Pith. sign in

REVIEW 6 major objections 5 minor 1 cited by

Electronic structure of SLSiN under charge density modulation

T0 review · 6 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Charging a monolayer of silicon nitride turns it from insulator to metal, simulations report.

desk verdict A routine charged-cell DFT study whose central claim is undermined by a known 2D electrostatics artifact and internal inconsistencies. read the letter →

arxiv 2507.15883 v1 pith:NQ3U3RRS submitted 2025-07-18 cond-mat.mtrl-sci

Ashkan Shekaari This is my paper · ORCID
classification cond-mat.mtrl-sci PACS 31.15.E65.40.-b73.22.-f
keywords SLSiNsiliconnitride2Dmaterialsdensity-functionaltheoryelectronicstructureinsulator-to-metaltransitionchargedopingband
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

This paper asks whether adding or removing electrons from a single layer of silicon nitride (SLSiN) changes its electronic behavior, and reports that it does: every charged configuration with net cell charge $n = \pm 1, \pm 2$, or $\pm 3$ shows bands crossing the Fermi level, so doping drives an insulator-to-metal transition. The neutral monolayer is an insulator with a roughly 4 eV band gap and is described as having zero electronegativity, meaning it neither attracts nor donates charge when placed in a heterostructure. Hole-doped cells ($n > 0$) show flat bands near the Fermi level and a larger density of states there, which the paper interprets as superior conductivity compared with electron-doped cells. If these results hold, charge control becomes a practical switch for turning SLSiN from a dielectric into a conductor.

What carries the argument

The argument is carried by periodic density-functional theory calculations in the generalized-gradient approximation, using plane waves and ultrasoft pseudopotentials. To make the charged periodic cells well-defined, a uniform jellium background charge is added to neutralize each cell, and equilibrium geometries are obtained by fitting energy–volume curves to the Murnaghan equation of state. The observable quantities are the band structure and density of states for each of the seven charge states, sampled along a $\Gamma$–M–K–$\Gamma$ path with a metal-friendly Brillouin-zone smearing scheme; the closing of the gap and the Fermi-level crossing in the charged states are what establish metallicity.

What would settle it

Repeat the charged-cell calculations with a neutralizing countercharge placed explicitly in the vacuum gap or with a dipole correction; if any charged configuration retains a finite band gap or fails to show bands crossing the Fermi level, the reported insulator-to-metal transition is an artifact of the jellium background.

Watch

Extended reading notes

Core claim

The central claim is that SLSiN, a two-dimensional allotrope of Si$_3$N$_4$, can be switched from insulating to metallic purely by varying the net charge of its unit cell. In the neutral reference state the band structure has a gap of about 4 eV; as the cell charge is tuned from $n = +3$ down to $n = -3$, the gap shifts rigidly upward under hole doping and downward under electron doping until bands cross the Fermi level in every charged case. The paper also finds that the lattice constant and Si–N bond length grow monotonically as the charge goes from $+3$ to $-3$ because added electrons amplify Coulomb repulsion, and that the neutral cell has the lowest ground-state energy, which it equates with zero electronegativity and stability against charge transfer in heterostructures.

Load-bearing premise

The claim rests on treating each charged periodic cell with a uniform jellium background, and if that background distorts the band energies of a truly two-dimensional film, the metallic Fermi-level crossings could be an artifact.

Editorial extensions

If this is right

  • A SLSiN monolayer could be toggled between insulator and metal by gating or contacting that controls its net charge, without chemical functionalization.
  • Hole-doped SLSiN is predicted to be the better conductor, so p-type doping or hole injection would be the preferred route for conductive applications.
  • The neutral monolayer's zero electronegativity would make it a chemically inert spacer or barrier layer in heterostructures, since it should not spontaneously transfer charge to neighbors.
  • The monotonic lattice expansion under electron doping means charged operation should be accompanied by measurable strain, relevant for electromechanical devices.
  • Flat bands near the Fermi level in hole-doped cells imply high effective masses and enhanced electronic response, which could be useful in devices exploiting localized carriers.

