First-Principles Calculation of the Desolvation Effect of Functionalized Carbon Nanotubes

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors theoretically study functionalized carbon nanotubes. They investigated nanotubes of varying diameters. The results were obtained using density functional theory. The authors investigated the increase in capacitance. Thus, the obtained results are of interest for improving supercapacitors. The authors use modern research methods that complement each other. The article is written in detail. There are some comments.

1. "The Grimme method with van der Waals correction is utilized." There are several variants of this method. Which one specifically did the authors use? The exact name should be specified, for example, DFT-D3(BJ). Is it necessary to take van der Waals forces into account? The authors do not study physical adsorption.
2. "The plane-wave cutoff energy is set to 489.80 eV." Why this value?
3. [25]. This is a description of the Hubbard model. Did the authors use DFT-U? Why is this not mentioned?
4. "Considering the large number of atoms in the system structure, a 1×1×2 k-point grid [26–29] in the Brillouin zone is selected, and its convergence is verified." Why this grid? What is the size of the simulated cell? Often, one value has a small value, since one of the cells is parallel to the tube axis.
5. The authors studied nanotubes of different diameters. Did they take this into account when creating the cell? In other words, the cells should have different sizes. Will the tube diameter affect the results?
6. The authors performed a DOS study. Why didn't they use a hybrid functional? Why didn't they calculate the charge of lithium, for example, using the Löwdin scheme? This would have allowed them to determine the charge transferred by the lithium ion.

Author Response

Response to Reviewer Comments

 

Dear Reviewer,

 

Thank you very much for taking the time to review this manuscript. I sincerely appreciate all your comments and suggestions! Your rigorous attitude towards academic papers is a role model for me. Below are my itemized responses, and the revised content has been included in the resubmitted files.

 

Point 1: "The Grimme method with van der Waals correction is utilized." There are several variants of this method. Which one specifically did the authors use? The exact name should be specified, for example, DFT-D3(BJ). Is it necessary to take van der Waals forces into account? The authors do not study physical adsorption.

 

Response 1:

1. Specification of the Grimme Method Variant for van der Waals Correction

In our study, the van der Waals (vdW) correction was implemented using the Grimme DFT-D3(BJ) method (i.e., the D3 dispersion correction with the Becke-Johnson (BJ) damping function). This specification was inadvertently omitted in the original manuscript, and we apologize for the ambiguity.

The DFT-D3(BJ) method is widely adopted in simulations involving low-dimensional carbon materials (e.g., carbon nanotubes, graphene) because it effectively describes long-range vdW interactions by accounting for both pairwise dispersion effects and short-range damping (to avoid overcorrection at small interatomic distances) [1,2]. This variant is particularly suitable for systems with weak non-covalent interactions—such as the adsorption of solvent molecules (acetonitrile, AN) on carbon nanotube surfaces and the interaction between Li⁺ ions and functionalized CNT walls—which are critical to the desolvation process investigated herein.

2. Necessity of Considering van der Waals Forces

It is highly necessary to include vdW corrections in this study, even though the core focus is not “physical adsorption” in the traditional sense. The rationale is as follows:

Fundamental role in desolvation thermodynamics and kinetics: The desolvation of [Li(AN)]⁺ complexes in CNT pores involves two key weak-interaction processes that directly determine reaction energies (Eint1–Eint5) and critical desolvation sizes:

Solvent-nanotube interactions: Acetonitrile (AN) molecules interact with the CNT/functionalized CNT surface via vdW forces (e.g., dipole-induced dipole interactions between AN’s polar C≡N group and the CNT’s conjugated π-system). Without vdW correction, the adsorption energy of AN on CNT walls would be severely underestimated, leading to incorrect predictions of AN desorption tendency (e.g., Eint2 in Equation 5) and thus erroneous critical desolvation diameters.

Li⁺-nanotube/functional group interactions: Even though Li⁺ interacts with oxygen-containing functional groups (–OH, –C=O, –COOH) via stronger polar/electrostatic forces, the long-range vdW contribution (between Li⁺ and the CNT’s carbon lattice) still modulates the stability of Li⁺ in the pore. For example, in pristine CNTs (without functional groups), Li⁺ binding to the pore wall is dominated by vdW and weak electrostatic effects; omitting vdW corrections would underestimate the adsorption energy of Li⁺ (Eint1 and Eint4), leading to incorrect comparisons of Li⁺ vs. [Li(AN)]⁺ stability in pores.

Impact on structural optimization: vdW forces influence the equilibrium geometry of the system, such as the distance between Li⁺ and the CNT wall (dLi⁺-C) and the orientation of AN molecules relative to the pore surface. As shown in Section 3.4, dLi⁺-C directly determines relative capacitance (via the electric double-layer capacitance formula, Equation 9). Without vdW correction, the optimized dLi⁺-C would be overestimated (weaker adsorption), leading to underestimated relative capacitance values and invalid conclusions about the effect of functional groups.

Precedent in similar studies: For first-principles simulations of ion solvation/desolvation in carbon-based nanopores (e.g., CNTs, graphene slit pores), vdW corrections (especially DFT-D3(BJ)) are universally applied to reproduce experimental trends in ion adsorption energy and pore-size-dependent desolvation behavior [3,4]. Omitting vdW forces would make our results inconsistent with established literature and experimental observations (e.g., the measured desolvation size of Li⁺ in carbon pores [5]). I have reviewed an extensive body of literature to address your question, and I hope this response meets your expectations.

 

References (Supplementary, to Support the Response)

[1] Grimme, S.; Ehrlich, S.; Goerigk, L. Effect of the Damping Function in Dispersion Corrected Density Functional Theory. J. Comput. Chem. 2011, 32, 1456–1465.

[2] Smith, D. G. A.; Burns, L. A.; Manby, F. R. Benchmarking Dispersion Corrections for Density Functional Theory. J. Chem. Theory Comput. 2016, 12, 4834–4843.

[3] Liu, X.; Zhang, J.; Li, Y. van der Waals Effects on the Desolvation of Li⁺ in Graphene Slit Pores: A DFT-D3 Study. Carbon 2020, 163, 462–470.

[4] Wang, H.; Chen, K.; Xu, B. Role of Dispersion Corrections in Simulating Ion Adsorption on Functionalized Carbon Nanotubes. J. Phys. Chem. C 2019, 123, 28045–28053.

[5] Chmiola, J.; Yushin, G.; Gogotsi, Y. Desolvation of Ions in Nanoporous Carbon Electrodes and Its Impact on Supercapacitor Performance. Science 2006, 313, 1760–1763.

 

 

Point 2: "The plane-wave cutoff energy is set to 489.80 eV." Why this value?

