An analysis based on the variation principle shows that in the molecules H2+, H2, B2, C2, N2, O2, F2, covalent bonding is driven by the attenuation of the kinetic energy that results from the delocalization of the electronic wave function. For molecular geometries around the equilibrium distance, two features of the wave function contribute to this delocalization: (i) Superposition of atomic orbitals extends the electronic wave function from one atom to two or more atoms; (ii) intra-atomic contraction of the atomic orbitals further increases the inter-atomic delocalization. The inter-atomic kinetic energy lowering that (perhaps counter-intuitively) is a consequence of the intra-atomic contractions drives these contractions (which per se would increase the energy). Since the contractions necessarily encompass both, the intra-atomic kinetic and potential energy changes (which add to a positive total), the fact that the intra-atomic potential energy change renders the total potential binding energy negative does not alter the fact that it is the kinetic delocalization energy that drives the bond formation.
REFERENCES
1.
Statement by
G. M.
Whitesides
, in the Opening Plenary Lecture of the 92nd Canadian Chemistry Conference
, 30 May 2009, Hamilton, Ontario
, Canada (personal communication by K.R.).2.
Regrettably, this misconception has been reiterated in the recent
Next Generation Science Standards (NGSS)
by the National Research Council
, Washington, DC
, 2013
(http://www.nextgenscience.org) which, according toM. M.
Cooper
, J. Chem. Educ.
90
, 679
(2013
), contains the following statements: “The first physical science core idea – PS1, Matter and its Interactions – is guided by the question: How can one explain the structure, properties, and interactions of matter?”; In high school, the “sub-atomic model and interactions between electric charges can be used to explain interactions of matter”; “The disciplinary core idea [is that] stable forms of matter are those in which the electric and magnetic field energy is minimized.” (Italics added by the present authors).3.
For instance, Isaac Newton surmised that, analogous to the gravitational forces between masses, there are additional forces between atoms that are attractive at large distances and repulsive at short distances. Berzelius believed all bonds to be due to electrostatic attractions. Helmholtz conjectured the existence of short-range potentials between atoms. See, e.g.,
K.
Ruedenberg
and W. H. E.
Schwarz
, “Three millennia of atoms and molecules
,” in Pioneers of Quantum Chemistry
, ACS Symposium Series
Vol. 1122
, edited by E. T.
Strom
and A. K.
Wilson
(ACS
, Washington DC
, 2013
).4.
This interpretation was first quoted by
J. C.
Slater
, J. Chem. Phys.
1
, 687
(1933
).5.
H.
Hellmann
, Z. Phys.
85
, 180
(1933
);6.
7.
Hellmann's interpretation was however used for solids in Sec. 5 of
R. E.
Peierls
, Quantum Theory of Solids
(Clarendon Press
, Oxford
, 1955
).8.
At the Boulder Conference of 1958,
C. A.
Coulson
famously expressed apprehension that the computer-generation of accurate, but complex wave functions might endanger conceptual interpretations, Rev. Mod. Phys.
32
, 170
(1960
).9.
K.
Ruedenberg
, Rev. Mod. Phys.
34
, 326
(1962
);C.
Edmiston
and K.
Ruedenberg
, J. Phys. Chem.
68
, 1628
(1964
);M. J.
Feinberg
, K.
Ruedenberg
, and E.
Mehler
, Advances in Quantum Chemistry
, edited by P. O.
Löwdin
(Academic Press
, 1970
), Vol. 5
, p. 27
;M. J.
Feinberg
and K.
Ruedenberg
, J. Chem. Phys.
54
, 1495
(1971
);M. J.
Feinberg
and K.
Ruedenberg
, J. Chem. Phys.
55
, 5804
(1971
);K.
Ruedenberg
, in Localization and Delocalization in Quantum Chemistry
, edited by R.
Daudel
(Reidel
, Dordrecht, Holland
, 1975
). Vol. 1
, p. 222
.10.
Hellmann's work was called to Ruedenberg's attention after he first communicated his conclusions.
11.
W. A.
Goddard
and C. W.
Wilson
, Theor. Chim. Acta
26
, 195
(1972
);W. A.
Goddard
and C. W.
Wilson
, Theor. Chim. Acta
26
, 211
(1972
);W.
Kutzelnigg
, Angew. Chem.
85
, 551
(1973
);K.
Fukui
, Chemical Reactions and Electronic Orbitals
(Maruzen Co
, Tokyo
, 1976
) (Kagaku Hannoh to Denshi no Kidoh) (in Japanese);R. S.
Mulliken
and W. C.
Ermler
, Diatomic Molecules
(Academic Press
, New York
, 1977
), Sec. II.F;T.