Reading between the lines

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

  • The jellium-background treatment may misplace the Fermi level for a genuinely two-dimensional film, so a direct test with an explicit countercharge sheet or slab-dipole correction would show whether the Fermi-level crossings survive.
  • If the transition is robust, SLSiN could serve as a tunable two-dimensional channel whose carrier density is set by an applied gate field, connecting this result to field-effect transistor design.
  • The same computational recipe could be applied to other predicted two-dimensional silicon nitride allotropes to see whether an insulator-to-metal response to charging is a family-wide feature.
  • The reported zero electronegativity suggests a design rule for heterostructures: match SLSiN with a material of similar electronegativity to keep the interface inert.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

6 major / 5 minor

Summary. The manuscript reports PBE-level plane-wave DFT calculations for a monolayer of Si3N4 (SLSiN) in seven charge states, n = 0, ±1, ±2, ±3, using Quantum ESPRESSO. The authors fit Murnaghan equations of state to obtain equilibrium lattice parameters and compute band structures and DOS for each charged cell. The central claim is that the neutral monolayer is an insulator with a ~4 eV gap, while all charged cells (both hole- and electron-doped) become metallic, and that hole-doped cells show flat bands near the Fermi level that the authors associate with 'superior electrical conductivity.' The paper also asserts that SLSiN has 'zero electronegativity' because the neutral state is the most stable. The reported calculations are straightforward in design, but the interpretation contains several serious conceptual and technical problems that bear directly on the central claims.

Significance. If the insulator-to-metal transition induced by integer charge injection were a genuine physical property of a two-dimensional Si3N4 monolayer, it could be of interest for nanoscale electronic devices. The paper is transparent about its computational setup, uses an open-source code, and makes its numerical data available in Table I. However, the conclusion rests on a charged-slab methodology that is known to be problematic for 2D materials, and several internal inconsistencies (e.g., flat bands claimed to give high conductivity; a 3D free-electron formula applied to a 2D system) further weaken the work. The significance is therefore not established by the evidence presented.

major comments (6)
  1. [Section II, Computational details] The charged-cell calculations use a uniform jellium background to neutralize the periodic array of charged unit cells. For a two-dimensional slab separated by vacuum, this 3D uniform compensating charge is a known crude approximation that introduces a spurious electrostatic potential, which can shift band positions and alter the Fermi level, potentially generating metallic crossings that are artifacts of the method. The manuscript provides no validation against established 2D-charged-slab corrections (e.g., planar-averaged counter-charge or Coulomb cutoff schemes), so the central result that all charged cells are metallic is not robustly established.
  2. [Section III.2, Fig. 4 and text] The central prediction that every charged configuration (n = ±1, ±2, ±3) is metallic is, to a large extent, a direct consequence of adding or removing electrons from a periodic cell: the Fermi level necessarily moves into the conduction or valence band under the rigid-band-like filling with a uniform background. The paper does not compare against a physically realistic doping model (e.g., substitutional dopants or a gate electrode that would keep the system neutral locally), so the alleged insulator-to-metal transition may not reflect a real tunable property of SLSiN.
  3. [Section III.2, Eq. (4) and associated text] The text states that flat bands at the Fermi level indicate high effective mass and low group velocity (vg ∝ 1/m*) and then concludes that these flat bands yield 'superior electrical conductivity' and amplify electronic responses. This is internally inconsistent: flat bands with high effective mass generally reduce carrier mobility and conductivity, not enhance it. The conclusion that hole-doped cells have higher conductivity than electron-doped cells is therefore not supported by the analysis.
  4. [Section III.1, Eq. (3)] Equation (3) is the Fermi energy of a three-dimensional non-interacting free-electron gas, EF = (ħ²/2m)(3π²N/V)^(2/3) in atomic units. Applying this formula to a two-dimensional monolayer SLSiN is dimensionally and physically incorrect; for a 2D electron gas, EF is proportional to N/A, not (N/V)^(2/3). The trend discussion for EF in Table I is therefore not a valid explanation, and the reported EF values cannot be interpreted with Eq. (3).
  5. [Table I] The fitted Murnaghan parameters contain suspicious coincidences: n = +2 and +3 share K0' = 15.0; n = -1, -2, -3 all have K0' = 1.0; and n = -2 and -3 have identical V0 = 812.8197 Å3 and a0 = 7.7710 Å while differing in Egs. These identical values to several decimal places are unlikely to reflect independent physical behavior and suggest either under-converged fits or a systematic effect of the jellium background. The authors should explain these coincidences or the equilibrium parameters should be re-fitted with a validated method.
  6. [Abstract and Section III.1] The assertion that SLSiN exhibits 'zero electronegativity' is a conceptual error. Electronegativity is a property of an atom or a bond that quantifies the tendency to attract electrons, not the stability of a neutral cell or its 'indifference' to added charge. The observation that the neutral cell has the lowest ground-state energy does not imply zero electronegativity, and this claim should be removed or reworded entirely.
minor comments (5)
  1. [Section IV, Conclusions] There is a typo: 'as nn goes from n = -3 to +3' should read 'as n goes from -3 to +3.'
  2. [Title page] The PACS line reads 'P ACS numbers' instead of 'PACS numbers.'
  3. [Section III.2] The band structure plots (Fig. 4) appear to be low-resolution; the Fermi-level crossings are difficult to inspect quantitatively. The authors should provide larger, high-resolution figures or include an inset of the band edges near the Fermi level.
  4. [Section III.1, Table I] The Fermi energy values are reported to four decimal places, but the physical meaning of EF for an insulator in a charged cell is ambiguous; the authors should define how EF is computed (e.g., the Kohn-Sham highest occupied state or the midpoint of the gap) for the neutral case.
  5. [References] The manuscript cites no recent methodological references on charged-slab corrections for 2D materials (for example, the work of Freysoldt and coworkers on electrostatic corrections); citing such literature would clarify the limitations of the employed jellium approach.

