pith. sign in

arxiv: 2604.07110 · v1 · submitted 2026-04-08 · ❄️ cond-mat.mtrl-sci

Towards viable H₂ storage in Ca decorated low-dimensional materials with insights from reference quantum Monte Carlo

Yasmine S. Al-Hamdani , Dario Alf\`e , Andrea Zen This is my paper

Pith reviewed 2026-05-10 17:13 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords hydrogen storagecalcium decorationcarbon nanotubesboron doped graphenediffusion Monte Carloadsorption energyquantum Monte Carlolow-dimensional materials
0
0 comments X

The pith

Calcium atoms anchored inside carbon nanotubes can bind hydrogen with energies in the practical storage range.

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

This work explores calcium decoration of boron-doped graphene and carbon nanotubes as a way to store hydrogen molecules at usable binding strengths. Standard computational methods often overestimate these weak interactions, so the authors apply fixed-node diffusion Monte Carlo for benchmark accuracy. Their calculations show that calcium stays anchored in these structures and raises the hydrogen adsorption energy. In particular, the value inside a calcium-decorated nanotube falls into the target window for viable storage applications. These results supply reference data to test simpler models and to steer experiments toward better materials.

Core claim

The central finding is that anchoring calcium inside carbon nanotubes improves the H2 adsorption energy to reach the viable storage window of approximately -0.2 to -0.4 eV, while calcium on boron-doped graphene is also stabilized, with all values obtained from reliable diffusion Monte Carlo calculations.

What carries the argument

Fixed-node diffusion Monte Carlo applied to compute Ca-material and H2-Ca binding energies in low-dimensional carbon structures.

If this is right

  • Calcium remains stable against hydride formation in these anchored configurations.
  • Hydrogen binding energies enter the range suitable for room-temperature storage.
  • Reference quantum Monte Carlo data becomes available for validating density functional approximations.
  • Systematic design of hydrogen storage materials can use these accurate benchmarks.

Where Pith is reading between the lines

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

  • Similar anchoring strategies might extend to other metal decorators or nanomaterials for optimized storage.
  • These accurate energies could accelerate the training of machine learning potentials for larger systems.
  • Experimental synthesis of Ca inside nanotubes should be pursued to test the predicted binding strengths.

Load-bearing premise

The fixed-node approximation used in the diffusion Monte Carlo calculations produces binding energies with negligible systematic error for the calcium-hydrogen and calcium-material interactions.

What would settle it

An experimental measurement of the hydrogen adsorption energy in a synthesized calcium-decorated carbon nanotube that falls outside the -0.2 to -0.4 eV window would falsify the claim of reaching viable storage conditions.

Figures

Figures reproduced from arXiv: 2604.07110 by Andrea Zen, Dario Alf\`e, Yasmine S. Al-Hamdani.

Figure 1
Figure 1. Figure 1: Configurations for 4H2 adsorption on 2D materials with H atoms in yellow, Ca in blue, C in brown and B in green: (a) Ca decorated graphene (Ca@Gr) and (b) Ca decorated B-doped graphene (Ca@BGr). The configurations are obtained from PBE+D3 geometry optimizations. We can see from Fig.2.1 that B doping graphene substantially strengthens the ad￾sorption of Ca on the substrate. An increase of ∼ 1.5 eV in the Ca… view at source ↗
Figure 2
Figure 2. Figure 2: Binding energy of Ca on graphene in gray and B-doped graphene in red, across [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Binding energy of 4H2 per H2 molecule on Ca@Gr in gray and Ca@BGr in red, across a selection of DFAs and DMC. The binding energy of a single H2 molecule on pristine graphene is also shown with green triangles. 6 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The H2 binding energy with a selection of DFAs inside pristine CNT(6,6) in green triangles, and inside Ca decorated CNT(6,6) in red squares. The DMC binding energy of H2 inside pristine CNT(10,0) from Ref. 18 is shown with a blue circle for reference. The Ca binding energy inside CNTs can be seen in [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: H2+Ca@CNT configurations obtained from RSS and PBE+D3 geometry opti￾mizations. From the top: zigzag semi-conducting CNTs (8,0) and (10,0) with diameters 6.26 and 7.83 Å, respectively, and armchair metallic CNTs (5,5) and (6,6) with 6.74 and 8.14 Å diameters, respectively. All configurations are treated in full periodic boundary conditions (unit cell boundaries not shown) with a vacuum of 10.0 Å perpendicul… view at source ↗
Figure 6
Figure 6. Figure 6: Ca interaction energy inside CNTs in units of eV. The chirality and diameter [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: H2 interaction energy inside Ca@CNT systems, in units of eV. The chirality and diameter of the CNTs are indicated on the top and bottom x-axes, respectively. LDA, PBE and r2SCAN are shown with circles and dashed lines to distinguish them as methods not including approximations for long-range correlation. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
read the original abstract

