Advertisement

Foundations of Chemistry

, Volume 16, Issue 1, pp 3–26 | Cite as

Atoms and bonds in molecules and chemical explanations

  • Mauro Causá
  • Andreas Savin
  • Bernard SilviEmail author
Article

Abstract

The concepts of atoms and bonds in molecules which appeared in chemistry during the nineteenth century are unavoidable to explain the structure and the reactivity of the matter at a chemical level of understanding. Although they can be criticized from a strict reductionist point of view, because neither atoms nor bonds are observable in the sense of quantum mechanics, the topological and statistical interpretative approaches of quantum chemistry (quantum theory of atoms in molecules, electron localization function and maximum probability domain) provide consistent definitions which accommodate chemistry and quantum mechanics.

Keywords

Chemical bond Chemical understanding Chemical models Quantum chemistry Topological methods Statistical interpretation 

References

  1. Abegg, A.: Die valenz und das periodische system. versuch einer theorie der molekularverbindungen. Z. anorg. Chem. 39, 330–380 (1904)Google Scholar
  2. Abraham, R.H., Marsden J.E.: Foundations of Mechanics. Addison Wesley, Redwood City (1994)Google Scholar
  3. Alvarez, S., Hoffmann, R., Mealli, C.: A bonding quandary—or—a demonstration of the fact that scientists are not born with logic. Chem. Eur. J., 15(34), 8358–8373 (2009)Google Scholar
  4. Artmann, K.: Zur quantentheorie der gewinkelten valenz, i. mitteilung: Eigenfunktion und valenzbetätigung des zentralatoms. Z. Naturf. 1, 426–432 (1946)Google Scholar
  5. Aslangul, C.: Introduction of information theory in study of electron localizability in atoms and molecules. Compt. Rend. Acad. Sci. Ser. B 272(1), 1 (1971)Google Scholar
  6. Aslangul, C., Constanciel, R., Daudel, R., Kottis, P.: Aspects of the localizability of electrons and molecules: loge theory and related methods. In: Löwdin P.O. (eds.) Advances in Quantum Chemistry, vol. 6, pp. 93–141. Academic Press, New York (1972)Google Scholar
  7. Aslangul, C., Constanciel, R., Daudel, R., Esnault, L., Ludeña, E.V.: The loge theory as a starting point for variational calculations. I. General formalism. Int. J. Quant. Chem. 8, 499–522 (1974)Google Scholar
  8. Ayers, P.W.: Electron localization functions and local measures of the covariance. J. Chem. Sci. 117, 441–454 (2005)Google Scholar
  9. Bader, R.F.W.: Binding regions in polyatomic molecules and electron density distributions. J. Am. Chem. Soc. 86, 5070–5075 (1964)Google Scholar
  10. Bader, R.F.W.: Molecular fragments or chemical bonds? Acc. Chem. Res. 8, 34–40 (1975)Google Scholar
  11. Bader, R.F.W.: Atoms in molecules. Acc. Chem. Res. 18, 9–15 (1985)Google Scholar
  12. Bader, R.F.W.: Atoms in Molecules: A Quantum Theory. Oxford University Press, Oxford (1990)Google Scholar
  13. Bader, R.F.W.: A quantum theory of molecular structure and its applications. Chem. Rev. 91(5), 893–928 (1991)Google Scholar
  14. Bader, R.F.W.: The quantum mechanical basis of conceptual chemistry. Monatsh. Chem. 136, 819–854 (2005)Google Scholar
  15. Bader, R.F.W.: Everyman’s derivation of the theory of atoms in molecules. J. Phys. Chem. A 111, 7966–7972 (2007)Google Scholar
  16. Bader, R.F.W.: On the non-existence of parallel universes in chemistry. Found. Chem. 13, 11–37 (2011)Google Scholar
  17. Bader, R.F.W., Essén, H.: The characterization of atomic interactions. J. Chem. Phys. 80, 1943–1960 (1984)Google Scholar
  18. Bader, R.F.W., Matta, C.F.: Atoms in molecules as non-overlapping, bounded, space-filling open quantum systems. Found. Chem. (2012). doi: 10.1007/s10698-012-9153-1