Circularity Check

1 steps flagged · score 6.0 of 10

The insulator-to-metal transition is a bookkeeping consequence of the fixed-charge setup, but the band-structure details remain independent first-principles output.

  1. self definitional [Section III.2 (Electronic structure), Fig. 4 caption and Conclusions]
    "In the neutral state (n = 0), the band structure displays an approximately 4 eV gap, confirming its insulating character. However, when the cell is hole-doped (n = + 1 through + 3) or electron-doped (n = − 1 through − 3), this gap shifts upward or downward, respectively, causing the bands to cross the Fermi level and render the system metallic. Consequently, every charged configuration behaves as a metal."

    The setup fixes the total electron count per cell (n = 0, ±1, ±2, ±3) and uses Methfessel–Paxton smearing to occupy Kohn–Sham states. Starting from a gapped n = 0 insulator, any nonzero integer n forces the electron count away from the neutral count, so the Fermi level must move into the valence band (hole doping) or conduction band (electron doping), producing partial occupation and band crossings by construction. The reported insulator-to-metal transition is therefore an arithmetic consequence of adding or removing a fixed number of electrons from a periodic gapped cell, not an independently derived electronic phase transition. The uniform jellium background is the computational enabler, but the metallicity follows already from the fixed-charge counting.

full rationale

The headline claim that precise charge-density control drives SLSiN across an insulator-to-metal transition is partially circular: because the neutral cell is an insulator with a ~4 eV gap and each doped cell has an integer electron excess or deficit, the Fermi level must lie inside a band, making 'every charged configuration behaves as a metal' essentially forced by the charge-counting setup. This is not a fitted parameter disguised as a prediction, but it is a prediction that reduces by construction. The remaining content—band dispersions, DOS features, flat bands, lattice-parameter trends, and the Murnaghan fits—is genuine first-principles output and is not circular. Self-citations (Refs. [31] and [36]) supply the SLSiN structure and prior motivation but are not load-bearing for the transition claim, and no uniqueness theorem is invoked. The jellium-background approximation is a methodological caveat about 2D charged-slab electrostatics, not itself a circularity. Score 6 reflects partial circularity of the central transition claim while acknowledging the independent quantitative results.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The paper introduces no new physical entities. Its free parameters are the Murnaghan fit coefficients, and its main assumptions are standard DFT practice plus the jellium background, with the misapplied 3D Fermi energy formula as an ad hoc step.

