Polarization, donor–acceptor interactions, and covalent contributions in weak interactions: a clarification

  • Timothy Clark
Original Paper
Part of the following topical collections:
  1. P. Politzer 80th Birthday Festschrift


The concepts of polarization (induction), charge transfer and covalent bonding contributions are discussed in terms of weak interactions. They are shown to be different incarnations of the same phenomenon, so that using polarization to describe them is most consistent as it is the only real, measurable and uniquely defined quantity of the three. Dispersion is discussed as a form of polarization within the Feynman description. Model calculations are described.

Graphical abstract

The electron density of a hydride ion (nucleus white) polarized by a single positive point charge (brown)


Bonding theory Hydrogen bonds Halogen bonds Polarization Charge transfer 



I thank above all Peter Politzer for discussions, instruction, and endless patience in turning weird ideas into equations named after bars on two continents.


  1. 1.
    Lewis GN (1916) The atom and the molecule. J Am Chem Soc 38:762–785CrossRefGoogle Scholar
  2. 2.
    Fukui K (1975) Theory of orientation and stereoselection. Springer, BerlinCrossRefGoogle Scholar
  3. 3.
    Chen J, Martínez T (2007) QTPIE: charge transfer with polarization current equalization. A fluctuating charge model with correct asymptotics. Chem Phys Lett 438:315–320CrossRefGoogle Scholar
  4. 4.
    Jansen HB, Ros P (1969) Non-empirical molecular orbital calculations on the protonation of carbon monoxide. Chem Phys Lett 3:140–143CrossRefGoogle Scholar
  5. 5.
    Liu B, McLean AD (1973) Accurate calculation of the attractive interaction of two ground state helium atoms. J Chem Phys 59:4557–4558CrossRefGoogle Scholar
  6. 6.
    Weinhold F, Landis CR (2005) Valency and bonding: a natural bond orbital donor-acceptor perspective. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  7. 7.
    Clark T, Hennemann M, Murray JS, Politzer P (2007) Halogen bonding: the σ-hole. J Mol Model 13:291–296CrossRefGoogle Scholar
  8. 8.
    Clark T (2013) σ-Holes. WIREs Comput Mol Sci 3:13–20CrossRefGoogle Scholar
  9. 9.
    Scheiner S (1997) Hydrogen bonding. Oxford University Press, OxfordGoogle Scholar
  10. 10.
    Jeffrey GA (1997) An introduction to hydrogen bonding. Oxford University Press, OxfordGoogle Scholar
  11. 11.
    Clark T (2017) Halogen bonds and σ-holes. “Halogen bonding in Supramolecular and solid state chemistry”. Faraday Discuss.
  12. 12.
    Extance A (2017) Do hydrogen bonds have covalent character? Chem World 14:39Google Scholar
  13. 13.
    Lennard-Jones J (1929) The electronic structure of some diatomic molecules. Trans Faraday Soc 25:668–686CrossRefGoogle Scholar
  14. 14.
    Kutzelnigg W (1996) Friedrich Hund and chemistry. Angew Chem Int Ed 35:572–586CrossRefGoogle Scholar
  15. 15.
    Coulson CA (1939) The electronic structure of some polyenes and aromatic molecules. VII. Bonds of fractional order by the molecular orbital method. Proc R Soc A169:413–428CrossRefGoogle Scholar
  16. 16.
    Mulliken RS (1955) Electronic population analysis on LCAOMO molecular wave functions. I. J Chem Phys 23:1833–1840CrossRefGoogle Scholar
  17. 17.
    Glendening ED, Landis CR, Weinhold F (2012) Natural bond orbital methods. WIREs Comput Mol Sci 2:1–42CrossRefGoogle Scholar
  18. 18.
    Khaliullin RZ, Bell AT, Head-Gordon M (2008) Analysis of charge transfer effects in molecular complexes based on absolutely localized molecular orbitals. J Chem Phys 128:184112CrossRefGoogle Scholar
