Predicting the binding affinity of ligands to protein pockets is key in the drug design pipeline. The flexibility of ligand-pocket motifs arises from a range of attractive and repulsive electronic interactions during binding. Accurately accounting for all interactions requires robust quantum-mechanical (QM) benchmarks, which are scarce for ligand-pocket systems. Additionally, disagreement between “gold standard” Coupled Cluster (CC) and Quantum Monte Carlo (QMC) methods casts doubt on many benchmarks for larger non-covalent systems. We introduce the “QUantum Interacting Dimer” (QUID) benchmark framework containing 170 non-covalent (non-)equilibrium systems modeling chemically and structurally diverse ligand-pocket motifs. Symmetry-adapted perturbation theory shows that QUID broadly covers non-covalent binding motifs and energetic contributions. Robust binding energies are obtained using complementary CC and QMC methods, achieving agreement of 0.5 kcal/mol. The benchmark data analysis reveals that several dispersion-inclusive density functional approximations provide accurate energy predictions, though their atomic van der Waals forces differ in magnitude and orientation. Contrarily, semiempirical methods and empirical force fields require improvements in capturing non-covalent interactions (NCIs) for out-of-equilibrium geometries. The wide span of NCIs, highly accurate interaction energies, and analysis of molecular properties take QUID beyond the “gold standard” for QM benchmarks of ligand-protein systems.

The EquiDTB framework leverages physics-inspired equivariant neural networks to parameterize generalizable many-body Δ _TB potentials, advancing the DFTB method for accurate simulations of large drug-like molecules and non-covalent systems.

Atomistic simulations are routinely employed in academia and industry to study the behavior of molecules, materials, and their interfaces. Central to these simulations are force fields (FF), whose development is challenged by intricate interatomic interactions at different spatio-temporal scales and the vast expanse of chemical space. Machine learning (ML) FFs, trained on quantum-mechanical energies and forces, have shown the capacity to achieve sub-kcal/(mol*A) accuracy while maintaining computational efficiency. The TEA Challenge 2023 rigorously evaluated commonly used MLFFs across diverse applications, highlighting their strengths and weaknesses. Participants trained their models using provided datasets, and the results were systematically analyzed to assess the MLFFs' ability to reproduce potential energy surfaces, handle incomplete reference data, manage multi-component systems, and model complex periodic structures. This publication describes the datasets, outlines the proposed challenges, and presents a detailed analysis of the accuracy, stability, and efficiency of the MACE, SO3krates, sGDML, SOAP/GAP, and FCHL19* architectures in molecular dynamics simulations. The models represent the MLFF developers who participated in the TEA Challenge 2023. All results presented correspond to the state of the ML architectures as of October 2023. A comprehensive analysis of the molecular dynamics results obtained with different MLFFs will be presented in the second part of this manuscript.

We present the second part of the rigorous evaluation of state-of-the-art machine learning force fields (MLFFs) within the TEA Challenge 2023. This study provides an in-depth analysis of the performance of MACE, SO3krates, sGDML, SOAP/GAP, and FCHL19* in modeling molecules, molecule-surface interfaces, and periodic materials. We compare observables obtained from molecular dynamics (MD) simulations using different MLFFs under identical conditions. Where applicable, density-functional theory (DFT) or experiment serves as a reference to reliably assess the performance of the machine learning models. In the absence of DFT benchmarks, we conduct a comparative analysis based on results from various MLFF architectures. Our findings indicate that at the current stage of MLFF development, the choice of the ML model is becoming less critical, as the resulting simulations are largely independent of the MLFF architecture. Instead, emphasis should be placed on developing complete, reliable, and representative training datasets. Nonetheless, long-range noncovalent interactions remain challenging for all MLFF models, necessitating special caution in simulations of physical systems where such interactions are prominent, such as molecule-surface interfaces. The findings presented here reflect the state of MLFF models as of October 2023.

Predicting the binding affinity of ligand molecules to protein pockets is a key step in the drug design pipeline. The flexibility of ligand-pocket motifs arises from a wide range of attractive and repulsive electronic interactions invoked upon binding. Accurately accounting for all these interactions on equal footing requires robust quantum-mechanical (QM) benchmarks, which are scarce for ligand-pocket systems. In addition, the puzzling disagreement between ``gold standard'' Coupled Cluster (CCSD(T)) and Quantum Monte Carlo (QMC) methods [Nat. Commun. 12, 3927 (2021)] casts doubt on many existing benchmarks for larger non-covalent systems. Here, we introduce the ``Quantum Interacting Dimer'' (QUID) benchmark framework containing 170 non-covalent systems spanning equilibrium and non-equilibrium geometries that model chemically and structurally diverse ligand-pocket motifs. Symmetry-adapted perturbation theory shows that QUID broadly covers non-covalent binding motifs and energetic (exchange-repulsion, electrostatic, induction, and dispersion) contributions. Robust and reproducible binding energies are obtained using two complementary QM methods: LNO-CCSD(T) and QMC, achieving mutual agreement of 0.3 kcal/mol. Analysis of this benchmark data reveals that several dispersion-inclusive density functional approximations provide accurate energy predictions, though they exhibit discrepancies in magnitude and orientation of atomic van der Waals forces, which could influence the dynamics of ligands within the pocket. On the contrary, semiempirical methods and widely used empirical force fields require improvements, particularly in capturing non-covalent interactions (NCIs) for out-of-equilibrium geometries. The wide span of molecular dipole moments and polarizabilities in QUID also demonstrates flexibility in designing pocket structures to achieve desired binding properties. Therefore, QUID sets a new ``platinum standard'' for reliable and reproducible QM benchmarks of NCIs in larger systems and enhances our understanding of biomolecular ligand-pocket interactions.

Semi-empirical electronic structure methods have become valuable tools for studying complex (bio)molecular systems due to their balance between computational efficiency and accuracy. A key aspect of these methods is their parameterization, which not only governs the reliability of the results but also provides an opportunity to enhance their overall performance. In our previous work [J. Phys. Chem. Lett. 11, 16 (2021)], we improved the accuracy of the semi-empirical density functional tight-binding (DFTB) method for computing multiple properties of small molecules by developing the machine learning (ML) potential NN$_{\rm rep}$ to bridge the gap between electronic DFTB components and those of the hybrid DFT-PBE0 functional. To overcome the limitations of NN$_{\rm rep}$, we introduce the EquiDTB framework, which leverages physics-inspired equivariant neural networks (NN) to parameterize scalable and transferable $\Delta_{\rm TB}$ many-body potentials, replacing the standard pairwise repulsive potential in the DFTB method. This advancement extends the applicability of our ML-corrected DFTB approach to larger molecules and non-covalent systems, going beyond the chemical space represented in the training quantum-mechanical datasets. Indeed, the enhanced performance of EquiDTB over the standard TB methods (DFTB and GFN2-xTB) is demonstrated by the accurate computation of the atomic forces of equilibrium and non-equilibrium small molecular dimers, as well as their interaction energies. Moreover, EquiDTB can be effectively employed to explore the potential energy surfaces of large and flexible drug-like molecules---for example, to determine the minimum energy path between isomers, analyze structural transitions during dynamical simulations, compute vibrational modes, and investigate energetic rankings. Therefore, our work highlights that an optimal integration of an equivariant NN with QM datasets can advance the DFTB method to achieve DFT-PBE0 level accuracy with high computational efficiency, paving the way for more reliable (bio)molecular simulations.