Absolutely Small - Michael D. Fayer [74]
In this chapter, we used the many electron energy level diagram (Figure 11.1), and the rules for filling the atomic orbitals (the Pauli Principle, lowest energy first if possible, Hund’s Rule) to discuss the Periodic Table. It was shown that very simple considerations can go a long way toward understanding the properties of the atomic elements and some aspects of chemical bond formation to make molecules. However, we did not use our ideas of quantum theory to discuss why chemical bonds should form and properties of molecules, such as their shapes, that arise from quantum considerations. We will begin the explication of the quantum theory of molecules with the simplest molecule, the hydrogen molecule H2, in Chapter 12.
12
The Hydrogen Molecule and the Covalent Bond
ONE OF THE GREAT TRIUMPHS of quantum mechanics is the theoretical explanation of the covalent bond. Two types of interactions hold atoms together, covalent bonds and ionic bonds. Ionic bonds are the type that occurs in a sodium chloride (NaCl) crystal. We know from Chapter 11 and our discussion of the Periodic Table that this salt crystal is composed of sodium cations, Na+1, and chloride anions, Cl-1. The ions in the crystal are held together by electrostatic interactions. Opposite charges attract. There are some complications because like charges repel, but it is possible to show that the attractions of the oppositely charged ions overcome the repulsions of the like charged ions. Such electrostatic interactions can be explained quite well with classical mechanics, although quantum theory is still needed to explain many properties in detail.
In contrast to ionic solids that are held together by electrostatic interactions, classical mechanics cannot explain the covalent bond. We saw in Chapter 11 that a hydrogen atom will tend to form one covalent bond with another atom to share one electron. This sharing brings the H atom to the helium closed shell configuration. But what is a covalent bond? Why do H atoms share electrons to form the H2 molecule, but helium atoms do not share electrons to form the He2 molecule? We will first investigate the nature of the covalent bond for the simplest molecule, H2, and then expand the discussion of covalent bonding for more complicated molecules in subsequent chapters. By the end of this chapter it will be clear why H2 exists and He2 does not exist.
TWO HYDROGEN ATOMS THAT ARE FAR APART
Two hydrogen atoms, call them a and b, do not interact with each other when they are very far apart. When they are separated by a large distance, the electron on hydrogen atom a will only feel the Coulomb attraction to the proton in hydrogen atom a. The electron on hydrogen atom b will only interact with the proton on hydrogen atom b. We know how to describe these separated hydrogen atoms. Let’s say both are in their lowest energy state, the 1s state. The electron is describe by the 1s wavefunction, which is an atomic orbital. It describes the probability amplitude of finding the electron in a given region of space. The square of the wavefunction gives the probability of finding the electron. The 1s state of the hydrogen atom was discussed in some detail in Chapter 10 (see Figures 10.2- 10.4).
TWO HYDROGEN ATOMS BROUGHT CLOSE TOGETHER
Now consider what happens when we start bringing the two hydrogen atoms closer and closer together. When they get close together but not too close they start to feel each other. This distance will be made quantitative below. The electron on hydrogen atom a starts to have attraction for the proton of hydrogen atom b, and it has repulsion for the electron on hydrogen atom b. In the same manner, the electron on hydrogen atom b is attracted to the proton of hydrogen atom a and is repelled by the electron of hydrogen atom a. In addition, the positively charged protons of hydrogen atom a and b repel each other because like