1. Introduction
Molecular hydrogen is the fundamental component in the interstellar medium and is prevalent in most interstellar environments. Collisions involving molecular hydrogen interacting with itself and other rotationally and vibrationally excited molecules are the essential components of astrophysics to understand the evolution of planetary gases.1,2 Since replicating the precise conditions of astrophysical environments in the laboratory is challenging, most collision studies involving molecular hydrogen and other molecules rely on quantum scattering calculations, necessitating an accurate understanding of the relevant interaction potential energy surface (PES). In recent years, researchers have addressed the potential energy surface of various systems involving molecular hydrogen, including H2 + H2,3 SiO2-H2,4 CN-H2,5 CO-H2,6 and others.7,8 Apart from these predominant molecules, the formation of molecules composed of elements with lower abundances also occurs. For instance, recently, sodium chloride has been discovered in Europa,9 in the disk around Orion Source I,10 as well as in other locations.11,12 Hence, the computation of a full-dimensional PES for the NaCl-H2 system is required to understand the collisions between them.
Previously, experimental and theoretical studies have been conducted to investigate the behavior of H2 on crystalline solid surfaces and in aqueous solutions of NaCl. For instance, Ewing, Heidberg, and others conducted multiple experiments to explore the adsorption of H2 on annealed NaCl films and NaCl(110) using infrared (IR) spectroscopy13−16 and He atom scattering.17 Additionally, Monte Carlo simulations and perturbation theory calculations were utilized to investigate the structure of monolayer and bilayer films of H2 molecules adsorbed on NaCl(001) at different temperatures.18 Recently, Zhu et al. developed an accurate model of H2 solubility in aqueous NaCl solution.19 To the best of our knowledge, no NaCl-H2 PES exists addressing the interaction between NaCl and H2.
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The accuracy of the PES for many atom systems, including biomolecules, condensed matter, and macromolecules, depends on the precise depiction of both short-range and long-range interactions. Therefore, accurately describing the long-range interaction potential is crucial to PES calculation20 and understanding phenomena such as molecular collisions,21,22 dispersion,23 and extended charge transfer.24,25 To achieve this goal, modeling long-range interactions using electrostatic, induction, and dispersion components yields computationally efficient and precise results.26
Describing long-range interactions is a challenge for the large class of atom-centered machine learning methods that use a strict cutoff for the interaction range to represent potentials.27,28 Quoting from Behler and co-workers in 2021, “Machine learning potentials···[that] rely on local properties···are unable to take global changes in the electronic structure into account, which result from long-range charge transfer or different charge states.”29 The authors then present ad hoc proposals to account for long-range interactions in their fourth-generation neural network approach. Namely, they include classical electrostatic interactions that are damped to zero in the short-range. This approach goes back to the origins of small molecule potentials30 and more modern versions of it have been incorporated into global methods that do not use range cutoffs, e.g., permutationally invariant polynomial (PIP)-based potentials. Examples include the PIP potentials for CH5+31 and (H2O)2.32 While these do fit data in the long-range, it was also clear that when available, switching to accurate long-range interactions made sense. For example, for the 2-body interaction in a many-body expansion of the water potential q-AQUA, the long-range interaction is switched to the dipole-dipole interaction33 using an accurate, flexible dipole moment surface.34 In order to avoid “ripples” in the final PES, it is important to verify that the machine-learned (ML) PES overlaps the long-range analytical potential accurately in the region of the switch, as was done in q-AQUA.33
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In the absence of a high-quality long-range interaction for flexible monomers, we have utilized two component fits.4 One component is a precise fit to data in the short-range, and the second one is a fit to data in the long-range. In the example in ref (4) for SiO + H2, the long-range data, i.e., CCSD(T) energies, extend to 11.1 Å. The RMS fitting error for the long-range data is 0.05 cm-1. This level of precision is just not feasible for a single fit to the entire data set.
In this paper, we present a full-dimensional potential energy surface for the NaCl-H2 system, including the correct long-range behavior. The structure of the paper is outlined as follows: Section 2 provides a detailed description of the theoretical and computational aspects, including ab initio calculations, the fitting procedure, long-range interaction, and DMC calculations. The results and properties of the fitted potential energy surface are discussed in Section 3, followed by the summary and conclusions in Section 4.
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