Lower and Upper Bound Estimates of Material Properties of Pristine Graphene: Using Quantum Espresso

  • T. Chaitanya Sagar
  • Viswanath ChinthapentaEmail author
Conference paper


In this paper, the basic groundstate (T = 0) properties of pristine graphene are calculated using first principles with the aid of Quantum Espresso (QE). QE software suite is a tool based on ab initio quantum chemistry methods to obtain the electronic structure for materials modeling. It is an open source package built basing on the formalism of density functional theory (DFT). Using QE, the band structure, cohesive energy, and second-order elastic constants are estimated for a pristine graphene. Upper bound estimates based on the generalized gradient approximation (GGA) and lower bound estimates based on local density approximation (LDA) are obtained. The cohesive energy is found to be −7.917 eV/atom using LDA and −5.673 eV/atom using GGA. Further, the elastic properties are determined using a post-processing tool ElaStic. The second-order elastic stiffness C 11 is found to be 491.5, and 506.7 GPa using LDA and GGA approaches, respectively.


Graphene DFT Quantum Espresso Band structure Cohesive energy and second-order elastic constants 



Density Functional Theory


Generalized Gradient Approximation


Integrated Computational Materials Engineering


Local Density Approximation


Molecular Dynamics


Pseudo Potentials


Quantum Espresso


Second-Order Elastic Constants


  1. 1.
    J.J. De Pablo, W.A. Curtin, J.J. de Pablo, Multiscale modeling in advanced materials research: challenges, novel methods, and emerging applications. MRS Bull. 32(11), 905–911 (2011)Google Scholar
  2. 2.
    M.F. Horstemeyer, Multiscale modeling: a review, in Practical Aspects of Computational Chemistry (Springer Netherlands, Dordrecht, 2009), pp. 87–135Google Scholar
  3. 3.
    R.E. Miller, E.B. Tadmor, A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods. Modell. Simul. Mater. Sci. Eng. 17(5), 53001 (2009)CrossRefGoogle Scholar
  4. 4.
    E.A. Carter, Challenges in modeling materials properties without experimental input. Science (80-.) 321(5890), 800–803 (2008)Google Scholar
  5. 5.
    R.W. Sullivan, S.M. Arnold, An annotative review of multiscale modeling and its application to scales inherent in the field of ICME, in Models, Databases, and Simulation Tools Needed for the Realization of Integrated Computational Material Engineering (2011), pp. 6–23Google Scholar
  6. 6.
    D.G.B. Pollock, M. Tresa, J.E. Allison, Integrated Computational Materials Engineering: A Transformational Discipline for Improved Competitiveness and National Security (Washington, DC: The National Academies Press, 2008)Google Scholar
  7. 7.
    M.F. Horstemeyer, From Atoms to Autos—A new Design Paradigm Using Microstructure-Property Modeling Part 1: Monotonic Loading Conditions (Albuquerque, NM, and Livermore, CA, 2001)Google Scholar
  8. 8.
    E.H. Falcao, F. Wudl, Carbon allotropes: beyond graphite and diamond. J. Chem. Technol. Biotechnol. 82(6), 524–531 (2007)CrossRefGoogle Scholar
  9. 9.
    J. Slonczewski, P. Weiss, Band structure of graphite. Phys. Rev. 109(2), 272–279 (1958)CrossRefGoogle Scholar
  10. 10.
    A.K. Geim, K.S. Novoselov, The rise of graphene. Nat. Mater. 6(3), 183–191 (2007)CrossRefGoogle Scholar