Bitter
, Doctoral Thesis (University Siegen
, 1982
);A.
Rozendaal
and E. J.
Baerends
, Chem. Phys.
95
, 57
(1985
);N. C.
Baird
, J. Chem. Educ.
63
, 660
(1986
);R. D.
Harcourt
, Am. J. Phys.
56
, 660
(1988
);W.
Kutzelnigg
, in The Concept of the Chemical Bond
, edited by Z. B.
Maksic
(Springer
, Berlin
, 1990
), Vol. 2
, p. 1
;F. E.
Harris
, in Encyclopedia of Physics
, 2nd ed., edited by R. G.
Lerner
and G. L.
Trig
(VCH Publishers, Inc.
, New York
, 1991
), p. 762
;F.
Rioux
, Chem. Educ.
2
(6
), 1
(1997
);G. B.
Bacskay
, J. R.
Reimers
, and S.
Nordholm
, J. Chem. Ed.
74
, 1494
(1997
);M. S.
Gordon
and J. H.
Jensen
, Encyclopedia of Computational Chemistry
, edited by P. v. R.
Schleyer
(John Wiley and Sons
, New York
, 1998
), pp. 3198
–3214
;M. S.
Gordon
and J. H.
Jensen
, Theor. Chem. Acc.
103
, 248
(2000
);F. M.
Bickelhaupt
and E. J.
Baerends
, Rev. Comput. Chem.
15
, 1
(2000
);F.
Rioux
, Chem. Educ.
6
(5
), 288
(2001
).12.
13.
G. B.
Bacskay
and S.
Nordholm
, J. Phys. Chem. A
117
, 7946
(2013
).14.
see also
J.
Jeans
, The Mathematical Theory of Electricity and Magnetism
(Cambridge University Press
, 1946
), pp. 167
–168
.15.
See, for instance,
L.
Pauling
, The Nature of the Chemical Bond
(Cornell University Press
, 1948
), Sec. 3.16.
The most accurate molecular values reported so far are 1.9971933199699992 bohrs for the equilibrium distance and 0.6026346191065398 hartree for the energy. See
T. C.
Scott
, M.
Aubert-Frecon
, and J.
Grotendorst
, Chem. Phys.
324
, 323
(2006
).17.
C. A.
Coulson
, Proc. R. Soc. Edinburgh A
61
, 20
(1941
).18.
A. D.
Buckingham
, Q. Rev. Chem. Soc.
13
, 183
(1959
).19.
This wave function was first determined by
B. N.
Finkelstein
and G. E.
Horowitz
, Z. Phys.
48
, 118
(1928
).20.
C. A.
Coulson
and R. P.
Bell
, Trans. Faraday Soc.
41
, 141
(1945
);P. O.
Löwdin
, J. Mol. Spectrosc.
3
, 46
(1959
).21.
M. W.
Schmidt
, J.
Ivanic
, and K.
Ruedenberg
, “The physical origin of covalent bonding
,” in The Chemical Bond. Fundamental Aspects of Chemical Bonding
, edited by G.
Frenking
and S.
Shaik
(Wiley-VCH Verlag
, 2014
), Chap. 1.22.
T. H.
Dunning
, J. Chem. Phys.
90
, 1007
(1989
). See also the website http://tyr0.chem.wsu.edu/~kipeters/Pages/cc_append.html.23.
A. C.
West
, M. W.
Schmidt
, M. S.
Gordon
, and K.
Ruedenberg
, J. Chem. Phys.
139
, 234107
(2013
);
[PubMed]
the quasi-atomic orbitals used in the present investigation were not orthogonalized between different atoms.
24.
See, e.g.,
J. S.
Boschen
, D.
Theis
, K.
Ruedenberg
, and T. L.
Windus
, Theor. Chem. Acc.
133
, 1425
(2013
).25.
T.
Bitter
, S. G.
Wang
, K.
Ruedenberg
, and W. H. E.
Schwarz
, Theor. Chem. Acc.
127
, 237
(2010
).26.
See, e.g.,
A. D.
Buckingham
, P. W.
Fowler
, and J. M.
Hudson
, Chem. Rev. Washington, D.C.
88
, 963
(1988
);G.
Chałasiński
and M. M.
Szczęśniak
, Chem. Rev. Washington, D.C.
100
, 4227
(2000
);27.
F.
London
, Trans. Faraday Soc.
33
, 8b
(1937
).28.
L.
Bytautas
and K.
Ruedenberg
, J. Chem. Phys.
130
, 204101
(2009
).© 2014 AIP Publishing LLC.
2014
AIP Publishing LLC
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