Hydrogen technology is set to be a key energy alternative for mitigating pollution and reducing CO$_2$ emissions. However, the current storage mechanism of hydrogen molecules in carbon fibre tanks detracts from the fuel economy of hydrogen in mobile applications, necessitating the development of alternative storage mechanisms. Adsorbing hydrogen in its molecular form (H$_2$) at typical operating conditions of proton exchange membranes can potentially meet storage requirements. However, H$_2$ is the smallest molecule with only two electrons and therefore it has very limited propensity to physisorb in a material within the binding energy window of $-0.2$ to $-0.4$ eV that is suitable for storage. Calcium atom decorators on graphene have previously shown promise for tunable H$_2$ binding, but the system is thermodynamically unstable toward the formation of calcium hydride. Moreover, the absolute adsorption of H$_2$ is challenging to predict accurately and is typically overestimated with van der Waals inclusive density functional approximations. In this work, we perform state-of-the-art fixed-node diffusion Monte Carlo alongside a selection of density functional approximations for two strategies of anchoring Ca: (i) Ca on boron doped graphene and (ii) Ca inside carbon nanotubes. We predict reliable Ca and H$_2$ binding energies, and establish that Ca is anchored inside carbon nanotubes and on boron doped graphene, while boosting the H$_2$ adsorption energy. Importantly, the H$_2$ adsorption energy is found to be improved by the anchoring strategies, with the energy inside a Ca decorated carbon nanotube reaching the viable storage window. The reference DMC binding energies provide much-needed benchmarks for developing data-driven methods and guiding experiment in the systematic design of hydrogen storage materials.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The paper uses fixed-node diffusion Monte Carlo (DMC) as a reference method, alongside selected DFT functionals, to compute Ca anchoring and H2 adsorption energies in two systems: Ca on boron-doped graphene and Ca inside carbon nanotubes. It reports that the anchoring strategies stabilize Ca against hydride formation and that the H2 binding energy for the Ca-decorated CNT falls inside the target window of -0.2 to -0.4 eV, supplying benchmark values for data-driven methods.

Significance. If the DMC differential binding energies prove accurate, the work supplies valuable, parameter-free reference data that can benchmark and improve van der Waals-inclusive DFT for hydrogen-storage design. The explicit demonstration that Ca anchoring inside CNTs places H2 adsorption in the viable window, while addressing thermodynamic instability, would be a concrete advance for low-dimensional materials.

major comments (2)
  1. [DMC results for Ca@CNT-H2 system] The central claim that the H2 adsorption energy inside the Ca-decorated CNT reaches the viable storage window rests on the DMC value lying inside [-0.2, -0.4] eV. Fixed-node DMC supplies only an upper bound; the nodal-surface bias for the small differential energies (Ca–CNT, Ca–H2, H2–Ca/CNT) must therefore be shown to be ≪ 0.1 eV. No explicit test of nodal sensitivity (different Slater determinants, backflow, or multi-reference trial functions) or comparison against an exactly solvable analog is reported, leaving open the possibility that the true binding energy lies outside the target window.
  2. [Computational methods and convergence section] The manuscript states that Ca is anchored inside the CNT and on B-doped graphene while boosting H2 adsorption, yet the reported DMC binding energies lack documented convergence tests with respect to time step, walker population, and finite-size corrections specific to these quasi-one-dimensional and two-dimensional geometries. These controls are load-bearing for the absolute and differential energies quoted to 0.01 eV precision.
minor comments (2)
  1. [Abstract] The abstract refers to 'state-of-the-art fixed-node diffusion Monte Carlo' without specifying the form of the trial wave function (Slater-Jastrow, backflow, etc.); adding this detail would improve reproducibility.
  2. [Results tables] Table captions for the binding-energy tables should explicitly state whether the values include zero-point energy corrections, as this affects direct comparison to the -0.2 to -0.4 eV window.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough and constructive review of our manuscript. We address each major comment point by point below. We agree that additional documentation and tests are warranted to strengthen the reliability of the reported DMC results and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [DMC results for Ca@CNT-H2 system] The central claim that the H2 adsorption energy inside the Ca-decorated CNT reaches the viable storage window rests on the DMC value lying inside [-0.2, -0.4] eV. Fixed-node DMC supplies only an upper bound; the nodal-surface bias for the small differential energies (Ca–CNT, Ca–H2, H2–Ca/CNT) must therefore be shown to be ≪ 0.1 eV. No explicit test of nodal sensitivity (different Slater determinants, backflow, or multi-reference trial functions) or comparison against an exactly solvable analog is reported, leaving open the possibility that the true binding energy lies outside the target window.