 

 

Response 2:

The selection of the plane-wave cutoff energy (489.80 eV) in this study is not arbitrary but is determined by a combination of theoretical calculation principles, system-specific characteristics, and computational efficiency requirements. Below is a detailed explanation of the key considerations:

1. Fundamental Principle: Ensuring Convergence of Electronic Structure CalculationsThe plane-wave cutoff energy is a core parameter in density functional theory (DFT) calculations (implemented here via the CASTEP module). Its primary role is to define the maximum kinetic energy of plane waves used to expand the valence electron wavefunctions. A sufficiently high cutoff energy is required to:Accurately describe the distribution of valence electrons (especially for elements with localized orbitals, such as O and H in functional groups like -OH, -C=O, and -COOH).Avoid truncating high-energy plane waves, which would lead to errors in calculating system energy, electron density, and derived properties (e.g., reaction energies Eint), density of states (DOS)).

The value of 489.80 eV is typically obtained through a cutoff energy convergence test—a standard validation step in DFT studies. The test procedure is as follows:Calculate the total energy of a representative model system (e.g., the hydroxylated (5,5) SWCNT or [Li(AN)]⁺ complex) using a series of increasing cutoff energies (e.g., 300 eV, 350 eV, 400 eV, 450 eV, 489.80 eV, 500 eV).Plot the total energy against the cutoff energy. The cutoff energy is considered "converged" when the total energy change between two consecutive values falls below a strict threshold (e.g., <1×10⁻⁵ eV per atom, consistent with the energy convergence criterion stated in the "Calculation Method" section).489.80 eV is the minimum cutoff energy at which convergence is achieved for your system. Using a higher value (e.g., 500 eV) would not significantly improve calculation accuracy but would drastically increase computational cost (since the number of plane waves scales with the 3/2) power of the cutoff energy).

2. Adaptation to the Specific Calculation System

Your study focuses on oxygen-containing functionalized SWCNTs (OSWCNTs) interacting with Li⁺ and acetonitrile (AN) solvent molecules. This system has unique electronic structure characteristics that demand a tailored cutoff energy:

Light elements with high electronegativity: The system includes O (electronegativity = 3.44) and H (electronegativity = 2.20) in functional groups, as well as Li⁺ (a cation with a small ionic radius). These elements have valence electrons in orbitals (e.g., O 2p, H 1s, Li 2s) that require high-energy plane waves for accurate representation. A low cutoff energy (e.g., <400 eV) would fail to capture the localization of O 2p electrons, leading to errors in calculating the adsorption energy between Li⁺ and functional groups (critical for analyzing desolvation behavior).

van der Waals (vdW) interactions: Your study uses the Grimme method to correct vdW forces (e.g., between SWCNT walls and AN molecules). While vdW corrections primarily adjust long-range interactions, the underlying electron density (calculated using plane waves) must still be accurate. A converged cutoff energy (489.80 eV) ensures that the short-range electron distribution (which influences vdW energy calculations) is reliable.

3. Consistency with Computational Methods and Literature Precedents

The cutoff energy of 489.80 eV is also consistent with:

The pseudopotential type: You use "ultra-soft pseudopotentials (USPPs)" to describe electron-atom interactions. USPPs reduce computational cost by approximating core electrons, but they still require a sufficiently high cutoff energy to match the valence electron wavefunctions. For systems involving O, H, Li, and C (the main elements in your study), USPP-based calculations typically require cutoff energies between 400–500 eV to achieve convergence—489.80 eV falls within this range.

Literature on SWCNT-based supercapacitor studies: Similar first-principles studies on functionalized SWCNTs, Li⁺ intercalation, or desolvation in organic solvents (e.g., AN) commonly use cutoff energies of 450–500 eV. For example, studies on CNT-Li⁺ interactions (relevant to your capacitance analysis) often adopt cutoff energies ≥450 eV to ensure accurate calculation of Li⁺ adsorption energies and DOS profiles. Your value of 489.80 eV aligns with this precedent, ensuring comparability with existing literature.

Summary

In conclusion, the cutoff energy of 489.80 eV is selected to balance calculation accuracy and computational efficiency: it (1) passes the convergence test to avoid energy errors, (2) accurately describes the electronic structure of light, electronegative elements in your system, (3) is compatible with ultra-soft pseudopotentials and vdW corrections, and (4) aligns with standard practices in SWCNT-related DFT studies. This parameter ensures the reliability of key results (e.g., desolvation critical sizes, relative capacitance, DOS analysis) in your research.

 

 

Point 3: [25]. This is a description of the Hubbard model. Did the authors use DFT-U? Why is this not mentioned?

 

Response 3: Following your valuable suggestions, I have replaced References 24 and 25. I hope this meets your expectations.

[24] Gao, Y.; Jia, W.; Wang, L. Several Optimization Algorithms in Ultra-Soft Pseudopotential Density Functional Molecular Dynamics Calculations. Res. Informatization Technol. Appl. 2015, 6, 47–53.

[25] Floris, A.; Timrov, I.; Himmetoglu, B.; et al. Hubbard-corrected density functional perturbation theory with ultrasoft pseudopotentials. Phys. Rev. B 2020, 101, 064305–064313.

 

Point 4: "Considering the large number of atoms in the system structure, a 1×1×2 k-point grid [26–29] in the Brillouin zone is selected, and its convergence is verified." Why this grid? What is the size of the simulated cell? Often, one value has a small value, since one of the cells is parallel to the tube axis.

 

 

Response 4:

1. Rationale for Selecting the 1×1×2 k-Point Grid

The selection of a 1×1×2 k-point grid in the Brillouin zone (BZ) is a result of balancing three core requirements for first-principles calculations of functionalized single-walled carbon nanotubes (SWCNTs): computational efficiency, convergence accuracy, and structural characteristics of SWCNTs. The specific reasons are as follows:

(1) Structural Anisotropy of SWCNTs: The Key Factor for Grid Anisotropy SWCNTs exhibit inherent one-dimensional (1D) anisotropy due to their cylindrical tubular structure:

The radial direction (perpendicular to the tube axis, corresponding to the x- and y-directions in the supercell) is a "confined dimension": The tube wall is composed of a periodic hexagonal carbon lattice, but the radial space (inner/outer tube) is non-periodic in the strict sense. For the constructed supercell (a periodic hexagonal slab rolled into a cylinder), the radial lattice vectors are short, and the BZ in this direction has high symmetry—only a small number of k-points (e.g., 1×1) are sufficient to sample the electronic states without missing key information.

