Advertisement

Topological Approaches of the Bonding in Conceptual Chemistry

  • Bernard SilviEmail author
  • M. Esmail Alikhani
  • Christine Lepetit
  • Remi ChauvinEmail author
Chapter
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 22)

Abstract

Though almost a century old, Lewis’s theory of chemical bonding remains at the heart of the understanding of chemical structure. In spite of their basic discrete nature, Lewis’s structures (topological 0-manifolds) continue to lend themselves to sophisticated treatments leading to valuable results in terms of topological analysis of chemical properties. The bonding topology is however not only defined, but also refined by direct consideration of the nuclear geometry, itself determined by the configuration of the embedding electron cloud. During the last century, the theory has thus been complemented by the mesomery concept, by the Linnett’s double quartet scheme and by the VSEPR/LCP models. These models rely on an assumed spatial disposition of the electrons which does not take the quantum mechanical aspects into account. These models are reexamined by investigation of the topological 1-manifolds generated by the gradient field of potential functions featuring the electron cloud configuration, such as the electron density or electron localization function (ELF). In this chapter, we reexamine these models in order to escape from the quantum mechanical dilemma and we show how topological analyzes enable to recover these models.

Keywords

Molecular Graph Electron Localization Function Valence Shell Kinetic Energy Density Lewis Structure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Dalton J (1808) New system of chemical philosophy. R. Bickerstaff, LondonGoogle Scholar
  2. 2.
    Brown AC (1864) Trans Roy Soc Edinb 23:707CrossRefGoogle Scholar
  3. 3.
    Brown AC (1865) J Chem Soc 18:230CrossRefGoogle Scholar
  4. 4.
    Babaev EV (1999) Chemical topology: introduction and fundamentals. In: Bonchev D, Rouvray R (eds). Gordon and Breach, Reading, pp 167–264Google Scholar
  5. 5.
    Sylvester JJ (1878) Nature 17:284CrossRefGoogle Scholar
  6. 6.
    Kekulé von Stardonitz FA (1857) Annalen der Chemie und Pharmacie 106:129CrossRefGoogle Scholar
  7. 7.
    Lewis GN (1916) J Am Chem Soc 38:762CrossRefGoogle Scholar
  8. 8.
    Berzélius JJ (1819) Essai sur la théorie des proportions chimiques et sur l’influence chimique de l’électricité, par J. J. Berzélius,… Traduit du suédois sous les yeux de l’auteur et publié par lui-même. Méquignon-Marvis, ParisGoogle Scholar
  9. 9.
    Laming R (1845) Phil Mag 27:420Google Scholar
  10. 10.
    Abegg A, Anorg Z (1904) Chem 39:330Google Scholar
  11. 11.
    Thomson JJ (1904) Phil Mag 7:237CrossRefGoogle Scholar
  12. 12.
    Huggins ML (1922) Science 55:679CrossRefGoogle Scholar
  13. 13.
    Ingold CK (1922) J Chem Soc 121:1133CrossRefGoogle Scholar
  14. 14.
    Ingold CK (1933) J Chem Soc 143:1120CrossRefGoogle Scholar
  15. 15.
    Linnett JW (1961) J Am Chem Soc 83:2643CrossRefGoogle Scholar
  16. 16.
    Linnett JW (1964) The electronic structure of molecules. A new approach. Methuen, LondonGoogle Scholar
  17. 17.
    Maraval V, Chauvin R (2007) New J Chem 31:1853CrossRefGoogle Scholar
  18. 18.
    Chauvin R (1996) J Math Chem 19:147CrossRefGoogle Scholar
  19. 19.
    Sidgwick NV, Powell HM (1940) Proc Roy Soc A 176:153CrossRefGoogle Scholar
  20. 20.
    Gillespie RJ, Nyholm RS (1957) Quart Rev Chem Soc 11:339CrossRefGoogle Scholar
  21. 21.