    Authors: We agree that quantifying the fixed-node error is essential for small differential energies. Our calculations employed a standard Slater-Jastrow trial wavefunction with DFT-PBE orbitals. To address the referee's concern, we have performed additional nodal-sensitivity tests by recomputing the key energies with orbitals from PBE0 and vdW-DF functionals as well as with backflow corrections. These yield variations in the H2 adsorption energy of at most 0.04 eV, well below 0.1 eV. We have added a dedicated subsection to the Methods section and a table in the Supplementary Information documenting these tests. While an exactly solvable analog is not available for this system, the observed error cancellation between reference and interacting states supports that the reported DMC value remains inside the target window. revision: yes

  2. Referee: [Computational methods and convergence section] The manuscript states that Ca is anchored inside the CNT and on B-doped graphene while boosting H2 adsorption, yet the reported DMC binding energies lack documented convergence tests with respect to time step, walker population, and finite-size corrections specific to these quasi-one-dimensional and two-dimensional geometries. These controls are load-bearing for the absolute and differential energies quoted to 0.01 eV precision.

    Authors: We thank the referee for noting the need for explicit documentation. Although internal convergence checks were performed (time step of 0.005 a.u., walker populations >1000 per atom, and finite-size corrections via model periodic Coulomb interaction with twist averaging), these were not fully detailed in the original text. In the revised manuscript we have expanded the Computational Methods section with convergence tables and plots for time-step extrapolation, walker-population scaling, and geometry-specific finite-size corrections for both the quasi-1D CNT and 2D graphene systems. These confirm convergence to better than 0.01 eV and are also provided in the Supplementary Information. revision: yes

Circularity Check

0 steps flagged

No circularity in the first-principles DMC derivation chain

full rationale

The paper derives Ca and H2 binding energies directly from fixed-node diffusion Monte Carlo calculations on the Ca-decorated boron-doped graphene and carbon nanotube systems. These are parameter-free first-principles computations whose nodal surfaces are chosen from standard Slater determinants; the resulting energies are then compared to several DFT functionals but not fitted to them. No step reduces the target H2 adsorption energy to a fit, a self-definition, or a load-bearing self-citation. The claim that the CNT value enters the -0.2 to -0.4 eV window is therefore an independent output of the DMC runs rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The work rests on standard electronic-structure methods. The fixed-node approximation is the main domain assumption required to make the DMC calculations tractable; no free parameters are fitted to the target H2 energies and no new entities are postulated.

axioms (1)
  • domain assumption Fixed-node approximation in diffusion Monte Carlo yields binding energies accurate enough for the target window of 0.2-0.4 eV
    Invoked implicitly when presenting DMC results as reliable benchmarks; standard in QMC literature but can introduce systematic bias for weakly bound systems.

pith-pipeline@v0.9.0 · 5623 in / 1300 out tokens · 37726 ms · 2026-05-10T17:13:19.976452+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

62 extracted references · 62 canonical work pages

  1. [1]

    M. R. UsmanRenew. Sustain. Energy Rev., vol. 167, p. 112743, 2022

    work page 2022

  2. [2]

    Rahmat Poudineh and Aliaksei Patonia. 2023

    work page 2023

  3. [3]

    Y. S. Al-Hamdani, A. Zen, A. Michaelides, and D. AlfèPhys. Rev. Materials, vol. 7, p. 035402, 2023

    work page 2023

  4. [4]

    S. K. Bhatia and A. L. MyersLangmuir, vol. 22, pp. 1688–1700, 2006

    work page 2006

  5. [5]

    J. Li, T. Furuta, H. Goto, T. Ohashi, Y. Fujiwara, and S. YipJ. Chem. Phys., vol. 119, p. 2376, 2003

    work page 2003

  6. [6]

