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REVIEW 3 major objections 5 minor 89 references

HOP-graphene: A high-capacity anode for Li/Na-ion batteries unveiled by first-principles calculations

T0 review · 3 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read HOP-graphene is a high-capacity anode for Li- and Na-ion batteries, with DFT-predicted capacities of 1338 and 1227 mAh/g.

desk verdict Competent, internally consistent DFT screening of HOP-graphene as a Li/Na anode, but the dismissal of a -0.5 THz imaginary phonon mode needs a real convergence test before the stability premise is fully trusted. read the letter →

arxiv 2505.04804 v1 pith:5D7QDOWY submitted 2025-05-07 cond-mat.mtrl-sci cond-mat.mes-hall

Nicolas F. Martins , José A. S. Laranjeira , Kleuton A. L. Lima , Luis A. Cabral , L.A. Ribeiro Junior , Julio R. Sambrano This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall
keywords HOP-graphene2Dcarbonallotropelithium-ionanodesodium-iondensityfunctionaltheorydiffusionbarriertheoreticalcapacityopen-circuitvoltage
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

With a porous two-dimensional carbon allotrope that has not yet been synthesized, the paper aims to show that HOP-graphene can outperform graphite as an anode in both lithium- and sodium-ion batteries. Density functional theory predicts theoretical capacities of 1338 mAh/g for Li and 1227 mAh/g for Na, roughly 3.6 and 35 times the graphite values, by adsorbing up to 24 Li or 22 Na atoms per 40-carbon cell. The same calculations report fast ion mobility, with lowest energy barriers of 0.70 eV for Li and 0.39 eV for Na, and average open-circuit voltages of 0.42 V and 0.33 V, within the safe anodic range. The sheet is described as metallic and mechanically stable both before and after full loading, which would let the electrode keep its conductivity during charge and discharge. If these first-principles predictions hold, HOP-graphene would be a concrete candidate for next-generation lithium- and sodium-ion anodes.

What carries the argument

The carrying object is the HOP-graphene lattice: a rectangular 10-carbon unit cell that tiles into octagons, hexagons, and pentagons. The octagonal hollow is the deepest adsorption site for both Li and Na, the pentagonal bridges connecting adjacent octagons form the lowest-energy migration paths, and a large vacuum gap isolates a true monolayer in the calculations. The argument itself is carried by a density-functional-theory workflow, including a generalized-gradient exchange-correlation functional, projector-augmented-wave potentials, a dispersion correction, nudged-elastic-band transition searches, and Bader charge decomposition, which converts the ring geometry into adsorption energies, diffusion barriers, capacities, open-circuit voltages, and charge transfer. The key structural statement is that the pentagonal motif, not the hexagon, is what gives fast diffusion, and the octagonal pore is what gives high storage.

What would settle it

A phonon calculation in larger supercells with different pseudopotentials that still shows the -0.5 THz mode would mean the free-standing monolayer is dynamically unstable; on the experimental side, a synthesized HOP-graphene with measured Li or Na capacity far below the predicted values would contradict the central claim.

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Extended reading notes

Core claim

The paper claims that HOP-graphene, a rectangular two-dimensional carbon allotrope made of five-, six-, and eight-membered rings, is a high-performance anode material for both lithium- and sodium-ion batteries. On the basis of density functional theory, it reports that the monolayer binds single Li and Na atoms most strongly at the octagonal hollow sites, with adsorption energies of -2.92 eV and -2.32 eV, and that full double-sided loading reaches 24 Li or 22 Na atoms per 40-carbon cell. From these loadings it derives theoretical capacities of 1338 mAh/g (Li) and 1227 mAh/g (Na), against 372 and 35 mAh/g for graphite. Diffusion calculations give minimum barriers of 0.70 eV for Li and 0.39 eV for Na, both along a path through pentagonal bridges, and Bader analysis shows +0.89 e and +0.87 e transferred from the metal atoms to the carbon sheet. Average open-circuit voltages of 0.42 V and 0.33 V place the electrode inside the safe operating window, and the metallic character of the sheet is reported to survive full loading.

Load-bearing premise

The load-bearing premise is that the small negative phonon frequency near -0.5 THz is a harmless numerical artifact; this is accepted on the authority of a cited -2 THz threshold instead of a convergence test, and if that mode is real the HOP-graphene sheet is unstable and none of the battery findings stand.

