CHEMICAL BONDING AND THE PROPERTIES OF MINERALS - Chemical Fundamentals of Geology and Environmental Geoscience - page 120

Suppose each of these atoms has a second unpaired
electron in a p-orbital perpendicular to those forming
the σ -bond. The two lobes of this orbital lie in the plane
of the diagram (large circles), and each can overlap side-
ways as shown with the corresponding lobe in the other
atom, generating two concentrations of electron density
(lighter stipple), above and below the σ -bond. Together
these constitute the molecular orbital of what is called a
π-bond between the two atoms. π -bonds form only in
conjunction with a σ -bond and are therefore characteris-
tic of molecules containing double or triple bonds . Such
molecules are not cylindrically symmetric. π -bonding
occurs in the doubly bonded oxygen molecule (O = O,
i.e. O 2 ), although the configuration is a little more com-
plicated than described above. The triple bond in the
nitrogen molecule (N ≡ N, i.e. N 2 ) consists of one σ -bond,
with two π -bonds in mutually perpendicular planes.

An unpaired valence electron achieves a lower
energy in a molecular orbital (if of the 'bonding' type -
Box 7.3) than in its own atomic orbital, which is why
molecules can be more stable than separate atoms. In
forming methane, carbon can promote an electron from
the 2 s orbital into the one 2p orbital that is still vacant:
the slight energy disadvantage in doing so (Figure 5.7)
is outweighed by having four unpaired electrons avail-
able to establish molecular orbitals with hydrogen
atoms, rather than just two (Figure 7.5a).
The Schrödinger wave analysis of the atom, as well
as defining the shape of individuals s- and p-orbitals,
offers the possibility of mixing their wave functions in
various proportions to produce hybrid orbitals of differ-
ent geometry. Hybridization is another consequence
of the wave model of the electron. Just as a guitar string
can simultaneously vibrate with two or more harmon-
ics of different frequencies (it is the combination of
multiple harmonics that gives the instrument its dis-
tinctive musical tone or 'timbre'), so a single atomic
electron can adopt more than one waveform. The com-
bined waveform (the 'hybrid' orbital) differs in shape
from the individual waveforms from which it is math-
ematically derived. The result of amalgamating the 2 s
and three 2p orbitals of carbon is called an sp 3 -hybrid . It
consists of four lobes of electron density, each accom-
modating an unpaired electron, projecting out from
the nucleus with tetrahedral symmetry. Each of these
lobes forms a separate σ -bond with a hydrogen atom in
the methane molecule.
The geometry of the ammonia molecule (NH 3 ) also
results from the sp 3 hybrid. Nitrogen has five electrons
in its valence shell (Figure 7.5b). Three of the lobes of
an sp 3 -hybrid are each occupied by an unpaired elec-
tron that forms a σ -bond with a hydrogen atom. The
fourth lobe accommodates the remaining two elec-
trons, which - being paired - are not available for
bonding that involves electron-sharing (covalent
bonding). The electron density of this lone pair repels
each of the N-H molecular orbitals slightly, leading to
a distorted hybrid in which the angle between the
bonds is only 107°. In the water molecule, two of the sp 3
lobes on the oxygen atom contain lone pairs, and their
combined repulsion closes the angle between the O-H
bonds still further (to 104° - Figure 7.5c).
The tetrahedral sp 3 hybrid can be recognized in the
structure of diamond too (Figure 7.5d), the unique
hardness of which reflects the strong bonds that each

Covalent crystals
It is only the lightest elements on the right of the
Periodic Table (N, O) that form multiple-bonded,
diatomic gas molecules. Heavier elements in the same
groups (V and VI) do not generally form stable multi-
ple bonds; instead they exist as solids consisting of
extended, singly bonded molecular structures. The
crystal structure of the element sulfur, for example,
consists of buckled rings of six or eight sulfur atoms in
which each is bonded to two others. These heavier
molecules have too much inertia to exist as gases at
room temperature.
In diamond (a form of crystalline carbon) and sil-
icon, each atom is bonded to four others in a continuous
three-dimensional network (Figure 7.5d). Each perfect
diamond crystal can therefore be regarded in a formal
sense as a single 'molecule' of carbon.

Molecular shape: hybridization

Methane (CH 4 ), the chief constituent of natural gas,
consists of molecules with a distinctive tetrahedral
shape. Four C-H bonds project from the central C
atom, as if towards the four 'corners' of a regular tetra-
hedron, at angles of 109° to one another (Figure 7.5a). It
is hard to reconcile this shape, and the existence of four
identical bonds, with the electronic configuration of
carbon (1s 2 2s 2 2p 2 ) in which the 2 s electrons are already
paired and therefore not available for bonding. Why,
in that case, is the valency of carbon 4, not 2?