Atoms and Molecules

The two simplest elements in the periodic table are hydrogen and helium. Both are gases under atmospheric conditions. Chemists have known for over a century that the formula for hydrogen gas is H₂ rather than H and that the formula for helium is He, not He₂. Why is it that one of these gases exists as a combination of two atoms while the other does not? The answer to this question will provide us with an introduction to the theory of chemical bonding. In order to answer the question, we need to be pragmatic. The fact that hydrogen exists as dihydrogen, H₂, rather than H indicates that the combination of two hydrogen atoms is a more stable arrangement than two separate atoms. Remember that in talking about the stability of an atom or a molecule we are talking about the potential energy of its electrons, which is determined by Coulomb's Law. Since dihydrogen is more stable than two isolated hydrogen atoms, it must mean that the attraction of the two nuclei for the two electrons is greater than the sum of the attractions each nucleus for its single electron.

Making Molecules

Imagine two hydrogen atoms that are initially very far apart. According to Coulomb's Law, any interactions between them would be very small.

Now imagine bringing these two atoms closer and closer together. At some point between an infinitely large separation and complete superposition, there must be an internuclear distance where the potential energy of the two atoms is a minimum. Figure 1 animates the changes in potential energy that accompany such an imaginary process. Click on the figure to start the animation.

Figure 1

Potential Energy Changes that Accompany Changes in the Internuclear Separation of Two Hydrogen Atoms

Why does the potential energy change in this manner? The rationalization that chemists have accepted is that as the two atoms approach each other, each nucleus exerts an attractive force not only on its own electron, but also on the the other atom's electron. In the case of two hydrogen atoms this reciprocal interaction reaches a maximum when the internuclear separation is 72 pm. The potential energy of the electrons in this arrangement is approximately 103 kcal/mol less than that of the electrons associated with the isolated hydrogen atoms. The mutual attraction of the two nuclei for the two electrons is what chemists call a chemical bond. The internuclear separation that corresponds to the energy minimum is called the bond length. The 103 kcal/mol required to separate the atoms from 74 pm to an infinite distance is called the bond strength.

Now let's consider how chemists have rationalized the stability of dihydrogen in terms of the filled shell rules, specifically the duet rule. The electron configuration of hydrogen is 1s¹. If a hydrogen were to "acquire" another electron, its electron configuration would become 1s², the same as helium. That is basically what happens in the process shown in Figure 1. The Coulombic attraction of one hydrogen nucleus for the electron of the other hydrogen atom amounts to the "acquisition" of that electron. Since this Coulombic attraction is a reciprocal one, each hydrogen atom "acquires" an electron from the other. The electron configuration of each hydrogen atom in dihydrogen becomes 1s². Of course this is all a bunch of hocus pocus; if the electron configuration of each hydrogen atom were really 1s², then dihydrogen would contain 4 electrons, not 2. In fact, as Figure 2 demonstrates, we are double counting when we say that the electron configuration of each hydrogen is 1s².

Figure 2

Counting Electrons in Dihydrogen

The chemical bond that is produced when atoms share valence electrons in this manner is called a covalent bond. The generalized description of the process just outlined constitutes what is known as valence bond theory.

Valence Bond Theory

Valence bond theory is the most popular theory among organic chemists because of its simplicity and its visual appeal. Despite its popularity with organic chemists, valence bond theory has some serious flaws. We will see how those blemishes led to the development of modifications and alternative theories.

Valence bond theory rests upon three assumptions.

1. A chemical bond between two atoms is formed when each atom shares one or more of its valence electrons with the other atom. Such a bond is called a covalent bond.
2. Stable molecules are formed when all the constituent atoms have filled valence shells.
3. Covalent bonds are localized bonds, which is to say that the shared electrons are restricted to the area between the two bonded atoms, the internuclear region.

Figure 3 animates the combination of a carbon atom with four hydrogen atoms to form methane, CH₄.

Figure 3

Putting It All Together-The Formation of Methane