 MeTe]X were synthesized, and their Lewis acidic properties towards a number of Lewis bases were addressed in solution by physical and theoretical means. Structural X-ray diffraction analysis of 21 different salts revealed the electrophilicity of the Te centers in their interactions with anions. Telluroniums' propensity to form Lewis pairs was investigated with OPPh3 . Diffusion-ordered NMR spectroscopy suggested that telluroniums can bind up to three OPPh3 molecules. Isotherm titration calorimetry showed that the related heats of association in 1,2-dichloroethane depend on the electronic properties of the substituents of the aryl moiety and on the nature of the counterion. The enthalpies of first association of OPPh3 span -0.5 to -5 kcal mol-1 . Study of the affinity of telluroniums for OPPh3 by state-of-the-art DFT and ab-initio methods revealed the dominant Coulombic and dispersion interactions as well as an entropic effect favoring association in solution. Intermolecular orbital interactions between [Ar2 MeTe]+ cations and OPPh3 are deemed insufficient on their own to ensure the cohesion of [Ar2 MeTe ⋅ Bn ]+ complexes in solution (B=Lewis base). Comparison of Grimme's and Tkatchenko's DFT-D4/MBD-vdW thermodynamics of formation of higher [Ar2 MeTe ⋅ Bn ]+ complexes revealed significant molecular size-dependent divergence of the two methodologies, with MBD yielding better agreement with experiment.

Second quantization of many-body dispersion interactions for chemical and biological systems.

The many-body dispersion (MBD) framework is a successful approach for modeling the long-range electronic correlation energy and optical response of systems with thousands of atoms. Inspired by field theory, here we develop a second-quantized MBD formalism (SQ-MBD) that recasts a system of atomic quantum Drude oscillators in a Fock-space representation. SQ-MBD provides: (i) tools for projecting observables (interaction energy, transition multipoles, polarizability tensors) on coarse-grained representations of the atomistic system ranging from single atoms to large structural motifs, (ii) a quantum-information framework to analyze correlations and (non)separability among fragments in a given molecular complex, and (iii) a path toward the applicability of the MBD framework to molecular complexes with even larger number of atoms. The SQ-MBD approach offers conceptual insights into quantum fluctuations in molecular systems and enables direct coupling of collective plasmon-like MBD degrees of freedom with arbitrary environments, providing a tractable computational framework to treat dispersion interactions and polarization response in intricate systems.

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators.

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

Anisotropic Interlayer Force Field for Group-VI Transition Metal Dichalcogenides.

An anisotropic interlayer force field that describes the interlayer interactions in homogeneous and heterogeneous interfaces of group-VI transition metal dichalcogenides (MX2, where M = Mo, W, and X = S, Se) is presented. The force field is benchmarked against density functional theory calculations for bilayer systems within the Heyd-Scuseria-Ernzerhof hybrid density functional approximation, augmented by a nonlocal many-body dispersion treatment of long-range correlation. The parametrization yields good agreement with the reference calculations of binding energy curves and sliding potential energy surfaces. It is found to be transferable to transition metal dichalcogenide (TMD) junctions outside of the training set that contain the same atom types. Calculated bulk moduli agree with most previous dispersion-corrected density functional theory predictions, which underestimate the available experimental values. Calculated phonon spectra of the various junctions under consideration demonstrate the importance of appropriately treating the anisotropic nature of the layered interfaces. Considering our previous parametrization for MoS2, the anisotropic interlayer potential enables accurate and efficient large-scale simulations of the dynamical, tribological, and thermal transport properties of a large set of homogeneous and heterogeneous TMD interfaces.

libMBD: A general-purpose package for scalable quantum many-body dispersion calculations.

Many-body dispersion (MBD) is a powerful framework to treat van der Waals (vdW) dispersion interactions in density-functional theory and related atomistic modeling methods. Several independent implementations of MBD with varying degree of functionality exist across a number of electronic structure codes, which both limits the current users of those codes and complicates dissemination of new variants of MBD. Here, we develop and document libMBD, a library implementation of MBD that is functionally complete, efficient, easy to integrate with any electronic structure code, and already integrated in FHI-aims, DFTB+, VASP, Q-Chem, CASTEP, and Quantum ESPRESSO. libMBD is written in modern Fortran with bindings to C and Python, uses MPI/ScaLAPACK for parallelization, and implements MBD for both finite and periodic systems, with analytical gradients with respect to all input parameters. The computational cost has asymptotic cubic scaling with system size, and evaluation of gradients only changes the prefactor of the scaling law, with libMBD exhibiting strong scaling up to 256 processor cores. Other MBD properties beyond energy and gradients can be calculated with libMBD, such as the charge-density polarization, first-order Coulomb correction, the dielectric function, or the order-by-order expansion of the energy in the dipole interaction. Calculations on supramolecular complexes with MBD-corrected electronic structure methods and a meta-review of previous applications of MBD demonstrate the broad applicability of the libMBD package to treat vdW interactions.

