Some molecules and ions cannot be described using a single Lewis structure. This is because of resonance, the bonding in molecules and ions that result in more than one Lewis structure. Resonance is a feature of the valence-bond theory. In the valence-bond theory, Schrödinger's equation is used to determine the structure of molecules. If more than one solution to Schrödinger's equation is possible, then more than one molecular structure must be possible. According to the valence bond theory, various combinations of the solutions to Schrödinger's equations depict possible molecular structures. These different structures are called resonance structures or contributing structures. The actual structure of the molecule is called the resonance hybrid, a structure which represents the average of each of the resonance structures. It was originally believed that a molecule resonated between the different possible structures, much like a plucked guitar string vibrates back and forth. These different structures were thought to transfer energy to and from each other, thus the term "resonance."
An example of a molecule which demonstrates resonance is ozone, O3 (Figure 1). Ozone can be represented by two different Lewis structures, O=O-O and O-O=O. Each structure represents two different bonds between the oxygen atoms, a single bond or a double bond. The difference between the two structures is the location of the double bond relative to the single bond. When resonance was first being investigated, scientists thought that ozone split its time between the two structures, spending half of its time with one structure and the other half with another structure. Later experiments showed, however, that both of the bonds involved in an ozone molecule are identical to each other. This resulted in a paradigm shift and scientists today theorize that ozone actually has one structure that is an average between the two possible Lewis structures. This average structure is the resonance hybrid for ozone. If drawing the Lewis structure for ozone, the two possible structures are drawn with a double headed arrow between them, showing that the ozone molecule exhibits resonance and exists in nature as a resonance hybrid.
Another example of a molecule which exists as a resonance hybrid in nature is NO2. This molecule has 17 valence electrons. The three atoms are arranged in a linear fashion, and the placement of the first four valence electrons can be determined quite easily. The problem lies in the placement of the remaining 13 electrons. Even with the use of double bonds, the last 13 valence electrons cannot be placed such that each atom has eight valence electrons, satisfying the octet rule. Instead of one structure, two are possible: O=N-O and O-N=O. Again, notice that the difference between the two structures is in the placement of the double bond relative to the single bond (Figure 2). Neither of these structures satisfies the octet rule. In each of the structures, one electron is left unpaired on the nitrogen atom. In nature, atoms are only stable if they contain paired electrons. If any unpaired electrons are present on an atom, the atom is said to be unstable. In this example, both structures are equally likely to occur and no single Lewis structure can accurately describe this molecule. Lewis structures are simply models for representing the structure of molecules and are not completely accurate. Experiments show that both of the bonds in an NO2 molecule are identical. The bond lengths between the atoms are between those found in single bonds and those found in double bonds. The resulting resonance hybrid is more stable than either Lewis structure.
In order to determine the Lewis structure of a molecule, one must know the number of valence electrons for the atoms involved and also understand the octet rule. The octet rule is the principle that describes the bonding in atoms. Individual atoms are unstable unless they have an octet of electrons in their highest energy level. The electrons in this level are called valence electrons. When atoms gain, lose, or share electrons with other atoms, they satisfy the octet rule and form chemical compounds. An example of this is the formation of molecular fluorine (F2) from two individual fluorine atoms. A fluorine atom has seven valence electrons. According to the octet rule, eight valence electrons is the most stable configuration, so each fluorine atom needs one more electron. If each fluorine atom shares one electron with the other, the octet rule will be satisfied and a covalent bond is formed. Another example of a molecule formed by covalent bonds in order to satisfy the octet rule is ammonia (NH3). A nitrogen atom has five valence electrons, so it needs three more to satisfy the octet rule. Hydrogen has one valence electron, so it needs one more to fill its outer energy level (hydrogen has electrons in only the first energy level, which fills when two electrons are present, unlike the other energy levels which require eight). If one nitrogen atom shares an electron with each of three hydrogen atoms, and the three hydrogen atoms each share an electron with the nitrogen atom, three covalent bonds are formed and the octet rule is satisfied for all four atoms.
The octet rule is more or less a guideline for the purpose of determining Lewis structures for molecules. It is not always strictly adhered to, as demonstrated by the hydrogen atom in the previous example. The octet rule is a useful way to determine the structure of common molecules, especially those important biologically. Even after the development of the octet rule, however, scientists still had difficulty determining the structure of benzene, C6H6. Chemists were baffled as to why the structure of a molecule with such a simple chemical formula could be so difficult to determine. In the early 1870s, a chemist named F. A. Kekulé (1829-1896) theorized that benzene could be represented using two structures and that the benzene molecule in nature actually resonated, or vibrated back and forth, between these two possibilites. Kekulé's theory was not entirely correct but was accepted for many years. Once the Schrödinger equation was developed and used to explain resonance structures, the true nature of benzene was discovered. Benzene exists in nature not as a molecule oscillating between two structures, but as a resonance hybrid representing the average of each of the possible structures (Figure 3).
The above examples demonstrated the problem of finding structures to represent molecules which contain multielectron atoms. Once the Schrödinger equation was developed to show the exact three-dimensional structure of the hydrogen atom, the theory of resonance was developed to explain the multiple solutions sometimes obtained using this equation. Another theory developed to explain molecular structure is the molecular orbital theory of hybridization. This theory is difficult to understand and requires complicated mathematics. The valence-bond theory, using Schrödinger's equation, is a very useful theory to scientists because it is easily understood and quite applicable. The resonance structures obtained by the Schrödinger equation are the Lewis structures which scientists are familiar with and are comfortable using. Originally, chemists often preferred resonance theory over molecular orbital theory because of these reasons. Recent developments in the study of molecular structure have shown that the resonance theory does have some limitations. It cannot be used to accurately describe all molecular structures, for example, that of cyclobutadiene. This molecule is very unstable despite its similarities to benzene. The molecular orbital theory can account for many of the properties of cyclobutadiene, including its instability. This theory is not as comfortable as resonance theory, that is, it does not use the familiar Lewis structures that scientists have used for years. Despite this deviation from the tenets of classical chemistry, the molecular orbital theory is used extensively. The molecular orbital theory has gained popularity with chemists, but the theory of resonance hybrids is still in use by many scientists today.
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