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

Abstract

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.

Role of Potassium in Electrocatalytic Water Oxidation Investigated in a Volume‐Active Cobalt Material at Neutral pH

“…This difference motivates our focus on the 20 K spectra. The coordination number ( N ) of hydrated K + is consistent with 6 ± 2 oxygen atoms (from water molecules or O‐atoms within CoCat) surrounding the K + ion; [ 57 ] a coordination number close to 7 seems likely [ 58,59 ] ( Figure , motif δ ). In our EXAFS simulations, the longer distances relating to peaks II and III in the FT‐spectrum are modeled as a KOPO 3 motif (peak II, KP around 3.5 Å, motif γ in Figure 4) and a KOCo motif (peak III, KCo around 4.1 Å, motif β in Figure 4).…”

Toward Data-Driven Many-Body Simulations of Biomolecules in Solution: N-Methyl Acetamide as a Proxy for the Protein Backbone

“…The differences between the EPSR-based and MB-nrg RDFs may be due to various reasons, including inaccuracies of the MB-nrg PEF which may be related to intrinsic inaccuracies of the DF-MP2/AVQZ training data and/or inaccuracies in the description of NMA–H 2 O n -body energies with n > 2 which are only represented by many-body polarization in the current MB-nrg PEF. In this regard, it was shown explicitly representing 3-body energies with a 3-body PIP, in some cases, slightly improves the agreement with experimental measurements of extended X-ray absorption fine structure (EXAFS) spectra. ,,, Another possible reason for the differences between the EPSR-based and MB-nrg RDFs may be related to the higher NMA concentration used in the experiments. In this regard, from the analyses of the NDIS measurements reported in ref , it was concluded that, at the concentration used in the experiments, NMA molecules can form hydrogen-bonded dimers and possibly chains.…”

“…The many-body expansion (MBE) of the energy allows for rigorously expressing the total energy of an N -body system as a sum of n -body energy contributions (1 ≤ n ≤ N ) according to Here, the 1-body energy, ε 1B ( i ), refers to the distortion energy of the i th monomer relative to its minimum-energy geometry, i.e., ε 1B ( i ) = E ( i ) – E eq ( i ), where E ( i ) and E eq ( i ) are the energies for the distorted and equilibrium geometries, respectively. For n ≥ 2, the n -body ( n B) energies are defined recursively through the following expression: Since the MBE converges quickly for nonmetallic systems, − eq provides a rigorous and efficient theoretical/computational framework for the development of full-dimensional PEFs where each n -body energy term is fitted to reproduce the corresponding reference values obtained from electronic structure calculations (see refs − , − , , , , , , , and − ). Examples of many-body PEFs derived from eq are the Thole-type-model energy (TTM-nrg) , and many-body energy (MB-nrg) , PEFs for generic solutes in water.…”

MB-pol(2023): Sub-chemical Accuracy for Water Simulations from the Gas to the Liquid Phase

“…It should be noted that MB-pol also represented the first step toward the development of the many-body energy (MB-nrg) theoretical/computational framework, which exploits the “nearsightedness” of electronic matter to rigorously represent the energy of a given molecular system in terms of individual many-body contributions . In this context, MB-pol was used to represent water in MB-nrg PEFs of various aqueous systems, including halide and alkali-metal ions in water, , CH 4 /H 2 O mixtures, , and CO 2 /H 2 O mixtures. , In particular, MB-nrg PEFs developed for alkali-metal and halide ions were shown to accurately predict the structures, binding and interaction energies, and vibrational spectra of small X – (H 2 O) N (with X = F, Cl, Br, and I) − and M + (H 2 O) N (with M = Li, Na, K, Rb, and Cs) clusters as well as the hydration structures of Cl – , Br – , I – , Na + , K + , and Cs + in solution. − …”