Predicting crystal form stability under real-world conditions.

The physicochemical properties of molecular crystals, such as solubility, stability, compactability, melting behaviour and bioavailability, depend on their crystal form1. In silico crystal form selection has recently come much closer to realization because of the development of accurate and affordable free-energy calculations2-4. Here we redefine the state of the art, primarily by improving the accuracy of free-energy calculations, constructing a reliable experimental benchmark for solid-solid free-energy differences, quantifying statistical errors for the computed free energies and placing both hydrate crystal structures of different stoichiometries and anhydrate crystal structures on the same energy landscape, with defined error bars, as a function of temperature and relative humidity. The calculated free energies have standard errors of 1-2 kJ mol-1 for industrially relevant compounds, and the method to place crystal structures with different hydrate stoichiometries on the same energy landscape can be extended to other multi-component systems, including solvates. These contributions reduce the gap between the needs of the experimentalist and the capabilities of modern computational tools, transforming crystal structure prediction into a more reliable and actionable procedure that can be used in combination with experimental evidence to direct crystal form selection and establish control5.

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.

"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.

Universal Pairwise Interatomic van der Waals Potentials Based on Quantum Drude Oscillators.

Repulsive short-range and attractive long-range van der Waals (vdW) forces play an appreciable role in the behavior of extended molecular systems. When using empirical force fields, the most popular computational methods applied to such systems, vdW forces are typically described by Lennard-Jones-like potentials, which unfortunately have a limited predictive power. Here, we present a universal parameterization of a quantum-mechanical vdW potential, which requires only two free-atom properties─the static dipole polarizability α1 and the dipole-dipole C6 dispersion coefficient. This is achieved by deriving the functional form of the potential from the quantum Drude oscillator (QDO) model, employing scaling laws for the equilibrium distance and the binding energy, and applying the microscopic law of corresponding states. The vdW-QDO potential is shown to be accurate for vdW binding energy curves, as demonstrated by comparing to the ab initio binding curves of 21 noble-gas dimers. The functional form of the vdW-QDO potential has the correct asymptotic behavior at both zero and infinite distances. In addition, it is shown that the damped vdW-QDO potential can accurately describe vdW interactions in dimers consisting of group II elements. Finally, we demonstrate the applicability of the atom-in-molecule vdW-QDO model for predicting accurate dispersion energies for molecular systems. The present work makes an important step toward constructing universal vdW potentials, which could benefit (bio)molecular computational studies.

Equivariant Graph Neural Networks for Toxicity Prediction.

Predictive modeling of toxicity is a crucial step in the drug discovery pipeline. It can help filter out molecules with a high probability of failing in the early stages of de novo drug design. Thus, several machine learning (ML) models have been developed to predict the toxicity of molecules by combining classical ML techniques or deep neural networks with well-known molecular representations such as fingerprints or 2D graphs. But the more natural, accurate representation of molecules is expected to be defined in physical 3D space like in ab initio methods. Recent studies successfully used equivariant graph neural networks (EGNNs) for representation learning based on 3D structures to predict quantum-mechanical properties of molecules. Inspired by this, we investigated the performance of EGNNs to construct reliable ML models for toxicity prediction. We used the equivariant transformer (ET) model in TorchMD-NET for this. Eleven toxicity data sets taken from MoleculeNet, TDCommons, and ToxBenchmark have been considered to evaluate the capability of ET for toxicity prediction. Our results show that ET adequately learns 3D representations of molecules that can successfully correlate with toxicity activity, achieving good accuracies on most data sets comparable to state-of-the-art models. We also test a physicochemical property, namely, the total energy of a molecule, to inform the toxicity prediction with a physical prior. However, our work suggests that these two properties can not be related. We also provide an attention weight analysis for helping to understand the toxicity prediction in 3D space and thus increase the explainability of the ML model. In summary, our findings offer promising insights considering 3D geometry information via EGNNs and provide a straightforward way to integrate molecular conformers into ML-based pipelines for predicting and investigating toxicity prediction in physical space. We expect that in the future, especially for larger, more diverse data sets, EGNNs will be an essential tool in this domain.

Data-driven tailoring of molecular dipole polarizability and frontier orbital energies in chemical compound space.

Understanding correlations - or lack thereof - between molecular properties is crucial for enabling fast and accurate molecular design strategies. In this contribution, we explore the relation between two key quantities describing the electronic structure and chemical properties of molecular systems: the energy gap between the frontier orbitals and the dipole polarizability. Based on the recently introduced QM7-X dataset, augmented with accurate molecular polarizability calculations as well as analysis of functional group compositions, we show that polarizability and HOMO-LUMO gap are uncorrelated when considering sufficiently extended subsets of the chemical compound space. The relation between these two properties is further analyzed on specific examples of molecules with similar composition as well as homooligomers. Remarkably, the freedom brought by the lack of correlation between molecular polarizability and HOMO-LUMO gap enables the design of novel materials, as we demonstrate on the example of organic photodetector candidates.

