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Chelation of the mercury ions by polyethyleneimine: Atomistic molecular dynamics study

T0 review · 4 major / 4 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A single linear polyethyleneimine chain with ten amino groups chelates up to four Hg2+ ions in water, with molecular dynamics and density functional theory agreeing on the complex structures.

desk verdict Plausible preliminary estimate of PEI-10's Hg2+ capacity, but the unbenchmarked Hg-N force field and a 0.35 Å MD/DFT distance gap keep the four-ion maximum conditional. read the letter →

arxiv 2506.18835 v1 pith:UWKHO5J2 submitted 2025-06-23 cond-mat.soft physics.chem-ph

Halyna Butovych , Jaroslav Ilnytskyi , Erkki Lahderanta , Taras Patsahan This is my paper · ORCID
classification cond-mat.softphysics.chem-ph
keywords mercurychelationpolyethyleneiminemoleculardynamicsOPLS/AAforcefieldradialdistributionfunctioncoordinationnumberDFTvalidationheavymetalremoval
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to establish the maximum mercury-chelating capacity of a single linear polyethyleneimine (PEI) chain in water and to describe the structure of the complexes. Using atomistic molecular dynamics with the OPLS/AA force field and SPC/E water, it simulates PEI chains with four, five, and ten nitrogen atoms (PEI-4, PEI-5, PEI-10) together with one to five Hg2+ ions. The central quantitative claim is that PEI-10 can stably coordinate up to four Hg2+ ions, while a fifth ion is driven away by Coulombic repulsion. Density functional theory optimizations of the MD-derived geometries give similar structures and Hg-N distances near 2.5 Å, and computed complexation free energies are negative for all stable complexes. If correct, the result gives a microscopic rule for how many mercury ions a short linear PEI chain can hold, which is the quantity relevant to PEI-based water purification materials.

What carries the argument

The load-bearing object is the Hg2+–nitrogen coordination shell, quantified by the Hg-N radial distribution function $g(r)$ and its running coordination number $n(r)$ from the production MD trajectories. The models use the OPLS/AA all-atom force field for PEI, the SPC/E model for water, and Lennard-Jones plus Coulombic interactions for Hg2+, with cross-interactions set by the geometric combination rule. Stability is checked by computing adsorption energies in MD and Gibbs free energies of complexation from DFT geometry optimizations at the M06-2X/LanL2DZ level, with the solvent treated implicitly.

What would settle it

Measure Hg-N distances and coordination numbers for PEI-Hg2+ complexes by EXAFS or X-ray absorption spectroscopy; if a PEI-10 chain is found to bind five Hg2+ ions, or if the Hg-N distances deviate from the predicted 2.15-2.5 Å range by more than about 0.1 Å, the force-field combination and the four-ion capacity would be falsified. Alternatively, recomputing the capacity with a Hg2+ parameter set fitted to Hg-amine reference data would provide a direct test.

Watch

Extended reading notes

Core claim

The paper's central discovery is that a neutral linear PEI molecule with ten amino groups binds up to four Hg2+ ions in aqueous solution, forming stable complexes in which each ion is held by two to five nitrogen atoms of the polymer and completed by water molecules in the first hydration shell. Shorter chains PEI-4 and PEI-5 wrap around a single ion with Hg-N coordination numbers of 3 and 5; PEI-10 uses four nitrogens for one ion and fewer per ion as loading increases. DFT-optimized structures reproduce the MD conformations and give Hg-N distances around 2.5 Å, and the complexation free energy is negative in every stable case. Attempts to load a fifth ion onto PEI-10 did not produce a stable complex, which is why the paper states the chelating capacity as four ions per PEI-10 chain.

Load-bearing premise

The whole capacity result rests on the assumption that the Hg2+ Lennard-Jones parameters fitted to mercury hydration, combined with the OPLS/AA PEI parameters through the geometric combination rule, correctly capture Hg-amine binding; the paper never tests this combination against known Hg-amine structures or binding energies.

