We shall illustrate these rules first with H2 and then with other diatomic molecules.
The same principles apply to polyatomic molecules, but their molecular orbitals
are more complicated and their energies are harder to predict. Mathematical software
for calculating the molecular orbitals and their energies is now widely available,
and we shall show some of the results that it provides.
In H2, two 1s-orbitals (one on each atom) merge to form two molecular orbitals.
We denote the bonding orbital 1s and the antibonding orbital 1s*. The 1s in
the notation shows the atomic orbitals from which the molecular orbitals are
formed. The indicates that we have built a “-orbital,” a sausage-shaped orbital.
More formally, a -orbital is a molecular orbital that has cylindrical symmetry and
no nodal plane that contains the internuclear axis. Two electrons, one from each H
atom, are available. Both occupy the bonding orbital (the lower-energy orbital) and
result in the configuration 1s
2 (FIG. 4.28). Because only the bonding orbital is occupied,
the energy of the molecule is lower than that of the separate atoms, and
hydrogen exists as H2 molecules. Two electrons in a -orbital form a -bond, like
the -bond in VB theory. However, even a single electron may be able to hold two
atoms together with about half the strength of an electron pair, and so—in contrast
to Lewis’s theory and VB theory—an electron pair is not required for a bond. A pair
is just the maximum number of electrons allowed by the Pauli exclusion principle
to occupy any one molecular orbital. Even a single electron can act to bond atoms
together.
Now we extend these ideas to other homonuclear diatomic molecules of
Period 2 elements. The first step is to build up the molecular orbital energy-level
diagram from the valence-shell atomic orbitals provided by the atoms. Because
Period 2 atoms have 2s- and 2p-orbitals in their valence shells, we form molecular
orbitals from the overlap of these atomic orbitals. There are a total of eight atomic
orbitals (one 2s- and three 2p-orbitals on each atom), so we can expect to build
eight molecular orbitals. The two 2s-orbitals overlap to form two -orbitals, one
bonding (the 2s-orbital) and the other antibonding (the 2s*-orbital); these orbitals
resemble the 1s- and 1s*-orbitals in H2. The six 2p-orbitals (three on each
neighboring atom) form the remaining six molecular orbitals. They can overlap in
two distinct ways. The two 2p-orbitals that are directed toward each other along
the internuclear axis form a bonding -orbital (2p) and an antibonding *-orbital
(2p*) where they overlap (FIG. 4.29). The two 2p-orbitals on each atom that are
perpendicular to the internuclear axis overlap side by side to form bonding and
antibonding “-orbitals” (FIG. 4.30). A -orbital is a molecular orbital with one
nodal plane that contains the internuclear axis. There are two 2p-orbitals on each
atom perpendicular to the internuclear axis, and so four molecular orbitals—two
bonding 2p-orbitals and two antibonding 2p*-orbitals—are formed by their
overlap.
Detailed calculation shows that there are some small differences in the order
of energy levels from molecule to molecule (BOX 4.3). FIGURE 4.31 shows the
order for the Period 2 elements, with the exception of O2 and F2, which lie in the
order shown in FIG. 4.32. The order of energy levels is easy to explain for these
two molecules. First, because each O and F atom has many electrons that contribute
to shielding, the 2s-orbitals lie well below the 2p-orbitals and we can think of
building -orbitals from the two sets of atomic orbitals separately. However,
because the atoms of elements earlier in the period have fewer electrons, their 2sand
2p-orbitals have more similar energies than in O and F. As a result, it is no
longer possible to think of a -orbital as being formed from either the 2s-orbitals
or the 2pz-orbitals separately, and all four of these orbitals must be used to build
the four -orbitals. It is then hard to predict without detailed calculation where
these four orbitals will lie, and it turns out that they in fact lie where we show
them in Fig. 4.31.
Once we know what molecular orbitals are available, we can derive the
ground-state electron configurations of the molecules by using the building-up
principle. For example, consider N2. Because nitrogen belongs to Group 15, each