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

Entropy of Liquid Water as Predicted by the Two-Phase Thermodynamic Model and Data-Driven Many-Body Potentials

We investigate the entropy of liquid water at ambient conditions using the two-phase thermodynamic (2PT) model, applied to both common pairwise-additive water models and the MB-pol and MB-pol(2023) data-driven many-body potentials. Our simulations demonstrate that the 2PT model yields entropy values in semiquantitative agreement with experimental data when using MB-pol and MB-pol(2023). Additionally, our analyses indicate that the entropy values predicted by pairwise-additive water models may benefit from error compensation between the inherent approximations of the 2PT model and the known limitations of these water models in describing many-body interactions. Despite its approximate nature, the simplicity of the 2PT model makes it a valuable tool for estimating relative entropy changes of liquid water across various environments, especially when combined with water models that provide a consistently robust representation of the structural, thermodynamic, and dynamical properties of liquid water.

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.

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.

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.

Accurate Modeling of Bromide and Iodide Hydration with Data-Driven Many-Body Potentials

Ion-water interactions play a central role in determining the properties of aqueous systems in a wide range of environments. However, a quantitative understanding of how the hydration properties of ions evolve from small aqueous clusters to bulk solutions and interfaces remains elusive. Here, we introduce the second generation of data-driven many-body energy (MB-nrg) potential energy functions (PEFs) representing bromide-water and iodide-water interactions. The MB-nrg PEFs use permutationally invariant polynomials to reproduce two-body and three-body energies calculated at the coupled cluster level of theory, and implicitly represent all higher-body energies using classical many-body polarization. A systematic analysis of the hydration structure of small Br^-(H₂O)_n and I^-(H₂O)_n clusters demonstrates that the MB-nrg PEFs predict interaction energies in quantitative agreement with "gold standard" coupled cluster reference values. Importantly, when used in molecular dynamics simulations carried out in the isothermal-isobaric ensemble for single bromide and iodide ions in liquid water, the MB-nrg PEFs predict extended X-ray absorption fine structure (EXAFS) spectra that accurately reproduce the experimental spectra, which thus allows for characterizing the hydration structure of the two ions with a high level of confidence.

Data-Driven Many-Body Potential Energy Functions for Generic Molecules: Linear Alkanes as a Proof-of-Concept Application

We present a generalization of the many-body energy (MB-nrg) theoretical/computational framework that enables the development of data-driven potential energy functions (PEFs) for generic covalently bonded molecules, with arbitrary quantum mechanical accuracy. The "nearsightedness of electronic matter" is exploited to define monomers as "natural building blocks" on the basis of their distinct chemical identity. The energy of generic molecules is then expressed as a sum of individual many-body energies of incrementally larger subsystems. The MB-nrg PEFs represent the low-order n-body energies, with n = 1-4, using permutationally invariant polynomials derived from electronic structure data carried out at an arbitrary quantum mechanical level of theory, while all higher-order n-body terms (n > 4) are represented by a classical many-body polarization term. As a proof-of-concept application of the general MB-nrg framework, we present MB-nrg PEFs for linear alkanes. The MB-nrg PEFs are shown to accurately reproduce reference energies, harmonic frequencies, and potential energy scans of alkanes, independently of their length. Since, by construction, the MB-nrg framework introduced here can be applied to generic covalently bonded molecules, we envision future computer simulations of complex molecular systems using data-driven MB-nrg PEFs, with arbitrary quantum mechanical accuracy.

The behavior of methane-water mixtures under elevated pressures from simulations using many-body potentials

Non-polarizable empirical potentials have been proven to be incapable of capturing the mixing of methane-water mixtures at elevated pressures. Although density functional theory-based ab initio simulations may circumvent this discrepancy, they are limited in terms of the relevant time and length scales associated with mixing phenomena. Here, we show that the many-body MB-nrg potential, designed to reproduce methane-water interactions with coupled cluster accuracy, successfully captures this phenomenon up to 3 GPa and 500 K with varying methane concentrations. Two-phase simulations and long time scales that are required to fully capture the mixing, affordable due to the speed and accuracy of the MBX software, are assessed. Constructing the methane-water equation of state across the phase diagram shows that the stable mixtures are denser than the sum of their parts at a given pressure and temperature. We find that many-body polarization plays a central role, enhancing the induced dipole moments of methane by 0.20 D during mixing under pressure. Overall, the mixed system adopts a denser state, which involves a significant enthalpic driving force as elucidated by a systematic many-body energy decomposition analysis.