free parameters (2)
  • K0 (bulk modulus), fitted per charge state = 149.411 to 660.933 kbar
    Obtained by fitting energy-volume data to the Murnaghan equation of state (Table I). These fitted moduli are not central to the insulator-metal claim but are reported as results.
  • K0' (pressure derivative of bulk modulus) = 1.0, 10.377, 11.221, 15.0
    Fitted in the same Murnaghan fit. Values of 1.0 and 15.0 are physically suspicious and suggest poor fit constraints. (Table I)
assumptions (3)
  • domain assumption PBE-DFT with ultrasoft pseudopotentials accurately describes the electronic structure of SLSiN.
    The paper uses the standard PBE functional (ref [40]) without benchmarking against higher-level methods or experiment. PBE is known to underestimate band gaps, so the reported ~4 eV gap is not a reliable prediction.
  • domain assumption A uniform jellium background correctly compensates the divergent electrostatic energy of charged periodic cells.
    Section II states this 'conventional approach' is used. For 2D materials, jellium is known to introduce artifacts; the paper does not discuss their impact on the metallic state.
  • ad hoc to paper The 3D free-electron Fermi energy formula (Eq. 3) applies to the 2D SLSiN monolayer.
    Eq. (3) is the Fermi energy of a 3D free-electron gas, but SLSiN is a 2D material. The paper uses it to explain the EF trend in Table I, which is an invalid application.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Electronic structure of SLSiN under charge density modulation." pith.science (2026). https://pith.science/paper/NQ3U3RRS

@misc{pith2026250715883,
  author       = {Pith},
  title        = {Pith review of: Electronic structure of SLSiN under charge density modulation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/NQ3U3RRS}},
  note         = {Machine review of arXiv:2507.15883}
}
abstract

First-principles density-functional theory calculations were carried out to assess how incremental unit-cell charging alters the electronic behavior of SLSiN (single-layer Si$_3$N$_4$). The net charge per cell was systematically tuned from $n\,=\,0$ (the neutral/reference configuration) to $n\,=\,\pm\,1,\pm\,2$, and $\pm\,3$ elementary charges, and for each charged configuration the band structure and density of states were evaluated at the PBE level. In its neutral state, SLSiN exhibits zero electronegativity, signifying both its indifference to additional electron density and its intrinsic stability when integrated into heterostructures. Altogether, these results reveal that precise control of the charge density can drive SLSiN across an insulator-to-metal transition.

Figures

Figures reproduced from arXiv: 2507.15883 by the authors.

Figure 1
Figure 1. FIG. 1. The [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. The internal energy [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The pressure [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Electronic band structures of SLSiN for charge states [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Electronic density of states (DOS) of SLSiN for unit-cell charges from + 3 to [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. First-principles study of the electronic structure and optical properties of two-dimensional $\alpha$-graphdiyne

    cond-mat.mtrl-sci 2026-07 conditional novelty 4.0 of 10

    Monolayer α-graphdiyne is a Dirac semimetal with strong optical anisotropy and plasma frequencies of ~3.21 eV (in-plane) and ~1.06 eV (out-of-plane).

Reference graph

Works this paper leans on

59 extracted references · 58 canonical work pages · cited by 1 Pith paper

  1. [1]

    McEntire, R

    B.J. McEntire, R. Lakshminarayanan, P. Thirug- nanasambandam, J. Seitz-Sampson, R. Bock, D. O’Brien, Processing and characterization of silicon ni- tride bioceramics, Bioceram. Dev. Appl. 6 (2016) 1

    work page 2016

  2. [2]

    Riley, Silicon nitride and related materials, J

    F.L. Riley, Silicon nitride and related materials, J. Am. Ceram. Soc. 83 (2000) 245

    work page 2000

  3. [3]

    Parr, G.F

    N.L. Parr, G.F. Martin, E.R.W. May, Preparation, microstructure, and mechanical properties of silicon nitride, Heywood Press, New York, 1960, pp. 102

    work page 1960

  4. [4]

