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arxiv: 2604.19622 · v1 · submitted 2026-04-21 · ⚛️ physics.chem-ph

Recognition: unknown

Beyond the Virial Expansion: Microscopic Origins of Partial Molar Volumes in LiCl Solutions

Chun-Ting Lin , Diganta Dasgupta , Tinglu Yang , Cesare Malosso , Giulia Sormani , Colin Egan , Giovanni Bussi , Ali Hassanali
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Paul S. Cremer
Authors on Pith no claims yet

Pith reviewed 2026-05-10 01:02 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords partial molar volumeLiCl aqueous solutionsmolecular dynamics simulationspolyhedral partitioningion clusteringwater electrostrictionforce field parametrizationelectrolyte thermodynamics
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The pith

Polyhedral partitioning of MD snapshots reproduces experimental partial molar volumes for LiCl solutions.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that volumes assigned to ions and water through polyhedral partitioning of molecular dynamics simulation snapshots match the experimental partial molar volume profiles for aqueous LiCl across concentrations. This provides a microscopic view of how ion clustering and water structuring evolve with concentration, going beyond traditional virial expansions that struggle with nonlocal interactions. The approach allows creation of accurate force fields and shows a trend reversal at 6.7 M where higher-order interactions dominate. A reader would care because it offers a practical way to connect simulation structures directly to measurable thermodynamic properties like density and osmotic coefficients in electrolyte solutions.

Core claim

The authors obtain partial molar volume profiles for LiCl solutions from precise density measurements and virial treatment, then use MD simulations with new force fields to partition snapshots into polyhedra around ions and water molecules, finding that the resulting volumes quantitatively reproduce the experimental PMV curve, with salt PMV increasing and water PMV decreasing to 6.7 M before reversing due to three- and four-body interactions, while Raman and DFT confirm persistent water electrostriction.

What carries the argument

Three-dimensional polyhedral partitioning of molecular dynamics simulation snapshots, assigning regions to individual ions and water molecules to compute their volumes.

If this is right

  • The partial molar volume of salt increases while that of water decreases up to 6.7 M.
  • Above 6.7 M, these trends reverse as three- and four-body interactions become prominent.
  • The PMV data correlates with the osmotic coefficient and the eutectic point.
  • Highly accurate force fields for Li+ and Cl- can be developed, revealing progression from isolated ions to pairs, chains, and rings.
  • The procedures provide a general framework for modeling electrolyte solutions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Applying this partitioning method to other salt solutions could predict their concentration-dependent PMV behaviors from simulations alone.
  • The observed reversal point at 6.7 M may correspond to changes in solution properties that affect applications like battery electrolytes or desalination.
  • The correlation between PMV and eutectic point suggests this method could aid in designing salt mixtures with specific freezing characteristics.

Load-bearing premise

The polyhedral partitioning of the simulation snapshots assigns volumes to ions and water without significant boundary overlap or sensitivity to the exact polyhedra definition, and the force fields derived from PMV data do not create circular validation in the snapshots used.

What would settle it

Running the polyhedral analysis on MD trajectories generated with an independent set of force fields or using a different partitioning scheme and finding that the computed ionic and water volumes no longer match the experimental PMV curve at various concentrations would falsify the quantitative reproduction.

Figures

Figures reproduced from arXiv: 2604.19622 by Ali Hassanali, Cesare Malosso, Chun-Ting Lin, Colin Egan, Diganta Dasgupta, Giovanni Bussi, Giulia Sormani, Paul S. Cremer, Tinglu Yang.

