sp3 Hybrid Orbitals and the Structure of Methane

The bonding in the hydrogen molecule is fairly straightforward, but the situation
is more complicated in organic molecules with tetravalent carbon
atoms. Take methane, CH4, for instance. As we’ve seen, carbon has four
valence electrons (2s2 2p2) and forms four bonds. Because carbon uses two
kinds of orbitals for bonding, 2s and 2p, we might expect methane to have
two kinds of C ] H bonds. In fact, though, all four C ] H bonds in methane are
identical and are spatially oriented toward the corners of a regular tetrahedron
(Figure 1.6). How can we explain this?
An answer was provided in 1931 by Linus Pauling, who showed mathematically
how an s orbital and three p orbitals on an atom can combine, or hybridize,
to form four equivalent atomic orbitals with tetrahedral orientation.
Shown in Figure , these tetrahedrally oriented orbitals are called
sp3 hybrids. Note that the superscript 3 in the name sp3 tells how many of
each type of atomic orbital combine to form the hybrid, not how many electrons
occupy it.

The concept of hybridization explains how carbon forms four equivalent
tetrahedral bonds but not why it does so. The shape of the hybrid orbital
suggests the answer. When an s orbital hybridizes with three p orbitals, the
resultant sp3 hybrid orbitals are unsymmetrical about the nucleus. One of
the two lobes is larger than the other and can therefore overlap more effectively
with an orbital from another atom to form a bond. As a result,
sp3 hybrid orbitals form stronger bonds than do unhybridized s or
p orbitals.

The asymmetry of sp3 orbitals arises because, as noted previously, the two
lobes of a p orbital have different algebraic signs, 1 and 2, in the wave function.
Thus, when a p orbital hybridizes with an s orbital, the positive p lobe adds
to the s orbital but the negative p lobe subtracts from the s orbital. The resultant
hybrid orbital is therefore unsymmetrical about the nucleus and is strongly
oriented in one direction.
When each of the four identical sp3 hybrid orbitals of a carbon atom overlaps
with the 1s orbital of a hydrogen atom, four identical C ] H bonds are formed
and methane results. Each C ] H bond in methane has a strength of 439 kJ/mol
(105 kcal/mol) and a length of 109 pm. Because the four bonds have a specific
geometry, we also can define a property called the bond angle. The angle
formed by each H ] C ] H is 109.5°, the so-called tetrahedral angle. Methane thus
has the structure shown in Figure