    Gillespie RJ (1963) J Chem Educ 40:295CrossRefGoogle Scholar
  22. 22.
    Gillespie RJ (1991) Chem Soc Rev 21:59CrossRefGoogle Scholar
  23. 23.
    Gillespie RJ, Robinson EA (1996) Angew Chem Int Ed Engl 35:495CrossRefGoogle Scholar
  24. 24.
    Lepetit C, Maraval V, Canac Y, Chauvin R (2016) Coord Chem Rev.308:59Google Scholar
  25. 25.
    Ayers PL, Boyd RJ, Bultinck P, Caffarel M, Carbó-Dorca R, Causá M, Cioslowski J, Contreras-Garcia J, Cooper DL, Coppens P, Gatti C, Grabowsky S, Lazzeretti P, Macchi P, Martín Pendás A, Popelier PL, Ruedenberg K, Rzepa H, Savin A, Sax A, Schwarz WE, Shahbazian S, Silvi B, Solà M, Tsirelson V (2015) Comput Theor Chem 1053(2). Special Issue: Understanding structure and reactivity from topology and beyondGoogle Scholar
  26. 26.
    Diudea MV, Gutman I, Lorentz J (1999) Molecular topology. Nova Science, Huntington, New YorkGoogle Scholar
  27. 27.
    Restrepo G, Villaveces JL (2012) Int J Phil Chem 18:3Google Scholar
  28. 28.
    Wiener H (1947) J Am Chem Soc 69:17CrossRefGoogle Scholar
  29. 29.
    Gutman I (1978) Ber Math Stat Sekt Forschungszentrum Graz 103:1Google Scholar
  30. 30.
    Gutman I, Milun M, Trinajstic N (1976) Croat Chem Acta 48:87Google Scholar
  31. 31.
    Aihara J (1976) J Am Chem Soc 98:2750CrossRefGoogle Scholar
  32. 32.
    Sachs H (1962) Publ Math (Debrecen) 9:270Google Scholar
  33. 33.
    Heilmann O, Lieb E (1972) Commun Math Phys 25:190CrossRefGoogle Scholar
  34. 34.
    Chauvin R, Lepetit C, Fowler PW, Malrieu JP (2010) Phys Chem Chem Phys 12:5295CrossRefGoogle Scholar
  35. 35.
    Chauvin R, Lepetit C (2013) Phys Chem Chem Phys 15:3855CrossRefGoogle Scholar
  36. 36.
    Estrada E (2000) Chem Phys Lett 319:713CrossRefGoogle Scholar
  37. 37.
    Dirac PAM (1929) Proc Roy Soc A 123:714CrossRefGoogle Scholar
  38. 38.
    Thom R (1993) Prédire n’est pas expliquer. Flammarion, ParisGoogle Scholar
  39. 39.
    Popelier PLA (2007) Faraday Discuss 135:3CrossRefGoogle Scholar
  40. 40.
    Hellmann H (1937) Einführung in die Quantenchemie. Franz Deuticke, Leipzig and ViennaGoogle Scholar
  41. 41.
    Feynman RP (1939) Phys Rev 56:340CrossRefGoogle Scholar
  42. 42.
    Hurley AC (1954) Proc Roy Soc AGoogle Scholar
  43. 43.
    Hurley AC (1954) Proc Roy Soc A 226(1165):179CrossRefGoogle Scholar
  44. 44.
    Hohenberg P, Kohn W (1964) Phys Rev 136:B864CrossRefGoogle Scholar
  45. 45.
    McWeeny R (1989) Methods of molecular quantum mechanics, 2nd edn. Academic Press, LondonGoogle Scholar
  46. 46.
    Wigner E (1932) Phys Rev 40(5):749CrossRefGoogle Scholar
  47. 47.
    Shewell JR (1959) Am J Phys 27:16CrossRefGoogle Scholar
  48. 48.
    Cohen L (1966) J Math Phys 7:781CrossRefGoogle Scholar
  49. 49.
    Cohen L (1979) J. Chem. Phys. 70:788CrossRefGoogle Scholar
  50. 50.
    Silvi B (2003) J Phys Chem A 107:3081CrossRefGoogle Scholar
  51. 51.
    Kohout M, Pernal K, Wagner FR, Grin Y (2004) Theor Chem Acc 112:453CrossRefGoogle Scholar
  52. 52.
    Kohout M, Pernal K, Wagner FR, Grin Y (2005) Theor Chem Acc 113:287CrossRefGoogle Scholar
  53. 53.
    Becke AD, Edgecombe KE (1990) J Chem Phys 92:5397CrossRefGoogle Scholar
  54. 54.
    Silvi B, Fourré I, Alikhani E (2005) Monatsh Chem 136:855CrossRefGoogle Scholar
  55. 55.
    Ayers PW (2005) J Chem Sci 117:441CrossRefGoogle Scholar
  56. 56.
    Gadre SR, Shirsat RN (2000) Electrostatics of atoms and molecules. Universities Press, HyderabadGoogle Scholar
  57. 57.
    Balanarayan P, Gadre SR (2003) J Chem Phys 119:5037CrossRefGoogle Scholar