Editorial extensions

If this is right

  • If the central claim is correct, the Li capacity of 1338 mAh/g is 3.6 times the 372 mAh/g of graphite anodes, so a HOP-graphene anode could cut anode mass roughly by that factor at full lithiation.
  • The Na capacity of 1227 mAh/g is 35 times the 35 mAh/g of graphite, making sodium-ion chemistry far more competitive than it is on carbon.
  • A room-temperature Na diffusion coefficient of 2.78e-6 cm2/s, with a 0.39 eV barrier, is orders of magnitude above Na in graphite, so fast charging would not be bottlenecked by sodium mobility.
  • Average open-circuit voltages near 0.42 V for Li and 0.33 V for Na sit below the 1 V threshold for practical anodes, balancing cell voltage against the risk of metal plating.
  • Because the monolayer is reported to remain metallic at full loading, the electrode would not lose its electrical conductivity as the battery charges.

Reading between the lines

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

  • The same 5-6-8 ring geometry could be screened for potassium, magnesium, calcium, or aluminum ions; the pore size and charge-transfer pattern reported here suggest those chemistries are a natural next test, but the paper does not run it.
  • The -0.5 THz mode is the cheapest place to check the prediction: a phonon calculation in larger supercells with different pseudopotentials would either confirm the artifact or invalidate the stability premise.
  • The present numbers describe a pristine, defect-free monolayer; a real electrode will contain grain boundaries, vacancies, and contact layers, so practical capacities are likely lower until those effects are included.
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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

3 major / 5 minor

Summary. The manuscript presents a first-principles study of HOP-graphene, a predicted 2D carbon allotrope with 5-6-8-membered rings, as an anode material for Li- and Na-ion batteries. Using PBE+DFT-D2, the authors compute the phonon dispersion, mechanical properties, adsorption energies, Bader charges, diffusion barriers via NEB, and open-circuit voltages. They report theoretical capacities of 1338 mAh/g for Li and 1227 mAh/g for Na, diffusion barriers of 0.70 eV (Li) and 0.39 eV (Na), and average OCVs of 0.42 V and 0.33 V, concluding that HOP-graphene is a promising high-capacity, safe anode.

Significance. If the reported properties are correct, HOP-graphene would compare favorably with previously proposed 2D carbon anodes, offering capacities more than three times that of graphite for Li and much higher for Na, while maintaining low diffusion barriers and safe OCV. The DFT calculations are performed with standard protocols, and the central quantities are derived directly from total energies with no fitting to target properties; the only empirical input is the attempt frequency in the Arrhenius diffusivity, which does not affect the barriers. The main weakness is the incomplete evidence for dynamic stability of the host structure, which underpins the adsorption, diffusion, capacity, and OCV calculations.

major comments (3)
  1. [Section 3.1, Fig. 1(b)] The -0.5 THz imaginary frequency near the Gamma point is dismissed by citing the -2 THz screening threshold of Wang et al. [55]. That threshold is an operational high-throughput criterion, not a demonstration that a Gamma-point acoustic mode is a numerical artifact. No convergence tests with respect to supercell size, k-point sampling, pseudopotential, or acoustic sum rule are reported. Because the dynamic stability of the pristine monolayer is the foundation for all subsequent adsorption, diffusion, capacity, and OCV calculations, the authors should provide a targeted phonon investigation (e.g., larger supercell, finite-displacement method with acoustic sum correction) to establish that the mode is an artifact. As written, the manuscript does not rule out the possibility that HOP-graphene is a saddle-point structure.
  2. [Sections 2 and 3.1/3.4] The AIMD simulations used as evidence of thermal stability are inconsistently described: Section 2 states a total simulation time of 5 ps, Section 3.1 reports 10 ps for the pristine monolayer, and Fig. 12 indicates 5 ps for the fully loaded systems. Moreover, a 5-10 ps trajectory is short relative to the period of a soft mode at -0.5 THz (about 2 ps) and cannot exclude a slow structural distortion. The authors should unify the reported times and, if the phonon convergence tests are inconclusive, extend the AIMD or perform replica exchange to justify the stability conclusion.
  3. [Section 3.4, Eq. (4)] The capacity calculation is not fully specified: the text reports a maximum loading of 24 Li and 22 Na atoms but never states the supercell size or the number of carbon atoms used for the host weight. The notation Li24C40 implies a 2x2 supercell of the 10-atom unit cell, but this is not stated explicitly, and the text also writes Na24C40 while reporting 22 Na atoms. Please specify the supercell, correct the Na formula, and confirm that the capacity values correspond to the stated loading.
minor comments (5)
  1. [Section 3.1] The extrema for Young's modulus and Poisson's ratio appear to be interchanged (313.45 vs. 347.67 N/m; 0.15 vs. 0.19), and the sentence describing negligible variation followed by exceptionally high anisotropy is contradictory. Please correct the numbers and wording.
  2. [Eq. (5)] The OCV formula is written with an unclear subscript E_substrate+xE_Li(Na) and appears to be missing the proper reference-state terms. Please rewrite the formula with consistent notation, for example OCV = -(E_{substrate+xA} - E_{substrate} - xE_A)/(xze).
  3. [Section 3.2] The figure callouts Figures 4(b) and 4(b) should be Figures 5(b) and 5(c).
  4. [Introduction and Sections 3.1/4] The ring composition is described as 4-, 5-, and 8-membered in the Introduction but as 5-, 6-, and 8-membered in the abstract and conclusions. Please harmonize these descriptions.
  5. [Data access statement] The statement that data can be accessed by contacting the corresponding author is not a reproducible data-sharing plan. Please provide a repository link or a detailed data availability statement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: all central quantities (barriers, capacities, OCVs) are direct DFT outputs with no fitting to the target claims.