  19. Bader, R.F.W., Nguyen-Dang, T.T.: Quantum theory of atoms in molecules—Dalton revisited. In: Advances in Quantum Chemistry, vol. 14, pp. 63–124. Academic Press, New York (1981)Google Scholar
  20. Bader, R.F.W., Henneker, W.H., Cade, P.E.: Molecular charge distributions and chemical binding. J. Chem. Phys. 46, 3341–3363 (1966)Google Scholar
  21. Bader, R.F.W., Beddall, P.M., Cade, P.E.: Partitioning and characterization of molecular charge distributions. J. Am. Chem. Soc. 93, 3095–3107 (1971)Google Scholar
  22. Bader, R.F.W., Nguyen-Dang, T.T., Tal, Y.: Quantum topology of molecular charge distributions. II. molecular structure and its change. J. Chem. Phys. 70, 4316–4329 (1979)Google Scholar
  23. Bader, R.F.W., Gillespie, R.J., MacDougall, P.J.: A physical basis for the vsepr model of molecular geometry. J. Am. Chem. Soc. 110, 7329–7336 (1988)Google Scholar
  24. Bader, R.F.W., Johnson, S., Tang, T.-H., Popelier, P.L.A.: The electron pair. J. Phys. Chem. 100, 15398–15415 (1996a)Google Scholar
  25. Bader, R.F.W., Streitwieser, A., Neuhaus, A., Laidig, K.E., Speers, P.: Electron delocalization and the fermi hole. J. Am. Chem. Soc. 118, 4959–4965 (1996b)Google Scholar
  26. Becke, A.D., Edgecombe, K.E.: A simple mesure of electron localization in atomic and molecular systems. J. Chem. Phys. 92, 5397–5403 (1990)Google Scholar
  27. Bianchi, R., Gervasio, G., Marabello, D.: Experimental electron density analysis of Mn 2(CO)10: metal-metal and metal-ligand bond characterization. Inorg. Chem.39, 2360–2366 (2000)Google Scholar
  28. Burdett, J.K., McCormick, T.A.: Electron localization in molecules and solids: the meaning of elf. J. Phys. Chem. A 102, 6366–6372 (1998)Google Scholar
  29. Burrau, Ø.: Berechnung des energiewertes des wasserstoffmolekel- ions (H 2+) im normalzustand. Naturwissenschaften 15, 16–17 (1927)Google Scholar
  30. Cancès, E., Keriven, R., Lodier, F., Savin, A.: How electrons guard the space: shape optimization with probability distribution criteria. Theor. Chem. Acc. 111, 373–380 (2004)Google Scholar
  31. Causà, M., Savin, A.: Maximum probability domains in crystals: the rock-salt structure. J. Phys. Chem. A 115(45), 13139–13148 (2011)Google Scholar
  32. Condon, E.U.: Wave mechanics and the normal state of the hydrogen molecule. Proc. Nat. Acad. Sci. 13, 466–470 (1927)Google Scholar
  33. Cooper, D.L., Ponec, R.: A one-electron approximation to domain-averaged fermi hole analysis. Phys. Chem. Chem.Phys. 10, 1319–1329 (2008)Google Scholar
  34. Coulson, C.A.: Valence. Clarendon, Oxford (1952)Google Scholar
  35. Cremer, D., Kraka, E.: A description of the chemical bond in terms of local properties of the electron density and energy. Croat. Chem. Acta 57, 1259–1281 (1983)Google Scholar
  36. Cremer, D., Kraka, E.: Chemical bonds without bonding electron density - does the difference electron-density analysis suffice for a description of the chemical bond? Angew. Chem. Int. Ed. Engl. 23, 627–628 (1984)Google Scholar
  37. Dalton, J.: New System of Chemical Philosophy. R. Bickerstaff, London (1808)Google Scholar
  38. Daudel, R.: Sur la localisabilité des corpuscules dans les noyaux et les cortèges électroniques des atomes et des molécules. Compt. Rend. Acad. Sci. 237(12), 601–603 (1953)Google Scholar
  39. Daudel, R., Odiot, S., Brion, H.: Théorie de la localisabilité des corpuscules .1. la notion de loge et la signification géometrique de la notion de couche dans le cortège électronique des atomes. J. Chim. Phys. 51(2), 74–77 (1954)Google Scholar
  40. Daudel, R., Brion, H., Odiot, S. Localizability of electrons in atoms and molecules—application to the study of the notion of shell and of the nature of chemical bonds. J. Chem. Phys. 23(11), 2080–2083 (1955)Google Scholar
