Journal of Molecular Modeling

, 23:271 | Cite as

On understanding the chemical origin of band gaps

  • J. Contreras-GarcíaEmail author
  • Carlos Cardenas
Original Paper
Part of the following topical collections:
  1. Festschrift in Honor of Henry Chermette


Conceptual DFT and quantum chemical topology provide two different approaches based on the electron density to grasp chemical concepts. We present a model merging both approaches, in order to obtain physical properties from chemically meaningful fragments (bonds, lone pairs) in the solid. One way to do so is to use an energetic model that includes chemical quantities explicitly, so that the properties provided by conceptual DFT are directly related to the inherent organization of electrons within the regions provided by topological analysis. An example of such energy model is the bond charge model (BCM) by Parr and collaborators. Bonds within an ELF-BCM coupled approach present very stable chemical features, with a bond length of ca. 1 Å and 2\(\bar {e}\). Whereas the 2\(\bar {e}\) corroborate classical views of chemical bonding, the fact that bonds always expand along 1 Å introduces the concept of geometrical transferability and enables estimating crystalline cell parameters. Moreover, combining these results with conceptual DFT enables deriving a model for the band gap where the chemical hardness of a solid is given by the bond properties, charge, length, and a Madelung factor, where the latter plays the major role. In short, the fundamental gap of zinc-blende solids can be understood as given by a 2\(\bar {e}\) bond particle asymmetrically located on a 1 Å length box and electrostatically interacting with other bonds and with a core matrix. This description is able to provide semi-quantitative insight into the band gap of zinc-blende semiconductors and insulators on equal footing, as well as a relationship between band gap and compressibility. In other words, merging these different approaches to bonding enables to connect measurable macroscopic behavior with microscopic electronic structure properties and to obtain microscopic insight into the chemical origin of band gaps, whose prediction is still nowadays a difficult task.
Graphical Abstract

Conceptual DFT couples to quatum chemcial topology to explain the band gap of zinc-blende solids


Conceptual DFT ELF Bond charge model Band gap Compressibility 



CC acknowledges support by the Fondo Nacional de Investigaciones Científicas y Tecnológicas (FONDECYT, Chile) under grant #1140313, Financiamiento Basal para Centros Científicos y Tecnológicos de Excelencia-FB0807, and project RC-130006 CILIS, granted by the fondo de Innovación para la competitividad Del Ministerio de Economia, Fomento y Turismo, Chile,


