Absolutely Small - Michael D. Fayer [80]
To see the predictive capabilities of the simple diagrams like those shown in Figures 12.7 and 12.8, consider four molecules, or possible molecules. They are the hydrogen molecule ion , the hydrogen molecule H2, the helium molecule ion , and the helium molecule He2. is composed of two hydrogen nuclei (protons) and one electron. Like the atomic cation ion Na+, it is positively charged because it has one fewer electrons than it has protons. is the molecular ion composed of two helium nuclei with two protons in each nucleus and three electrons. So it has four positive charges (four protons) and three negatively charged electrons.
Figure 12.9 shows the MO energy level diagrams for the four molecules. The atomic energy levels have been omitted. has only one electron, so it goes into the lowest energy level, the bonding MO. The energy is lower than the separated atoms, but by only approximately half as much as for the H2 molecule, which has two electrons in the bonding MO. H2 has a full covalent bond. We say it has a bond order of 1. has a bond order of 1/2. has three electrons. The first two can go into the bonding MO, but, because of the Pauli Principle, the third electron must go into the antibonding MO. Two electrons lower the energy relative to the separated atoms, but one electron raises the energy. There is a net lowering of the energy. The molecular ion exists in nature, and it has a bond order of 1/2. As discussed, He2 has two bonding electrons and two antibonding electrons. It has no bond. The bond order is zero. The He2 molecule does not exist.
FIGURE 12.9. The MO energy level diagrams for four molecules, the hydrogen molecule ion , the hydrogen molecule H2, the helium molecule ion , and the helium molecule He2.
Table 12.1 gives some quantitative information about these four molecules. It gives the number of bonding electrons, the number of antibonding electrons, and the net, which is the number of bonding electrons minus the number of antibonding electrons. It also gives the bond order. The last two columns are of particular interest.
These are the results of experimental measurements on the molecules. First consider the bond length. The lengths are in Å (Ångstroms, 10-10 m). The molecule has a bond order of 1/2 and a bond length of 1.06 Å. In contrast, H2, which has a full bond with bond order 1, has a bond length of 0.74 Å. The additional bonding electron in the H2 bonding MO holds the atoms together tighter and therefore, closer. has a bond order of 1/2 and a bond length of 1.08 Å, which is only a little longer than . Of course, He2 is not a molecule, so it does not have a bond length. The last column is the bond energy in units of 10-19 J. The relative strength of the bonds is interesting. The H2 molecule with a bond order of 1 has a considerably stronger bond than the two molecular ions, which have bond orders of 1/2. These simple MO diagrams allow us to see if a bond will exist, and they give information on how strong the bond will be.
TBLE 12.1. Properties of the hydrogen molecule ion , the hydrogen molecule H2, the helium molecule ion , and the helium molecule He2.
In this chapter, we have used the ideas of molecular orbitals to look at the simplest molecules. The discussion only involved atoms that have 1s electrons. All other atoms and molecules involve more electrons and more orbitals. In the next chapter, the ideas introduced here will be used to examine diatomic molecules involving larger atoms, such as the oxygen molecule, O2, and the nitrogen molecule, N2. These two molecules are the major components of the air we breathe.
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What Holds Atoms Together: Diatomic Molecules
THE HYDROGEN MOLECULE is a diatomic molecule, that is, a molecule composed of only two atoms. Our investigation of hydrogen revealed