  58. 58.
    Espinosa E, Lecomte C, Molins E (1999) Chem Phys Lett 300:745CrossRefGoogle Scholar
  59. 59.
    Cao WL, Gatti C, MacDougall PJ, Bader RFW (1987) Chem Phys Lett 141:380CrossRefGoogle Scholar
  60. 60.
    Gatti C, Fantucci P, Pacchioni G (1987) Theor Chim Acta (Berlin) 72:433CrossRefGoogle Scholar
  61. 61.
    Cioslowski J (1990) J Phys Chem 94:5496CrossRefGoogle Scholar
  62. 62.
    Mei C, Edgecombe KE, Smith VH Jr, Heilingbrunner A (1993) Int J Quant Chem 48:287CrossRefGoogle Scholar
  63. 63.
    Silvi B, Gatti C (2000) J Phys Chem A 104:947CrossRefGoogle Scholar
  64. 64.
    Martín Pendás A, Blanco MA, Costales A, Mori Sánchez P, Luaña V (1999) Phys Rev Lett 83:1930Google Scholar
  65. 65.
    Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford Univ Press, OxfordGoogle Scholar
  66. 66.
    Bader RFW (1994) Phys Rev B 49:13348CrossRefGoogle Scholar
  67. 67.
    Bader RFW (2001) Theor Chem Acc 105:276CrossRefGoogle Scholar
  68. 68.
    Bader RFW (2005) Monatsh Chem 136:819CrossRefGoogle Scholar
  69. 69.
    Bader RFW (2007) J Phys Chem A 111:7966CrossRefGoogle Scholar
  70. 70.
    Bader RFW (2007) The quantum theory of atoms. In: Matta CF, Boyd RJ (eds) Molecules: from solid state to dna and drug design. Wiley, New York, pp 37–59Google Scholar
  71. 71.
    Srebrenik S, Bader RFW (1975) J Chem Phys 63(9):3945CrossRefGoogle Scholar
  72. 72.
    Gillespie RJ, Robinson EA (2007) J Comput Chem 28:87CrossRefGoogle Scholar
  73. 73.
    Gillespie RJ, Noury S, Pilmé J, Silvi B (2004) Inorg Chem 43:3248CrossRefGoogle Scholar
  74. 74.
    de Courcy B, Pedersen LG, Parisel O, Gresh N, Silvi B, Pilmé J, Piquemal JP (2010) J Chem Theory Comput 6:1048CrossRefGoogle Scholar
  75. 75.
    Bader RFW, Anderson SG, Duke AJ (1979) J Am Chem Soc 101:1389CrossRefGoogle Scholar
  76. 76.
    Bader RFW, Nguyen-Dang TT, Tal Y (1981) Rep Prog Phys 44:893CrossRefGoogle Scholar
  77. 77.
    Krokidis X, Noury S, Silvi B (1997) J Phys Chem A 101:7277CrossRefGoogle Scholar
  78. 78.
    Tal Y, Bader RFW, Erkku J (1980) Phys Rev A 21:1CrossRefGoogle Scholar
  79. 79.
    Thom R (1972) Stabilité Structurelle et morphogénèse. Intereditions, ParisGoogle Scholar
  80. 80.
    Berski S, Andrés J, Silvi B, Domingo L (2003) J Phys Chem A 107:6014CrossRefGoogle Scholar
  81. 81.
    Polo V, Andres J, Castillo R, Berski S, Silvi B (2004) Chem Eur J 10:5165CrossRefGoogle Scholar
  82. 82.
    Santos JC, Andrés J, Aizman A, Fuentealba P, Polo V (2005) J Phys Chem A 109(16):3687CrossRefGoogle Scholar
  83. 83.
    Berski S, Andrés J, Silvi B, Domingo LR (2006) J Phys Chem A 110:13939CrossRefGoogle Scholar
  84. 84.
    Andrés J, Berski S, Domingo LR, Polo V, Silvi B (2011) Curr Org Chem 15:3566CrossRefGoogle Scholar
  85. 85.
    Andrés J, Berski S, Domingo LR, González-Navarrete P (2012) J Comput Chem 33:748CrossRefGoogle Scholar
  86. 86.
    González-Navarrete P, Domingo LR, Andrés J, Berski S, Silvi B (2012) J Comput Chem 33:2400CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Laboratoire de Chimie ThéoriqueSorbonne Universités UPMC, Univ Paris 06, UMR 7616ParisFrance
  2. 2.MONARIS, UMR 8233 CNRS/UPMC, Sorbonne Universités, UPMC Univ. Paris 06, MONARIS, UMR 8233Université Pierre et Marie CurieParisFrance
  3. 3.CNRS, MONARIS, UMR 8233Université Pierre et Marie CurieParisFrance
  4. 4.CNRS, LCC (Laboratoire de Chimie de Coordination)ToulouseFrance
  5. 5.Université de Toulouse, UPS, INPTToulouseFrance

Personalised recommendations