  11. 11.
    K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless Dirac fermions in graphene. Nature 438(7065), 197–200 (2005)Google Scholar
  12. 12.
    A.A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C.N. Lau, Superior thermal conductivity of single-layer graphene. Nano Lett. 8(3), 902–907 (2008)Google Scholar
  13. 13.
    C. Berger, Z. Song, T. Li, X. Li, A.Y. Ogbazghi, R. Feng, Z. Dai, A.N. Marchenkov, E.H. Conrad, P.N. First, W.A. de Heer, Ultrathin epitaxial graphite: 2D electron gas properties and a route toward graphene-based nanoelectronics. J. Phys. Chem. B 108(52), 19912–19916 (2004)Google Scholar
  14. 14.
    S. Ghosh, I. Calizo, D. Teweldebrhan, E.P. Pokatilov, D.L. Nika, A.A. Balandin, W. Bao, F. Miao, C.N. Lau, Extremely high thermal conductivity of graphene: prospects for thermal management applications in nanoelectronic circuits. Appl. Phys. Lett. 92(15), 151911 (2008)CrossRefGoogle Scholar
  15. 15.
    J.H. Seol, I. Jo, A.L. Moore, L. Lindsay, Z.H. Aitken, M.T. Pettes, X. Li, Z. Yao, R. Huang, D. Broido, N. Mingo, R.S. Ruoff, L. Shi, Two-dimensional phonon transport in supported graphene. Science (80-.) 328(5975), 213–216 (2010)Google Scholar
  16. 16.
    T. Schwamb, B.R. Burg, N.C. Schirmer, D. Poulikakos, An electrical method for the measurement of the thermal and electrical conductivity of reduced graphene oxide nanostructures. Nanotechnology 20(40), 405704 (2009)CrossRefGoogle Scholar
  17. 17.
    C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene. Science (80-.) 321(5887), 385–388 (2008)Google Scholar
  18. 18.
    G. Tsoukleri, J. Parthenios, K. Papagelis, R. Jalil, A.C. Ferrari, A.K. Geim, K.S. Novoselov, C. Galiotis, Subjecting a graphene monolayer to tension and compression. Small 5(21), 2397–2402 (2009)CrossRefGoogle Scholar
  19. 19.
    C. Lee, X.D. Wei, Q.Y. Li, R. Carpick, J.W. Kysar, J. Hone, Elastic and frictional properties of graphene. Phys. Status Solidi B-Basic Solid State Phys. 246(11–12), 2562–2567 (2009)CrossRefGoogle Scholar
  20. 20.
    V. Singh, D. Joung, L. Zhai, S. Das, S.I. Khondaker, S. Seal, Graphene based materials: the past, present, and future. Prog. Mater Sci. 56(8), 1178–1271 (2011)CrossRefGoogle Scholar
  21. 21.
    K.S. Novoselov, V.I. Fal’ko, L. Colombo, P.R. Gellert, M.G. Schwab, K. Kim, A roadmap for graphene. Nature 490(7419), 192–200 (2012)Google Scholar
  22. 22.
    X. Wei, B. Fragneaud, C.A. Marianetti, J.W. Kysar, Nonlinear elastic behavior of graphene: Ab initio calculations to continuum description. Phys. Rev. B Condens. Matter Mater. Phys. 80(20), 1–8 (2009)Google Scholar
  23. 23.
    F. Liu, P. Ming, J. Li, Ab initio calculation of ideal strength and phonon instability of graphene under tension. Phys. Rev. B Condens. Matter Mater. Phys. 76(6), 1–7 (2007)Google Scholar
  24. 24.
    K.N. Kudin, G.E. Scuseria, B.I. Yakobson, C2F, BN, and C nanoshell elasticity from ab initio computations. Phys. Rev. B 64(23), 235406 (2001)CrossRefGoogle Scholar
  25. 25.
    G. Van Lier, C. Van Alsenoy, V. Van Doren, P. Geerlings, Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene. Chem. Phys. Lett. 326(1–2), 181–185 (2000)CrossRefGoogle Scholar
  26. 26.