Editorial extensions

If this is right

  • A single PEI-10 chain saturates at four Hg2+ ions; a fifth ion is not stably bound because Hg-Hg Coulombic repulsion wins.
  • For one ion, shorter chains wrap more completely: PEI-5 coordinates five nitrogens and binds more strongly (MD binding energy -670 ± 21 kJ/mol) than PEI-4 or PEI-10.
  • Each additional Hg2+ on PEI-10 lowers the per-ion binding strength, so the Gibbs free energy per ion becomes less negative, from -61 kJ/mol for one ion to -21 kJ/mol for four ions at the mixed-basis DFT level.
  • In multi-ion complexes the chain stretches: Hg-Hg minimum distances are about 5.55 Å for four ions and larger for fewer ions, and each ion keeps only two nitrogen contacts.
  • DFT-optimized structures agree qualitatively with MD for all stable complexes, supporting the use of this MD protocol to screen PEI architectures for mercury binding.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Extending the paper's result, the four-ion ceiling is a property of a 10-nitrogen neutral chain; longer or branched PEI chains might bind more ions per molecule, but the per-amine ceiling may not scale linearly because Coulombic repulsion between bound ions becomes the limiting factor.
  • The paper does not benchmark the Hg2+ force field against known Hg-amine complexes; a reparameterization using Hg-N reference data could change the predicted coordination numbers and the four-ion capacity, so the capacity should be read as model-dependent until such a benchmark exists.
  • Since the simulations use neutral PEI chains, the capacity at low pH with protonated amines is likely lower; testing the same protocol at different protonation states would connect the model to realistic wastewater conditions.
  • The DFT Hg-N distances of about 2.5 Å are systematically longer than the MD first-peak distances of about 2.15 Å, suggesting the MD force field underestimates Hg-N contact length; comparing against EXAFS could decide which is closer to reality.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The manuscript reports atomistic molecular dynamics simulations of linear polyethyleneimine chains (PEI-4, PEI-5, PEI-10) complexed with Hg2+ ions in explicit SPC/E water, using OPLS/AA parameters for PEI and Babu-Lim parameters for Hg2+. Complexes are pre-formed in vacuum (Stage 1), solvated and equilibrated for 3 ns, then simulated for 4 ns in the production stage. The authors compute Hg-N, Hg-Ow, N-N, and Hg-Hg radial distribution functions and coordination numbers, and they supplement the MD with M06-2X/LanL2DZ DFT geometry optimizations, adsorption energies, and Gibbs free energies of complexation. The central claim is that one linear PEI-10 chain can coordinate up to four Hg2+ ions, with five ions being unstable.

Significance. If established, the predicted capacity of four Hg2+ ions per PEI-10 chain is a concrete, design-relevant quantity for PEI-based water-treatment adsorbents, and the paper usefully combines MD structural analysis with DFT checks. The study is also clearly written and parameter-free in the sense that no new force-field parameters are fitted. However, the central claim is not yet supported at the required level because (i) the Hg2+-amine cross-interaction is unvalidated and internally inconsistent with the paper's own DFT distances, (ii) all simulations start from pre-formed complexes, and (iii) all structural numbers come from single short trajectories without error estimates. These issues are fixable in principle, so the manuscript merits major revision rather than rejection.