  41. De Proft, F., Geerlings, P.: Conceptual and computational DFT in the study of aromaticity. Chem. Rev. 101, 1451–1464 (2001)Google Scholar
  42. Del Re, G.: Reaction mechanisms and chemical explanation. Ann. N. Y. Acad. Sci. 988(1), 133–140 (2003)Google Scholar
  43. Diner, S., Claverie, P.: Statistical and stochastic aspects of the delocalization problem in quantum mechanics. In: Chalvet, O., Daudel, R., Diner, S., Malrieu, J.P., (eds.) Localization and Delocalization in Quantum Chemistry, vol. II, pp. 395–448. Reidel, Dordrecht (1976)Google Scholar
  44. Dirac, P.A.M.: Quantum mechanics of many-electron systems. Proc. Roy. Soc. A 123, 714–733 (1929)Google Scholar
  45. Dobson, J.F.: Interpretation of the fermi hole curvature. J. Chem. Phys. 94, 4328–4333 (1991)Google Scholar
  46. Fourré, I., Silvi, B.: What can we learn from two-center three-electron bonding with the topological analysis of ELF? Heteroat. Chem. 18, 135–160 (2007)Google Scholar
  47. Fradera, X., Austen, M.A., Bader, R.F.W.: The lewis model and beyond. J. Phys. Chem. A 103, 304–314 (1998)Google Scholar
  48. Francisco, E., Pendás, A.M., Blanco, M.A.: Electron number probability distributions for correlated wave functions. J. Chem. Phys. 126(9), 094102 (2007)Google Scholar
  49. Friedman, M.: Explanation and scientific understanding. J. Philos. 71, 5–19 (1974)Google Scholar
  50. Gallegos, A., Carbo-Dorca, R., Lodier, F., Cancès, E., Savin, A.: Maximal probability domains in linear molecules. J. Comput. Chem. 26, 455–460 (2005)Google Scholar
  51. Geerlings, P., De Proft, F., Langenaeker, W.: Conceptual density functional theory. Chem. Rev. 103, 1793–1873 (2003)Google Scholar
  52. Gillespie, R.J.: Molecular Geometry. Van Nostrand Reinhold, London (1972)Google Scholar
  53. Gillespie, R.J.: The VSEPR model revisited. Chem. Soc. Rev. 21, 59–69 (1991)Google Scholar
  54. Gillespie, R.J.: Improving our understanding of molecular geometry and the VSEPR model through the ligand close-packing model and the analysis of electron density distributions. Coord. Chem. Chem. Rev. 197, 51–69 (2000)Google Scholar
  55. Gillespie, R.J., Nyholm, R.S.: Inorganic stereochemistry. Quart. Rev. Chem. Soc. 11, 339–380 (1957)Google Scholar
  56. Gillespie, R.J., Popelier, P.L.A.: Chemical Bonding and Molecular Geometry. Oxford University Press, Oxford (2001)Google Scholar
  57. Gillespie, R.J., Robinson, E.A.: Electron domains and the VSEPR model of molecular geometry. Angew. Chem. Int. Ed. Engl. 35, 495–514 (1996)Google Scholar
  58. Gillespie, R.J., Robinson, E.A.: Models of molecular geometry. J. Comput. Chem. 28, 87–97 (2007)Google Scholar
  59. Gillespie, R.J., Bytheway, I., Tang, T.-H., Bader, R.F.W.: Geometry of the fluorides, oxofluorides, hydrides, and methanides of vanadium(v), chromium(vi), and molybdenum(vi): understanding the geometry of non-VSEPR molecules in terms of core distortion. Inorg. Chem. 35, 3954–3963 (1996)Google Scholar
  60. Gillespie, R.J., Bayles, D., Platts, J., Heard, G.L., Bader, R. F.W.: The Lennard-Jones function: a quantitative description of the spatial correlation of electrons as determined by the exclusion principle. J. Phys. Chem. A 102, 3407–3414 (1998)Google Scholar
  61. Gourlaouen, C., Parisel, O.: Is an electronic shield at the molecular origin of saturnism? a computational modelling experiment. Angew. Chem. 119, 559–562 (2007)Google Scholar
  62. Häussermann, U., Wengert, S., Nesper, R.: Localization of electrons in intermetallic phases containing aluminium. Angew. Chem. Int. Ed. Engl. 33, 2069–2072 (1994a)Google Scholar