full rationale

The paper's derivation chain is first-principles throughout. Adsorption energies use Eq. (1) as direct DFT total-energy differences; NEB barriers are computed on the DFT potential-energy surface; capacities follow from Eq. (4) with n set by DFT loading; OCVs follow from Eq. (5) using the same adsorption energies. No parameter is fitted to the reported capacities, barriers, or voltages. The only empirical prefactor, nu0 = 1 x 10^13 Hz in Eq. (3), is a standard order-of-magnitude attempt frequency and affects D, not the barriers or capacities. Self-citations (refs. 19, 21, 38, 69, etc.) are used as literature comparisons or as prior structural characterizations, but the central HOP-graphene claims do not reduce to them. The apparent weak point—the -0.5 THz imaginary phonon mode dismissed via the -2 THz threshold of Wang et al. [55]—is a correctness/stability-convergence concern, not a circularity: the threshold is an external screening criterion, and the paper's own AIMD is independent evidence. Therefore no circular step can be quoted, and the appropriate score is 0.

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

The central claim rests on standard DFT approximations, a widely used dispersion correction, a heuristic stability threshold for imaginary phonons, and a short AIMD simulation. No new physical entities are introduced.

free parameters (1)
  • Attempt frequency ν0 = 1×10^13 Hz
    Used as empirical pre-factor in Arrhenius diffusion coefficient (Eq. 3); a typical value for lattice vibrations, not fitted to specific data. Affects the reported D values but not the diffusion barriers.
assumptions (5)
  • domain assumption PBE-GGA exchange-correlation functional with PAW method gives accurate energetics for Li/Na adsorption and diffusion on carbon allotropes.
    Standard DFT choice used throughout; no benchmark against experiment or higher-level theory for these specific systems.
  • domain assumption DFT-D2 dispersion correction adequately captures van der Waals interactions between alkali metals and carbon substrate.
    Paper uses Grimme DFT-D2; other dispersion schemes may give different adsorption energies and barriers.
  • domain assumption Imaginary phonon frequencies down to -2 THz do not indicate dynamic instability.
    The paper cites Wang et al. to justify the -0.5 THz imaginary mode near Gamma as acceptable; this is a heuristic threshold, not a rigorous criterion.
  • domain assumption A 5 ps AIMD simulation at 300 K is sufficient to demonstrate thermodynamic stability of the fully lithiated/sodiated structures.
    Short simulation time may not capture slow diffusion or cluster formation; the paper uses it as evidence of no metal aggregation.
  • standard math Born-Huang stability criteria for orthorhombic crystals are appropriate for evaluating mechanical stability of a 2D rectangular lattice.
    Standard elasticity criteria applied in Sec 3.1.

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Cite this review

Pith. "Pith review of HOP-graphene: A high-capacity anode for Li/Na-ion batteries unveiled by first-principles calculations." pith.science (2026). https://pith.science/paper/5D7QDOWY

@misc{pith2026250504804,
  author       = {Pith},
  title        = {Pith review of: HOP-graphene: A high-capacity anode for Li/Na-ion batteries unveiled by first-principles calculations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5D7QDOWY}},
  note         = {Machine review of arXiv:2505.04804}
}
read the original abstract

The growing demand for efficient energy storage has driven the search for advanced anode materials for lithium- and sodium-ion batteries (LIBs and SIBs). In this context, we report the application of HOP-graphene (a 5-6-8-membered 2D carbon framework) as a high-performance anode material for LIBs and SIBs using density functional theory simulations. Diffusion studies reveal low energy barriers of 0.70 eV for Li and 0.39 eV for Na, indicating superior mobility at room temperature compared to other carbon allotropes, like graphite. Full lithiation and sodiation accommodate 24 Li and 22 Na atoms, respectively, delivering outstanding theoretical capacities of 1338 mAh/g (Li) and 1227 mAh/g (Na). Bader charge analysis and charge density difference maps confirm substantial electron transfer from the alkali metals to the substrate. Average open-circuit voltages of 0.42 V (Li) and 0.33 V (Na) suggest favorable electrochemical performance. HOP-graphene also demonstrates excellent mechanical strength. These findings position HOP-graphene as a promising candidate for next-generation LIB and SIB anodes.

