Nature of Halide–Water Interactions: Insights from Many-Body Representations and Density Functional Theory

Molecular Insights into the Influence of Ions on the Water Structure. I. Alkali Metal Ions in Solution

In this study, we explore the impact of alkali metal ions (Li+, Na+, K+, Rb+, and Cs+) on the hydration structure of water using molecular dynamics simulations carried out with MB-nrg potential energy functions (PEFs). Our analyses include radial distribution functions, coordination numbers, dipole moments, and infrared spectra of water molecules, calculated as a function of solvation shells. The results collectively indicate a highly local influence of all of the alkali metal ions on the hydrogen-bond network established by the surrounding water molecules, with the smallest and most densely charged Li+ ion exerting the most pronounced effect. Remarkably, the MB-nrg PEFs demonstrate excellent agreement with available experimental data for the position and size of the first solvation shells, underscoring their potential as predictive models for realistic simulations of ionic aqueous solutions across various thermodynamic conditions and environments.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Novel Computational Chemistry Infrastructure for Simulating Astatide in Water: From Basis Sets to Force Fields Using Particle Swarm Optimization

Using the example of astatine, the heaviest naturally occurring halogen whose isotope At-211 has promising medical applications, we propose a new infrastructure for large-scale computational models of heavy elements with strong relativistic effects. In particular, we focus on developing an accurate force field for At- in water based on reliable relativistic density functional theory (DFT) calculations. To ensure the reliability of such calculations, we design novel basis sets for relativistic DFT, via the particle swarm optimization algorithm to optimize the coefficients of the new basis sets and the polarization-consistent basis set idea's extension to heavy elements to eliminate the basis set error from DFT calculations. The resulting basis sets enable the well-grounded evaluation of relativistic DFT against "gold-standard" CCSD(T) results. Accounting for strong relativistic effects, including spin-orbit interaction, via our redesigned infrastructure, we elucidate a noticeable dissimilarity between At- and I- in halide-water force field parameters, radial distribution functions, diffusion coefficients, and hydration energies. This work establishes the framework for the systematic development of polarization-consistent basis sets for relativistic DFT and accurate force fields for molecular dynamics simulations to be used in large-scale models of complex molecular systems with elements from the bottom of the periodic table, including actinides and even superheavy elements.

Consistent density functional theory-based description of ion hydration through density-corrected many-body representations

Delocalization error constrains the accuracy of density functional theory in describing molecular interactions in ion-water systems. Using Na+ and Cl- in water as model systems, we calculate the effects of delocalization error in the SCAN functional for describing ion-water and water-water interactions in hydrated ions, and demonstrate that density-corrected SCAN (DC-SCAN) predicts n-body and interaction energies with an accuracy approaching coupled cluster theory. The performance of DC-SCAN is size-consistent, maintaining an accurate description of molecular interactions well beyond the first solvation shell. Molecular dynamics simulations at ambient conditions with many-body MB-SCAN(DC) potentials, derived from the many-body expansion, predict the solvation structure of Na+ and Cl- in quantitative agreement with reference data, while simultaneously reproducing the structure of liquid water. Beyond rationalizing the accuracy of density-corrected models of ion hydration, our findings suggest that our unified density-corrected MB formalism holds great promise for efficient DFT-based simulations of condensed-phase systems with chemical accuracy.

Neural network potential energy surfaces and dipole moment surfaces for SO2(H2O) and SO2(H2O)2 complexes

Full-dimensional, ab initio-based many-body potential energy surfaces and dipole moment surfaces constructed using the neural network method for SO2(H2O)n (n = 1,2) complexes are reported. The database of the SO2 1-body PES, SO2(H2O) 2-body PES and SO2(H2O)2 3-body PES consists of 11 952, 79 882 and 84 159 ab initio energies, respectively. All 1-body energies were calculated at the CCSD(T)/CBS(AVTZ:AVQZ) level and all 2,3-body energies were calculated at the DSD-PBEP86/AVTZ level. The database of DMSs is the same as that of PESs and all dipole moments were calculated at the MP2/AVTZ level. Harmonic frequencies and dissociation energies of SO2(H2O) and SO2(H2O)2 were calculated on these PESs and compared with ab initio results to examine the fidelity of these PESs.

