On understanding the chemical origin of band gaps

Abstract

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.

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

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Notes

  1. 1.

    Available upon request at the Oviedo Quantum Chemistry Group (http://azufre.quimica.uniovi.es/qcg-home.html)

References

  1. 1.

    Cohen AJ, Mori-Sánchez P, Yang W (2002) Science 321:792

    Article  Google Scholar 

  2. 2.

    Kohn W, Sham LJ (1965) Phys Rev 140:A1133

    Article  Google Scholar 

  3. 3.

    Parr RG, Yang W (1989) Density functional theory of atoms and molecules. Oxford University Press, New York

    Google Scholar 

  4. 4.

    Hohenberg PC, Kohn W (1964) Phys Rev 136:B864

    Article  Google Scholar 

  5. 5.

    Chermette H (1998) Coord Chem Rev 180:699

    Article  Google Scholar 

  6. 6.

    Fuentealba P, Cardenas C (2015) Chem Model 11:151

    Google Scholar 

  7. 7.

    Liu S-B (2009) Acta Phys -Chim Sin 25:590

    CAS  Google Scholar 

  8. 8.

    Gazquez J (2008) J Mex Soc 52:3

    CAS  Google Scholar 

  9. 9.

    Chattaraj PK, Sarkar U, Roy DR (2006) Chem Rev 106:2065

    CAS  Article  Google Scholar 

  10. 10.

    Ayers PW, Anderson JSM, Bartolotti LJ (2005) Int J Quantum Chem 101:520

    CAS  Article  Google Scholar 

  11. 11.

    Geerlings P, de Proft F, Langenaeker W (2003) Chem Rev 103:1793

    CAS  Article  Google Scholar 

  12. 12.

    Pearson RG (1986) Proc Nati Acad Sci USA 83:8440

    CAS  Article  Google Scholar 

  13. 13.

    Parr RG, Pearson RG (1983) JACS 105:7512

    CAS  Article  Google Scholar 

  14. 14.

    Ayers PW (2007) Faraday Discuss 135:161

    CAS  Article  Google Scholar 

  15. 15.

    Fuentealba P, Cardenas C (2013) J Molec Model 19:2849

    Article  Google Scholar 

  16. 16.

    Noorizadeh S, Shakerzadeh E (2008) J Phys Chem A 112:3486

    CAS  Article  Google Scholar 

  17. 17.

    Noorizadeh S, Parsa H (2013) J Phys Chem A 117:939

    CAS  Article  Google 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 660:307

    CAS  Article  Google Scholar 

  19. 19.

    Parr RG, Donnelly RA, Levy M, Palke WE (1978) J Chem Phys 68:3801

    CAS  Article  Google Scholar 

  20. 20.

    Bader RFW (1990) Atoms in molecules, a quantum theory. Clarendon, Oxford

    Google 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, UK

    Google Scholar 

  22. 22.

    Becke AD, Edgecombe K (1990) J Chem Phys 92:5397

    CAS  Article  Google Scholar 

  23. 23.

    Savin A, Jepsen O, Flad J, Andersen L, Preuss H (1992) Angew Chem Int Ed Engl 31:187

    Article  Google Scholar 

  24. 24.

    Silvi B, Savin A (1994) Nature 371:683

    CAS  Article  Google Scholar 

  25. 25.

    Bader RFW, Slee T, Cremer D, Kraka E (1983) J Am Chem Soc 105:5061

    CAS  Article  Google Scholar 

  26. 26.

    Jenkins S (2002) J Phys Condens Matter 14:10251

    CAS  Article  Google Scholar 

  27. 27.

    Jenkins S, Ayers PW, Kirk SR, Mori-Sánchez P, Martín Pendás A (2009) A Chem Phys Lett 471:174

    CAS  Article  Google Scholar 

  28. 28.

    Seriani N (2010) J Phys Condens Matter 22:255502

    Article  Google Scholar 

  29. 29.

    Bader RFW, MacDougall P, Lau C (1984) J Am Chem Soc 106:1594

    CAS  Article  Google 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, Weinheim

  31. 31.

    Contreras-García J, Recio JM (2011) Theor Chem Acc 128:411

    Article  Google Scholar 

  32. 32.

    Marques M, Santoro M, Guillaume CL, Gorelli F, Contreras-García J, Howie R, Goncharov AF, Gregoryanz E (2011) Phys Rev B 83:184106

    Article  Google Scholar 

  33. 33.

    Marques M, Ackland GJ, Lundegaard LF, Contreras-García J, McMahon MI (2009) Phys Rev Lett 103:115501

    CAS  Article  Google Scholar 

  34. 34.

    Popelier PLA Wales DJ (ed) (2005) Quantum chemical topology: on bonds and potentials. Springer, Heidelberg

  35. 35.

    Popelier PLA, Bremond EAG (2009) Int J Quantum Chem 109:2542

    CAS  Article  Google Scholar 

  36. 36.