  19. 19.
    Azar RJ, Head-Gordon M (2012) An energy decomposition analysis for intermolecular interactions from an absolutely localized molecular orbital reference at the coupled cluster singles and doubles level. J Chem Phys 136:024103CrossRefGoogle Scholar
  20. 20.
    Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theor Chim Acta 44:129–138CrossRefGoogle Scholar
  21. 21.
    Bader RF (1994) Atoms in molecules: a quantum theory (international series of monographs on chemistry 22). Clarendon, OxfordGoogle Scholar
  22. 22.
    Alcoba DR, Lain L, Torre A, Bochicchio RC (2005). Chem Phys Lett 407:379–383CrossRefGoogle Scholar
  23. 23.
    Timerghazin QK, Peslherbe GH (2007) Non-nuclear attractor of electron density as a manifestation of the solvated electron. J Chem Phys 127:064108CrossRefGoogle Scholar
  24. 24.
    Bader RWF, Slee TS, Cremer D, Kraka E (1983) Description of conjugation and hyperconjugation in terms of electron distributions. J Am Chem Soc 105:5061–5068CrossRefGoogle Scholar
  25. 25.
    Vries RY, Briels W, Feil D (1996) Critical analysis of non-nuclear electron-density maxima and the maximum entropy method. Phys Rev Lett 77:1719–1722CrossRefGoogle Scholar
  26. 26.
    Bader RFW, Matta CF (2004) Atomic charges are measurable quantum expectation values: a rebuttal of criticisms of QTAIM charges. J Phys Chem A 108:8385–8394CrossRefGoogle Scholar
  27. 27.
    Hellmann H (1933) Zur Rolle der kinetischen Elektronenenergie für die zwischenatomaren Kräfte. Z Phys 35:180–190CrossRefGoogle Scholar
  28. 28.
    Feynman RP (1939) Forces in molecules. Phys Rev 56:340–343CrossRefGoogle Scholar
  29. 29.
    Stone AJ, Misquitta AJ (2009) Charge-transfer in symmetry-adapted perturbation theory. Chem Phys Lett 473:201–205CrossRefGoogle Scholar
  30. 30.
    Scuseria GE, Janssen CL, Schaefer III HF (1988) An efficient reformulation of the closed-shell coupled cluster single and double excitation (CCSD) equations. J Chem Phys 89:7382–7387CrossRefGoogle Scholar
  31. 31.
    Wilson AK, van Mourik T, Dunning Jr TH (1996) Gaussian basis sets for use in correlated molecular calculations. VI. Sextuple zeta correlation consistent basis sets for boron through neon. J Mol Struct (THEOCHEM) 388:339–349CrossRefGoogle Scholar
  32. 32.
    Peterson KA, Woon DE, Dunning Jr TH (1994) Benchmark calculations with correlated molecular wave functions. IV. The classical barrier height of the H+H2 → H2+H reaction. J Chem Phys 100:7410–7415CrossRefGoogle Scholar
  33. 33.
    Woon DE, Dunning Jr TH (1993) Gaussian-basis sets for use in correlated molecular calculations. 3. The atoms aluminum through argon. J Chem Phys 98:1358–1371CrossRefGoogle Scholar
  34. 34.
    Dunning Jr TH (1989) Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J Chem Phys 90:1007–1023CrossRefGoogle Scholar
  35. 35.
    Hehre WJ, Stewart RF, Pople JA (1969) Self-consistent molecular orbital methods. 1. Use of Gaussian expansions of Slater-type atomic orbitals. J Chem Phys 51:2657–2664CrossRefGoogle Scholar
  36. 36.
    Jordan KD, Wang F (2003) Theory of dipole-bound anions. Annu Rev Phys Chem 54:367–396CrossRefGoogle Scholar
  37. 37.
    Clark T, Politzer P, Murray JS (2015) Correct electrostatic treatment of non-covalent interactions: the importance of polarisation. WIREs Comput Mol Sci 2015:169–177CrossRefGoogle Scholar
  38. 38.
    Politzer P, Murray JS, Clark T (2015) σ-Hole bonding: a physical interpretation. Top Curr Chem 358:19–42CrossRefGoogle Scholar