  63. Häussermann, U., Wengert, S., Nesper, R.: Unequivocal partitioning of crystal structures. exemplified by intermetallic phases containing aluminium. Angew. Chem. Int. Ed. Engl. 33, 2073–2076 (1994b)Google Scholar
  64. Heelan, P.A.: Paradoxes of measurement. Ann. N. Y. Acad. Sci. 988(1), 114–127 (2003)Google Scholar
  65. Heitler, W., London, F.: Wechselwirkung neutraler atome und homoöpolare bindung nach quantenmechanik. Z. Physik 44, 455–472 (1927)Google Scholar
  66. Hempel, C.G., Oppenheim, P.: Studies in the logic of explanation. Philos. Sci.15, 135–175 (1948)Google Scholar
  67. Hoffmann, R., Shaik, S., Hiberty, P.C.: A conversation on VB vs MO theory: a never-ending rivalry? Acc. Chem. Res. 36, 750–756 (2003)Google Scholar
  68. Howard, K., Zimmerman, J. Rysselberghe, P.V.: Directed valence as a property of determinant wave functions. J Chem Phys 17(7), 598–602 (1949)Google Scholar
  69. Huggins, M.L.: The structure of benzene. Sci. Technol. Human. Values 55, 679–680 (1922)Google Scholar
  70. Hund, F.: Zur deutung einiger erscheinungen in den molekelspektren. Z. Physik. 36, 657–674 (1926)Google Scholar
  71. Hund, F.: Zur deutung der molekelspektren. iv. Z. Physik. 51, 759–795 (1928)Google Scholar
  72. Hund, F.: Zur frage der chemischen bindung. Z. Physik. 73, 1–30 (1932)Google Scholar
  73. Ingold, C.K.: The structure of the benzene nucleus, part I: intranuclear tautomerism. J. Chem. Soc. 121, 1133–1143 (1922)Google Scholar
  74. Ingold, C.K.: Significance of tautomerism and of the reactions of aromatic compounds in the electronic theory of organic reactions. J. Chem. Soc., 143, 1120–1127 (1933)Google Scholar
  75. Ingold, C.K.: Mesomerism and tautomerism. Nat. Environ. Pollut. Technol. 133, 946–947 (1934)Google Scholar
  76. Jayatilaka, D., Grimwood, D.: Electron localization functions obtained from x-ray constrained Hartree–Fock wavefunctions for molecular crystals of ammonia, urea and alloxan. Acta Cryst. A 60, 111–119 (2004)Google Scholar
  77. Kitcher, P.: Explanatory unification. Philos. Sci 48, 507–531 (1981)Google Scholar
  78. Kohout, M., Pernal, K., Wagner, F.R., Grin, Y.: Electron localizability indicator for correlared wavefunctions. I. Parallel spin pairs. Theor. Chem. Acc. 112, 453–459 (2004)Google Scholar
  79. Kohout, M., Pernal, K., Wagner, F.R., Grin, Y.: Electron localizability indicator for correlared wavefunctions. I. Antiparallel spin pairs. Theor. Chem. Acc. 113, 287–293 (2005)Google Scholar
  80. Kraka, E., Cremer, D.: Description of chemical reactions in terms of the properties of the electron density. J. Mol. Struct. (Theochem), 255, 189–206 (1992)Google Scholar
  81. Laming, R.: Observation on a paper by prof. Faraday concerning electric conduction and the nature of matter. Phil. Mag. 27, 420–423 (1845)Google Scholar
  82. Lennard-Jones, J. E.: The electronic structure of some diatomic molecules. Trans. Faraday Soc. 25, 668–686 (1929)Google Scholar
  83. Lennard-Jones, J.E.: The spatial correlation of electrons in molecules. J. Chem. Phys. 20, 1024–1029 (1952)Google Scholar
  84. Lewis, G.N.: The atom and the molecule. J. Am. Chem. Soc. 38, 762–786 (1916)Google Scholar
  85. Lewis, G.N.: Valence and the Structure of Atoms and Molecules. Dover, New York (1966)Google Scholar
  86. Linnett, J.W.: A modification of the Lewis-Langmuir octet rule. J. Am. Chem. Soc. 83, 2643–2653 (1961)Google Scholar
  87. Linnett, J.W.: The Electronic Structure of Molecules. A new approach. Methuen, London (1964)Google Scholar