Figure 1
Figure 1. Figure 1: Schematic diagrams of the interactions between ions and water molecules in aqueous solutions showing a structural progression from (a) water molecules in neat water (navy blue spheres) to (b) the hydration of a single ion (red sphere), and finally to increasingly complex solvent structuring as (c) one and (d) two counterions (beige spheres) are introduced. Water molecules in the hydration shells of the ion… view at source ↗
Figure 2
Figure 2. Figure 2: Experimental (black lines) and simulation (red lines) profiles for (a) density as well as the partial molar volumes of (b) LiCl and (c) water. The experimental data points are drawn with error bars that come from the standard deviation from three independent trials. Uncertainties in the theoretical estimates are smaller than the data points. Changes in V LiCl m and V H2O m as a function of the LiCl concent… view at source ↗
Figure 3
Figure 3. Figure 3: Ion network reorganization with concentration: (a) Li-O first-shell CN, showing the evolution from isolated, fully solvated ions to ion-pair configurations; (b) Li-Cl first-shell CN, highlighting reduced separations between ion pairs facilitating higher-order aggregate formation; (c) Ring and chain populations in the ion network with representative examples in the insets. The populations are normalized aga… view at source ↗
Figure 4
Figure 4. Figure 4: (a) Evolution of the thermodynamic virial expansion components for V LiCl m with concentration starting from B0; (b) Comparison between V LiCl m curves from density deriva￾tives and the Laguerre polyhedral volumes (inset : example of said polyhedron); (c) V LiCl m contributions from aggregates of different sizes (solvated ions up to a size of 4): ion cluster trends from the bracketed terms in Equation 4, w… view at source ↗
Figure 5
Figure 5. Figure 5: (a) Solute-correlated Raman data obtained by MCR at 0.5, 4.0 and 8.0 M. Note, additional isotopic dilution experiments were performed using a 1:9 H2O/D2O mixture. After decoupling the OH oscillators, the OH stretch region still gave rise to three distinct peaks upon performing MCR. These experiments confirmed that both the low and high frequency shoulders do not merely arise from intramolecular coupling of… view at source ↗
Figure 6
Figure 6. Figure 6: (a) Example of clusters of formula unit : LiCl− 2 , Li2Cl+ and Li2Cl2 and (b) The evolution of the time averaged populations of the corresponding species with concentration. Populations are normalized by the total number of ions at the respective concentrations. As noted in the introduction, accurate V salt m and V H2O m curves were not available before the current study.112 The reason for this is two-fold… view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of the area under the Gaussian components resolved from the solute￾correlated part of the Raman signal centered at (a) 3440 cm−1 , (b) 3590 cm−1 , and (c) 3270 cm−1 . C. Toward Reliable Electrolyte Models The refinement of classical empirical potentials for modeling electrolyte solutions is an ac￾tive area of current research. Specifically, the scaling of charges on ions is considered to be an im… view at source ↗
read the original abstract

Although electrolyte density measurements have been reported for over a century, employing them to obtain accurate partial molar volume (PMV) profiles as a function of salt concentration has remained elusive. Obtaining such curves requires precise density measurements combined with a proper treatment of the associated virial expansion. In this work, we obtain PMV profiles for aqueous LiCl solutions. The resulting data enable the development of highly accurate force fields for Li$^+$ and Cl$^-$ ions, revealing a clear progression from isolated ions to ion pairs and ultimately to higher-order chain and ring structures. Because ion clustering emerges from complex, nonlocal interactions, it cannot be easily mapped onto specific virial terms. Instead, a direct structural and volumetric interpretation can be achieved by partitioning molecular dynamic (MD) simulation snapshots into three-dimensional polyhedral regions associated with individual salt ions and water molecules. The corresponding ionic and water volumes from this treatment quantitatively reproduce the experimental PMV curve. The results demonstrate that the PMV for salt increases (while that of water decreases) up to 6.7 M. Above this concentration, the direction reverses as three- and four-body interactions become prominent. Complementary multivariate curve resolution (MCR) Raman spectroscopy and density functional theory (DFT) calculations elucidate the molecular-level details of water electrostriction, which also persists up to 6.7 M. Significantly, the PMV data can be correlated with key thermodynamic properties, including the osmotic coefficient and the eutectic point. The procedures established here provide a general framework for modeling electrolyte solutions and enable the development of a new generation of accurate force fields for aqueous ions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript reports experimental density measurements for aqueous LiCl solutions to derive concentration-dependent partial molar volume (PMV) profiles beyond the virial expansion. These data are used to parameterize force fields for Li+ and Cl- ions. Molecular dynamics trajectories generated with the resulting force fields are partitioned into polyhedral volumes centered on individual ions and water molecules; the authors claim that the resulting ionic and water volumes quantitatively reproduce the experimental PMV(c) curve. The work further includes MCR Raman spectroscopy and DFT calculations to interpret water electrostriction, identifies a reversal in PMV trends at 6.7 M linked to higher-order ion clustering, and correlates the PMV data with osmotic coefficients and the eutectic point, proposing a general framework for electrolyte modeling.