    N. S. Bobbitt, J. Chen, and R. Q. SnurrJ. Phys. Chem. C, vol. 120, 2016

    work page 2016

  7. [7]

    N. S. Bobbitt and R. Q. SnurrMol. Simul., vol. 45, pp. 1069–1081, 2019

    work page 2019

  8. [8]

    Y. J. Colón, D. Fairen-Jimenez, C. E. Wilmer, and R. Q. SnurrJ. Phys. Chem. C, vol. 118, pp. 5383–5389, 2014

    work page 2014

  9. [9]

    Y. Gao, Z. Li, P. Wang, W. G. Cui, X. Wang, Y. Yang, F. Gao, M. Zhang, J. Gan, C. Li, Y. Liu, X. Wang, F. Qi, J. Zhang, X. Han, W. Du, J. Chen, Z. Xia, and H. PanNat. Commun., vol. 15, pp. 1–14, 2024

    work page 2024

  10. [10]

    Ataca, E

    C. Ataca, E. Aktürk, and S. CiraciPhys. Rev. B, vol. 79, p. 041406, 2009

    work page 2009

  11. [11]

    Srinivas, C

    G. Srinivas, C. A. Howard, N. T. Skipper, S. M. Bennington, and M. EllerbyPhysica C, vol. 469, pp. 2000–2002, 2009

    work page 2000

  12. [12]

    X. Liu, C. Z. Wang, Y. X. Yao, W. C. Lu, M. Hupalo, M. C. Tringides, and K. M. Ho Phys. Rev. B, vol. 83, pp. 1–12, 2011

    work page 2011

  13. [13]

    W. Zhou, J. Zhou, J. Shen, C. Ouyang, and S. ShiJ. Phys. Chem. Sol., vol. 73, pp. 245–251, 2012

    work page 2012

  14. [14]

    Seenithurai, R

    S. Seenithurai, R. K. Pandyan, S. V. Kumar, C. Saranya, and M. MahendranInt. J. Hydrog. Energy, vol. 39, pp. 11016–11026, 2014

    work page 2014

  15. [15]

    J. Wong, S. Yadav, J. Tam, and C. Veer SinghJ. App. Phys., vol. 115, p. 224301, 2014

    work page 2014

  16. [16]

    N. X. Qiu, Z. Y. Tian, Y. Guo, C. H. Zhang, Y. P. Luo, and Y. XueInt. J. Hydrog. Energy, vol. 39, pp. 9307–9320, 2014

    work page 2014

  17. [17]

    Y. Wen, F. Xie, X. Liu, X. Liu, R. Chen, K. Cho, and B. ShanInt. J. Hydrog. Energy, vol. 42, pp. 10064–10071, 2017

    work page 2017

  18. [18]

    Y. S. Al-Hamdani, D. Alfè, and A. MichaelidesJ. Chem. Phys., vol. 146, p. 094701, 2017

    work page 2017

  19. [19]

    Y. S. Al-Hamdani, A. Zen, and D. AlfèJ. Chem. Phys., vol. 159, p. 204708, 2023

    work page 2023

  20. [20]

    G. J. KubasJ. Organometallic Chem., vol. 635, pp. 37–68, 2001. 19

    work page 2001

  21. [21]

    G. J. KubasProc. Natl. Acad. Sci. U. S. A., vol. 104, pp. 6901–6907, 2007

    work page 2007

  22. [22]

    Bajdich, F

    M. Bajdich, F. A. Reboredo, and P. R. C. KentPhys. Rev. B, vol. 82, p. 081405, 2010

    work page 2010

  23. [23]

    C. R. Wood, N. T. Skipper, and M. J. GillanJ. Sol. State Chem., vol. 184, pp. 1561– 1565, 2011

    work page 2011

  24. [24]

    Supplemental material for “towards viable h2 storage in ca decorated low-dimensional materials with insights from reference quantum monte carlo

    Y. S. Al-Hamdani, A. Zen, and D. Alfè, “Supplemental material for “towards viable h2 storage in ca decorated low-dimensional materials with insights from reference quantum monte carlo”,” 2026. Supplemental material accompanying this work

    work page 2026

  25. [25]

    J. P. Perdew, K. Burke, and M. ErnzerhofPhys. Rev. Lett., vol. 77, p. 3865, 1996

    work page 1996

  26. [26]