  1. 1.
    Cohen AJ, Mori-Sánchez P, Yang W (2002) Science 321:792CrossRefGoogle Scholar
  2. 2.
    Kohn W, Sham LJ (1965) Phys Rev 140:A1133CrossRefGoogle Scholar
  3. 3.
    Parr RG, Yang W (1989) Density functional theory of atoms and molecules. Oxford University Press, New YorkGoogle Scholar
  4. 4.
    Hohenberg PC, Kohn W (1964) Phys Rev 136:B864CrossRefGoogle Scholar
  5. 5.
    Chermette H (1998) Coord Chem Rev 180:699CrossRefGoogle Scholar
  6. 6.
    Fuentealba P, Cardenas C (2015) Chem Model 11:151Google Scholar
  7. 7.
    Liu S-B (2009) Acta Phys -Chim Sin 25:590Google Scholar
  8. 8.
    Gazquez J (2008) J Mex Soc 52:3Google Scholar
  9. 9.
    Chattaraj PK, Sarkar U, Roy DR (2006) Chem Rev 106:2065CrossRefGoogle Scholar
  10. 10.
    Ayers PW, Anderson JSM, Bartolotti LJ (2005) Int J Quantum Chem 101:520CrossRefGoogle Scholar
  11. 11.
    Geerlings P, de Proft F, Langenaeker W (2003) Chem Rev 103:1793CrossRefGoogle Scholar
  12. 12.
    Pearson RG (1986) Proc Nati Acad Sci USA 83:8440CrossRefGoogle Scholar
  13. 13.
    Parr RG, Pearson RG (1983) JACS 105:7512CrossRefGoogle Scholar
  14. 14.
    Ayers PW (2007) Faraday Discuss 135:161CrossRefGoogle Scholar
  15. 15.
    Fuentealba P, Cardenas C (2013) J Molec Model 19:2849CrossRefGoogle Scholar
  16. 16.
    Noorizadeh S, Shakerzadeh E (2008) J Phys Chem A 112:3486CrossRefGoogle Scholar
  17. 17.
    Noorizadeh S, Parsa H (2013) J Phys Chem A 117:939CrossRefGoogle Scholar
  18. 18.
    Heidar-Zadeh F, Richer M, Fias S, Miranda-Quintana RA, Chan M, Franco-Pérez M, González-Espinoza C, Cristina E, Kim TD, Lanssens C, Caitlin, Patel AHG et al (2016) Chem Phys Lett 660:307CrossRefGoogle Scholar
  19. 19.
    Parr RG, Donnelly RA, Levy M, Palke WE (1978) J Chem Phys 68:3801CrossRefGoogle Scholar
  20. 20.
    Bader RFW (1990) Atoms in molecules, a quantum theory. Clarendon, OxfordGoogle Scholar
  21. 21.
    Bader RFW, Schleyer P, Alinger NL, Clark T, Gasteiger J, Kollman PA, Schaefer HF, Schreiner PR (1998) . In: The encyclopedia of computational chemistry. Wiley, Chichester, UKGoogle Scholar
  22. 22.
    Becke AD, Edgecombe K (1990) J Chem Phys 92:5397CrossRefGoogle Scholar
  23. 23.
    Savin A, Jepsen O, Flad J, Andersen L, Preuss H (1992) Angew Chem Int Ed Engl 31:187CrossRefGoogle Scholar
  24. 24.
    Silvi B, Savin A (1994) Nature 371:683CrossRefGoogle Scholar
  25. 25.
    Bader RFW, Slee T, Cremer D, Kraka E (1983) J Am Chem Soc 105:5061CrossRefGoogle Scholar
  26. 26.
    Jenkins S (2002) J Phys Condens Matter 14:10251CrossRefGoogle Scholar
  27. 27.
    Jenkins S, Ayers PW, Kirk SR, Mori-Sánchez P, Martín Pendás A (2009) A Chem Phys Lett 471:174CrossRefGoogle Scholar
  28. 28.
    Seriani N (2010) J Phys Condens Matter 22:255502CrossRefGoogle Scholar
  29. 29.
    Bader RFW, MacDougall P, Lau C (1984) J Am Chem Soc 106:1594CrossRefGoogle Scholar
  30. 30.
    Matta CF, Boyd RJ (eds) (2007) The quantum theory of atoms in molecules. From solid state to DNA and drug design. Wiley-VCH, WeinheimGoogle Scholar
  31. 31.
    Contreras-García J, Recio JM (2011) Theor Chem Acc 128:411CrossRefGoogle Scholar
  32. 32.
    Marques M, Santoro M, Guillaume CL, Gorelli F, Contreras-García J, Howie R, Goncharov AF, Gregoryanz E (2011) Phys Rev B 83:184106CrossRefGoogle Scholar
  33. 33.
    Marques M, Ackland GJ, Lundegaard LF, Contreras-García J, McMahon MI (2009) Phys Rev Lett 103:115501CrossRefGoogle Scholar
  34. 34.
    Popelier PLA Wales DJ (ed) (2005) Quantum chemical topology: on bonds and potentials. Springer, HeidelbergGoogle Scholar
  35. 35.