    D. Sánchez-Portal, E. Artacho, J.M. Soler, A. Rubio, P. Ordejón, Ab initio structural, elastic, and vibrational properties of carbon nanotubes. Phys. Rev. B 59(19), 12678–12688 (1999)CrossRefGoogle Scholar
  27. 27.
    E. Konstantinova, S.O. Dantas, P.M.V.B. Barone, Electronic and elastic properties of two-dimensional carbon planes. Phys. Rev. B Condens. Matter Mater. Phys. 74(3), 1–6 (2006)Google Scholar
  28. 28.
    J.P. Perdew, K. Burke, M. Ernzerhof, Generalized gradient approximation made simple. Phys. Rev. Lett. 77(18), 3865–3868 (1996)CrossRefGoogle Scholar
  29. 29.
    W. Kohn, L.J. Sham, Self-Consistent Equations Including Exchange and Correlation Effects, vol. 385, no. 1951 (1965)Google Scholar
  30. 30.
    J.P. Perdew, J.A. Chevary, S.H. Vosko, K.A. Jackson, M.R. Pederson, D.J. Singh, C. Fiolhais, Atoms, molecules, solids, and surfaces: applications of the generalized gradient approximation for exchange and correlation. Phys. Rev. B 46(11), 6671–6687 (1992)CrossRefGoogle Scholar
  31. 31.
    Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., … Wentzcovitch, R. M. . QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials.J. Phys. Condens. Matter  21(39), 395502 (2009)Google Scholar
  32. 32.
    M. Born, Dynamical theory of crystal lattices. Am. J. Phys. 23(7), 474 (1955)CrossRefGoogle Scholar
  33. 33.
    B.Z. Yanchitsky, A.N. Timoshevskii, Determination of the space group and unit cell for a periodic solid. Comput. Phys. Commun. 139(2), 235–242 (2001)CrossRefzbMATHGoogle Scholar
  34. 34.
    R. Golesorkhtabar, P. Pavone, J. Spitaler, P. Puschnig, C. Draxl, ElaStic: a tool for calculating second-order elastic constants from first principles. Comput. Phys. Commun. 184(8), 1861–1873 (2013)CrossRefGoogle Scholar
  35. 35.
    R. Yu, J. Zhu, H.Q. Ye, Calculations of single-crystal elastic constants made simple. Comput. Phys. Commun. 181(3), 671–675 (2010)CrossRefzbMATHGoogle Scholar
  36. 36.
    O. Hassel, H. Mark, Uber die Kristallstruktur des Graphits. Zeitschrift fur Phys. 25(1), 317–337 (1924)CrossRefGoogle Scholar
  37. 37.
    P. Hofmann, Solid State Physics: An Introduction (Wiley, 2015)Google Scholar
  38. 38.
    P.R. Wallace, The band theory of graphite. Phys. Rev. 71(9), 622–634 (1947)CrossRefzbMATHGoogle Scholar
  39. 39.
    L.-F. Huang, Y.-L. Li, M.-Y. Ni et al., Lattice dynamics of hydrogen-substituted graphene systems. Acta Phys. Sin. 58(13), S306–S312 (2009)Google Scholar
  40. 40.
    H. Shin, S. Kang, J. Koo, H. Lee, J. Kim, Y. Kwon, Cohesion energetics of carbon allotropes: quantum Monte Carlo study. J. Chem. Phys. 140(11), 114702 (2014)CrossRefGoogle Scholar
  41. 41.
    R. Hill, The elastic behaviour of a crystalline aggregate. Proc. Phys. Soc. London, Sect. A 65(389), 349–354 (1952)CrossRefGoogle Scholar
  42. 42.
    B. Aufray, A. Kara, Ś. Vizzini, H. Oughaddou, C. Ĺandri, B. Ealet, G. Le Lay, Graphene-like silicon nanoribbons on Ag(110): a possible formation of silicene. Appl. Phys. Lett. 96(18), 10–12 (2010)CrossRefGoogle Scholar
  43. 43.
    O.L. Blakslee, Elastic constants of compression-annealed pyrolytic graphite. J. Appl. Phys. 41(8), 3373 (1970)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Micro-Mechanics LabIndian Institute of Technology HyderabadKandi, SangareddyIndia

Personalised recommendations