Absolutely Small - Michael D. Fayer [78]
FIGURE 12.4. The left side is a schematic of two hydrogen atom 1s orbitals that are being added together. Note that the probability amplitude waves have opposite signs. The two atomic orbitals combine to make a molecular orbital. Because of the opposite signs, there is destructive interference, in contrast to Figure 12.2.
The molecular orbital that arises from constructive interference of the 1s atomic orbitals (see Figures 12.2 and 12.3), which is responsible for the H2 chemical bond, is called a bonding molecular orbital, or bonding MO. The molecular orbital that arises from destructive interference between the atomic orbitals is called an antibonding MO because it does not give rise to a bond, and in fact increases the energy as the atoms are brought together.
Figure 12.5 is a schematic of the energy curves for the bonding and antibonding MOs of the H2 molecule. As discussed in connection with Figure 12.1, as the two hydrogen atoms are brought together, the energy goes down and reaches a minimum before increasing again. This is the bonding MO curve. In contrast, the curve for the antibonding MO shows that the energy increases as the two atoms get close enough together to feel each other. The energy continues to increase as the atoms get progressively closer together. There is no reduction in energy. If the electrons are in the antibonding MO, the two atoms will not form a bond because the energy of the system is always higher than having separated atoms.
PUTTING ELECTRONS IN MOLECULAR ORBITALS
We started with two atomic orbitals, 1sa and 1sb, that were associated with two hydrogen atoms, Ha and Hb. These two atomic orbitals give rise to two molecular orbitals, the bonding and antibonding MOs. The rules we used for filling the atomic orbitals with electrons apply here as well. The Pauli Principle says no more than two electrons can go into an MO and they must have opposite spins (spins paired, one up arrow and one down arrow). Electrons go into the lowest energy levels first so long as this doesn’t violate the Pauli Principle. Hund’s Rule states that electrons will be unpaired if that doesn’t violate the first two rules. We will not need Hund’s Rule until the next chapter when we talk about larger molecules. Now we are in a position to see why the hydrogen molecule H2 exists, but the helium molecule He2 does not exist.
FIGURE 12.5. A schematic plot of the energy curves of the bonding and antibonding molecular orbitals for two hydrogen atoms as they are brought closer together. In contrast to the bonding MO, the energy of the antibonding MO increases as the atomic separation is decreased.
THE HYDROGEN MOLECULE EXISTS BUT THE HELIUM MOLECULE DOESN’T
At the atomic separation that corresponds to the bond length, that is, the separation you find in the actual molecule, the bonding MO is always lower in energy than the separated atoms and the antibonding MO is always higher in energy. This is a rigorous result from quantum mechanics. It is a good approximation to say that the energy decrease of the bonding MO is equal to the energy increase of the antibonding MO.
A simple diagram that is used to reflect the atomic orbitals coming together to form molecular orbitals is shown in Figure 12.6. We will use this type of diagram in subsequent chapters. The two 1s atomic orbitals, one for each H atom, are depicted on the left and right sides of the figure. The lines through them are the zero