CHEMICAL BONDING AND THE PROPERTIES OF MINERALS - Chemical Fundamentals of Geology and Environmental Geoscience - page 119

Box 7.3 The mechanism of covalent bonding

When two hydrogen atoms come into contact and their
electron orbitals overlap (Figure 7.3.1a), each electron
feels the electrostatic attraction of a second nucleus.
Both electrons modify their standing waves to extend
across the two atoms, forming a molecular orbital
(Figure 7.3.1b) in which the electrons are identified with
the h 2 molecule instead of with the separate h atoms . the
wave function of the molecular orbital can be regarded as
the sum of the separate atomic wave functions
(Figure 7.3.1c). the electron density ( ψ 2 ) in the region
between the two nuclei is enhanced (shaded area) at the
expense of other parts of the molecule, and screens the
nuclei from each other. the molecular orbital offers each
electron a lower energy than it had in the isolated atom
(Figure 7.3.1d). any two atoms having valence electrons in
such bonding orbitals have a lower energy together than
separately, in spite of the internuclear repulsion. For this
reason the hydrogen molecule h 2 is more stable than
atomic hydrogen.
a bonding orbital accepts two electrons with opposed
spins, accommodating the unpaired electron contributed
by each of the bonding atoms. the overlap of atomic orbit-
als that each contain two electrons (as when two helium
atoms touch) does not lead to bond formation. the add-
itional two electrons establish a complementary molecular
orbital configuration (an anti-bonding orbital, with dimin-
ished electron density between the nuclei) whose energy
is higher than the corresponding atomic orbitals (see
Figure 7.3.1d). With electrons occupying bonding and
anti-bonding orbitals, there is no net energy advantage in

forming a molecule. thus helium, having no unpaired elec-
trons, cannot form a stable he 2 molecule.

(a)

1s

1s

Orbital overlap

r 0

(b)

Electron
density
in molecular
orbital

ψ 2 for molecular
orbital. Stippled area
shows increase in ψ 2
between nuclei.
ψ 2 for atomic orbital

(c)

ψ 2

(d)

Anti-bonding
Atom 2

1s σ *

Atom 1
1s

1s

Electron energy

Bonding

1s σ
Unpaired electrons in hydrogen atoms

Additional electrons in helium atoms

Figure 7.3.1 Ways of looking at a covalent bond. r 0
represents the equilibrium internuclear distance.

(a) (c)

Sideways overlap
of p orbitals

1s 1s

2p 2p

1s σ

Molecular
orbital of
2p π bond

(b)

Figure 7.4 Orbital overlap in σ - and π -bonds.
The stippled areas show the approximate
disposition of the associated bonding
molecular orbitals. (a) 1s σ bond in the
hydrogen molecule H 2 . Note the cylindrical
symmetry. (b) 2p 1s σ bonds in the water
molecule H 2 O. (c) 2p σ and 2p π bonds in a
double-bonded molecule such as O 2 .

2p y

2p x

O

Molecular
orbital of
2p σ bond

H H

1s

1s

104°