major comments (4)
  1. [Section 3 (Stage 1) and Section 4] The preparation protocol places the Hg2+ ion 'in close proximity' to the PEI molecule and runs Stage 1 in vacuum, so the production runs test only whether pre-formed Hg-N contacts remain bound, not whether complexes assemble from unbound components. Since the abstract's capacity claim ('capable of coordinating up to four Hg2+ ions') is about what a chain can do in solution, the manuscript should add simulations initialized from unbound or randomly placed ions (and from partially bound states) and show that the four-ion complex forms reproducibly. Without such a test, the 'up to four' statement could reflect kinetic trapping rather than thermodynamic capacity.
  2. [Section 4 and Table 2] The MD Hg-N first peak is reported at approximately 2.15 Å (Figs. 4, 7, 8), while all DFT-optimized Hg-N distances in Table 2 are 2.48-2.57 Å. This roughly 0.35 Å discrepancy is internal evidence that the Hg2+-amine Lennard-Jones interaction, built from Babu-Lim hydration-fitted parameters (Table 1, ref. 36) via the geometric combination rule (Section 3), is miscalibrated for Hg-amine binding. Because the DFT optimizations start from MD-selected conformations, they do not repair this issue. The authors should benchmark the Hg2+-amine model against known Hg2+-amine complexes or high-level calculations (e.g., binding energies and distances for small model amines) and/or perform a sensitivity analysis over the Hg2+ epsilon and sigma parameters; the capacity claim should be shown to be robust under that uncertainty.
  3. [Section 5] The DFT validation is not independent of the MD force field: the authors 'selected several typical configurations ... obtained from our MD simulations and used them as input for structure optimization using DFT.' This confirms that the MD-generated coordination topologies are local minima at the DFT level, but it cannot establish that the MD sampling produced the correct Hg-amine interaction or that the four-ion complex is the thermodynamically preferred state. The authors should also run DFT optimizations starting from alternative, non-MD initial geometries (e.g., unbound ions, different coordination numbers) and compare relative energies, to test whether the four-ion complex is preferred over other stoichiometries.
  4. [Section 4 and Stage 4] All coordination numbers and RDFs are derived from a single 4 ns production trajectory per system (trajectory stored at 1 ps), with no replicate simulations, block averaging, or error bars. Quantities like 'average Hg-N coordination number is 2.5' for PEI-10 + 2 Hg2+ are therefore presented without statistical uncertainty, and the conclusion that five ions are unstable rests on one short run. Please report statistical uncertainties and, ideally, multiple independent initial configurations; this is essential for the capacity claim because coordination numbers directly determine the maximum ion load.
minor comments (4)
  1. [Section 5, Table 3] The column header 'MD Binding enegry, MD' contains a typo ('enegry') and a duplicated 'MD'; the table would be clearer with explicit level-of-theory labels in each column header.
  2. [Section 2] The paper does not explicitly state the protonation state of PEI; the assigned charges correspond to neutral amines, but PEI chelation is pH-dependent. This assumption should be stated and justified in the context of water-treatment conditions.
  3. [Data Availability] 'Data will be made available on request' is not sufficient for a computational study of this type; depositing input topologies, force-field parameter files, and starting coordinates would substantially improve reproducibility.
  4. [Figures 11 and 12] The alignment procedure used to superimpose MD and DFT structures is not described, and the color code in the captions is not explained in the main text; a sentence in Section 5 describing the best-fit alignment would help.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: no fitted parameters or self-citation chain; DFT is an independent check, and the MD/DFT distance discrepancy is a correctness risk, not a circular reduction.

full rationale

The prediction that a single PEI-10 chain coordinates up to four Hg2+ ions emerges from the simulation protocol rather than being encoded in the model. The force field uses OPLS/AA parameters for PEI, SPC/E water, and Babu-Lim Hg2+ parameters taken from previous publications; no parameter in this paper is fitted to the capacity claim. The four-ion maximum is inferred from the observed instability of the PEI-10 + 5 Hg2+ system and from running coordination numbers, not from a definition or from a fitted quantity. The DFT validation is an independent electronic-structure method applied to MD-derived starting geometries, and although starting from MD structures biases the conformational search, DFT optimizations are not equivalent by construction to the MD force field. There are no load-bearing self-citations and no uniqueness argument imported from the authors' prior work. The internal inconsistency between MD Hg-N distances (~2.15 Å) and DFT Hg-N distances (~2.5 Å) is a genuine accuracy concern about the Hg2+ amine cross-interaction, but it does not make the derivation circular. The central claim is therefore self-contained against the model assumptions, and any weakness lies in force-field transferability, not in circular reasoning.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim depends on standard force-field and DFT assumptions, plus one parameter set (Hg2+ LJ) taken from prior hydration fits. The paper introduces no new fitted parameters or invented entities. The main unvalidated transfer is the Hg2+ parameters to Hg-amine binding.

