A PARADIGM SHIFT 257
bonding. Bonds could either be
strong “sigma” bonds, in which
orbitals overlap head-on, or weaker,
more diffuse “pi” bonds, in which
orbitals are parallel to each other.
Pauling came up with the idea
that in a molecule, as opposed to a
bare atom, carbon’s atomic orbitals
could combine, or “hybridize,”
to give stronger bonds to other
atoms. He showed that the s and p
orbitals could hybridize to form
four sp^3 hybrids, which would all be
equivalent, and would project from
the nucleus toward the corners of a
tetrahedron, with inter-bond angles
of 109.5°. Each sp^3 orbital can form
a sigma bond with another atom.
This is consistent with the fact
that all the hydrogen atoms in
methane (CH 4 ), and all the chlorine
atoms in carbon tetrachloride
(CCl 4 ), behave the same way.
As the structures of various carbon
compounds were studied, the four
closest neighboring atoms were
often found in a tetrahedral
arrangement. The crystal structure
of diamond was among the first
structures to be resolved by
X-ray crystallography, in 1914.See also: August Kekulé 160–65 ■ Max Planck 202–05 ■ Erwin Schrödinger 226–33 ■ Harry Kroto 320–21
By 1935, I felt I had an
essentially complete
understanding of the nature
of the chemical bond.
Linus PaulingDiamondFour electrons in the
carbon atom hybridize to
form four sp^3 orbitals.
Each carbon atom in a diamond
is bonded by sp^3 hybrids to four
other atoms to form the corner
of a tetrahedron. The result is an
infinite lattice held together by
covalent carbon–carbon bonds,
which are immensely strong.CHHHHCHHMethane
HCEthyleneThree electrons in the carbon atoms hybridize
to form three sp^2 orbitals. The remaining
unhybridized orbitals form a second pi bond
between the carbon atoms.Two electrons in
the carbon atom form
two sp orbitals, each
of which bonds with
an oxygen atom.
The remaining two
orbitals bond to the
oxygen in a pi bond.OCCarbon dioxideDiamond is pure carbon, and in
the crystal each carbon atom
is bonded to four others by
sigma bonds at the corners of
a tetrahedron. This structure
explains diamond’s hardness.
Another possible way for carbon
atoms to bond to other atoms is
for an s-orbital to mix with two
p-orbitals to form three sp^2 hybrids.
These stick out from the nucleus
in one plane, with angles of 120°
between them. This is consistent
with the geometry of molecules
such as ethylene, which has the
double-bond structure H 2 C=CH 2.
Here, a sigma bond is formed
between the carbon atoms by one
of the sp^2 hybrids, and a pi bond by
the fourth, unhybridized orbital.
Lastly, an s-orbital can mix with
one p-orbital to form two sp hybrids,
whose lobes stick out in a straight
line, 180° apart. This is consistent ❯❯Hsigma bondOpi bondsigma bondpi bond