Figures

Figures reproduced from arXiv: 2505.04804 by the authors.

Figure 1
Figure 1. Structural and stability characterization of HOP-graphene. (a) Unit cell and extended supercell of HOP-graphene, highlighting the periodic arrangement of octagons (cyan), hexagons (yellow), and pentagons (green), with optimized lattice constants. (b) Phonon dispersion spectrum along high-symmetry paths of the Brillouin zone. (c) The total energy profile from AIMD simulations at 300 K over 10 ps. The inset shows top … view at source ↗
Figure 2
Figure 2. Band structure and projected density of states (PDOS) for pristine HOP-graphene. Fermi level is fixed at zero eV for better illustration. variation, ranging from a maximum of 0.15 to a minimum of 0.19, resulting in an exceptionally high anisotropy. This way, HOP-graphene can be classified as an almost isotropic material concerning its mechanical properties. The mechan￾ical stability of HOP-graphene was evaluated in … view at source ↗
Figure 3
Figure 3. Polar diagrams representing (a) Young Modulus (𝑌 ), (b) Shear Modulus (𝐺), and (c) Poisson’s ratio (𝜈) of HOP￾graphene. H1 H2 H3 C1 C2 C3 L1 L2 L3 L4 L5 L6 H1 H3 Hollow sites C1 C3 Atomic sites L1 L6 Bridge sites [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (9 more)
Figure 4
Figure 4. Figure 4: Different Li and Na adsorption sites over HOP￾graphene monolayer. (H1), indicating that the octagonal hollow site (H1) is the most favorable location for adsorbing both alkali metals. The moderate strength of these adsorption energies helps prevent the aggregation of L…
Figure 6
Figure 6. Figure 6: Charge density difference map for single (a) Li and (b) Na adsorption on HOP-graphene structure, where yellow and cyan represent charge accumulation and depletion, respectively. plot (see Fig.6, following the relation: Δ𝜌 = 𝜌HOP-graphene+Li(Na) − 𝜌HOP-graphene − 𝜌Li(Na…
Figure 7
Figure 7. Figure 7: Diffusion pathways and energy barriers for Li and Na migration on HOP-graphene. (a) Top view of the HOP-graphene monolayer showing the two selected diffusion paths: Path 1 (magenta) across hexagonal units and Path 2 (blue) across pentagonal bridges, both connecting adj…
Figure 8
Figure 8. Figure 8: Temperature-dependent diffusion coefficients of Li and Na on HOP-graphene. (a) Diffusion coefficients for Li along Path 1 (magenta) and Path 2 (blue) as a function of temperature, calculated using the Arrhenius equation. (b) Corresponding diffusion behavior for Na. Ver…
Figure 9
Figure 9. Figure 9: Side and top perspectives for maximum capacity achieved for (a) Li and (b) Na ions over HOP-graphene monolayer. Based on this calculation, the HOP-graphene monolayer exhibits remarkable storage capacities of 1338 mAh/g for Li and 1227 mAh/g for Na, respectively. These …
Figure 10
Figure 10. Figure 10: Adsorption energy (Eads) as a function of number of (a) Li and (b) Na atoms adsorbed into HOP-graphene. practical anode applications, the operating potential should typically remain below 1.0 V [86]. The OCV profiles for Li and Na adsorption on HOP-graphene are shown …
Figure 11
Figure 11. Figure 11: Projected density of states (PDOS) analysis for different concentrations of (a) Li and (b) Na on HOP-graphene structure [PITH_FULL_IMAGE:figures/full_fig_p009_11.png]
Figure 12
Figure 12. Figure 12: AIMD simulations at 300 K for the fully (a) lithiated and (b) sodiated HOP-graphene. [2] Jana Vejpravová. Mixed sp2–sp3 nanocarbon materials: a status quo review. Nanomaterials, 11(10):2469, 2021. [3] Andre K Geim and Konstantin S Novoselov. The rise of graphene. Natu…
Figure 13
Figure 13. Figure 13: Open-circuit voltage (OCV) profile for (a) Li and (b) Na storage on HOP-graphene monolayer. of two-dimensional planar sp2 carbon space associated with a la￾beled quotient graph. The Journal of Physical Chemistry Letters, 12(47):11511–11519, 2021. [14] Zhenzhe Zhang, H…

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.