free parameters (1)
  • Hg2+ Lennard-Jones parameters (epsilon, sigma) = epsilon = 0.0409 kcal/mol, sigma = 2.36 Å
    Taken from Babu and Lim via refs 33-35, fitted to Hg2+ hydration properties. Used here for Hg-water, Hg-counterion, and Hg-amine interactions through combination rules; transferability to Hg-amine binding is assumed without revalidation.
assumptions (5)
  • domain assumption OPLS/AA force field accurately models linear PEI chains in water.
    Used throughout Section 2; standard force field, but its accuracy for PEI-Hg2+ binding is not benchmarked here.
  • domain assumption Geometric combination rule for cross Lennard-Jones interactions is appropriate for Hg-N and Hg-O pairs.
    Section 3 states the rule; it determines the balance between Hg-water and Hg-amine attractions that sets coordination numbers.
  • domain assumption SPC/E water model adequately represents hydration of Hg2+ and PEI.
    Section 2; standard rigid water model, used without revalidation.
  • ad hoc to paper 4 ns production runs are long enough to judge complex stability.
    Section 3; no convergence analysis is shown, and the choice of 3 ns equilibration plus 4 ns production appears arbitrary.
  • domain assumption M06-2X/LanL2DZ with implicit water reliably ranks the relative stability of these complexes.
    Section 5; the level of theory is reasonable for heavy-metal systems but is not benchmarked against experimental Hg-amine binding energies.

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Pith. "Pith review of Chelation of the mercury ions by polyethyleneimine: Atomistic molecular dynamics study." pith.science (2026). https://pith.science/paper/UWKHO5J2

@misc{pith2026250618835,
  author       = {Pith},
  title        = {Pith review of: Chelation of the mercury ions by polyethyleneimine: Atomistic molecular dynamics study},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/UWKHO5J2}},
  note         = {Machine review of arXiv:2506.18835}
}
read the original abstract

Contamination of water by heavy metal ions represents a significant environmental concern. Among various remediation methods, chelation has proven to be an effective technique in water treatment processes. This study investigates the chelating properties of linear polyethyleneimine (PEI) and its complexation with divalent mercury ions (Hg2+) in aqueous solution. Atomistic molecular dynamics (MD) simulations were carried out using the OPLS/AA force field to examine the microscopic structure of PEI-Hg2+ complexes. PEI chains of varying lengths were considered, and it was found that a single linear PEI molecule containing ten amino groups is capable of coordinating up to four Hg2+ ions. The stability of the resulting complexes was further supported by density functional theory (DFT) calculations.

Figures

Figures reproduced from arXiv: 2506.18835 by the authors.