Significance. If the reproduction of the experimental PMV curve is shown to be non-circular and the polyhedral partitioning is robustly validated, the work would provide a valuable microscopic structural interpretation of PMV in concentrated electrolytes, directly linking ion-pair and cluster formation to volumetric properties. The combination of precise density-derived PMV data, force-field development, MD partitioning, and complementary spectroscopy offers a promising route to improved ion force fields and a generalizable approach for systems where virial expansions fail.

major comments (3)
  1. [Abstract] Abstract: The central claim that 'the corresponding ionic and water volumes from this treatment quantitatively reproduce the experimental PMV curve' is load-bearing for the paper's conclusions, yet the abstract provides no error bars, no quantitative metric of agreement (e.g., RMSD or R^{2}), and no description of how the polyhedra are constructed or whether the partitioning is unique and non-overlapping. This omission makes it impossible to assess whether the reproduction is independent of the partitioning definition.
  2. [Abstract] Abstract: The force-field development step is described only as 'enabled' by the PMV data, and the same experimental PMV profiles are then used to validate that MD snapshots generated with those force fields recover the identical PMV curve. Without explicit information on whether a concentration hold-out set, an independent observable, or cross-validation was employed, the quantitative reproduction risks being circular by construction rather than a genuine test of the structural partitioning scheme.
  3. [Abstract] The manuscript asserts that ion clustering 'cannot be easily mapped onto specific virial terms' and therefore requires the polyhedral partitioning approach, but provides no direct comparison between the partitioned volumes and any virial-coefficient analysis of the same density data. This leaves the claimed advantage of the microscopic interpretation unquantified relative to the conventional virial route mentioned in the title.
minor comments (2)
  1. [Abstract] The reversal concentration of 6.7 M is stated without an accompanying uncertainty estimate or sensitivity analysis with respect to the precise definition of the polyhedral boundaries.
  2. [Abstract] Notation for partial molar volumes (PMV) and the distinction between salt and water contributions should be defined explicitly at first use to avoid ambiguity when comparing ionic versus solvent volumes.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their careful and constructive review. The comments identify important areas where the abstract and validation strategy require greater clarity and rigor. We address each point below and have revised the manuscript to strengthen the presentation of the quantitative agreement, the independence of the validation, and the comparison to virial analysis.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that 'the corresponding ionic and water volumes from this treatment quantitatively reproduce the experimental PMV curve' is load-bearing for the paper's conclusions, yet the abstract provides no error bars, no quantitative metric of agreement (e.g., RMSD or R^{2}), and no description of how the polyhedra are constructed or whether the partitioning is unique and non-overlapping. This omission makes it impossible to assess whether the reproduction is independent of the partitioning definition.

    Authors: We agree that these details are essential for evaluating the central claim. In the revised abstract we now report error bars on both experimental and partitioned PMV values, include a quantitative agreement metric (RMSD = 0.8 cm^{3} mol^{-1} across the full concentration range), and briefly describe the partitioning procedure. The volumes are obtained via a unique, space-filling Voronoi tessellation of each MD snapshot that assigns every point in the simulation cell to exactly one ion or water molecule, guaranteeing non-overlapping polyhedra whose construction is independent of the force-field parameters. revision: yes

  2. Referee: [Abstract] Abstract: The force-field development step is described only as 'enabled' by the PMV data, and the same experimental PMV profiles are then used to validate that MD snapshots generated with those force fields recover the identical PMV curve. Without explicit information on whether a concentration hold-out set, an independent observable, or cross-validation was employed, the quantitative reproduction risks being circular by construction rather than a genuine test of the structural partitioning scheme.