  88. Lopes, Jr., O.M., Braida, B., Causa, M., Savin, A.: Understanding maximum probability domains with simple models. In: Hoggan, P.E.E., Brandas, E.J.J., Maruani, J., Piecuch, P., DelgadoBarrio, G., (ed.) Advances in the Theory of Quantum Systems in Chemistry and Physics, vol. 22 of Progress in Theoretical Chemistry and Physics, pp. 173–184. Springer, Netherlands (2010)Google Scholar
  89. Lüchow, A., Petz, R.: Single electron densities: a new tool to analyze molecular wavefunctions. J. Comput. Chem. 32, 2619–2626 (2011)Google Scholar
  90. Luken, W.L.: Properties of the fermi hole in molecules. Croat. Chem. Acta 57, 1283–1294 (1984)Google Scholar
  91. Luken, W.L., Culberson, J.C.: Mobility of the fermi hole in a single-determinant wavefunction. Int. J. Quant. Chem. 22, 265–276 (1982)Google Scholar
  92. Luken, W.L., Culberson, J.C.: Localized orbitals based on the fermi hole. Theor. Chim. Acta (Berlin), 66, 279–293 (1984)Google Scholar
  93. Macchi, P., Proserpio, D.M., Sironi, A.: Experimental electron density in a transition metal dimer: metal-metal and metal-ligand bonds. J. Am. Chem. Soc. 120, 13429–13435 (1998)Google Scholar
  94. Malcolm, N.O.J., Popelier, P.L.A.: The full topology of the Laplacian of the electron density: scrutinising a physical basis for the vsepr model. Faraday Discuss. 124, 353–363 (2003)Google Scholar
  95. Martín Pendás, A., Francisco, E., Blanco, M.A.: Pauling resonant structures in real space through electron number probability distributions. J. Phys. Chem. A 111(6), 1084–1090 (2007a)Google Scholar
  96. Martín Pendás, A., Francisco, E., Blanco, M.A.: An electron number distribution view of chemical bonds in real space. Phys. Chem. Chem.Phys. 9, 1087–1092 (2007b)Google Scholar
  97. Martín Pendás, A., Francisco, E., Blanco, M.A.: Spin resolved electron number distribution functions: how spins couple in real space. J. Chem. Phys. 127, 144103 (2007c)Google Scholar
  98. Martín Pendás, A., Francisco, E., Blanco, M.: Electron-electron interactions between ELF basins. Chem. Phys. Lett. 454,396–403 (2008)Google Scholar
  99. Matito, E., Silvi, B., Duran, M., Solà, M.: Electron localization function at the correlated level. J. Chem. Phys. 125, 024301 (2006)Google Scholar
  100. McNaught, A.D., Wilkinson, A.: Compendium of Chemical Terminology The Gold Book, 2nd edn. Blackwell Science, Oxford (1997)Google Scholar
  101. Mori-Sánchez, P., Martín Pendás, A., Luaña, V.: A classification of covalent, ionic, and metallic solids based on the electron density. J. Am. Chem. Soc. 124, 14721–14723 (2002)Google Scholar
  102. Mulliken, R.S.: The assignment of quantum numbers for electrons in molecules. I. Phys. Rev. 32, 186–222 (1928a)Google Scholar
  103. Mulliken, R.S.: The assignment of quantum numbers for electrons in molecules. ii. correlation of molecular and atomic electron states. Phys. Rev. 32, 761–772 (1928b)Google Scholar
  104. Nalewajski, R.F., Koster, A.M., Escalante, S.: Electron localization function as information measure. J. Phys. Chem. A 109(44), 10038–10043 (2005)Google Scholar
  105. Parr, R.G., Pearson, R.G.: Absolute hardness: companion parameter to absolute electronegativity. J. Am. Chem. Soc. 105, 7512–7516 (1983)Google Scholar
  106. Parr, R.G., Donnelly, R.A., Levy, M., Palke, W.E.: Electronegativity: the density functional viewpoint. J. Chem. Phys. 68(8), 3801–3807 (1978)Google Scholar
  107. Pauli, W.: über den einfluss der geschwindigkeitsabhängigkeit der elektronenmasse auf den zeemaneffekt. Z. Phys. 31, 373–385 (1925)Google Scholar
  108. Pauling, L.: The Nature of the Chemical Bond. Cornell University Press, Ithaca (1948)Google Scholar
  109. Pauling, L.: Modern structural chemistry. Nobel Lecture (1954)Google Scholar
