Physical understanding through variational reasoning: Electron sharing and covalent bonding

Journal of Physical Chemistry A

Volumn 113, Issue 10, 2009, Pages 1954-1968

  Ruedenberg, Klaus ^a   Schmidt, Michael W ^a  

^a IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AB-INITIO; COVALENT BONDINGS; ELECTRON CLOUDS; ELECTRON-SHARING; ELECTRONIC WAVE FUNCTIONS; ELECTROSTATIC POTENTIALS; ENERGY CHANGES; ENERGY FUNCTIONAL; ENERGY MINIMIZATIONS; GEOMETRIC PARAMETERS; GROUND-STATE WAVE FUNCTIONS; HYDROGEN ATOMS; HYDROGEN MOLECULES; KINETIC PRESSURES; POTENTIAL ENERGY FUNCTIONALS; STATIONARY STATE; VIRIAL THEOREMS;

BINDING ENERGY; ELECTRON ENERGY LOSS SPECTROSCOPY; GROUND STATE; HYDROGEN; KINETIC ENERGY; MOLECULAR ORBITALS; MOLECULES; POTENTIAL ENERGY; WAVE FUNCTIONS;

ATOMS;

EID: 63849224067     PISSN: 10895639     EISSN: None     Source Type: Journal    
DOI: 10.1021/jp807973x     Document Type: Article

References (54)

