For instance, in h1 the s- and p-orbitals all have their usual signs and their amplitudes
add together where they are all positive. In h2, however, the signs of px and
py are reversed, and so the resulting interference pattern is different.
The four hybrid orbitals that we have constructed differ only in their orientation,
with one pointing toward each corner of a tetrahedron (FIG. 4.13); in all other
respects, they are identical. These four hybrid orbitals are called sp3 hybrids because
they are formed from one s-orbital and three p-orbitals. In an orbital-energy diagram,
we represent the hybridization as the formation of four orbitals of equal
energy. That energy lies between the energies of the s- and p-orbitals from which
the hybrid orbitals are constructed (37). The hybrids are colored green to remind
us that they are a blend of (blue) s-orbitals and (yellow) p-orbitals. An sp3 hybrid
orbital has two lobes, but one lobe extends farther than those of the contributing
p-orbitals and the other lobe is shortened. The fact that hybrid orbitals have their
amplitudes concentrated on one side of the nucleus allows them to overlap more
effectively with other orbitals, and as a result the bonds that they form are stronger
than in the absence of hybridization.
We are now ready to account for the bonding in methane. In the promoted,
hybridized atom, each of the electrons in the four sp3 hybrid orbitals can pair with
an electron in a hydrogen 1s-orbital. Their overlapping orbitals form four _-bonds
that point toward the corners of a tetrahedron (FIG. 4.14). The valence-bond
description is now consistent with experimental data on molecular geometry.
When there is more than one “central” atom in a molecule, we concentrate on
each atom in turn and match the hybridization of each atom to the shape at that
atom predicted by VSEPR. For example, in ethane, C2H6 (38), the two carbon atoms are both “central” atoms. According to the VSEPR model, the four electron
pairs around each carbon atom take up a tetrahedral arrangement. This arrangement
suggests the same sp3 hybridization of the carbon atoms as in methane (see
Fig. 4.14). Each C atom has one unpaired electron in each of its four sp3 hybrid
orbitals and can therefore form four -bonds that point toward the corners of a
regular tetrahedron. The CßC bond is formed by spin-pairing of the electrons in
one sp3 hybrid orbital of each C atom. We label this bond (C2sp3,C2sp3) to show
its composition: C2sp3 denotes an sp3 hybrid orbital composed of 2s- and 2p-orbitals
on a carbon atom, and the parentheses show which orbitals on each atom overlap
(FIG. 4.15). Each CßH bond is formed by spin-pairing of an electron in one of the
remaining sp3 hybrid orbitals with an electron in a 1s-orbital of an H atom (denoted
H1s). These bonds are denoted (C2sp3,H1s).
We can extend these ideas to molecules, such as ammonia (NH3), that have a
lone pair of electrons on the central atom. According to the VSEPR model, the four
electron pairs in NH3 take up a tetrahedral electron arrangement, so we describe the
nitrogen atom in terms of four sp3 hybrid orbitals. Because nitrogen has five valence
electrons, one of these hybrid orbitals is already doubly occupied (39). The three
unpaired electrons in the remaining sp3 hybrid orbitals pair with the 1s-electrons of
the three hydrogen atoms to form three NßH -bonds. Whenever an atom in a
molecule has a tetrahedral electron arrangement, we say that it is sp3 hybridized.