In the previous section, we introduced bonding and anti-bonding MOs. Bonding MOs have more electron density between the nuclei, and lower energy than the atomic orbitals they were made from. Putting electrons in bonding orbitals tends to make a bond between the nuclei, because when the electrons spend time between the nuclei, both nuclei are attracted to the negative charge between them.
Anti-bonding orbitals have less electron density between the nuclei, because they have a node there. They have higher energy than the AOs they were made of. Putting electrons in anti-bonding orbitals tends to break bonds, because with the electrons on the outside, the nuclei repel each other and all the electrons repel each other.
There is a third type of MO: non-bonding MOs. In order to make a
bond, orbitals have to have net overlap, which
means that if you multiply them together and take the integral over
the whole molecule, the integral isn't 0. Consider the HF
molecule. The H 1s orbital can make a bond with the F 2s or F
2pz orbital. However, there is no net overlap between the H
1s and the F 2px and 2py. This is shown in the
figure. When we
multiply Ψ1s times Ψ2p, the top half is + * +
= +. The bottom half is + * — = —. Except for the sign,
the top half and bottom half are symmetrical, so when we add up the
values of Ψ1sΨ2p everywhere, the top
half and bottom half cancel out, and ∫
Ψ1sΨ2p dV = 0. (Note that multiplying
the wavefunctions is different from adding them, which would give us
the wave interference patterns we saw in hybrids and MOs.) For this reason, the F 2px and 2py
orbitals in HF are called non-bonding orbitals. In contrast, the
2pz orbital does have net overlap with 1s, because
│Ψ1sΨ2p│ on the red
side in the figure is bigger than
│Ψ1sΨ2p│ on the blue side.
The bonding and antibonding MOs shown above are both σ-type MOs. Recall from the section on multiple bonds that we can classify bonds as σ or π bonds. σ-bonds are symmetrical around the bond (if you rotate them around the bond, they don't change). π-bonds change sign when you rotate them 180° around the bond.
If we think about making MOs for F2, we can imagine
making a bonding and antibonding combination of the 2pz
orbitals, which point toward each other. This will make a
σ-bonding MO and an σ-anti-bonding MO. We can also make
σ-type combinations of the 2s orbitals. When we combine the
2px and 2py orbitals, these are perpendicular to
each other, so they will make π-type bonding and anti-bonding
combinations. These are shown below. Note that for both σ
combinations and π combinations electron density increases between
the nuclei in bonding MOs and decreases between nuclei in anti-bonding MOs.
The easiest way to name and label MOs is using σ and π. Anti-bonding character is shown using a *, such as π* which means a π-type anti-bonding orbital. Each MO in the figure above is labeled in this way. There are other more complicated ways to name MOs, but you won't learn them unless you take Inorganic Chemistry.