Figure 1
Figure 1. Atomistic model of PEI molecule containing 4 nitrogen atoms (referred to as PEI-4) described using the OPLS/AA force field (see parameters in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Simulation box with a PEI-10 + 2 Hg2+ ions complex (in the middle) and 4 counterions (at the boundary). Water molecules are seen as small red dots. The simulations comprised four sequential stages: 1) formation of a PEI-Hg2+ complex in a vacuum, i.e. without water molecules; 2) then, the complex of PEI-Hg2+ is introduced in the water environment and the volume of the simulation box is relaxed at the ambient conditio… view at source ↗
Figure 3
Figure 3. Examples of the PEI + Hg2+ complex with water molecules in the first hydration shell. Carbon atoms are shown in cyan, nitrogen atoms – in blue, hydrogen atoms – in light-grey, mercury ion – in brown, oxygen and hydrogen atoms of water molecules are shown as red and light-grey spheres respectively. At the first stage (Stage 1), the PEI molecule and the Hg2+ ion are placed in the simulation box in close prox￾imity to … view at source ↗
Figures from the paper (13 more)
Figure 4
Figure 4. Figure 4: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) Hg-N for PEI-4 + 1 Hg2+ (left) and PEI-5 + 1 Hg2+ (right) complexes. 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 Hg−Ow g(r) n(r) r, Å 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 Hg−Ow g…
Figure 5
Figure 5. Figure 5: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) Hg-Ow for PEI-4 + 1 Hg2+ (left) and PEI-5 + 1 Hg2+ (right) complexes. whether they did not approach the couterions. We noticed that the complex was moving randomly with …
Figure 6
Figure 6. Figure 6: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) N-N for PEI-4 + 1 Hg2+ (left) and PEI-5 + 1 Hg2+ (right) complexes. 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 Hg−N g(r) n(r) r, Å 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 Hg−N g(r)…
Figure 7
Figure 7. Figure 7: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) Hg-N for PEI-10 + 1 Hg2+ (left) and PEI-10 + 2 Hg2+ (right) complexes. associates with 3 nitrogen atoms of the PEI-4 polymer at the distance of ∼ 2.15 Å and at the same …
Figure 8
Figure 8. Figure 8: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) Hg-N for PEI-10 + 3 Hg2+ (left) and PEI-10 + 4 Hg2+ (right) complexes. For the longer PEI polymer consisting of 10 nitrogen atoms (PEI-10) the picture is more complicate…
Figure 9
Figure 9. Figure 9: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) Hg-Ow for PEI-10 + 1 Hg2+ (left) and PEI-10 + 2 Hg2+ (right) complexes. 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 Hg−Ow g(r) n(r) r, Å 0 2 4 6 8 10 0 1 2 3 4 5 6 7 8 9 10 Hg−O…
Figure 10
Figure 10. Figure 10: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) Hg-Ow for PEI-10 + 3 Hg2+ (left) and PEI-10 + 4 Hg2+ (right) complexes. shell of mercury allowing one more water molecule to coordinate to the ion ( [PITH_FULL_IMAGE:f…
Figure 11
Figure 11. Figure 11: Comparison of DFT and MD conformations of PEI-4, PEI-5 and PEI-10 with 1 Hg2+ (MD: Carbon atoms are shown in cyan, nitrogen atoms – in blue, mercury ion – in orange, DFT: Carbon atoms are shown in green, nitrogen atoms – in yellow, mercury ion – in grey, the pictures …
Figure 12
Figure 12. Figure 12: Comparison of DFT and MD conformations of PEI-10 with 2, 3 and 4 Hg2+ ions (same colours as in [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]
Figure 13
Figure 13. Figure 13: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) N-N for PEI-10 + 1 Hg2+ (left) and PEI-10 + 2 Hg2+ (right) complexes. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_13.png]
Figure 14
Figure 14. Figure 14: Radial distribution functions g(r) (solid line) and running coordination numbers n(r) (dashed line) N-N for PEI-10 + 3 Hg2+ (left) and PEI-10 + 4 Hg2+ (right) complexes. 0 5 10 15 20 25 30 0 1 2 3 4 5 6 7 8 9 10 Hg−Hg g(r) n(r) r, Å 0 5 10 15 20 25 30 0 1 2 3 4 5 6 7 …
Figure 15
Figure 15. Figure 15: Radial distribution function, g(r) (solid line), and running coordination number, n(r) (dashed line), for Hg– Hg pairs, obtained from MD simulations of the PEI-10+2 Hg2+ (top left), PEI-10+3 Hg2+ (top right), and PEI-10+4 Hg2+ (bottom) complexes. There is considerable…
Figure 16
Figure 16. Figure 16: Complexation energies per Hg 2+ ion (see [PITH_FULL_IMAGE:figures/full_fig_p011_16.png]

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Pith tools

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