MBX: A many-body energy and force calculator for data-driven many-body simulations

Many-Body eXpansion (MBX) is a C++ library that implements many-body potential energy functions (PEFs) within the "many-body energy" (MB-nrg) formalism. MB-nrg PEFs integrate an underlying polarizable model with explicit machine-learned representations of many-body interactions to achieve chemical accuracy from the gas to the condensed phases. MBX can be employed either as a stand-alone package or as an energy/force engine that can be integrated with generic software for molecular dynamics and Monte Carlo simulations. MBX is parallelized internally using Open Multi-Processing and can utilize Message Passing Interface when available in interfaced molecular simulation software. MBX enables classical and quantum molecular simulations with MB-nrg PEFs, as well as hybrid simulations that combine conventional force fields and MB-nrg PEFs, for diverse systems ranging from small gas-phase clusters to aqueous solutions and molecular fluids to biomolecular systems and metal-organic frameworks.

A "short blanket" dilemma for a state-of-the-art neural network potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions?

Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven, many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water, but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties, but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict the properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.

Hydration Structure of Na+ and K+ Ions in Solution Predicted by Data-Driven Many-Body Potentials

The hydration structure of Na⁺ and K⁺ ions in solution is systematically investigated using a hierarchy of molecular models that progressively include more accurate representations of many-body interactions. We found that a conventional empirical pairwise additive force field that is commonly used in biomolecular simulations is unable to reproduce the extended X-ray absorption fine structure (EXAFS) spectra for both ions. In contrast, progressive inclusion of many-body effects rigorously derived from the many-body expansion of the energy allows the MB-nrg potential energy functions (PEFs) to achieve nearly quantitative agreement with the experimental EXAFS spectra, thus enabling the development of a molecular-level picture of the hydration structure of both Na⁺ and K⁺ in solution. Since the MB-nrg PEFs have already been shown to accurately describe isomeric equilibria and vibrational spectra of small ion-water clusters in the gas phase, the present study demonstrates that the MB-nrg PEFs effectively represent the long-sought-after models able to correctly predict the properties of ionic aqueous systems from the gas to the liquid phase, which has so far remained elusive.

A Benchmark Protocol for DFT Approaches and Data-Driven Models for Halide-Water Clusters

Dissolved ions in aqueous media are ubiquitous in many physicochemical processes, with a direct impact on research fields, such as chemistry, climate, biology, and industry. Ions play a crucial role in the structure of the surrounding network of water molecules as they can either weaken or strengthen it. Gaining a thorough understanding of the underlying forces from small clusters to bulk solutions is still challenging, which motivates further investigations. Through a systematic analysis of the interaction energies obtained from high-level electronic structure methodologies, we assessed various dispersion-corrected density functional approaches, as well as ab initio-based data-driven potential models for halide ion-water clusters. We introduced an active learning scheme to automate the generation of optimally weighted datasets, required for the development of efficient bottom-up anion-water models. Using an evolutionary programming procedure, we determined optimized and reference configurations for such polarizable and first-principles-based representation of the potentials, and we analyzed their structural characteristics and energetics in comparison with estimates from DF-MP2 and DFT+D quantum chemistry computations. Moreover, we presented new benchmark datasets, considering both equilibrium and non-equilibrium configurations of higher-order species with an increasing number of water molecules up to 54 for each F, Cl, Br, and I anions, and we proposed a validation protocol to cross-check methods and approaches. In this way, we aim to improve the predictive ability of future molecular computer simulations for determining the ongoing conflicting distribution of different ions in aqueous environments, as well as the transition from nanoscale clusters to macroscopic condensed phases.

MB-Fit: Software infrastructure for data-driven many-body potential energy functions

Many-body potential energy functions (MB-PEFs), which integrate data-driven representations of many-body short-range quantum mechanical interactions with physics-based representations of many-body polarization and long-range interactions, have recently been shown to provide high accuracy in the description of molecular interactions from the gas to the condensed phase. Here, we present MB-Fit, a software infrastructure for the automated development of MB-PEFs for generic molecules within the TTM-nrg (Thole-type model energy) and MB-nrg (many-body energy) theoretical frameworks. Besides providing all the necessary computational tools for generating TTM-nrg and MB-nrg PEFs, MB-Fit provides a seamless interface with the MBX software, a many-body energy and force calculator for computer simulations. Given the demonstrated accuracy of the MB-PEFs, particularly within the MB-nrg framework, we believe that MB-Fit will enable routine predictive computer simulations of generic (small) molecules in the gas, liquid, and solid phases, including, but not limited to, the modeling of quantum isomeric equilibria in molecular clusters, solvation processes, molecular crystals, and phase diagrams.

