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

Molecule-Environment Embedding with Quantum Monte Carlo: Electrons Interacting with Drude Oscillators

We present a comprehensive investigation of the El-QDO embedding method [Phys. Rev. Lett. 131, 228001 (2023)], where molecular systems described through the electronic Hamiltonian are immersed in a bath of charged quantum harmonic oscillators, i.e., quantum Drude oscillators (QDOs). In the El-QDO model, the entire system of electrons and drudons─the quantum particles in the QDOs─is modeled through a single Hamiltonian which is solved through quantum Monte Carlo (QMC) methods. We first describe the details of the El-QDO Hamiltonian, of the proposed El-QDO ansatz, and of the QMC algorithms implemented to integrate both electronic and drudonic degrees of freedom. Then we analyze short-range regularization functions for the interacting potential between electrons and QDOs in order to accurately treat equilibrium and repulsive regions, resolving the overpolarization error that occurs between the electronic system and the environment. After benchmarking various regularization (damping) functions on the cases of argon and water dimers, the El-QDO method is applied to study the solvation energies of the benzene and water dimers, verifying the accuracy of the El-QDO approach compared to accurate fully electronic ab initio calculations. Furthermore, through the comparison of the El-QDO interaction energies with the components of Symmetry-Adapted Perturbation Theory calculations, we illustrate the El-QDO's explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the electronic subsystem and the environment.

Experimental evidence of quantum Drude oscillator behavior in liquids revealed with probabilistic iterative Boltzmann inversion

The first experimental evidence of quantum Drude oscillator behavior in liquids is uncovered using probabilistic machine learning-augmented iterative Boltzmann inversion applied to noble gas radial distribution functions. Furthermore, classical force fields for noble gases are shown to be reduced to a single parameter through simple empirical relations linked to atomic dipole polarizability. These findings highlight how neutron scattering data can inspire innovative force field design and offer insight into interatomic forces to advance molecular simulations.

Imaging the Rovibrational Ground State of the Helium-Neon Dimers 4He20Ne and 4He22Ne

The helium-neon dimer has been subject to many theoretical studies, in which the interaction potential of the helium-neon system has been calculated with ever increasing accuracy. Calculations predict that the helium-neon system supports only a few bound states, which makes the system inaccessible to standard spectroscopic techniques. Previous experiments have probed the helium-neon potential by comparing measured and predicted scattering cross sections. However, the spatial structure and energetics of the bound states of the helium-neon system have not been studied experimentally in great detail. We employ Coulomb explosion imaging (CEI) to measure the pair distance distributions of the helium-neon dimers 4He20Ne and 4He22Ne in their rovibrational ground state. For each dimer, the binding energy is extracted from the measured pair distance distribution. Additionally, the pair distance distribution provides access to the helium-neon potential.

Organic Molecule Adsorption on Barite (001)─A Density Functional Theory Study

Scale formation is a continuous and expensive challenge in several industries such as water treatment systems, oil and gas production, and desalination plants. Density functional theory (DFT) calculations were employed to explore the adsorption mechanisms of a diverse set of organic molecules on the barite (001) surface relevant for scale inhibition application. Our study focuses on understanding how different functional groups influence adsorption energy, surface affinity, and potential inhibition effectiveness. Results reveal that molecules with strong dispersion interactions, such as aromatic compounds with heteroatoms (e.g., phenol and pyrrole), bind strongly to barite, suggesting their potential as effective scale inhibitors and simultaneously the potential for these molecules to cover the already formed scale, making dissolution more difficult. The study also examines the impact of solvation on adsorption energy, confirming that the same compounds are expected to bind strongly, even from solution. These insights can inform the design of more efficient scale inhibitors for barite, contributing to better management of mineral scaling in industrial applications. The research underscores the importance of molecular-level interactions for optimizing scale inhibition strategies and offers a foundation for future studies on other mineral surfaces and inhibitor designs.