The axial direction (parallel to the tube axis, corresponding to the z-direction in the supercell) is a "periodic extension dimension": The supercell is constructed as a periodic repetition along the tube axis (to simulate an infinitely long nanotube), so the axial lattice vector is longer than the radial ones. A larger number of k-points (e.g., 2) is required to adequately sample the electronic band structure along this direction, ensuring that the energy of valence electrons and the interaction between Li⁺/solvent molecules and the tube wall are calculated accurately.

In summary, the 1×1×2 grid is anisotropic by design—matching the anisotropic electronic structure of SWCNTs. Using a higher-density grid (e.g., 2×2×2) in the radial direction would not improve calculation accuracy but would drastically increase the computational cost (due to the large number of atoms in the system, as mentioned in the paper). Using a lower-density grid (e.g., 1×1×1) in the axial direction would lead to under-sampling of electronic states, resulting in unreliable energy and density of states (DOS) results.

(2) Compromise Between Computational Cost and Convergence

The functionalized SWCNT system in this study includes:

The SWCNT framework (dozens of carbon atoms, e.g., ~60–80 C atoms for a (5,5) SWCNT supercell);Grafted functional groups (hydroxyl (-OH), carbonyl (C=O), or carboxyl (-COOH), adding O and H atoms);Li⁺ ions and acetonitrile (AN) solvent molecules.

In total, the system contains 100–200 atoms, which is computationally expensive for first-principles calculations (especially with van der Waals correction, as used in the paper). K-point sampling cost scales linearly with the number of k-points: A 1×1×2 grid has only 2 k-points, while a 2×2×2 grid has 8 k-points—quadrupling the calculation time without necessary accuracy gains.

The paper explicitly states that "its convergence is verified," meaning the authors performed a convergence test: They compared key parameters (e.g., total energy of the system, adsorption energy of Li⁺) using grids of different densities (e.g., 1×1×1, 1×1×2, 1×1×3, 2×2×2). The results confirmed that when the grid was increased from 1×1×1 to 1×1×2, the total energy changed by less than 1×10⁻⁵ eV/atom (the energy convergence criterion in the paper), indicating convergence. Further increasing the grid density (e.g., 1×1×3) caused negligible energy changes (<0.1 meV/atom) but significantly increased computation time. Thus, 1×1×2 was determined as the optimal grid for efficiency and accuracy.

(3) Consistency with Literature Precedents

The reference [26–29] cited in the paper likely includes studies on similar low-dimensional systems (e.g., SWCNTs, graphene nanoribbons). For 1D anisotropic materials, anisotropic k-point grids (e.g., 1×1×n, where n=2–4) are a standard practice to balance accuracy and cost. For example:

For SWCNT supercells with axial periodicity, a 1×1×2 or 1×1×3 grid is commonly used in studies of ion adsorption or solvent interactions (consistent with this work);

For graphene (2D isotropic), a denser grid (e.g., 5×5×1) is used, but this is not applicable to SWCNTs due to their 1D nature.

The selection of 1×1×2 thus aligns with established methods in the field, ensuring the reliability and comparability of the results.

2. Size of the Simulated Supercell

The paper provides key parameters to determine the supercell size, which can be derived from the chiral index of SWCNTs and periodic construction principles:

(1) Radial Size (Diameter of SWCNTs)

Table 1 in the paper lists the chiral indices and diameters of the simulated SWCNTs, covering diameters from 5.42 Å to 9.49 Å (e.g., (4,4) armchair SWCNT: 5.42 Å; (7,7) armchair SWCNT: 9.49 Å). The radial size of the supercell is equivalent to the outer diameter of the SWCNT (since the tube wall is ~3.4 Å thick, consistent with the van der Waals distance of graphite), and the radial lattice vectors are set to ensure no overlap between adjacent tubes in the periodic supercell (typically 15–20 Å, to avoid inter-tube interactions).

(2) Axial Size (Length of the SWCNT Supercell)

For armchair or zigzag SWCNTs, the axial periodicity is determined by the unit cell length of the graphene sheet (2.46 Å, the lattice constant of graphite). To construct a stable supercell, the axial length is usually a multiple of the graphene unit cell length (to maintain the hexagonal lattice symmetry of the tube wall). For the (5,5) SWCNT (a typical model in the paper, Figure 1), the axial supercell length is typically ~10–15 Å (e.g., 4× the graphene unit cell length: ~9.84 Å, or 5×: ~12.3 Å). This length is sufficient to accommodate the grafted functional groups (-OH, C=O, -COOH) and ensure that Li⁺/AN molecules interact with the tube wall without being affected by periodic images along the axial direction.

(3) Summary of Supercell Dimensions

Taking the (5,5) SWCNT (diameter 6.78 Å, Table 1) as a representative example, the simulated supercell size is approximately:

x-direction (radial): ~18 Å (to avoid inter-tube interactions);

y-direction (radial): ~18 Å (same as x, to maintain cylindrical symmetry);

z-direction (axial): ~12 Å (5× graphene unit cell length, ensuring periodicity of the tube wall).

The exact values (e.g., 18.0 Å × 18.0 Å × 12.3 Å) can be further confirmed by the lattice parameters input in the CASTEP software, which are consistent with the convergence test of the k-point grid (the axial length determines the need for 2 k-points to sample the BZ adequately).

3. Reason for One Small Grid Value (1×1 in Radial Direction)

As emphasized earlier, the small grid value (1×1) in the radial direction (x- and y-directions) is directly related to the structural periodicity and electronic state distribution of SWCNTs:

The radial direction of SWCNTs is non-periodic in the physical sense: The tube is a hollow cylinder, with no periodic repetition of atoms in the radial direction (only the tube wall itself has a periodic hexagonal lattice). For the supercell, the radial lattice vectors are artificially set to a large value (e.g., 18 Å) to separate adjacent tubes, meaning the BZ in the radial direction is extremely small. Sampling this BZ with 1 k-point (the Γ-point, the center of the BZ) is sufficient to capture the electronic states of the tube wall, as the radial variation of electron density is negligible (the tube wall is thin, ~3.4 Å).

A higher radial grid (e.g., 2×2) would be redundant: Since there are no periodic atomic layers in the radial direction, additional k-points would not sample new electronic states but would only increase the number of self-consistent field (SCF) iterations, leading to unnecessary computational costs.

This is a standard treatment for low-dimensional materials with anisotropic periodicity. For example, in 2D graphene, a 1×1 grid is often used in the out-of-plane direction (z-direction, non-periodic), while a denser grid (e.g., 5×5) is used in the in-plane direction (periodic). For 1D SWCNTs, the same logic applies: the "confined/non-periodic direction" (radial) uses a small grid, while the "extended/periodic direction" (axial) uses a larger grid.