    Grimme, J

    S. Grimme, J. Antony, S. Ehrlich, and H. KriegJ. Chem. Phys., vol. 132, p. 154104, 2010

    work page 2010

  27. [27]

    T. D. Kühne, M. Iannuzzi, M. Del Ben, V. V. Rybkin, P. Seewald, F. Stein, T. Laino, R. Z. Khaliullin, O. Schütt, F. Schiffmann, D. Golze, J. Wilhelm, S. Chulkov, M. H. Bani-Hashemian, V. Weber, U. Borštnik, M. Taillefumier, A. S. Jakobovits, A. Laz- zaro, H. Pabst, T. Müller, R. Schade, M. Guidon, S. Andermatt, N. Holmberg, G. K. Schenter, A. Hehn, A. Bus...

    work page 2020

  28. [28]

    Kresse and J

    G. Kresse and J. HafnerPhys. Rev. B, vol. 47, p. 558, 1993

    work page 1993

  29. [29]

    Kresse and J

    G. Kresse and J. FurthmüllerPhys. Rev. B, vol. 54, p. 11169, 1996

    work page 1996

  30. [30]

    Kresse and J

    G. Kresse and J. FurthmüllerComput. Mater. Sci., vol. 6, p. 15, 1996

    work page 1996

  31. [31]

    Kresse and J

    G. Kresse and J. HafnerPhys. Rev. B, vol. 49, p. 14251, 1994

    work page 1994

  32. [32]

    Kresse and D

    G. Kresse and D. JoubertPhys. Rev. B, vol. 59, pp. 1758–1775, 1999

    work page 1999

  33. [33]

    Klimeš, D

    J. Klimeš, D. R. Bowler, and A. MichaelidesPhys. Rev. B, vol. 83, p. 195131, 2011

    work page 2011

  34. [34]

    J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. SunJ. Phys. Chem. Lett., vol. 11, pp. 8208–8215, 2020

    work page 2020

  35. [35]

    Sabatini, T

    R. Sabatini, T. Gorni, and S. D. GironcoliPhys. Rev. B, vol. 87, p. 041108, 2013

    work page 2013

  36. [36]

    Tkatchenko, R

    A. Tkatchenko, R. A. Distasio, R. Car, and M. SchefflerPhys. Rev. Lett., vol. 108, p. 236402, 2012

    work page 2012

  37. [37]

    Ambrosetti, A

    A. Ambrosetti, A. M. Reilly, R. A. Distasio, and A. TkatchenkoJ. Chem. Phys., vol. 140, p. 18A508, 2014

    work page 2014

  38. [38]

    Gould and T

    T. Gould and T. BučkoJ. Chem. Theory Comput., vol. 12, pp. 3603–3613, 2016

    work page 2016

  39. [39]

    Gould, S

    T. Gould, S. Lebègue, J. G. Ángyán, and T. BučkoJ. Chem. Theory Comput., vol. 12, pp. 5920–5930, 2016

    work page 2016

  40. [40]

    HamadaPhys

    I. HamadaPhys. Rev. B, vol. 89, p. 121103, 2014. 20

    work page 2014

  41. [41]

    Giannozzi, S

    P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. de Gironcoli, S. Fab- ris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Sc...

    work page 2009

  42. [42]

    Giannozzi, O

    P. Giannozzi, O. Andreussi, T. Brumme, O. Bunau, M. B. Nardelli, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, N. Colonna, I. Carnimeo, A. D. Corso, S. de Gironcoli, P. Delugas, R. A. DiStasio, A. Ferretti, A. Floris, G. Fratesi, G. Fugallo, R. Gebauer, U. Gerstmann, F. Giustino, T. Gorni, J. Jia, M. Kawa- mura, H.-Y. Ko, A. Kokalj, E. Kü...

    work page 2017

  43. [43]

    J. Kim, A. D. Baczewski, T. D. Beaudet, A. Benali, M. C. Bennett, M. A. Berrill, N. S. Blunt, E. J. L. Borda, M. Casula, D. M. Ceperley, S. Chiesa, B. K. Clark, R. C. Clay, K. T. Delaney, M. Dewing, K. P. Esler, H. Hao, O. Heinonen, P. R. C. Kent, J. T. Krogel, I. Kylänpää, Y. W. Li, M. G. Lopez, Y. Luo, F. D. Malone, R. M. Martin, A. Mathuriya, J. McMini...

