Quantum mechanics/molecular mechanics (QM/ MM) molecular dynamics (MD) simulations have been developed to simulate molecular systems, where an explicit description of changes in the electronic structure is necessary. However, QM/MM MD simulations are computationally expensive compared to fully classical simulations as all valence electrons are treated explicitly and a self-consistent field (SCF) procedure is required. Recently, approaches have been proposed to replace the QM description with machine-learned (ML) models. However, condensed-phase systems pose a challenge for these approaches due to long-range interactions. Here, we establish a workflow, which incorporates the MM environment as an element type in a high-dimensional neural network potential (HDNNP). The fitted HDNNP describes the potential-energy surface of the QM particles with an electrostatic embedding scheme. Thus, the MM particles feel a force from the polarized QM particles. To achieve chemical accuracy, we find that even simple systems require models with a strong gradient regularization, a large number of data points, and a substantial number of parameters. To address this issue, we extend our approach to a Δ-learning scheme, where the ML model learns the difference between a reference method (density functional theory (DFT)) and a cheaper semiempirical method (density functional tight binding (DFTB)). We show that such a scheme reaches the accuracy of the DFT reference method while requiring significantly less parameters. Furthermore, the Δ-learning scheme is capable of correctly incorporating long-range interactions within a cutoff of 1.4 nm. It is validated by performing MD simulations of retinoic acid in water and the interaction between S-adenoslymethioniat and cytosine in water. The presented results indicate that Δ-learning is a promising approach for (QM)ML/MM MD simulations of condensed-phase systems.

The accurate description of electrostatic interactions remains a challenging problem for classical potential-energy functions. The commonly used fixed partial-charge approximation fails to reproduce the electrostatic potential at short range due to its insensitivity to conformational changes and anisotropic effects. At the same time, possibly more accurate machine-learned (ML) potentials struggle with the long-range behavior due to their inherent locality ansatz. Employing a multipole expansion offers in principle an exact treatment of the electrostatic potential such that the long-range and short-range electrostatic interactions can be treated simultaneously with high accuracy. However, such an expansion requires the calculation of the electron density using computationally expensive quantum-mechanical (QM) methods. Here, we introduce an equivariant graph neural network (GNN) to address this issue. The proposed model predicts atomic multipoles up to the quadrupole, circumventing the need for expensive QM computations. By using an equivariant architecture, the model enforces the correct symmetry by design without relying on local reference frames. The GNN reproduces the electrostatic potential of various systems with high fidelity. Possible uses for such an approach include the separate treatment of long-range interactions in ML potentials, the analysis of electrostatic potential surfaces, and static multipoles in polarizable force fields.

Experimental determination of the absolute stereochemistry of chiral molecules has been a fundamental challenge in natural sciences for decades. Vibrational circular dichroism (VCD) spectroscopy represents an attractive alternative to traditional methods like X-ray crystallography due to the use of molecules in solution. The interpretation of measured VCD spectra and thus the assignment of the absolute configuration relies on quantum-mechanical calculations. While such calculations are straightforward for rigid molecules with a single conformation, the need to estimate the correct conformational ensemble and energy landscape to obtain the appropriate theoretical spectra poses significant challenges for flexible molecules. In this work, we present the development of a VCD spectra alignment (VSA) algorithm to compare theoretical and experimental VCD spectra. The algorithm determines which enantiomer is more likely to reproduce the experimental spectrum and thus allows the correct assignment of the absolute stereochemistry. The VSA algorithm is successfully applied to determine the absolute chirality of highly flexible molecules, including commercial drug substances. Furthermore, we show that the computational cost can be reduced by performing the full frequency calculation only for a reduced set of conformers. The presented approach has the potential to allow the determination of the absolute configuration of chiral molecules in a robust and efficient manner.

The relative stereochemistry and isomeric substitution pattern of organic molecules is typically determined using nuclear magnetic resonance spectroscopy (NMR). However, NMR spectra are sometimes nonconclusive, e.g., if spectra are extremely crowded, coupling patterns are not resolved, or if symmetry reasons preclude interpretation. Infrared spectroscopy (IR) can provide additional information in such cases, because IR represents a molecule comprehensively by depiction of the complete set of its normal vibrations. The challenge is thereby that diastereomers and substitution isomers often give rise to highly similar IR spectra, and visual distinction is insufficient and may be biased. Here we show the adaptation of an alignment algorithm, originally developed for vibrational circular dichroism (VCD) spectroscopy, to automatically match IR spectra and provide a quantitative measure of the goodness of fit, which can be used to distinguish isomers. The performance of the approach is demonstrated for different use cases: diastereomers of flexible druglike molecules, E/Z-isomers, and substitution isomers of pyrazine and naphthalene. It can be applied to IR spectra measured both in the gas phase (gas chromatography IR) and in solution.

Simulations of molecular systems using electronic structure methods are still not feasible for many systems of biological importance. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. The parametrization of FF is, however, time-consuming and has traditionally been based on experimental data. Recent years have therefore seen increasing efforts to automatize FF parametrization or to replace FF with machine-learning (ML) based potentials. Here, we propose an alternative strategy to parametrize FF, which makes use of ML and gradient-descent based optimization while retaining a functional form founded in physics. Using a predefined functional form is shown to enable interpretability, robustness, and efficient simulations of large systems over long time scales. To demonstrate the strength of the proposed method, a fixed-charge and a polarizable model are trained on ab initio potential-energy surfaces. Given only information about the constituting elements, the molecular topology, and reference potential energies, the models successfully learn to assign atom types and corresponding FF parameters from scratch. The resulting models and parameters are validated on a wide range of experimentally and computationally derived properties of systems including dimers, pure liquids, and molecular crystals.