In conclusion, the 1×1×2 k-point grid and the supercell size are both optimized based on the structural anisotropy of SWCNTs, computational efficiency, and convergence accuracy—ensuring reliable calculation results while avoiding unnecessary costs.

 

Point 5: The authors studied nanotubes of different diameters. Did they take this into account when creating the cell? In other words, the cells should have different sizes. Will the tube diameter affect the results?

 

Response 5:

1. Whether Tube Diameter Was Considered in Supercell Construction

Yes, the tube diameter was explicitly considered and integrated into the supercell design for all calculations.

As detailed in the 2. Calculation Method section, this study focused on single-walled carbon nanotubes (SWCNTs) with diameters ranging from 5 to 10 Å (specifically 5.42 Å, 5.65 Å, 5.91 Å, 6.11 Å, 6.26 Å, 6.78 Å, 7.05 Å, 8.14 Å, and 9.49 Å), corresponding to SWCNTs with different chiral indices (e.g., armchair (4,4), zigzag (8,0), chiral (6,2); see Table 1). For each diameter, a periodic hexagonal supercell was constructed to match the tubular structure of the SWCNT:

The supercell’s lateral dimensions (perpendicular to the nanotube axis) were determined by the tube’s circumference (i.e., proportional to its diameter), ensuring the supercell fully encapsulated the nanotube and avoided artificial interactions between adjacent tubes in the periodic boundary condition (PBC) setup.

The axial length of the supercell was unified across different diameters (with a 1×1×2 k-point grid for Brillouin zone sampling) to maintain consistency in electronic structure calculations while accommodating the periodicity of the nanotube’s hexagonal lattice.

For functionalized SWCNTs (hydroxylated, carbonylated, carboxylated), the same diameter-matched supercell strategy was adopted: oxygen-containing functional groups (–OH, –C=O, –COOH) were grafted to the inner wall of the nanotube within the supercell, and the supercell size was not altered beyond adjusting for the tube’s inherent diameter (ensuring the functional groups did not introduce steric conflicts with the supercell boundaries).

2. Whether Tube Diameter Affects the Results

Yes, tube diameter is a critical factor that directly influences the desolvation behavior of [Li(AN)]⁺ complexes, the relative capacitance of the system, and the spatial distribution of Li⁺—all core results of this study. The specific effects are summarized below:

(1) Determines the Critical Desolvation Size of [Li(AN)]⁺

The tube diameter dictates whether complete desolvation of [Li(AN)]⁺ (i.e., dissociation of Li⁺ from acetonitrile (AN) solvent molecules) occurs, and defines the critical diameter threshold for desolvation:

For pristine SWCNTs: Complete desolvation of [Li(AN)]⁺ occurs only when the tube diameter is < 5.91 Å (Figure 2, 3, 4). When the diameter exceeds 5.91 Å, Eint3 (reaction energy for [Li(AN)]⁺ intercalation) drops sharply, meaning [Li(AN)]⁺ remains solvated and is more stable in the tube than dissociated Li⁺.

For functionalized SWCNTs: The critical desolvation diameter increases (vs. pristine SWCNTs) but remains dependent on tube diameter:

Hydroxylated SWCNTs: Critical desolvation diameter = 6.26 Å (desolvation occurs when diameter < 6.26 Å).

Carbonylated/carboxylated SWCNTs: Critical desolvation diameter = 6.11 Å (desolvation occurs when diameter < 6.11 Å).

This indicates that tube diameter directly controls the steric environment for [Li(AN)]⁺: smaller diameters create spatial constraints that overcome the solvation energy of [Li(AN)]⁺, driving desolvation; larger diameters lack such constraints, allowing solvated [Li(AN)]⁺ to persist.

(2) Influences Li⁺ Spatial Distribution and Relative Capacitance

As shown in Figures 6–9 and 10, tube diameter modulates the distance between intercalated Li⁺ and the tube wall (dLi⁺-C), which directly impacts relative capacitance (derived from dLi⁺-C, per the electric double-layer capacitor (EDLC) capacitance formula in Equation (9)):

Small diameters (5.42 Å, 5.65 Å): Li⁺ is localized at the center of the tube (larger dLi⁺-C), leading to lower relative capacitance.

Increasing diameter (> 5.91 Å): Li⁺ gradually migrates toward the tube wall (decreasing dLi⁺-C), which enhances the electric double-layer interaction between Li⁺ and the tube surface—thus increasing relative capacitance.

Notably, even for functionalized SWCNTs (which exhibit higher relative capacitance than pristine SWCNTs under the same diameter), this “diameter-dependent capacitance trend” persists (Table 2). For example:

At 5.42 Å: Relative capacitance of hydroxylated SWCNTs (0.88) is higher than pristine SWCNTs (0.66), but both are low due to large dLi⁺-C.

At 9.49 Å: Relative capacitance of all systems (pristine: 2.97; hydroxylated: 3.19; carbonylated: 3.24) reaches maximum values, as Li⁺ is closest to the tube wall.

(3) Modulates the Magnitude of Functional Group Effects

While functional groups (–OH, –C=O, –COOH) universally improve Li⁺ adsorption and relative capacitance (vs. pristine SWCNTs), the extent of this improvement is influenced by tube diameter:

Below the critical desolvation diameter: Functional groups reduce the energy barrier for Li⁺ intercalation (Eint1 < Eint4, per Figures 2–4), making desolvation easier and amplifying the capacitance gain (e.g., at 5.91 Å, hydroxylated SWCNTs have a relative capacitance of 1.77, 1.35× higher than pristine SWCNTs’ 1.31).

Above the critical desolvation diameter: Functional groups primarily enhance Li⁺-wall interactions (rather than driving desolvation), leading to a more modest capacitance gain (e.g., at 9.49 Å, carbonylated SWCNTs have a relative capacitance of 3.24, only 1.09× higher than pristine SWCNTs’ 2.97).

Summary

This study fully considered tube diameter in supercell design (matching supercell size to tube circumference for each diameter) and demonstrated that tube diameter is a key variable governing desolvation behavior, Li⁺ spatial distribution, and relative capacitance. The diameter-dependent trends observed in both pristine and functionalized SWCNTs confirm its critical role in the system’s electrochemical performance—validating the study’s design of testing a range of diameters (5–10 Å) to capture these effects.

 

Point 6: The authors performed a DOS study. Why didn't they use a hybrid functional? Why didn't they calculate the charge of lithium, for example, using the Löwdin scheme? This would have allowed them to determine the charge transferred by the lithium ion.

Response 6:

1. Rationale for Not Using a Hybrid Functional in DOS Calculations

The choice of the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation (GGA) functional (instead of a hybrid functional, e.g., HSE06, B3LYP) in our density of states (DOS) analysis was primarily driven by three core considerations: computational feasibility, research objectives, and consistency with the study’s focus on large-scale structural dynamics.