Nonbonded Force Field Parameters Derived from Atoms-in-Molecules Methods Reproduce Interactions in Proteins from First-Principles

Noncovalent interactions govern many chemical and biological phenomena and are crucial in protein-protein interactions, enzyme catalysis, and DNA folding. The size of these macromolecules and their various conformations demand computationally inexpensive force fields that can accurately mimic the quantum chemical nature of the atomic noncovalent interactions. Accurate force fields, coupled with increasingly longer molecular dynamics simulations, may empower us to predict conformational changes associated with the biochemical function of proteins. Here, we aim to derive nonbonded protein force field parameters from the partitioned electron density of amino acids, the fundamental units of proteins, via the atoms-in-molecules (AIM) approach. The AIM parameters are validated using a database of charged, aromatic, and hydrophilic side-chain interactions in 610 conformations, primarily involving π-π interactions, as recently reported by one of us (Carter-Fenk et al., 2023). Electrostatic and van der Waals interaction energies calculated with nonbonded force field parameters from different AIM methodologies were compared to first-principles interaction energies from absolute localized molecular orbital-energy decomposition analysis (ALMO-EDA) at the ωB97XV/def2-TZVPD level. Our findings show that electrostatic interactions between side chains are accurately reproduced by atomic charges from the minimal basis iterative stockholder (MBIS) scheme with mean absolute errors of 4-7 kJ/mol. Meanwhile, C6 coefficients from the MBIS AIM method effectively predict dispersion interactions with a mean error of -2 kJ/mol and a maximal error of -5 kJ/mol. As an outlook to use AIM methods in the development of protein force fields, we present the constrained AIM method that allows one to fix backbone parameters during the optimization of side-chain interactions. Backbone dihedral parameters have been optimized to reproduce secondary structure elements in proteins, and not altering them maintains compatibility with conventional protein force fields while improving the description of side-chain interactions. Our validated AIM methods allow for the depiction of noncovalent, long-range interactions in proteins using cost-effective force fields that achieve chemical precision.

Alchemical harmonic approximation based potential for iso-electronic diatomics: Foundational baseline for Δ-machine learning

We introduce the alchemical harmonic approximation (AHA) of the absolute electronic energy for charge-neutral iso-electronic diatomics at fixed interatomic distance d0. To account for variations in distance, we combine AHA with this ansatz for the electronic binding potential, E(d)=(Eu-Es)Ec-EsEu-Esd/d0+Es, where Eu, Ec, Es correspond to the energies of the united atom, calibration at d0, and the sum of infinitely separated atoms, respectively. Our model covers the two-dimensional electronic potential energy surface spanned by distances of 0.7-2.5 Å and differences in nuclear charge from which only one single point (with elements of nuclear charge Z1, Z2, and distance d0) is drawn to calibrate Ec. Using reference data from pbe0/cc-pVDZ, we present numerical evidence for the electronic ground-state of all neutral diatomics with 8, 10, 12, and 14 electrons. We assess the validity of our model by comparison to legacy interatomic potentials (harmonic oscillator, Lennard-Jones, and Morse) within the most relevant range of binding (0.7-2.5 Å) and find comparable accuracy if restricted to single diatomics and significantly better predictive power when extrapolating to the entire iso-electronic series. We also investigated Δ-learning of the electronic absolute energy using our model as a baseline. This baseline model results in a systematic improvement, effectively reducing training data needed for reaching chemical accuracy by up to an order of magnitude from ∼1000 to ∼100. By contrast, using AHA+Morse as a baseline hardly leads to any improvement and sometimes even deteriorates the predictive power. Inferring the energy of unseen CO converges to a prediction error of ∼0.1 Ha in direct learning and ∼0.04 Ha with our baseline.

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.