    Popelier PLA, Bremond EAG (2009) Int J Quantum Chem 109:2542CrossRefGoogle Scholar
  36. 36.
    Cortés-Guzmán F, Bader RFW (2005) Coord Chem Rev 249:633CrossRefGoogle Scholar
  37. 37.
    Merino G, Vela A, Heine T (2005) Chem Rev 105:3812CrossRefGoogle Scholar
  38. 38.
    Popelier PLA, Smith PJ (2002) In: Hinchliffe A (ed) Specialist periodical reports chemical modelling: applications and theory;. The Royal Society of Chemistry, Cambridge, p 391Google Scholar
  39. 39.
    Popelier PLA, Aicken FM, O’Brien SE (2000) In: A Hinchliffe (ed) Specialist periodical reports chemical modelling: applications and theory. The Royal Society of Chemistry, Cambridge, p 143Google Scholar
  40. 40.
    Berski S, Andrés J, Silvi B, Domingo LR (2006) J Phys Chem A 110:13939CrossRefGoogle Scholar
  41. 41.
    Poater J, Duran M, Sola M, Silvi B (2005) Chem Rev 105:3911CrossRefGoogle Scholar
  42. 42.
    Berges J, Fourre I, Pilmé J, Kozelka J (2013) Inorg Chem 52:1217CrossRefGoogle Scholar
  43. 43.
    Silvi B (2003) J Phys Chem A 107:3081CrossRefGoogle Scholar
  44. 44.
    Borkman RF, Parr RG (1968) J Chem Phys 48:1116CrossRefGoogle Scholar
  45. 45.
    Boyd RJ, Edgecombe KE (1988) J Am Chem Soc 110:4182CrossRefGoogle Scholar
  46. 46.
    Komorowski L, Boyd SL, Boyd RJ (1996) J Phys Chem 100:3448CrossRefGoogle Scholar
  47. 47.
    Boyd RJ, Boyd SL (1992) J Am Chem Soc 114:1652CrossRefGoogle Scholar
  48. 48.
    Berlin T (1951) J Chem Phys 19:208CrossRefGoogle Scholar
  49. 49.
    Contreras-Garcia J, Marques M, Menendez JM, Recio JM (2015) Int J Mol Sci 16:8151CrossRefGoogle Scholar
  50. 50.
    Perdew JP, Wang Y (1992) Phys Rev B 45:13244CrossRefGoogle Scholar
  51. 51.
    Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865CrossRefGoogle Scholar
  52. 52.
    DW Palmer (2008)
  53. 53.
    Contreras-García J, Martin Pendás A, Silvi B, Recio JM (2008) J Phys Chem Solids 69:2204CrossRefGoogle Scholar
  54. 54.
    Contreras-García J, Silvi B, Martín Pendás A, Recio JM (2009) J Chem Theory Comput 5:164CrossRefGoogle Scholar
  55. 55.
    Cohen ML (1985) Phys Rev B 32:7988CrossRefGoogle Scholar
  56. 56.
    Manca P (1961) J Phys Chem Solids 20:268CrossRefGoogle Scholar
  57. 57.
    Martin RM (1968) Chem Phys Lett 2:268CrossRefGoogle Scholar
  58. 58.
    Kohout M, Savin A (1996) Int J Quant Chem 60:875CrossRefGoogle Scholar
  59. 59.
    Gasquez JL, Ortiz E (1984) J Chem Phys 81:2741CrossRefGoogle Scholar
  60. 60.
    Cardenas C, Ayers PW, de Proft F, Tozer DJ, Geerlings P (2011) Phys Chem Chem Phys 13:2285CrossRefGoogle Scholar
  61. 61.
    Cardenas C (2011) Chem Phys Lett 513:127CrossRefGoogle Scholar
  62. 62.
    Cardenas C, Tiznado W, Ayers PW, Fuentealba P (2011) J Phys Chem A 115:2325CrossRefGoogle Scholar
  63. 63.
    Glasser L (2012) Inorg Chem 51:2420CrossRefGoogle Scholar
  64. 64.
    Yang W, Parr R (1987) Phys Chem Miner 15:191CrossRefGoogle Scholar
  65. 65.
    Contreras-Garcia J, Mori-Sánchez P, Silvi B, Recio JM (2009) J Chem Theor Comp 5:2108CrossRefGoogle Scholar
  66. 66.
    Martín Pendás A, Costales A, Blanco MA, Recio JM, Luaña V (2000) Phys Rev B 62:13970CrossRefGoogle Scholar
  67. 67.
    Fuentealba P (2016) Solvay workshop “Conceptual quantum chemistry: Present aspects and challenges for the future”. Brussels, BelgiumGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Laboratoire de Chimie Théorique, UPMCSorbonne Universités and CNRSParisFrance
  2. 2.Departamento de Física, Facultad de CienciasUniversidad de ChileSantiagoChile
  3. 3.Centro para el Desarrollo de la Nanociencia y la Nanotecnología (CEDENNA)SantiagoChile

Personalised recommendations