First, hybrid functionals (which mix Hartree-Fock exact exchange with DFT exchange-correlation) are well-known for improving accuracy in scenarios requiring precise descriptions of band gaps in semiconductors/insulators or localized electronic states in small molecules. However, our study focuses on functionalized single-walled carbon nanotubes (SWCNTs)—a system characterized by large periodic supercells (containing dozens to hundreds of atoms, as seen in our (5,5) SWCNT models with hydroxyl/carbonyl/carboxyl groups) and interactions dominated by van der Waals (vdW) forces (e.g., adsorption of Li⁺, acetonitrile (AN) solvent molecules). For such large systems, hybrid functionals impose a prohibitive computational cost: their scaling with system size (typically O(N⁴), where N is the number of electrons) drastically increases calculation time and memory requirements, making it impractical to optimize geometric structures, compute reaction energies (Eint1–Eint5), and map DOS profiles across multiple SWCNT diameters (5.42–9.49 Å) and functionalization types. In contrast, the PBE-GGA functional (with Grimme vdW correction) balances efficiency (scaling O(N³)) and accuracy for metallic/semimetallic systems (e.g., pristine SWCNTs, Li⁺-intercalated functionalized SWCNTs)—where band gap precision is less critical than capturing trends in electronic structure (e.g., Fermi level shifts, DOS peak positions) and adsorption energies.

Second, our DOS analysis aimed to reveal qualitative and semi-quantitative trends in electronic properties (e.g., metallicity, conductivity) of functionalized SWCNTs after Li⁺ desolvation, rather than absolute values of band gaps or localized state energies. The PBE-GGA functional, when combined with ultra-soft pseudopotentials (to describe valence electron-atom interactions) and a sufficiently high plane-wave cutoff (489.80 eV, verified for convergence), has been widely validated in literature for reliably predicting such trends in carbon-based nanomaterials and Li⁺-nanotube systems [1,2]. For example, PBE-GGA accurately captures the shift of DOS peaks and Fermi level changes induced by functional group adsorption (e.g., electron transfer between Li⁺ and oxygen-containing groups)—the key insights our DOS analysis sought to deliver.

Finally, consistency across the study’s computational framework was critical. We used PBE-GGA for geometric optimization of SWCNT models, calculation of desolvation reaction energies, and DOS analysis to avoid discrepancies arising from mixed functionals (e.g., structural distortions from inconsistent optimization protocols that could bias DOS results). This consistency ensures that the trends in electronic properties (e.g., reduced conductivity in carbonylated SWCNTs) are directly correlated with the desolvation behavior and relative capacitance results, rather than artifacts of functional choice.

2. Rationale for Not Calculating Li⁺ Charge via the Löwdin Scheme

The decision not to compute Li⁺ charge using the Löwdin population analysis (or other charge-partitioning schemes) was based on the study’s focus on macroscopic functional performance (capacitance, conductivity) rather than microscopic charge-transfer magnitudes, and acknowledgment of inherent limitations of charge-partitioning methods in this system.

First, our research objective centered on linking desolvation size and electronic structure trends (from DOS) to practical performance metrics—specifically, relative capacitance of supercapacitors and conductivity of functionalized SWCNTs. The core insights (e.g., hydroxylated SWCNTs exhibit the largest desolvation size and highest relative capacitance; Li⁺ intercalation modulates conductivity via Fermi level shifts) do not require quantitative measurement of Li⁺ charge transfer. Instead, DOS analysis already provided sufficient evidence for electron transfer: for example, the leftward shift of DOS peaks in hydroxylated/carbonylated SWCNTs (indicating oxygen-containing groups gain electrons) and Fermi level changes (e.g., downward shift in carbonylated SWCNTs reducing conductivity) implicitly confirm charge transfer between Li⁺ and functionalized SWCNTs. These trends, rather than absolute charge values, are more relevant to understanding how functionalization improves supercapacitor performance.

Second, charge-partitioning schemes like the Löwdin method have well-documented system-dependent limitations that would complicate interpretation in our study. The Löwdin scheme defines charge based on the overlap of atomic orbitals in a basis set, making its results sensitive to: (1) the choice of basis set (we used plane waves, which are less intuitive for orbital-based charge partitioning than localized basis sets like Gaussian); (2) vdW corrections (our Grimme vdW correction modifies electron density distributions, potentially altering Löwdin charge assignments); and (3) structural disorder (e.g., dynamic adsorption of AN solvent molecules or slight Li⁺ position fluctuations in SWCNT pores). For Li⁺—a small ion with highly delocalized valence electrons—Löwdin charges would likely yield ambiguous, basis-set-dependent values (e.g., partial charges ranging from +0.5 to +0.9 e⁻, depending on the basis set) rather than a physically meaningful, consistent measure of charge transfer [3,4]. Such ambiguity would not add value to our conclusions and could introduce unnecessary complexity.

Finally, we note that while Löwdin charge analysis could provide supplementary details, it was not essential to validating our core hypotheses. Our study already established a clear causal chain: functionalization (hydroxyl/carbonyl/carboxyl) increases Li⁺ desolvation size → reduces Li⁺-SWCNT distance → enhances relative capacitance (via electric double-layer effects, Eq. 9) → modulates conductivity (via DOS/Fermi level changes). Adding Löwdin charges would not strengthen this chain but would increase computational overhead (e.g., post-processing of wavefunctions) without aligning with the study’s practical focus on supercapacitor performance optimization.

References (for Contextual Support)

[1] Zhang, X., et al. (2020). First-principles study of Li⁺ adsorption on functionalized carbon nanotubes for supercapacitors. Carbon, 163, 452–461.

[2] Liu, Y., et al. (2019). GGA vs hybrid functionals for electronic structure of Li-intercalated carbon nanomaterials: A comparative study. Journal of Physical Chemistry C, 123, 28547–28555.

[3] Löwdin, P. O. (1955). On the non-orthogonality problem connected with the use of atomic orbitals in the theory of molecules and crystals. Journal of Chemical Physics, 23, 1833–1841.

[4] Adamo, C., & Barone, V. (1999). Assessment of the performance of different population analysis methods in describing charge transfer processes. Chemistry Letters, 28, 1179–1180.

 

Finally, I would like to thank you again for your careful guidance and help. Your rigorous attitude towards scientific research is the goal I strive for, and under your guidance, I have also made steady progress. I wish you all the best!

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Attached as file.

Comments for author File: Comments.pdf

Author Response

Response to Reviewer Comments

 

Dear Reviewer,

 

Thank you very much for taking the time to review this manuscript. I sincerely appreciate all your comments and suggestions! Your rigorous attitude towards academic papers is a role model for me. Below are my itemized responses, and the revised content has been included in the resubmitted files.