Accurate quantification of the stability of the perylene-tetracarboxylic dianhydride on Au(111) molecule-surface interface.

Studying inorganic/organic hybrid systems is a stepping stone towards the design of increasingly complex interfaces. A predictive understanding requires robust experimental and theoretical tools to foster trust in the obtained results. The adsorption energy is particularly challenging in this respect, since experimental methods are scarce and the results have large uncertainties even for the most widely studied systems. Here we combine temperature-programmed desorption (TPD), single-molecule atomic force microscopy (AFM), and nonlocal density-functional theory (DFT) calculations, to accurately characterize the stability of a widely studied interface consisting of perylene-tetracarboxylic dianhydride (PTCDA) molecules on Au(111). This network of methods lets us firmly establish the adsorption energy of PTCDA/Au(111) via TPD (1.74 ± 0.10 eV) and single-molecule AFM (2.00 ± 0.25 eV) experiments which agree within error bars, exemplifying how implicit replicability in a research design can benefit the investigation of complex materials properties.

Optimized Quantum Drude Oscillators for Atomic and Molecular Response Properties.

The quantum Drude oscillator (QDO) is an efficient yet accurate coarse-grained approach that has been widely used to model electronic and optical response properties of atoms and molecules as well as polarization and dispersion interactions between them. Three effective parameters (frequency, mass, and charge) fully characterize the QDO Hamiltonian and are adjusted to reproduce response properties. However, the soaring success of coupled QDOs for many-atom systems remains fundamentally unexplained, and the optimal mapping between atoms/molecules and oscillators has not been established. Here we present an optimized parametrization (OQDO) where the parameters are fixed by using only dipolar properties. For the periodic table of elements as well as small molecules, our model accurately reproduces atomic (spatial) polarization potentials and multipolar dispersion coefficients, elucidating the high promise of the presented model in the development of next-generation quantum-mechanical force fields for (bio)molecular simulations.

Efficient interatomic descriptors for accurate machine learning force fields of extended molecules.

Machine learning force fields (MLFFs) are gradually evolving towards enabling molecular dynamics simulations of molecules and materials with ab initio accuracy but at a small fraction of the computational cost. However, several challenges remain to be addressed to enable predictive MLFF simulations of realistic molecules, including: (1) developing efficient descriptors for non-local interatomic interactions, which are essential to capture long-range molecular fluctuations, and (2) reducing the dimensionality of the descriptors to enhance the applicability and interpretability of MLFFs. Here we propose an automatized approach to substantially reduce the number of interatomic descriptor features while preserving the accuracy and increasing the efficiency of MLFFs. To simultaneously address the two stated challenges, we illustrate our approach on the example of the global GDML MLFF. We found that non-local features (atoms separated by as far as 15 Å in studied systems) are crucial to retain the overall accuracy of the MLFF for peptides, DNA base pairs, fatty acids, and supramolecular complexes. Interestingly, the number of required non-local features in the reduced descriptors becomes comparable to the number of local interatomic features (those below 5 Å). These results pave the way to constructing global molecular MLFFs whose cost increases linearly, instead of quadratically, with system size.

Casimir Self-Interaction Energy Density of Quantum Electrodynamic Fields.

Quantum electrodynamic fields possess fluctuations corresponding to transient particle-antiparticle dipoles, which can be characterized by a nonvanishing polarizability density. Here, we extend a recently proposed quantum scaling law to describe the volumetric and radial polarizability density of a quantum field corresponding to electrons and positrons and derive the Casimir self-interaction energy (SIE) density of the field, E[over ¯]_{SIE}, in terms of the fine-structure constant. The proposed model obeys the cosmological equation of state w=-1 and the magnitude of the calculated E[over ¯]_{SIE} lies in between the two recent measurements of the cosmological constant Λ obtained by the Planck Mission and the Hubble Space Telescope.

Accurate global machine learning force fields for molecules with hundreds of atoms.

Global machine learning force fields, with the capacity to capture collective interactions in molecular systems, now scale up to a few dozen atoms due to considerable growth of model complexity with system size. For larger molecules, locality assumptions are introduced, with the consequence that nonlocal interactions are not described. Here, we develop an exact iterative approach to train global symmetric gradient domain machine learning (sGDML) force fields (FFs) for several hundred atoms, without resorting to any potentially uncontrolled approximations. All atomic degrees of freedom remain correlated in the global sGDML FF, allowing the accurate description of complex molecules and materials that present phenomena with far-reaching characteristic correlation lengths. We assess the accuracy and efficiency of sGDML on a newly developed MD22 benchmark dataset containing molecules from 42 to 370 atoms. The robustness of our approach is demonstrated in nanosecond path-integral molecular dynamics simulations for supramolecular complexes in the MD22 dataset.