1. References and details regarding the early history sketched in this paragraph can be found in A. J. Rocke's book Chemical Atomism in the Nineteenth Century; Ohio State University Press: Columbus, OH, 1984.
2. See, e.g., Helmholtz's Faraday address of 1881 at the Royal Institution in London, as reported in Leo Koenigsberger's book Hermann von Helmholtz; Verlag Vieweg: Braunschweig, Germany, 1902; Vol. II, pp 278-284.
3. Earnshaw, S. Trans. Cambridge Philos. Soc. 1842, 7, 97.
4. Lewis, G. N. J. Am. Chem. Soc. 1916, 38, 762. See also: Valence and the Structure of Atoms and Molecules; ACS-sponsored monograph by the Chemical Catalog Co., 1923; republished by Dover, New York, 1966.
5. Heitler, W.; London, F. Z. Phys. 1927, 44, 455.
6. Burreau, Ø. Det. Kgl. Danske Vid. Selskab. 1927, 7, 1.
7. Pauling, L. Chem. Rev. 1928, 5, 173.
8. Finkelstein, B. N.; Horowitz, G. E. Z. Phys. 1928, 48, 118.
9. Guillemin, V.; Zener, C. Proc. Natl. Acad. Sci. U.S.A. 1929, 15, 314.
10. Hylleraas, E.A. Z. Phys. 1931, 71, 739.
11. See, e.g.: (a) Schwarz, W. H. E.; Bitter, Th. Ber. Bunsen-Ges. Phys. Chem. 1976, 80, 1231.
12. (b) Kutzelnigg, W. Einführung in die Theoretische Chemie; Verlag Chemie: Weinheim, Germany, 1978; Vol. 2.
13. (c) Bickelhaupt, F. M.; Baerends, E. J. Rev. Comput. Chem. 2000, 15, 1.
14. (d) Kovacs, A.; Esterhuysen, C.; Frenking, G. Chem.-Eur. J. 2005,11, 1813.
15. (e) Bitter, Th.; Wang, S. G.; Ruedenberg, K.; Schwarz, W. H. E. J. Comput. Chem. 2007, 28, 411.
16. Rozendahl, A.; Baerends, E. J. Chem. Phys. 1985, 95, 57.
17. Ruedenberg, K.; Schmidt, M. W. J. Comput. Chem. 2007, 28, 391.
18. Scott, T. C.; Aubert-Frecon, M.; Grotendorst, J. Chem. Phys. 2006, 324, 323. Other important accurate earlier work at R = 2.0 bohr and other distances includes Wind, H. J. Chem. Phys. 1965, 42, 2371 for the ground state and Bates, D. R.; Reid, R. H. G. Adv. At. Mol. Phys. 1968, 4, 13 for the ground and various exited states. The experimental value of 1.988 bohr is of course not the exact minimum of the electronic potential energy curve.
19. Ruedenberg, K. Rev. Mod. Phys. 1962, 34, 326, Section 7.
20. Feinberg M. J.; Ruedenberg K.; Mehler, E. In Advances in Quantum Chemistry; Lowdin, P. O., Ed.; Academic Press: New York, 1970; Vol. 5, p 27.
21. Feinberg, M. J.; Ruedenberg, K. J. Chem. Phys. 1971, 54, 1495.
22. Feinberg, M. J.; Ruedenberg, K. J. Chem. Phys. 1971, 55, 5804.
23. Ruedenberg, K. In Localization and Derealization in Quantum Chemistry; Daudel, R., Ed.; Reidel Publishing Co.: Dordrecht, The Netherlands, 1975; Vol. 1, p 222.
24. Kutzelnigg, W. Angew. Chem. 1973, 85, 551; Angew. Chem., Int. Ed. Engl. 1973, 12, 46.
25. Goddard, W. A.; Wilson, C. W. Theor. Chim. Acta 1972, 26, 195, 211.
26. Fukui, K. Chemical Reactions and Electronic Orbitals; Muruzen Co.: Tokyo, 1976; in Japanese only (Kagaku Hannoh to Denshi no Kidoh).
27. Mulliken, R. S.; Ermler, W. C. Diatomic Molecules; Academic Press: New York, 1977; Section II.F.
28. Kutzelnigg, W. Einführung in die Theoretische Chemie; Verlag Chemie: Weinheim, Germany, 1978; Vol. 2, Section 3.3.
29. Kutzelnigg, W. In The Concept of the Chemical Bond; Maksic, Z. B., Ed.; Springer: Berlin, 1990; Vol. 2, p 1.
30. Steiner, E. The Determination and Interpretation of Molecular Wave Functions; Cambridge University Press: Cambridge, U.K., 1975.
31. Klapötke, T. M.; Schulz, A.; Harcourt, R. D. Quantum chemical methods in main-group chemistry; Wiley: New York, 1998.
32. (a) See e.g. Bacskay, G. B.; Reimers, J. R.; Nordholm, S. J. Chem. Ed. 1997, 74, 1494.
33. (b) At the International Conference on Quantum Chemistry, June 12-26, 2002, at St. John's College, Cambridge, U.K., Chr. Longuet-Higgins addressed K.R. at breakfast in the presence of I. Shavitt, starting the conversation with "Forty years ago we questioned your ideas on chemical binding, but I have to hand it to you, you were right all along."
34. Hellmann, H. Z. Phys. 1933, 35, 180. See also his book Quan-tenchemie; Deuticke: Vienna, Austria, 1937.
35. Slater, J. C. J. Chem. Phys. 1933, 1, 687.
36. See, e.g.: Piatt, J. R. Encyclopedia of Physics; Springer Verlag: Berlin, 1961; Vol. 37/2.
37. See, e.g.: Peierls, R. E. Quantum Theory of Solids; Clarendon Press: Oxford, U.K., 1955; Section 5.
38. Coulson, C. A. Valence; Clarendon Press: Oxford, U.K., 1952; Section 4.5.
39. See, e.g.: Pauli, W. Die allgemeinen Prinzipien der Wellenmechanik. Handbuch der Physik; Springer: Berlin, 1933; Chapter 2, eq 150.
40. (a) Schrödinger, E. Ann. Phys. 1926, 79, 361.
41. (b) See also: Pauli, W. Die allgemeinen Prinzipien der Wellenmechanik. Handbuch der Physik; Springer: Berlin, 1933; Chapter 2, eq 148. Note for instance that a Dirac-type Hamiltonian does not have a lowest eigenvalue.
42. Löwdin, P. O. J. Mol. Spectroscopy 1959, 3, 46.
43. See ref 1 la.
44. + wave function have been elucidated by Kutzelnigg, W.; Schwarz, W. H. E. Phys. Rev. A 1982, 26, 2361.
45. A is a single Is orbital, whose orbital exponent ζ = 1.237 is obtained by energy minimization. It is very similar to the value ζ* = 1.2654, quoted after eq 4.13, which is obtained by overlap maximization.
46. Dickinson introduced the polarizing scaled p orbital: Dickinson, B. N. J. Chem. Phys. 1933, 1, 317. He found that the optimal 2ps orbital had the exponential factor exp(-ζ*r), with ζ* equal to that of the 1s* orbital in eq 4.13. Thus, the polarizing orbital was contracted to the size of the contracted 1s* orbital.
47. See refs 16 and 17.
48. A detailed discussion of this point is given in ref 17. This cancellation may also be relevant in a broader context, e.g., in the discussion of Walsh's rules. See: Buenker, R. J.; Peyerimhoff, S. D. Chem. Rev. 1974, 74, 127.
49. See ref lie, p 127.
50. See ref 15.
51. See ref 11d.
52. See ref 1la.
53. Kolos, W. J. Chem. Phys. 1994, 101, 1330. Nakatsuji, H. Phys. Rev. Lett. 2004, 93, 030403.
54. Jensen's "PC3" basis sets were used for fluorine and oxygen. They contain the following numbers of contracted orbitals: 6s, 5p, 4d, 2f, lg. See: Jensen, F. J. Chem. Phys. 2001, 115, 9113.