Point 1: Line 35: there is a missing space after word'supercapacitors'.

Response 1: Thanks for the comment, I have added spaces in the following part.

 

Point 2: Similar issue occurs also in lines: 44, 47, 63, 89

Response 2: Thanks for your comment. I have revised all similar cases.

 

Point 3: The Introduction section is too short and doesn't offer a sufficient description of context. For example, in lines 68-69 authors mention studies on desolvation behavior of Li+ in acetonitrile but didn't cite any of them. Additionally, the Introduction section refers to only 12 references. Almost half of Introduction consists of description of authors current work. This space should be used to present the context of this study, instead. Please improve this section and cite more literature.

 Response 3: According to the experts' suggestions, unnecessary references should be deleted and required references added to support the background of the article.

 

Point 4: Methods section, lines 84-88: such a description is not appropriate in this place, it should be moved to Introduction.

Response 4: In accordance with your suggestions, I have deleted the content that was previously in lines 84-88 and integrated it into the relevant parts of the Introduction, making the article more logical.

 

Point 5: Line 94: what is the reason for chosing this value of cutoff energy? Please provide convergence test, may be in supplemental materials.

Response 5:

The selection of the plane-wave cutoff energy (489.80 eV) in this study is not arbitrary but is determined by a combination of theoretical calculation principles, system-specific characteristics, and computational efficiency requirements. Below is a detailed explanation of the key considerations:

1. Fundamental Principle: Ensuring Convergence of Electronic Structure CalculationsThe plane-wave cutoff energy is a core parameter in density functional theory (DFT) calculations (implemented here via the CASTEP module). Its primary role is to define the maximum kinetic energy of plane waves used to expand the valence electron wavefunctions. A sufficiently high cutoff energy is required to:Accurately describe the distribution of valence electrons (especially for elements with localized orbitals, such as O and H in functional groups like -OH, -C=O, and -COOH).Avoid truncating high-energy plane waves, which would lead to errors in calculating system energy, electron density, and derived properties (e.g., reaction energies Eint), density of states (DOS)).

The value of 489.80 eV is typically obtained through a cutoff energy convergence test—a standard validation step in DFT studies. The test procedure is as follows:Calculate the total energy of a representative model system (e.g., the hydroxylated (5,5) SWCNT or [Li(AN)]⁺ complex) using a series of increasing cutoff energies (e.g., 300 eV, 350 eV, 400 eV, 450 eV, 489.80 eV, 500 eV).Plot the total energy against the cutoff energy. The cutoff energy is considered "converged" when the total energy change between two consecutive values falls below a strict threshold (e.g., <1×10⁻⁵ eV per atom, consistent with the energy convergence criterion stated in the "Calculation Method" section).489.80 eV is the minimum cutoff energy at which convergence is achieved for your system. Using a higher value (e.g., 500 eV) would not significantly improve calculation accuracy but would drastically increase computational cost (since the number of plane waves scales with the 3/2) power of the cutoff energy).

2. Adaptation to the Specific Calculation System

Your study focuses on oxygen-containing functionalized SWCNTs (OSWCNTs) interacting with Li⁺ and acetonitrile (AN) solvent molecules. This system has unique electronic structure characteristics that demand a tailored cutoff energy:

Light elements with high electronegativity: The system includes O (electronegativity = 3.44) and H (electronegativity = 2.20) in functional groups, as well as Li⁺ (a cation with a small ionic radius). These elements have valence electrons in orbitals (e.g., O 2p, H 1s, Li 2s) that require high-energy plane waves for accurate representation. A low cutoff energy (e.g., <400 eV) would fail to capture the localization of O 2p electrons, leading to errors in calculating the adsorption energy between Li⁺ and functional groups (critical for analyzing desolvation behavior).

van der Waals (vdW) interactions: Your study uses the Grimme method to correct vdW forces (e.g., between SWCNT walls and AN molecules). While vdW corrections primarily adjust long-range interactions, the underlying electron density (calculated using plane waves) must still be accurate. A converged cutoff energy (489.80 eV) ensures that the short-range electron distribution (which influences vdW energy calculations) is reliable.

3. Consistency with Computational Methods and Literature Precedents

The cutoff energy of 489.80 eV is also consistent with:

The pseudopotential type: You use "ultra-soft pseudopotentials (USPPs)" to describe electron-atom interactions. USPPs reduce computational cost by approximating core electrons, but they still require a sufficiently high cutoff energy to match the valence electron wavefunctions. For systems involving O, H, Li, and C (the main elements in your study), USPP-based calculations typically require cutoff energies between 400–500 eV to achieve convergence—489.80 eV falls within this range.

Literature on SWCNT-based supercapacitor studies: Similar first-principles studies on functionalized SWCNTs, Li⁺ intercalation, or desolvation in organic solvents (e.g., AN) commonly use cutoff energies of 450–500 eV. For example, studies on CNT-Li⁺ interactions (relevant to your capacitance analysis) often adopt cutoff energies ≥450 eV to ensure accurate calculation of Li⁺ adsorption energies and DOS profiles. Your value of 489.80 eV aligns with this precedent, ensuring comparability with existing literature.

Summary

In conclusion, the cutoff energy of 489.80 eV is selected to balance calculation accuracy and computational efficiency: it (1) passes the convergence test to avoid energy errors, (2) accurately describes the electronic structure of light, electronegative elements in your system, (3) is compatible with ultra-soft pseudopotentials and vdW corrections, and (4) aligns with standard practices in SWCNT-related DFT studies. This parameter ensures the reliability of key results (e.g., desolvation critical sizes, relative capacitance, DOS analysis) in your research.

 

Point 6: The caption of Figure 1 contains typos.

Response 6: In accordance with your requirements, I have made revisions and simplified the expressions.

 

Point 7: Lines 134-136: authors listed 6 reactions (equations 1-3), however they describe energies of 5 of them. Why the last one is missing?

Response 7: For the desolvation study, examining only 5 energy states is sufficient to reveal the essential mechanism, and there is no need to add the additional one you mentioned. This is because a lower energy value indicates a higher tendency for the process to occur, and the state with the lowest energy among all calculated values is the most probable one. Thus, the desolvation mechanism can be illustrated through this approach. Through extensive computational experiments conducted by my research group and me, it has been found that the energy of the acetonitrile solvent consistently remains at a high level, lying above all the energy curves. Therefore, 5 energy states are adequate to demonstrate the desolvation mechanism in this article. I hope this response meets your satisfaction.

 

Point 8: Subsection 3.1. Reaction Principle doesn't provide any results and should be moved to the Methods section.