    Cortés-Guzmán F, Bader RFW (2005) Coord Chem Rev 249:633

    Article  Google Scholar 

  37. 37.

    Merino G, Vela A, Heine T (2005) Chem Rev 105:3812

    CAS  Article  Google 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 391

    Google 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 143

  40. 40.

    Berski S, Andrés J, Silvi B, Domingo LR (2006) J Phys Chem A 110:13939

    CAS  Article  Google Scholar 

  41. 41.

    Poater J, Duran M, Sola M, Silvi B (2005) Chem Rev 105:3911

    CAS  Article  Google Scholar 

  42. 42.

    Berges J, Fourre I, Pilmé J, Kozelka J (2013) Inorg Chem 52:1217

    CAS  Article  Google Scholar 

  43. 43.

    Silvi B (2003) J Phys Chem A 107:3081

    CAS  Article  Google Scholar 

  44. 44.

    Borkman RF, Parr RG (1968) J Chem Phys 48:1116

    CAS  Article  Google Scholar 

  45. 45.

    Boyd RJ, Edgecombe KE (1988) J Am Chem Soc 110:4182

    CAS  Article  Google Scholar 

  46. 46.

    Komorowski L, Boyd SL, Boyd RJ (1996) J Phys Chem 100:3448

    CAS  Article  Google Scholar 

  47. 47.

    Boyd RJ, Boyd SL (1992) J Am Chem Soc 114:1652

    CAS  Article  Google Scholar 

  48. 48.

    Berlin T (1951) J Chem Phys 19:208

    CAS  Article  Google Scholar 

  49. 49.

    Contreras-Garcia J, Marques M, Menendez JM, Recio JM (2015) Int J Mol Sci 16:8151

    CAS  Article  Google Scholar 

  50. 50.

    Perdew JP, Wang Y (1992) Phys Rev B 45:13244

    CAS  Article  Google Scholar 

  51. 51.

    Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865

    CAS  Article  Google Scholar 

  52. 52.

    DW Palmer (2008) www.semiconductors.co.uk

  53. 53.

    Contreras-García J, Martin Pendás A, Silvi B, Recio JM (2008) J Phys Chem Solids 69:2204

    Article  Google Scholar 

  54. 54.

    Contreras-García J, Silvi B, Martín Pendás A, Recio JM (2009) J Chem Theory Comput 5:164

    Article  Google Scholar 

  55. 55.

    Cohen ML (1985) Phys Rev B 32:7988

    CAS  Article  Google Scholar 

  56. 56.

    Manca P (1961) J Phys Chem Solids 20:268

    CAS  Article  Google Scholar 

  57. 57.

    Martin RM (1968) Chem Phys Lett 2:268

    CAS  Article  Google Scholar 

  58. 58.

    Kohout M, Savin A (1996) Int J Quant Chem 60:875

    CAS  Article  Google Scholar 

  59. 59.

    Gasquez JL, Ortiz E (1984) J Chem Phys 81:2741

    Article  Google Scholar 

  60. 60.

    Cardenas C, Ayers PW, de Proft F, Tozer DJ, Geerlings P (2011) Phys Chem Chem Phys 13:2285

    CAS  Article  Google Scholar 

  61. 61.

    Cardenas C (2011) Chem Phys Lett 513:127

    CAS  Article  Google Scholar 

  62. 62.

    Cardenas C, Tiznado W, Ayers PW, Fuentealba P (2011) J Phys Chem A 115:2325

    CAS  Article  Google Scholar 

  63. 63.

    Glasser L (2012) Inorg Chem 51:2420

    CAS  Article  Google Scholar 

  64. 64.

    Yang W, Parr R (1987) Phys Chem Miner 15:191

    CAS  Article  Google Scholar 

  65. 65.

    Contreras-Garcia J, Mori-Sánchez P, Silvi B, Recio JM (2009) J Chem Theor Comp 5:2108

    CAS  Article  Google Scholar 

  66. 66.

    Martín Pendás A, Costales A, Blanco MA, Recio JM, Luaña V (2000) Phys Rev B 62:13970

    Article  Google Scholar 

  67. 67.

    Fuentealba P (2016) Solvay workshop “Conceptual quantum chemistry: Present aspects and challenges for the future”. Brussels, Belgium

Download references

Acknowledgments

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,

Author information

Affiliations

Authors

Corresponding author

Correspondence to J. Contreras-García.

Additional information

This paper belongs to Topical Collection Festschrift in Honor of Henry Chermette

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Contreras-García, J., Cardenas, C. On understanding the chemical origin of band gaps. J Mol Model 23, 271 (2017). https://doi.org/10.1007/s00894-017-3434-5

Download citation

Keywords

  • Conceptual DFT
  • ELF
  • Bond charge model
  • Band gap
  • Compressibility