Machine learning models are poised to make a transformative impact on chemical sciences by dramatically accelerating computational algorithms and amplifying insights available from computational chemistry methods. However, achieving this requires a confluence and coaction of expertise in computer science and physical sciences. This Review is written for new and experienced researchers working at the intersection of both fields. We first provide concise tutorials of computational chemistry and machine learning methods, showing how insights involving both can be achieved. We follow with a critical review of noteworthy applications that demonstrate how computational chemistry and machine learning can be used together to provide insightful (and useful) predictions in molecular and materials modeling, retrosyntheses, catalysis, and drug design.

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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.

Nuclear quantum effects (NQE) tend to generate delocalized molecular dynamics due to the inclusion of the zero point energy and its coupling with the anharmonicities in interatomic interactions. Here, we present evidence that NQE often enhance electronic interactions and, in turn, can result in dynamical molecular stabilization at finite temperature. The underlying physical mechanism promoted by NQE depends on the particular interaction under consideration. First, the effective reduction of interatomic distances between functional groups within a molecule can enhance the n → π* interaction by increasing the overlap between molecular orbitals or by strengthening electrostatic interactions between neighboring charge densities. Second, NQE can localize methyl rotors by temporarily changing molecular bond orders and leading to the emergence of localized transient rotor states. Third, for noncovalent van der Waals interactions the strengthening comes from the increase of the polarizability given the expanded average interatomic distances induced by NQE. The implications of these boosted interactions include counterintuitive hydroxyl–hydroxyl bonding, hindered methyl rotor dynamics, and molecular stiffening which generates smoother free-energy surfaces. Our findings yield new insights into the versatile role of nuclear quantum fluctuations in molecules and materials.

Dynamics of flexible molecules are often determined by an interplay between local chemical bond fluctuations and conformational changes driven by long-range electrostatics and van der Waals interactions. This interplay between interactions yields complex potential-energy surfaces (PESs) with multiple minima and transition paths between them. In this work, we assess the performance of the state-of-the-art Machine Learning (ML) models, namely, sGDML, SchNet, Gaussian Approximation Potentials/Smooth Overlap of Atomic Positions (GAPs/SOAPs), and Behler-Parrinello neural networks, for reproducing such PESs, while using limited amounts of reference data. As a benchmark, we use the cis to trans thermal relaxation in an azobenzene molecule, where at least three different transition mechanisms should be considered. Although GAP/SOAP, SchNet, and sGDML models can globally achieve a chemical accuracy of 1 kcal mol −1 with fewer than 1000 training points, predictions greatly depend on the ML method used and on the local region of the PES being sampled. Within a given ML method, large differences can be found between predictions of close-to-equilibrium and transition regions, as well as for different transition mechanisms. We identify key challenges that the ML models face mainly due to the intrinsic limitations of commonly used atom-based descriptors. All in all, our results suggest switching from learning the entire PES within a single model to using multiple local models with optimized descriptors, training sets, and architectures for different parts of the complex PES.

Viable planar pentacoordinate carbon (ppC) systems with a ppC bonded to a transition metal and embedded in a metallocene framework are reported. Our detailed global minima search shows that CAlMX (M = Zr and Hf; X = F-I and CH) clusters with ppCs are appropriate candidates for experimental realization in the gas phase. The fulfillment of the 18 electron rule and electron delocalization is found to be crucial for the stabilization of these ppC arrangements.

The training set of atomic configurations is key to the performance of any Machine Learning Force Field (MLFF) and, as such, the training set selection determines the applicability of the MLFF model for predictive molecular simulations. However, most atomistic reference datasets are inhomogeneously distributed across configurational space (CS), and thus, choosing the training set randomly or according to the probability distribution of the data leads to models whose accuracy is mainly defined by the most common close-to-equilibrium configurations in the reference data. In this work, we combine unsupervised and supervised ML methods to bypass the inherent bias of the data for common configurations, effectively widening the applicability range of the MLFF to the fullest capabilities of the dataset. To achieve this goal, we first cluster the CS into subregions similar in terms of geometry and energetics. We iteratively test a given MLFF performance on each subregion and fill the training set of the model with the representatives of the most inaccurate parts of the CS. The proposed approach has been applied to a set of small organic molecules and alanine tetrapeptide, demonstrating an up to twofold decrease in the root mean squared errors for force predictions on non-equilibrium geometries of these molecules. Furthermore, our ML models demonstrate superior stability over the default training approaches, allowing reliable study of processes involving highly out-of-equilibrium molecular configurations. These results hold for both kernel-based methods (sGDML and GAP/SOAP models) and deep neural networks (SchNet model).

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.