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.

General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case Study

We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantum-mechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from density functionals belonging to different rungs across Jacob's ladder of approximations within density functional theory (MB-DFT) and from Møller-Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using density-corrected functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.

Discrete Oligomers and Polymers of Chloride Monohydrate Can Form in Encapsulated Environments: Structures and Infrared Spectra of [Cl4 (H2 O)4 ]4- and {[Cl(H2 O)]- }∞

A discrete tetrachloride tetrahydrate cluster, [Cl₄ (H₂ O)₄ ]^4- , was obtained with a partially-fluorinated triaminocyclopropenium cation, [C₃ (N(CH₂ CF₃ )₂ )(NEt₂ )(NPr₂ )]⁺ . The cluster consists of a [Cl₂ (H₂ O)₂ ]^2- square with each Cl^- coordinated by another H₂ O bridged to another Cl^- . A 1D polymer of chloride monohydrate, {[Cl(H₂ O)]^- }_∞ , was obtained with [C₃ (N(CH₂ CF₃ )₂ )₂ (NBuMe)]⁺ . The tetrameric and polymeric structures were found to be computationally-unstable in the gas phase which indicates that an encapsulated environment is essential for their isolation. DFT and DFTB calculations were carried out on gas-phase [Cl₄ (H₂ O)₄ ]^4- to assist the infrared assignments. Anharmonically-corrected B3LYP transition frequencies were in close agreement with experiment, but DFTB models were only appropriate for qualitative interpretation. Solid-state DFTB calculations allowed the vibrational modes to be assigned. The results found are consistent with "discrete" chloride hydrates.

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.

Highly Accurate Many-Body Potentials for Simulations of N2O5 in Water: Benchmarks, Development, and Validation

Dinitrogen pentoxide (N₂O₅) is an important intermediate in the atmospheric chemistry of nitrogen oxides. Although there has been much research, the processes that govern the physical interactions between N₂O₅ and water are still not fully understood at a molecular level. Gaining a quantitative insight from computer simulations requires going beyond the accuracy of classical force fields while accessing length scales and time scales that are out of reach for high-level quantum-chemical approaches. To this end, we present the development of MB-nrg many-body potential energy functions for nonreactive simulations of N₂O₅ in water. This MB-nrg model is based on electronic structure calculations at the coupled cluster level of theory and is compatible with the successful MB-pol model for water. It provides a physically correct description of long-range many-body interactions in combination with an explicit representation of up to three-body short-range interactions in terms of multidimensional permutationally invariant polynomials. In order to further investigate the importance of the underlying interactions in the model, a TTM-nrg model was also devised. TTM-nrg is a more simplistic representation that contains only two-body short-range interactions represented through Born-Mayer functions. In this work, an active learning approach was employed to efficiently build representative training sets of monomer, dimer, and trimer structures, and benchmarks are presented to determine the accuracy of our new models in comparison to a range of density functional theory methods. By assessing the binding curves, distortion energies of N₂O₅, and interaction energies in clusters of N₂O₅ and water, we evaluate the importance of two-body and three-body short-range potentials. The results demonstrate that our MB-nrg model has high accuracy with respect to the coupled cluster reference, outperforms current density functional theory models, and thus enables highly accurate simulations of N₂O₅ in aqueous environments.

Competition between Solvent-Solvent and Solvent-Solute Interactions in the Microhydration of the Hexafluorophosphate Anion, PF6-(H2O)n=1,2

