Absolutely Small - Michael D. Fayer [79]
FIGURE 12.6. An energy level diagram that represents the combination of the two atomic 1s orbitals to form the bonding and antibonding MOs at the bond length separation r0, which is the distance of the energy minimum of the bonding MO. The bonding MO is lower in energy and the antibonding MO is higher in energy than the atomic orbitals by the same amount. The bonding MO is called σb, and the antibonding MO is called σ*.
Figure 12.6 shows the MO energy level diagram for the two energy states that are involved in forming a hydrogen molecule. We have not “put in” the two electrons yet. This diagram is analogous to the many electron energy level diagram, Figure 11.1. We have the energy levels, but now we need to put in the electrons to see what happens. There are two electrons, one from each of the hydrogen atoms. We know that electrons are placed in the lowest possible energy level so long as the number of electrons does not violate the Pauli Principle, that is, at most two electrons can be in any given orbital with spins paired. This applies to MOs as well as atomic orbitals. Figure 12.7 shows the MO energy level diagram with the two electrons (arrows). The two electrons go into the lowest energy level, σb, with spins paired. When the atoms are well separated, the electrons have the energy represented by the lines though the 1s atomic orbitals. The bonding MO has substantially lower energy. It is this reduction in energy that holds the molecule together. The two electrons are in a molecular orbital. Neither is associated with a particular atom. A covalent bond involves sharing of the electrons by the atoms.
Why doesn’t the helium molecule, He2, exist? Two separated He atoms each have 1s orbitals with two electrons in them. Therefore the MO diagram is the same as that shown in Figure 12.6. However, now we need to put four electrons into the MO energy levels. Figure 12.8 shows the MO diagram with the four electrons. The first electron goes into the bonding MO because it is the lowest energy state. The second electron also goes into the bonding MO with the opposite spin of the first. The Pauli Principle says that no two electrons can have all of their quantum numbers the same. The two electrons in the bonding MO have different spin quantum numbers, s = +1/2 and s = -1/2. There are only these two spin quantum numbers, so the third electron cannot go into the bonding MO. It must go into the next lowest energy level, which is the antibonding MO. The fourth electron can also go into the antibonding MO with the opposite spin. There are two electrons in the bonding MO and two electrons in the antibonding MO. The two electrons in the bonding MO lower the energy relative to the separated atoms, but the two electrons in the antibonding MO raise the energy just as much as the bonding electrons lowered the energy. The net result is that there is no decease in energy relative to the separated atoms. A molecule is held together because the bonded atoms have lower energy than the separated atoms. For helium atoms, there is no reduction in energy that would produce a stable configuration. Therefore, there is no bond. We will see this same type of behavior for the noble gas neon in the next chapter.
FIGURE 12.7. The MO diagram for the hydrogen molecule. The two electrons (arrows), one from each hydrogen atom, go into the lowest energy level with their spins paired. The energy is lower than the separated atoms. An electron pair sharing bond is formed.
FIGURE 12.8.