4.5 Electron Promotion and the Hybridization of Orbitals
When we try to apply VB theory to methane, we run into difficulties. A carbon
atom has the configuration [He]2s22px
12py
1 with four valence electrons (34).
However, two valence electrons are already paired, and only the two half-filled
2p-orbitals appear to be available for bonding. It looks as though a carbon atom
should have a valence of 2 and form two perpendicular bonds, but in fact it almost
always has a valence of 4 (it is commonly “tetravalent”) and in CH4 has a tetrahedral
arrangement of bonds.
To account for the four bonds we note that a carbon atom would have four
unpaired electrons available for bonding if an electron is promoted—that is,
has been relocated to a higher-energy orbital. When a 2s-electron is promoted
into an empty 2p-orbital, we get the configuration [He]2s12px
12py
12pz
1 (35).
Without promotion, a carbon atom can form only two bonds; after promotion,
it can form four bonds. Although it takes energy to promote an electron, the
overall energy of the CH4 molecule is lower than if carbon formed only two
CßH bonds.
The characteristic tetravalence of carbon is due to the small promotion
energy of a carbon atom. The promotion energy is small because a 2s-electron is
transferred from an orbital that it shares with another electron to an empty
2p-orbital. Although the promoted electron enters an orbital of higher energy,
it experiences less repulsion from other electrons than before it was promoted.
As a result, only a little energy is needed to promote the electron. Nitrogen,
carbon’s neighbor in the periodic table, cannot use promotion to increase the
number of bonds it can form, because it has no empty p-orbitals (36). The same
is true of oxygen and fluorine. Promotion of an electron is possible if the overall
change, taking account of all contributions to the energy and especially the
greater number of bonds that can thereby be formed, is toward lower energy.
Boron, [He]2s22p1, like carbon, is an element in which promotion can lead to the
formation of more bonds (three in boron’s case), and boron does typically form
three bonds.
At this stage, it looks as though electron promotion should result in two different
types of bonds in methane, one bond from the overlap of a hydrogen 1s-orbital
and a carbon 2s-orbital, and three more bonds from the overlap of hydrogen
1s-orbitals with each of the three carbon 2p-orbitals. The overlap with the 2p-orbitals
should result in three -bonds at 90 to one another. However, this arrangement is
inconsistent with the known tetrahedral structure of methane, which is four equivalent
bonds.