Effective Two-Body Interactions

Cooperative or nonadditive effects contribute to the pairwise noncovalent interaction of two molecules in a cluster or the condensed phase in ways that depend on the specific arrangements and interactions of the other surrounding molecules that constitute their environment. General expressions for an effective two-body interaction are presented, which are correct to increasing orders in the many-body expansion. The simplest result, correct through third order, requires only seven individual calculations, in contrast to a linear number of three-body contributions. Two applications are presented. First, an error analysis is performed on a model (H₂O)₈ cluster which completes the first solvation shell of a central water-water hydrogen bond. Energy decomposition analysis is performed to show that the largest effects of cooperativity on the central hydrogen bond arise from electrical polarization. Second, the nature of cooperative effects on proton transfer in an HCl + (H₂O)₄ cluster is characterized.

Data-driven many-body models enable a quantitative description of chloride hydration from clusters to bulk

We present a new data-driven potential energy function (PEF) describing chloride-water interactions, which is developed within the many-body-energy (MB-nrg) theoretical framework. Besides quantitatively reproducing low-order many-body energy contributions, the new MB-nrg PEF is able to correctly predict the interaction energies of small chloride-water clusters calculated at the coupled cluster level of theory. Importantly, classical and quantum molecular dynamics simulations of a single chloride ion in water demonstrate that the new MB-nrg PEF predicts x-ray spectra in close agreement with the experimental results. Comparisons with an popular empirical model and a polarizable PEF emphasize the importance of an accurate representation of short-range many-body effect while demonstrating that pairwise additive representations of chloride-water and water-water interactions are inadequate for correctly representing the hydration structure of chloride in both gas-phase clusters and solution. We believe that the analyses presented in this study provide additional evidence for the accuracy and predictive ability of the MB-nrg PEFs, which can then enable more realistic simulations of ionic aqueous systems in different environments.

Self-interaction error overbinds water clusters but cancels in structural energy differences

We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi-Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction-corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/[Formula: see text] from about 42 meV/[Formula: see text] for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction-corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

The Born model can accurately describe electrostatic ion solvation

The solvation free energies of ions in water are consistent with the Born linear response model if the centre on which the ion–water repulsion force acts is moved from the oxygen atom towards the hydrogens.

Quantifying the hydration structure of sodium and potassium ions: taking additional steps on Jacob's Ladder

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena.

Aqueous solvation of the chloride ion revisited with density functional theory: impact of correlation and exchange approximations

Aqueous chloride is simulated using PBE-D3, PBE0-D3, and SCAN to investigate the impact of exchange and correlation approximations; we find the exact exchange fraction strongly impacts the energetics and polarizability of solvated chloride.

Specific Ion Effects on Hydrogen-Bond Rearrangements in the Halide-Dihydrate Complexes

Small aqueous ionic clusters represent ideal systems to investigate the microscopic hydrogen-bonding structure and dynamics in ion hydration shells. In this context, halide-dihydrate complexes are the smallest systems where the interplay between halide-water and water-water interactions can be studied simultaneously. Here, quantum molecular dynamics simulations unravel specific ion effects on the temperature-dependent structural transition in X^-(H₂O)₂ complexes (X = Cl, Br, and I), which is induced by the breaking of the water-water hydrogen bond. A systematic analysis of the hydrogen-bonding rearrangements at low temperature provides fundamental insights into the competition between halide-water and water-water interactions depending on the properties of the halide ion. While the halide-water hydrogen-bond strength decreases going from Cl^-(H₂O)₂ to I^-(H₂O)₂, the opposite trend in observed in the strength of the water-water hydrogen-bond, suggesting that nontrivial many-body effects may also be at play in the hydration shells of halide ions in solution, especially in frustrated systems (e.g., interfaces) where the water molecules can have dangling OH bonds.