    Deeley, J.M

    G.G. Deeley, J.M. Herbert, N.C. Moore, Dense silicon nitride, Pow. Metal 4 (1961) 145

    work page 1961

  5. [5]

    Lange, The sophistication of ceramic science through silicon nitride studies, J

    F.F. Lange, The sophistication of ceramic science through silicon nitride studies, J. Ceram. Soc. Japan 114 (2006) 873

    work page 2006

  6. [6]

    C.W. Li, J. Yamanis, Super-tough silicon nitride with r-curve behavior, Ceram. Eng. Sci. Proc. 10 (1989) 632

    work page 1989

  7. [7]

    Tajima, Development of high performance silicon nitride ceramics and their applications, Cambridge University Press, Pittsburg, 1992

    Y. Tajima, Development of high performance silicon nitride ceramics and their applications, Cambridge University Press, Pittsburg, 1992

    work page 1992

  8. [8]

    Hoffmann, Relationship between microstructure and mechanical properties of silicon nitride ceramics, Pure Appl

    M.J. Hoffmann, Relationship between microstructure and mechanical properties of silicon nitride ceramics, Pure Appl. Chem. 67 (1995) 939

    work page 1995

Show all 59 references
  1. [9]

    Becher, E.Y

    P.F. Becher, E.Y. Sun, K.P. Plucknett, K.B. Alexan- der, C. Hsueh, C.G. Westmoreland, Microstructural design of silicon nitride with improved fracture tough- ness: I, Effects of grain shape and size, J. Am. Ceram. Soc. 81 (1998) 2821

    1998

  2. [10]

    Sun, P.F

    E.Y. Sun, P.F. Becher, K. Plucknett, C.-H. Hsueh, K.B. Alexander, S.B. Waters, K. Hirao, M. Brito, Mi- crostructural design of silicon nitride with improved fracture toughness: II, Effects of yttria and alumina additives, J. Am. Ceram. Soc. 81 (1998) 2831

    1998

  3. [11]

    Bressiani, V

    J.C. Bressiani, V. Izhevskyi, A.H.A. Bressiani, De- velopment of the microstructure of the silicon nitride based ceramics, Mater. Res. 2 (1999) 165

    1999

  4. [12]

    Prescher, J.G

    T. Prescher, J.G. Heinrich, Microstructure-properties correlation of continuously sintered silicon nitride, Ce- ram. Forum Int. 81 (2004) E37

    2004

  5. [13]

    Katz, High-temperature structural ceramics, Science 208 (1980) 841

    R.N. Katz, High-temperature structural ceramics, Science 208 (1980) 841

    1980

  6. [14]

    Riley, Applications of silicon nitride ceramics, Key Eng

    F.L. Riley, Applications of silicon nitride ceramics, Key Eng. Mater. 122 (1996) 479

    1996

  7. [15]

    https://materialsproject.org/materials/mp-988/

  8. [16]

    Wiederhorn, M.K

    S.M. Wiederhorn, M.K. Ferber, Silicon nitride for gas turbines, Curr. Opin. Solid State Mater. Sci. 5 (2011) 8 311

    2011

  9. [17]

    Danzer, M

    R. Danzer, M. Lengauer, Silicon nitride materials for hot working of high strength metal wires, Eng. Failure Anal. 17 (2010) 596

    2010

  10. [18]

    Khader, A

    I. Khader, A. Kailer, Damage mechanisms in silicon nitride wire-rolling tools: lab-scale experiments and correlation with finite element modelling, J. Mater. Process Technol. 210 (2010) 1314

    2010

  11. [19]

    Hampshire, Silicon nitride ceramics – review of structure, processing and properties, J

    S. Hampshire, Silicon nitride ceramics – review of structure, processing and properties, J. Achiev. Mater. Manuf. Eng. 24 (2007) 43

    2007

  12. [20]

    Souza, M.C.A

    J.V.C. Souza, M.C.A. Nono, M.V. Ribeiro, J.P.B. Machado, O.M.M. Silva, Cutting forces in turning of gray cast iron using silicon nitride based cutting tool, Mater. Des. 30 (2009) 2715