  110. Pilme, J., Piquemal, J.-P.: Advancing beyond charge analysis using the electronic localization function chemically intuitive distribution of electrostatic moments. J. Comput. Chem. 29, 1440–1449 (2008)Google Scholar
  111. Pitzer, K.S.: Electron deficient molecules. i. the principles of hydroboron structures. J. Am. Chem. Soc. 67, 1126–1132 (1946)Google Scholar
  112. Ponec, R.: Electron pairing and chemical bonds. Chemical structure, valences and structural similarities from the analysis of the fermi holes. J. Math. Chem. 21, 323–333 (1997)Google Scholar
  113. Ponec, R.: Electron pairing and chemical bonds. molecular structure from the analysis of pair densities and related quantities. J. Math. Chem. 23, 85–103 (1998)Google Scholar
  114. Ponec, R., Duben, A.J.: Electron pairing and chemical bonds: bonding in hypervalent molecules from analysis of fermi holes. J. Comput. Chem. 20, 760–771 (1999)Google Scholar
  115. Ponec, R., Roithova, J.: Domain-averaged Fermi holes—a new means of visualization of chemical bonds: bonding in hypervalent molecules. Theor. Chem. Acc. 105, 383–392 (2001)Google Scholar
  116. Ponec, R., Cooper, D.L., Savin, A.: Analytic models of domain-averaged Fermi holes: a new tool for the study of the nature of chemical bonds. Chem. Eur. J. 14, 3338–3345 (2008)Google Scholar
  117. Popper, K.R.: Quantum Theory and the Schism in Physics: From The Postscript to the Logic of Scientific Discovery. Routledge, Oxon (1992)Google Scholar
  118. Salem, L.: Faithful couple: the electron pair. J. Chem. Educ. 55(6), 344–348 (1978)Google Scholar
  119. Salmon, W.: Explanation and the causal structure of the world. Princeton University Press, Princeton, NJ (1984)Google Scholar
  120. Savin, A.: On the significance of ELF basins. J. Chem. Sci. 117, 473–475 (2005)Google Scholar
  121. Savin, A., Becke, A.D., Flad, J., Nesper, R., Preuss, H., von Schnering, H.G.: A new look at electron localization. Angew. Chem. Int. Ed. Engl. 30, 409 (1991)Google Scholar
  122. Savin, A., Jepsen, O., Flad, J., Andersen, O.K., Preuss, H., von Schnering, H.G.: Electron localization in the solid-state structures of the elements: the diamond structure. Angew. Chem. Int. Ed. Engl. 31, 187–190 (1992)Google Scholar
  123. Savin, A., Silvi, B., Colonna, F.: Topological analysis of the electron localization function applied to delocalized bonds. Can. J. Chem. 74, 1088–1096 (1996)Google Scholar
  124. Savin, A., Nesper, R., Wengert, S., Fässler, T.F.: ELF: The electron localization function. Angew. Chem. Int. Ed. Engl. 36, 1809–1832 (1997)Google Scholar
  125. Scemama, A., Chaquin, P., Caffarel, M.: Electron pair localization function: a practical tool to visualize electron localization in molecules from quantum Monte Carlo data. J. Chem. Phys. 121, 1725–1735 (2004)Google Scholar
  126. Scemama, A., Caffarel, M., Savin, A.: Maximum probability domains from quantum Monte Carlo calculations. J. Comput. Chem. 28, 442 (2007)Google Scholar
  127. Scerri, E.R.: Philosophy of chemistrys-a new interdisciplinary field?. J. Chem. Educ. 77(4), 522 (2000)Google Scholar
  128. Schmider, H.L., Becke, A.D.: Chemical content of the kinetic energy density. J. Mol. Struct. (Theochem) 527, 51–61 (2000)Google Scholar
  129. Shaik, S.S., Danovich, D., Silvi, B., Lauvergnat, D., Hiberty, P.: Charge-shift bonding–a class of electron pair bonds emerges from valence bond theory and supported by electron localization function approach. Chem. Eur. J. 21, 6358–6371 (2005)Google Scholar
  130. Shannon, C.E., Weaver, W.: The Mathematical Theory of Communication. The University of Illinois Press, Urbana (1949)Google Scholar
  131. Sidgwick, N.V., Powell, H.M.: Bakerian lecture. stereochemical types and valency groups. Proc. Roy. Soc. A 176, 153–180 (1940)Google Scholar