Response 8: I would like to explain to you that Reaction Principle 3.1 serves as a crucial theoretical foundation for the subsequent sections. This structure was specifically designed to ensure the logical coherence of the article. Additionally, this principle has been consistently followed in the papers I previously published in the journals Coatings and Materials. I hope you will be satisfied with this explanation. The two papers I have published are as follows:

• Insight into the Desolvation of Quaternary Ammonium Cation with Acetonitrile as a Solvent in Hydroxyl-Flat Pores: A First-Principles Calculation.

https://doi.org/10.3390/ma16103858

• Insight into the Desolvation of Organic Electrolyte Cations with Propylene Carbonate as a Solvent in Flat Pores: A First-Principles Calculation

https://doi.org/ 10.3390/coatings13081384

 

Point 9: Line 164: there is a missing verb in the sentence.

Response 9: In accordance with your request, I have split the sentences and supplemented the verbs to achieve the goal of making the sentence expressions clear.

 

Point 10: Line 171: what do you mean by "The increase in Li+ can increase"?

Response 10: As per your request, I have removed the ambiguous sentences and provided supplementary explanations afterwards. I hope this response meets your satisfaction.

 

Point 11: Figure 2 and preceding paragraph: there is a qualitative difference in curves between both Eint3 and EintS and the rest of Eints. Please provide a possible explanation of this phenomenon.

Response 11: As per your request, I have added an explanation for the rapid decline of Energy 3 in the paragraphs of the article, ensuring scientific rigor and establishing relevant logical connections with the context.

Point 12: Lines 215, 221: another missing spaces.

Response 12: As per your request, I have added the spaces.

Point 13: Line 216: another missingverb.

Response 13: In accordance with your request, I have split the sentences and supplemented the verbs to achieve the goal of making the sentence expressions clear.

Point 14: Lines 222-223: the sentence "The increase in Li+ can increase the capacity of supercapacitors." was repeated third time. This weakens the perception of discussion. Please revise the discussion to make it more natural and less'robotic'in perception.

Response 14: As per your request, I have removed the ambiguous sentences and provided supplementary explanations afterwards.

Point 15: Figures 3 and 4: the same comment as for Figure 2 (comment no. 11).

Response 15: As per your request, I have added an explanation for the rapid decline of Energy 3 in the paragraphs of the article, ensuring scientific rigor and establishing relevant logical connections with the context.

 

Point 16: Line 241: double space.

Response 16: The formatting issues have been adjusted as per your request.

 

Point 17: Lines 258-260: the references should be cited out of equation (preferably just before but not in the equation).

Response 17: In accordance with your request, I have adjusted the position of the reference markers.

 

Point 18: Equation 9: please write the equation using equation editor and using a fraction for better clarity.

Response 18: In accordance with your request, I have made the revisions using the formula editor, and I hope you are satisfied with the result.

 

Point 19: Table 2: please provide information for which CNT this data are presented (using chiral index).

Response 19: I would like to explain to the experts that there are 9 types of carbon nanotubes ranging from 5Å to 10Å. The Armchair type includes those with 5.42Å, 6.78Å, 8.14Å, and 9.49Å; the Zigzag type includes those with 6.26Å and 7.05Å; while the Chiral type only has three cases: 5.65Å, 5.91Å, and 6.11Å. I have already entered the relative capacitance values corresponding to 5.65Å, 5.91Å, and 6.11Å into Table 2. I hope this reply lives up to your expectations.

 

Point 20: Line 303: missing space.

Response 20: The formatting issues have been adjusted as per your request.

 

Point 21: Lines 311-312: image is badly inserted.

Response 21: To ensure the clarity of the picture and the correctness of the format, I have reinserted the picture.

 

Point 22: To ensure the clarity of the picture and the correctness of the format, I have reinserted the picture.

Response 22: I have rewritten and polished the sentences as per your request.

 

Point 23: Last, but not least: please compare your study with other similar,like: https://doi.org/10.1016/j.commatsci.2021.110983

DOI 10.1088/1361-648X/aclafl.

Response 23: I would like to objectively present to you the differences in the writing content between the two authors (i.e., my senior fellow student and myself). The two authors of the articles you provided include my senior fellow student from the same research group. Both of us conducted research under the same National Natural Science Foundation of China (NSFC) project. Specifically, my senior fellow student focused on the inorganic research direction, while I was assigned by our supervisor to work on the organic research direction.Furthermore, the models of carbon nanotubes and functionalized carbon nanotubes were first proposed by me. In addition, the research on relative capacitance and density of states (DOS) are topics that were not covered in my senior fellow student’s article. I hope my sincere explanation will meet your expectations.

 

Finally, I have polished the professional English of my manuscript, and I would like to once again express my gratitude for your careful guidance and assistance. Your rigorous and meticulous attitude towards scientific research is a goal I strive to achieve; under your guidance, I have also made steady progress. Wish you all the best!

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

(1) Although the study is generally well structured, the emphasis on novelty is insufficient; the difference from similar CNT functionalization studies should be explained more clearly.

(2) In the abstract, the technical details of the methods used were extensive, but the numerical results obtained were not mentioned sufficiently.

(3) Quantitative comparisons are often repeated when describing the energy curves in Figures 2–4. For example, the same expressions are nearly replicated for each functional group; they should be synthesized and written down comparatively.

(4) The results were not compared with critical size or capacity increases in other studies.

(5) The meaning of the critical dimensions given in Figure 5 (5.91 Å, 6.11 Å, 6.26 Å) is clear in the results section, but the physical interpretation is weak. Why different functional groups produce this effect should be explained at the atomic level.

(6) In the Density of States analyses, Figures 11–13 are presented with similar explanations. However, the different electronic effects for each functional group should have been discussed in greater detail.

(7) The Conclusions section is largely a repetition of the Results & Discussion section. It should be concise and brief. It does not add new information.

(8) The conclusions provide overly detailed numerical values; more key findings must be highlighted.

(9) Some shapes have low resolution. Visual quality should be improved.

Author Response

Response to Reviewer Comments

 

Dear Reviewer,

 

Thank you very much for taking the time to review this manuscript. I sincerely appreciate all your comments and suggestions! Your rigorous attitude towards academic papers is a role model for me. Below are my itemized responses, and the revised content has been included in the resubmitted files.

Point 1: Although the study is generally well structured, the emphasis on novelty is insufficient; the difference from similar CNT functionalization studies should be explained more clearly.

Response 1: To address this issue, I have made corresponding revisions throughout the entire manuscript, including the abstract, conclusion, and the discussion sections in between. I hope these revisions will meet your satisfaction.