A Simple Model for the Pauli Repulsion with Possible Utility in QM, MM and Chemical Education

The Pauli repulsion is the intermolecular force responsible for the volume and low compressibility of condensed-phase matter at normal conditions. A simple model for this force is presented, wherein per-atom electron densities are represented as spherical charge distributions that are prevented from significantly overlapping. In the example of two noble gas atoms approaching one another beyond their van der Waals radii, the distance between the centers of the electronic charge distributions becomes larger than the distance between the nuclei, giving rise to an unfavorable electrostatic interaction. For the purpose of calculating this interaction, the model is further simplified by representing the per-atom electron density as a negative point charge, loosely inspired by the classical Drude oscillator. The dispersion interaction is simplified to an R-6 term, centered on the aforementioned point charges. Despite the gross simplicity of the resulting formalism, near-quantitative agreement with high-level QM interaction energies of noble gas dimers is achieved. Accordingly, the present model is thought to have utility in force fields, in post-HF and post-DFT dispersion corrections, and in chemical education.

Impact of Combination Rules, Level of Theory, and Potential Function on the Modeling of Gas- and Condensed-Phase Properties of Noble Gases

The systems of noble gases are particularly instructive for molecular modeling due to the elemental nature of their interactions. They do not normally form bonds nor possess a (permanent) dipole moment, and the only forces determining their bonding/clustering stems from van der Waals forces─dispersion and Pauli repulsion, which can be modeled by empirical potential functions. Combination rules, that is, formulas to derive parameters for pair potentials of heterodimers from parameters of corresponding homodimers, have been studied at length for the Lennard-Jones 12-6 potentials but not in great detail for other, more accurate, potentials. In this work, we examine the usefulness of nine empirical potentials in their ability to reproduce quantum mechanical (QM) benchmark dissociation curves of noble gas dimers (He, Ne, Ar, Kr, and Xe homo- and heterodimers), and we systematically study the efficacy of different permutations of combination relations for each parameter of the potentials. Our QM benchmark comprises dissociation curves computed by several different coupled cluster implementations as well as symmetry-adapted perturbation theory. The two-parameter Lennard-Jones potentials were decisively outperformed by more elaborate potentials that sport a 25-30 times lower root-mean-square error (RMSE) when fitted to QM dissociation curves. Very good fits to the QM dissociation curves can be achieved with relatively inexpensive four- or even three-parameter potentials, for instance, the damped 14-7 potential (Halgren, J. Am. Chem. Soc. 1992, 114, 7827-7843), a four-parameter Buckingham potential (Werhahn et al., Chem. Phys. Lett. 2015, 619, 133-138), or the three-parameter Morse potential (Morse, Phys. Rev. 1929, 34, 57-64). Potentials for heterodimers that are generated from combination rules have an RMSE that is up to 20 times higher than potentials that are directly fitted to the QM dissociation curves. This means that the RMSE, in particular, for light atoms, is comparable in magnitude to the well-depth of the potential. Based on a systematic permutation of combination rules, we present one or more combination rules for each potential tested that yield a relatively low RMSE. Two new combination rules are introduced that perform well, one for the van der Waals radius σij as ( 1 2 ( σ i 3 + σ j 3 ) ) 1 / 3 and one for the well-depth ϵij as ( 1 2 ( ϵ i - 2 + ϵ j - 2 ) ) - 1 / 2 . The QM data and the fitted potentials were evaluated in the gas phase against experimental second virial coefficients for homo- and heterodimers, the latter of which allowed evaluation of the combination rules. The fitted models were used to perform condensed phase molecular dynamics simulations to verify the melting points, liquid densities at the melting point, and the enthalpies of vaporization produced by the models for pure substances. Subtle differences in the benchmark potentials, in particular, the well-depth, due to the level of theory used were found here to have a profound effect on the macroscopic properties of noble gases: second virial coefficients or the bulk properties in simulations. By explicitly including three-body dispersion in molecular simulations employing the best pair potential, we were able to obtain accurate melting points as well as satisfactory densities and enthalpies of vaporization.

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.