This study systematically examines the interactions of the hexafluorophosphate anion (PF₆^-) with one or two solvent water molecules (PF₆^-(H₂O)_n where n = 1, 2). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed on each stationary point using a variety of common density functional theory methods (B3LYP, B3LYP-D3, M06-2X, and ωB97XD) and the MP2 and CCSD(T) ab initio methods with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for P, O, and F; denoted as haTZ). Five new stationary points of PF₆^-(H₂O)₂ have been identified, one of which has an electronic energy of approximately 2 kcal mol^-1 lower than the only other dihydrate structure reported for this system. The CCSD(T) computations also reveal that the detailed interactions between PF₆^- and H₂O can be quite difficult to model reliably, with some methods struggling to correctly characterize stationary points for n = 1 or accurately reproduce the vibrational frequency shifts induced by the formation of the hydrated complex. Although the interactions between the solvent and ionic solute are quite strong (CCSD(T) electronic dissociation energy ≈10 kcal mol^-1 for the monohydrate minimum), the solvent-solvent interactions in the lowest-energy PF₆^-(H₂O)₂ minimum give rise to appreciable cooperative effects not observed in the other dihydrate minima. In addition, this newly identified structure exhibits the largest frequency shifts in the OH stretching vibrations for the waters of hydration (with Δω exceeding -100 cm^-1 relative to the values for an isolated H₂O molecule).

A Series of Discrete Dichloride Dihydrates: Characterisation and Symmetry Effects

A series of three discrete dichloride dihydrates [Cl₂ (H₂ O)₂ ]^2- have been isolated with different triaminocyclopropenium (TAC) cations and with different crystallographic symmetries. The cluster exhibits D_2h symmetry with the tris(dimethylamino)cyclopropenium cation [C₃ (NMe₂ )₃ ]⁺ , C_2h symmetry with the fluorinated cation [C₃ (N(CH₂ CF₃ )₂ )(NBu₂ )₂ ]⁺ (containing two 2,2,2-trifluoroethyl substituents) and C_2v symmetry with the more fluorinated [C₃ (N(CH₂ CF₃ )₂ )₂ (NBu₂ )]⁺ cation. The effect of symmetry on the infrared spectra of the dichloride ion-pair clusters, as well as deuterated analogues, has been investigated. The D_2h - and C_2h -symmetric clusters each exhibit two stretching bands in the infrared at 3427 and 3368 cm^-1 for D_2h symmetry and 3444 and 3392 cm^-1 for C_2h symmetry, whereas the C_2v -symmetric cluster exhibits three bands at 3475, 3426 and 3373 cm^-1 . Computational studies were carried out on a [Cl₂ (H₂ O)₂ ]^2- cluster with C_2v symmetry to aid the infrared band assignments.

One water to bind a chloride-chloride ion pair: isolation of discrete [Cl2(H2O)]2- in the solid state

A discrete dichloride ion pair in the form of a monohydrate, [Cl₂(H₂O)]^2-, was isolated using the triaminocyclopropenium cation [C₃(NHex₂)(N(CH₂CF₃)₂)₂]⁺. Although this ion pair is calculated to be unstable in the gas phase, the ionic lattice and weak CH-Cl hydrogen bonds assist the stabilization of the cluster. The D₂O and HDO isotopomers were also prepared and characterized.

A Discrete Dichloride Tetrahydrate Trapped by a Cyclopropenium Cation: Structure and Spectroscopic Properties

A discrete dichloride tetrahydrate cluster, [Cl₂ (H₂ O)₄ ]^2- , was obtained as a salt of the bis(diphenylamino)diethylamino cyclopropenium cation [C₃ (NPh₂ )₂ (NEt₂ )]⁺ and characterized by single-crystal X-ray diffraction and infrared spectroscopy. This chloride-chloride ion-pair cluster consists of a [Cl₂ (H₂ O)₂ ]^2- square with opposite edges bridged by water molecules to give a chair-like structure of the non-hydrogen atoms. The solid-state structure is essentially the same as the calculated gas-phase structure. Infrared spectra were also collected on the deuterium analogue [Cl₂ (D₂ O)₄ ]^2- . Computational studies were carried out on gas-phase [Cl₂ (H₂ O)₄ ]^2- to confirm the infrared band assignments in the solid state. The structure and infrared spectrum are consistent with the discrete nature of the cluster.

Deep Undercooling of Aqueous Droplets on a Superhydrophobic Surface: The Specific Role of Cation Hydration

An extraordinary prolonged freezing delay was detected for the first time for deeply undercooled sessile droplets of aqueous solutions of alkali metal chlorides deposited onto a superhydrophobic surface. Accounting for the variation in the hydration energy of ions, their distribution in the vicinity of charged interfaces of solution/air and solution/superhydrophobic surface allows qualitative description of the observed ice nucleation kinetics and ionic specificity in freezing phenomena.