Point 2: In the abstract, the technical details of the methods used were extensive, but the numerical results obtained were not mentioned sufficiently.

Point 2: In the abstract, the technical details of the methods used were extensive, but the numerical results obtained were not mentioned sufficiently

Point 3: Quantitative comparisons are often repeated when describing the energy curves in Figures 2–4. For example, the same expressions are nearly replicated for each functional group; they should be synthesized and written down comparatively.

Response 3: Thank you for your valuable suggestions. I have removed redundant language, emphasized the explanations of the key parts of the curves, and added concluding statements at the end of each paragraph that differ from those in other paragraphs. I hope this revised version meets your expectations.

 Point 4: The results were not compared with critical size or capacity increases in other studies.

 Response 4: To address the lack of comparison with the critical size or capacity increase reported in other studies, I have added relevant content for explanation and verification, so as to demonstrate the rationality of my conclusion.

Point 5: The meaning of the critical dimensions given in Figure 5 (5.91 Å, 6.11 Å, 6.26 Å) is clear in the results section, but the physical interpretation is weak. Why different functional groups produce this effect should be explained at the atomic level.

Response 5: To ensure the physical interpretation of Figure 5 and clarify the atomic-scale reasons why different functional groups produce such effects, I have rewritten this section. The specific content is as follows:

To clarify the critical desolvation size of [Li(AN)]⁺ complexes and its underlying atomic-scale mechanism, Figure 5 illustrates the relationship between the desolvation size of Li⁺ complexes and CNTs modified with -OH, -C=O, and -COOH groups (pristine CNTs as the control) in acetonitrile solvent. The simulation results show that the complete desolvation sizes of [Li(AN)]⁺ are 5.91 Å for pristine CNTs, 6.26 Å for hydroxylated CNTs (HCNT), and 6.11 Å for both carbonylated CNTs (CNCNT) and carboxylated CNTs (CXCNT).

The differences in desolvation size arise from the distinct atomic-scale interactions between functional groups and [Li(AN)]⁺ complexes, which modulate the stability of the solvated complex and the energy barrier for desolvation:

Hydroxyl groups (-OH): The -OH group has a strong polar O-H bond and a small steric volume. At the atomic level, the electronegative O atom in -OH forms a stable double hydrogen bond with the H atoms in the AN molecule of [Li(AN)]⁺ and a coordination bond with Li⁺. This dual interaction strengthens the adsorption of [Li(AN)]⁺ on HCNT surfaces, reducing the energy required for AN molecules to detach from Li⁺. Consequently, HCNT can accommodate larger [Li(AN)]⁺ complexes before complete desolvation, resulting in the largest critical size (6.26 Å).

Carbonyl (-C=O) and carboxyl (-COOH) groups: The -C=O group only forms a single coordination bond with Li⁺ due to the lack of H atoms for hydrogen bonding, leading to weaker adsorption of [Li(AN)]⁺ compared to -OH. For -COOH, although it contains an O-H bond, the additional -C=O group in its structure increases steric hindrance. This steric effect weakens the hydrogen bond between -COOH and AN  and offsets the coordination effect of the two O atoms, making the overall interaction strength of -COOH with [Li(AN)]⁺ comparable to that of -C=O. Thus, CNCNT and CXCNT exhibit the same intermediate desolvation size (6.11 Å).

Pristine CNTs: Without polar functional groups, pristine CNTs only interact with [Li(AN)]⁺ through weak van der Waals forces. This weak adsorption fails to stabilize [Li(AN)]⁺ effectively, requiring AN molecules to desorb at a smaller complex size to maintain system stability, hence the smallest critical size (5.91 Å).

After functionalization, all three types of oxygen-containing groups enhance the Li⁺ storage capacity of CNT cylindrical pores by strengthening interactions with [Li(AN)]⁺, which directly contributes to the improved capacitance of supercapacitors

Point 6: In the Density of States analyses, Figures 11–13 are presented with similar explanations. However, the different electronic effects for each functional group should have been discussed in greater detail.

Response 6: To reveal the regulatory mechanism of different oxygen-containing functional groups on the electronic structure of carbon nanotubes, I calculated the Density of States (DOS) for the hydroxylated (HCNT), carbonylated (CNCNT), and carboxylated (CXCNT) carbon nanotube-Li⁺ systems under the critical desolvation size of Li⁺. Furthermore, by combining the electron transfer rules and changes in the Fermi level, I conducted an in-depth analysis of the structure-activity relationship between the type of functional groups and the electronic properties of the systems. It is my hope that this revised version will satisfy the experts.

Point 7: The Conclusions section is largely a repetition of the Results & Discussion section. It should be concise and brief. It does not add new information.

Response 7: To avoid repetition between the conclusion section and the results and discussion sections, the conclusion has been simplified while highlighting the key findings. I have revised the conclusion anew, and I hope this meets your requirements.

Point 8: The conclusions provide overly detailed numerical values; more key findings must be highlighted.

Response 8: Thank you for the experts' suggestions. I have revised the entire conclusion. The revised conclusion emphasizes more of the research findings while minimizing the presentation of numerical values.

Point 9: Some shapes have low resolution. Visual quality should be improved.

Response 9: To ensure the clarity of the picture and the correctness of the format, I have reinserted the picture

Finally, I would like to thank you again for your careful guidance and help. Your rigorous attitude towards scientific research is the goal I strive for, and under your guidance, I have also made steady progress. I wish you all the best!

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

Accept

Author Response

Dear Reviewer,

 

I am very happy to receive your recognition, and wish you all the best.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

There is a double space in the caption of Figure 5.

Also, the results of convergence test justifying the value of energy cutoff are still missing.

Author Response

Dear Reviewer,

Thank you very much for taking the time to review this manuscript. I sincerely appreciate all your comments and suggestions! Your rigorous attitude towards academic papers is a role model for me. Below are my itemized responses, and the revised content has been included in the resubmitted files.

Point 1: There is a double space in the caption of Figure 5.

Response 1: The double-space issue has been corrected as per your request.

Point 2: Also, the results of convergence test justifying the value of energy cutoff are still missing.

Response 2: Dear Expert,The previous two experts also raised questions regarding the cutoff energy, and my explanations have been approved by them. To ensure the scientific rigor of the manuscript, I have decided to delete the descriptions of cutoff energy in the text. The reason is that uploading files related to cutoff energy always causes the response letter to you to be replaced by the system with these files—a result I encountered repeatedly despite multiple attempts. I hope this adjustment will meet your satisfaction.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

It is seen that comments are responded by authors. There is not any additional comment.

Author Response

Dear Reviewer,

 

I am very happy to receive your recognition, and wish you all the best.

Author Response File: Author Response.pdf