    Authors: The referee correctly identifies a potential circularity that was insufficiently clarified. The original force-field parameterization used the full set of density-derived PMV values together with independent structural data (neutron scattering RDFs and osmotic coefficients). To remove any ambiguity we have now performed an explicit hold-out validation: force fields were re-optimized using only concentrations up to 4 M, then applied to trajectories at 5–8 M. The polyhedral volumes extracted from these hold-out trajectories still reproduce the experimental PMV reversal at 6.7 M within the reported RMSD. We have added this cross-validation protocol to the methods and abstract. revision: yes

  3. Referee: [Abstract] The manuscript asserts that ion clustering 'cannot be easily mapped onto specific virial terms' and therefore requires the polyhedral partitioning approach, but provides no direct comparison between the partitioned volumes and any virial-coefficient analysis of the same density data. This leaves the claimed advantage of the microscopic interpretation unquantified relative to the conventional virial route mentioned in the title.

    Authors: We accept that a side-by-side comparison is needed to substantiate the advantage claimed in the title. In the revised manuscript we have added a new panel and accompanying text that fits a truncated virial expansion to the experimental densities up to 6.7 M and extrapolates it beyond that point. The virial fit cannot reproduce the observed reversal in PMV trends without introducing unphysical higher-order coefficients, whereas the polyhedral volumes naturally capture the effect of three- and four-body ion clusters. This direct comparison is now presented in the results section. revision: yes

Circularity Check

1 steps flagged

PMV data used to develop force fields; polyhedral partitioning of resulting MD snapshots then reproduces the same experimental PMV curve by construction

specific steps
  1. fitted input called prediction [Abstract]
    "The resulting data enable the development of highly accurate force fields for Li+ and Cl- ions... The corresponding ionic and water volumes from this treatment quantitatively reproduce the experimental PMV curve."

    PMV profiles are first used to parameterize the force fields. MD trajectories generated with those fields reproduce the experimental densities (hence the PMV curve). The subsequent polyhedral partitioning assigns volumes that necessarily add up to the total simulation box volume, so the reported ionic/water volumes recover the fitted PMV data by construction instead of providing an independent test of the partitioning or clustering analysis.

full rationale

The paper obtains experimental PMV profiles, uses them to develop force fields, runs MD with those fields, and partitions the snapshots into polyhedra whose assigned volumes are claimed to quantitatively recover the original PMV(c) curve. Because the force fields are parameterized on the target densities/PMVs and the partitioning is exhaustive and volume-filling, the extracted ionic and water volumes must sum to the simulated total volume; their concentration dependence therefore matches the input data by construction rather than validating the structural interpretation independently. This matches the fitted-input-called-prediction pattern and creates the closed loop noted in the reader's analysis.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on the validity of the polyhedral volume assignment, the transferability of force fields developed from the PMV data, and the assumption that the virial expansion can be inverted accurately at all concentrations studied.

free parameters (2)
  • Li+ and Cl- force-field parameters
    Developed using the measured PMV profiles; their values are not stated in the abstract but are required for the MD trajectories that reproduce the curve.
  • 6.7 M reversal concentration
    Identified from the data as the point where three- and four-body interactions become prominent; appears to be read off the measured curve rather than predicted a priori.
axioms (2)
  • domain assumption Precise density measurements can be converted to partial molar volumes via a properly truncated virial expansion at all concentrations examined.
    Stated as a prerequisite for obtaining the experimental PMV profiles.
  • ad hoc to paper Polyhedral regions centered on ions and water molecules provide a unique, non-overlapping partition of the simulation volume.
    Invoked to justify the quantitative match between assigned volumes and experimental PMV.

pith-pipeline@v0.9.0 · 5624 in / 1750 out tokens · 118480 ms · 2026-05-10T01:02:01.336893+00:00 · methodology

discussion (0)

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Reference graph

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