  39. 39.
    Politzer P, Murray JS, Clark T (2015) Mathematical modeling and physical reality in noncovalent interactions. J Mol Model 21:52CrossRefGoogle Scholar
  40. 40.
    Pauli W (1980) General principles of quantum mechanics. Springer, Berlin, pp 103–129CrossRefGoogle Scholar
  41. 41.
    Oliveira de Sousa DW, Chaer Nascimento MA (2017) Are one-electron bonds any different from standard two-electron covalent bonds? Acc Chem Res 50:2264–2272.
  42. 42.
    Mulliken RS (1932) Electronic structures of polyatomic molecules and valence. II. General considerations. Phys Rev 41:49–71CrossRefGoogle Scholar
  43. 43.
    Hoffmann R (1982) Building bridges between inorganic and organic chemistry (Nobel lecture). Angew Chem Int Ed 21:711–724CrossRefGoogle Scholar
  44. 44.
    Haselbach E, Klemm U, Gschwind R, Bally T, Chassot L, Nitsche S (1982) ‘Non-Koopmans’ states in Stilbene Cations and a remarkable example to the “SDT-equation”: Indeno [2,1-a]indene. Helv Chim Acta 65:2464–2471CrossRefGoogle Scholar
  45. 45.
    Reed AE, Weinhold F, Curtiss LA, Pochatko DJ (1986) Natural bond orbital analysis of molecular interactions: theoretical studies of binary complexes of HF, H2O, NH3, N2, O2, F2, CO and CO2 with HF, H2O and NH3. J Chem Phys 84:5687–5705CrossRefGoogle Scholar
  46. 46.
    Stone A (2017) Natural bond orbitals and the nature of the hydrogen bond. J Phys Chem A 121:1531–1534CrossRefGoogle Scholar
  47. 47.
    Bauzá A, Frontera A (2016) RCH3⋯O interactions in biological systems: are they trifurcated H-bonds or noncovalent carbon bonds? Crystals 6:26CrossRefGoogle Scholar
  48. 48.
    El Kerdawy A, Murray JS, Politzer P, Bleiziffer P, Heßelmann A, Görling A, Clark T (2013) Directional non-covalent interactions: repulsion and dispersion. J Chem Theory Comput 9:2264–2275CrossRefGoogle Scholar
  49. 49.
    Eisenschitz R, London F (1930) Über das Verhältnis der van der Waalsschen Kräfte zu den homöopolaren Bindungskräften. Z Phys 60:491–527CrossRefGoogle Scholar
  50. 50.
    Hunt KLC (1989) Dispersion dipoles and dispersion forces: proof of Feynman’s “conjecture” and generalization to interacting molecules of arbitrary symmetry. J Chem Phys 92:1180–1187CrossRefGoogle Scholar
  51. 51.
    Odbadrakh TT, Jordan KD (2016) Dispersion dipoles for coupled Drude oscillators. J Chem Phys 144:034111CrossRefGoogle Scholar
  52. 52.
    Stone AJ (1993) Computation of charge-transfer energies by perturbation theory. Chem Phys Lett 211:101–109CrossRefGoogle Scholar
  53. 53.
    Glendening ED, Landis CR, Weinhold F (2012) Natural bond orbital methods. WIREs Comp Mol Sci 2:1–42CrossRefGoogle Scholar
  54. 54.
    Misquitta AJ (2013) Charge transfer from regularized symmetry adapted perturbation theory. J Chem Theory Comput 9:5313–5326CrossRefGoogle Scholar
  55. 55.
    Gupta K, Ghanty TK, Ghosh SK (2012) Polarizability, ionization potential, and softness of water and methanol clusters: an interrelation. J Phys Chem A 116:6831–6836CrossRefGoogle Scholar
  56. 56.
    Chandrakumar KRS, Ghanty TK, Ghosh SK (2004) Relationship between ionization potential, polarizability, and softness: a case study of lithium and sodium metal clusters. J Phys Chem A 108:6661–6666CrossRefGoogle Scholar
  57. 57.

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Computer-Chemie-Centrum, Department of Chemistry and PharmacyFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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