    2009

  13. [21]

    J.W. Kim, B. Chmielak, H. Lerch, U. Plachetka, Fab- rication of photonic integrated circuits in silicon ni- tride using substrate conformal imprint lithography, Microelectron. Eng. 176 (2017) 11

    2017

  14. [22]

    Mu˜ noz, G

    P. Mu˜ noz, G. Mic´ o, L.A. Bru, D. Pastor, D. P´ erez, J.D. Dom´ enech, J. Fern´ andez, R. Ba˜ nos, B. Gargallo, R. Alemany, A.M. S´ anchez, J.M. Cirera, R. Mas, C. Dom ´ ınguez, Silicon nitride photonic integration plat- forms for visible, near-infrared and mid-infrared ap- ...

    2017

  15. [23]

    M.L. Bloo, H. Haitjema, W.O. Pril, Deformation and wear of pyramidal, silicon-nitride AFM tips scanning micrometre-size features in contact mode, Measure- ment 25 (1999) 203

    1999

  16. [24]

    Carrapichano, J.R

    J.M. Carrapichano, J.R. Gomes, F.J. Oliveira, R.F. Silva, Si 3N4 and Si 3N4/SiC composite rings for dy- namic sealing of circulating fluids, Wear 255 (2003) 695

    2003

  17. [25]

    Carrapichano, F.J

    J.M. Carrapichano, F.J. Oliveira, R.F. Silva, J.R. Gomes, Functionality diagrams for hybrid mechanical seals with silicon nitride rings, J. Am. Ceram. Soc. 88 (2005) 2177

    2005

  18. [26]

    Shekaari, M

    A. Shekaari, M. Jafari, Biocompatibility of 2D silicon nitride: interaction at the nano-bio interface, Mater. Res. Express 8 (2021) 095404

    2021

  19. [27]

    Olofsson, T.M

    J. Olofsson, T.M. Grehk, T. Berlind, C. Persson, S. Jacobson, H. Engqvist, Evaluation of silicon nitride as a wear resistant and resorbable alternative for total hip joint replacement, Biomatter. 2 (2012) 94

    2012

  20. [28]

    Mazzocchi, A

    M. Mazzocchi, A. Bellosi, On the possibility of sili- con nitride as a ceramic for structural orthopaedic im- plants. Part I: processing, microstructure, mechanical properties, cytotoxicity, J. Mater. Sci. Mater. Med. 19 (2008) 2881

    2008

  21. [29]

    Webster, A.A

    T.J. Webster, A.A. Patel, M.N. Rahaman, B. Sonny Bal, Anti-infective and osteointegration properties of silicon nitride, poly(ether ether ketone), and titanium implants, Acta Biomater. 8 (2012) 4447

    2012

  22. [30]

    Anderson, R

    M.C. Anderson, R. Olsen, Bone ingrowth into porous silicon nitride, J. Biomed. Mater. Res. A 92 (2010) 1598

    2010

  23. [31]

    Shekaari, M

    A. Shekaari, M. Jafari, Unveiling the first post- graphene member of silicon nitrides: A novel 2D ma- terial, Comput. Mater. Sci. 180 (2020) 109693

    2020

  24. [32]

    Humphrey, A

    W. Humphrey, A. Dalke, K. Schulten, VMD: visual molecular dynamics, J. Molec. Graphics 14 (1996) 33

    1996

  25. [33]

    http://jedi.ks.uiuc.edu/ ∼johns/raytracer/

  26. [34]

    Geim, K.S

    A.K. Geim, K.S. Novoselov, The rise of graphene, Nat. Mater. 6 (2007) 183

    2007

  27. [35]

    R.G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford University Press, New York, Oxford, 1989

    1989

  28. [36]

    Shekaari, M.R

    A. Shekaari, M.R. Abolhassani, Metallic modification of molybdenum disulfide monolayer via doping charge carriers: A DFT investigation, Chem. Phys. Lett. 684 (2017) 158

    2017

  29. [37]

