Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. Here, 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 inter- actions, which implies that DNN potentials may have limited ability to predict 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.

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.

For the past 50 years, researchers have sought molecular models that can accurately reproduce water's microscopic structure and thermophysical properties across broad ranges of its complex phase diagram. Herein, molecular dynamics simulations with the many-body MB-pol model are performed to monitor the thermodynamic response functions and local structure of liquid water from the boiling point down to deeply supercooled temperatures at ambient pressure. The isothermal compressibility and isobaric heat capacity show maxima near 223 K, in excellent agreement with recent experiments, and the liquid density exhibits a minimum at ∼208 K. A local tetrahedral arrangement, where each water molecule accepts and donates two hydrogen bonds, is found to be the most probable hydrogen-bonding topology at all temperatures. This work suggests that MB-pol may provide predictive capability for studies of liquid water's physical properties across broad ranges of thermodynamic states, including the so-called water's "no man's land" which is difficult to probe experimentally.

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.

The efficient selection of representative configurations that are used in high-level electronic structure calculations needed for the development of many-body molecular models poses a challenge to current data-driven approaches to molecular simulations. Here, we introduce an active learning (AL) framework for generating training sets corresponding to individual many-body contributions to the energy of an N-body system, which are required for the development of MB-nrg potential energy functions (PEFs). Our AL framework is based on uncertainty and error estimation and uses Gaussian process regression to identify the most relevant configurations that are needed for an accurate representation of the energy landscape of the molecular system under examination. Taking the Cs+–water system as a case study, we demonstrate that the application of our AL framework results in significantly smaller training sets than previously used in the development of the original MB-nrg PEF, without loss of accuracy. Considering the computational cost associated with high-level electronic structure calculations, our AL framework is particularly well-suited to the development of many-body PEFs, with chemical and spectroscopic accuracy, for molecular-level computer simulations from the gas to the condensed phase.