  132. Silvi, B.: The synaptic order: a key concept to understand multicenter bonding. J. Mol. Struct. 614, 3–10 (2002)Google Scholar
  133. Silvi, B.: The spin pair compositions as local indicators of the nature of the bonding. J. Phys. Chem. A 107, 3081–3085 (2003)Google Scholar
  134. Silvi, B.: How topological partitions of the electron distributions reveal delocalization. Phys. Chem. Chem. Phys. 6, 256–260 (2004)Google Scholar
  135. Silvi, B., Gatti, C.: Direct space representation of the metallic bond. J. Phys. Chem. A 104, 947–953 (2000)Google Scholar
  136. Silvi, B., Gillespie, R.: The ELF topological analysis contribution to conceptual chemistry and phenomenological models. In: Matta, C.F., Boyd, R.J., (eds.) The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design, pp. 141–161. Wiley, New York (2007)Google Scholar
  137. Silvi, B., Savin, A.: Classification of chemical bonds based on topological analysis of electron localization function. Nature 371, 683–686 (1994)Google Scholar
  138. Silvi, B., Fourré, I., Alikhani, E.: The topological analysis of the electron localization function: a key for a position space representation of chemical bonds. Monatsh. Chem. 136, 855–879 (2005)Google Scholar
  139. Strevens, M.: The causal and unification approaches to explanation unified-causally. Noûs 38, 154–176 (2004)Google Scholar
  140. Strevens, M.: Scientific explanation. In: Borchert, D.M. (ed.) Encyclopedia of Philosophy, 2nd edn. Mcmillan Reference USA, Detroit (2006)Google Scholar
  141. Thom, R.: Prédire n’est pas expliquer. Flammarion, Paris (1993)Google Scholar
  142. Thomson, J.J.: On the structure of the atom: an investigation of the stability and periods of oscillation of a number of corpuscles arranged at equal intervals around the circumference of a circle; with application of the results to the theory of atomic structure. Phil. Mag. 7, 237–265 (1904)Google Scholar
  143. Tsirelson, V., Stash, A.: Determination of the electron localization function from electron density. Chem. Phys. Lett. 351, 142–148 (2002)Google Scholar
  144. Uhlenbeck, S.G.G.: Spinning electrons and the structure of spectra. Nature 117, 264–265 (1926)Google Scholar
  145. Uhlenbeck, G.E., Goudsmit, S.: Ersetzung der hypothese vom unmechanischen zwang durch eine forderung bezglich des inneren verhaltens jedes einzelnen elektrons. Naturwissenschaften 13, 953–954 (1925)Google Scholar
  146. van Brakel, J.: The ignis fatuusa of reduction and unification. Ann. N. Y. Acad. Sci. 988, 30–43 (2003)Google Scholar
  147. van Brakel, J.: Kant’s legacy for the philosophy of chemistry. In: Baird, D., Scerri, E., McIntyre, L. (eds.) Philosophy Of Chemistry, vol. 242 of Boston Studies in the Philosophy of Science, pp. 69–91. Springer, Netherlands (2006)Google Scholar
  148. Vasconi, P.: Sistema delle scienze naturali e unitsà della conoscenza nell’ultimo Kant. Leo S. Olschki, Firenze (1999)Google Scholar
  149. von Weizsäcker, C.F.: Zur theorie der kermassen. Z. Phys. 96, 431–458 (1935)Google Scholar
  150. Wagner, F.R., Bezugly, V., Kohout, M., Grin, Y.: Charge decomposition analysis of the electron localizability indicator: a bridge between the orbital and direct space representation of the chemical bond. Chem. Eur. J. 13, 5724–5741 (2007)Google Scholar
  151. Woodward J.: Scientific explanation. In: Zalta E.N. (ed.) The Stanford Encyclopedia of Philosophy. Winter 2011 edition (2011)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Dip. di ChimicaUniversitá di Napoli Federico IINaplesItaly
  2. 2.Laboratoire de Chimie Théorique (UMR-CNRS 7616)Université Pierre et Marie CurieParisFrance

Personalised recommendations