    Wang, B.A

    R. Wang, B.A. Ruzicka, N. Kumar, M.Z. Bellus, H.-Y. Chiu, H. Zhao, Ultrafast and spatially resolved stud- ies of charge carriers in atomically thin molybdenum disulfide, Phys. Rev. B 86 (2012) 045406

    2012

  30. [38]

    Kohn, L.J

    W. Kohn, L.J. Sham, Self-consistent equations includ- ing exchange and correlation effects, Phys. Rev. 140 (1965) A1133

    1965

  31. [39]

    Pickett, Pseudopotential methods in condensed matter applications, Comput

    W.E. Pickett, Pseudopotential methods in condensed matter applications, Comput. Phys. Rep. 9 (1989) 115

    1989

  32. [40]

    Perdew, K

    J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77 (1996) 3865

    1996

  33. [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. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri...

    2009

  34. [42]

    Torvalds, The Linux edge, Commun

    L. Torvalds, The Linux edge, Commun. ACM 42 (1999) 38

    1999

  35. [43]

    https://www.debian.org/

  36. [44]

    https://www.open-mpi.org/

  37. [45]

    Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys

    D. Vanderbilt, Soft self-consistent pseudopotentials in a generalized eigenvalue formalism, Phys. Rev. B 41 (1990) 7892

    1990

  38. [46]

    Laasonen, A

    K. Laasonen, A. Pasquarello, R. Car, C. Lee, D. Van- derbilt, Car-Parrinello molecular dynamics with Van- derbilt ultrasoft pseudopotentials, Phys. Rev. B 47 (1993) 10142

    1993

  39. [47]

    http://www.quantum-espresso.org

  40. [48]

    Rappe, K.M

    A.M. Rappe, K.M. Rabe, E. Kaxiras, J.D. Joannopou- los, Optimized pseudopotentials, Phys. Rev. B 41 (1990) 1227

    1990

  41. [49]

    Louie, S

    S.G. Louie, S. Froyen, M.L. Cohen, Nonlinear ionic pseudopotentials in spin-density-functional calcula- tions, Phys. Rev. B 26 (1982) 1738

    1982

  42. [50]

    Giannozzi, F

    P. Giannozzi, F. De Angelis, R. Car, First-principle molecular dynamics with ultrasoft pseudopotentials: parallel implementation and application to extended bioinorganic systems, J. Chem. Phys. 120 (2004) 5903

    2004

  43. [51]

    I. Dabo, B. Kozinsky, N.E. Singh-Miller, N. Marzari, Electrostatics in periodic boundary conditions and real-space corrections, Phys. Rev. B 77 (2008) 115139

    2008

  44. [52]

    Murnaghan, The compressibility of media under extreme pressures, Proc

    F.D. Murnaghan, The compressibility of media under extreme pressures, Proc. Natl. Acad. Sci. U. S. A. 30 (1944) 244

    1944

  45. [53]

    Birch, Finite elastic strain of cubic crystals, Phys

    F. Birch, Finite elastic strain of cubic crystals, Phys. Rev. 71 (1947) 809

    1947

  46. [54]

    Billeter, A.J

    S.R. Billeter, A.J. Turnera, W. Thiel, Linear scaling geometry optimisation and transition state search in 9 hybrid delocalised internal coordinates, Phys. Chem. Chem. Phys. 2 (2000) 2177

    2000

  47. [55]

    Billeter, A

    S.R. Billeter, A. Curioni, W. Andreoni, Efficient lin- ear scaling geometry optimization and transition-state search for direct wavefunction optimization schemes in density functional theory using a plane-wave basis, Comput. Mater. Sci. 27 (2003) 437

    2003

  48. [56]

    Methfessel, A.T

    M. Methfessel, A.T. Paxton, High-precision sampling for Brillouin-zone integration in metals, Phys. Rev. B 40 (1989) 3616

    1989

  49. [57]

    https://www.gnu.org/licenses/gpl-3.0.en.html

  50. [58]

    http://www.gnuplot.info/

  51. [59]

    Ashcroft, N.D

    N.W. Ashcroft, N.D. Mermin, Solid State Physics, Philadelphia, PA: Saunders College Publishing, 1976

    1976

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.