Absolutely Small - Michael D. Fayer [83]
The lower portion of Figure 13.3 shows the π antibonding MO. The two p atomic orbitals come together side to side, but the positive lobe of one orbital overlaps the negative lobe of the other orbital, and vice versa. The result is destructive interference between the lobes giving rise to the π antibonding MO. The antibonding MO has much less electron density between the nuclei. The result is that the energy is higher than the separated atoms, so this configuration of atomic orbitals produces an antibonding MO.
FIGURE 13.3. Upper potion: a pair of p orbitals are overlapped side to side to give a π bonding molecular orbital (constructive interference). There is no electron density along the line connecting the nuclei. Lower portion: a pair of p orbitals are overlapped side to side to give a π antibonding molecular orbital (destructive interference). Note the signs of the lobes of the p atomic orbitals. The antibonding MO has a node between the nuclei.
BONDING IN DIATOMIC MOLECULES: THE FLUORINE MOLECULE
We are now ready to discuss bonding for diatomics with atoms other than hydrogen. Let’s start with the diatomic, F2, the fluorine molecule. We will use the same approach as we did for H2, but now there are more orbitals and more electrons involved. We imagine bringing two F atoms together and stopping at the point where the energy is lowest. This is the separation of the two F atoms when they are bonded (assuming they form a bond), as in Figure 12.5. We can draw an energy level diagram, as in Figure 12.6. We need to define the axis along which the two atoms approach each other because we have pz, px, and py orbitals. It matters whether we bring p orbitals together end to end or side to side. When the two atoms (labeled a and b) approach along the z axis (see Figure 13.4), the pz orbitals will come together end to end, while the px and py orbitals will come together side to side. Therefore, the pz atomic orbitals will form σ MOs and the px and py atomic orbitals will form π MOs.
Figure 13.5 shows the energy level diagram for two F atoms brought together along the z axis. In the diagram, the energy levels for the atomic orbitals for the two atoms (a and b) are shown on the right and left sides of the diagram. The corresponding bonding (b) and antibonding (*) MOs are shown in the center. σ MOs formed from s atomic orbitals have a subscript s. σ MOs formed from pz atomic orbitals have a subscript z, and π MOs formed from px or py atomic orbitals have a subscript x or y. The bonding MO is always lower in energy than the atomic orbitals that formed it, and the antibonding MO is always higher in energy. The three p atomic orbitals have the same energy. When quantum states have the same energy, they are said to be degenerate. In the diagram, the three p atomic orbitals are shown as three closely spaced lines even though they are degenerate. As shown, only the matching atomic orbitals of the same energy combine to make MOs. Quantum theory gives this result. States of identical energy can readily combine to make superposition states. In this case, atomic orbitals of identical energy on two different atoms can combine to make molecular orbitals. In general, only atomic states with similar energy can combine to make MOs. This will be important when we discuss heteronuclear diatomics below. For the homonuclear diatomics, the atomic orbitals are identical in energy. In the diagram, the three p orbitals on each atom, a total of six atomic orbitals, combine to form six molecular orbitals. The pz atomic orbitals produce the σ bonding and antibonding MOs, which are different in energy from the bonding and antibonding πx and πy MOs formed from the px and py atomic orbitals. However, the πx and πy bonding MOs have the same energy, and the πx and πy antibonding MOs have the same energy. The degenerate pairs of π MOs are shown as two closely spaced lines.