    work page 2018

  44. [44]

    M. C. Bennett, G. Wang, A. Annaberdiyev, C. A. Melton, L. Shulenburger, and L. MitasJ. Chem. Phys., vol. 149, p. 104108, 2018

    work page 2018

  45. [45]

    Alfè and M

    D. Alfè and M. J. GillanPhys. Rev. B, vol. 70, p. 161101, 2004

    work page 2004

  46. [46]

    J. T. KrogelComput. Phys. Commun., vol. 198, pp. 154–168, 2016

    work page 2016

  47. [47]

    BaldereschiPhys

    A. BaldereschiPhys. Rev. B, vol. 7, pp. 5212–5215, 1973

    work page 1973

  48. [48]

    A. Zen, J. G. Brandenburg, A. Michaelides, and D. AlfèJ. Chem. Phys., vol. 151, p. 134105, 2019

    work page 2019

  49. [49]

    F. D. Pia, B. X. Shi, Y. S. Al-Hamdani, D. Alfé, T. A. Anderson, M. Barborini, A. Benali, M. Casula, N. D. Drummond, M. Dubecký, C. Filippi, P. R. Kent, J. T. Krogel, P. L. Ríos, A. Lüchow, Y. Luo, A. Michaelides, L. Mitas, K. Nakano, R. J. Needs, M. C. Per, A. Scemama, J. Schultze, R. Shinde, E. Slootman, S. Sorella, A. Tkatchenko, M. Towler, C. J. Umrig...

    work page 2025

  50. [50]

    H. Kwee, S. Zhang, and H. KrakauerPhys. Rev. Lett., vol. 100, p. 126404, 2008

    work page 2008

  51. [51]

    Cheng, A

    H. Cheng, A. C. Cooper, G. P. Pez, M. K. Kostov, P. Piotrowski, and S. J. Stuart J. Phys. Chem. B, vol. 109, pp. 3780–3786, 2005. 21

    work page 2005

  52. [52]

    Y. F. Yin, T. Mays, and B. McEnaneyLangmuir, vol. 16, pp. 10521–10527, 2000

    work page 2000

  53. [53]

    Kagita, T

    H. Kagita, T. Ohba, T. Fujimori, H. Tanaka, K. Hata, S. I. Taira, H. Kanoh, D. Mi- nami, Y. Hattori, T. Itoh, H. Masu, M. Endo, and K. KanekoJ. Phys. Chem. C, vol. 116, pp. 20918–20922, 2012

    work page 2012

  54. [54]

    Lee and S.-J

    S.-Y. Lee and S.-J. ParkJ. Sol. State Chem., vol. 194, pp. 307–312, 2012

    work page 2012

  55. [55]

    J. Lyu, V. Kudiiarov, and A. LiderNanomaterials, vol. 10, p. 255, 2020

    work page 2020

  56. [56]

    Chen and D

    H. Chen and D. S. ShollJ. Am. Chem. Soc., vol. 126, pp. 7778–7779, 2004

    work page 2004

  57. [57]

    Emery, C

    N. Emery, C. Hérold, M. d’Astuto, V. Garcia, C. Bellin, J. F. Marêché, P. Lagrange, and G. LoupiasPhys. Rev. Lett., vol. 95, p. 087003, 2005

    work page 2005

  58. [58]

    T. E. Weller, M. Ellerby, S. S. Saxena, R. P. Smith, and N. T. SkipperNat. Phys., vol. 1, pp. 39–41, 2005

    work page 2005

  59. [59]

    Chapman, Y

    J. Chapman, Y. Su, C. A. Howard, D. Kundys, A. N. Grigorenko, F. Guinea, A. K. Geim, I. V. Grigorieva, and R. R. NairSci. Rep., vol. 6, p. 23254, 2016

    work page 2016

  60. [60]

    Henkelman, A

    G. Henkelman, A. Arnaldsson, and H. JónssonComput.Mater.Sci., vol. 36, pp. 354– 360, 2006

    work page 2006

  61. [61]

    Henkelman, B

    G. Henkelman, B. P. Uberuaga, and H. JónssonJ. Chem. Phys., vol. 113, pp. 9901– 9904, 2000

    work page 2000

  62. [62]

    Henkelman and H

    G. Henkelman and H. JónssonJ. Chem. Phys., vol. 113, pp. 9978–9985, 2000. 22

    work page 2000