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.

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 to
M. 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.
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, “
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, edited by
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and
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ACS
,
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,
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).
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This interpretation was first quoted by
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[PubMed]
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At the Boulder Conference of 1958,
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[PubMed]
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G. B.
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S.
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see also
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.
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See, for instance,
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(
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,
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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.
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A. D.
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This wave function was first determined by
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and
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C. A.
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M. W.
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K.
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and
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). See also the website http://tyr0.chem.wsu.edu/~kipeters/Pages/cc_append.html.
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A. C.
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M. W.
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,
M. S.
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[PubMed]
the quasi-atomic orbitals used in the present investigation were not orthogonalized between different atoms.
24.
See, e.g.,
J. S.
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D.
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K.
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K.
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[PubMed]
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See, e.g.,
A. D.
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,
P. W.
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, and
J. M.
Hudson
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88
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G.
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100
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A. J.
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F.
London
,
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33
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L.
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and
K.
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).
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