8.4 Resonance

One of the postulates of the Lewis Dot Structure for representing molecules is that a bond is the result of a pair of electrons being shared between two different nuclei, and as such, can be represented as a line between the two nuclei (actually, this is normally a line between the letters that represent the elements involved). but what if the electrons are shared between more than two nuclei? When this happens, there is no one Lewis Dot Structure that accurately describes the molecule, and you sort of have to average all the structures.

NOTE: Resonance structures represent different ways of placing electrons on the atoms in a molecule's Lewis dot structure. All resonance structures have the same connectivity. If you change the connectivity, you change the molecule, and that is not a resonance structure. In section 8.5 we will cover drawing Lewis dot structures and you will learn how to recognize if they exist while you are drawing them. But before we draw them, we want to define and describe them. So the following examples should help you identify and describe resonance structures.

Lets start with a look at the Lewis Dot Structure of Ozone

Ozone (O₃)

Fig. 8.3.1: Lewis dot structure of ozone.

In figure 8.3.1 we see that the Lewis Dot Structure of Ozone has a dobule bond between the left and center oxygens, and a single between the right and center. But we could have written as in figure 8.3.2, where we switched the double and single bonds.

Fig. 8.3.2: another valid Lewis dot structure of ozone

So which of the above two structures is the correct one that accurately describes ozone?

Neither, as both bonds are between oxygen and oxygen, and so should be of the same length. That is, if you think about it, a double bond should be shorter than a single bond. There are two facets of logic to this. First, the double bond is stronger, because if you break the double bond, you end up with the single bond. Second, the stronger the bond attraction, the closer the nuclei, and so the stronger double bond will be shorter than the weaker single bond. But the bonds are between identical atoms with identical connectivity, and so they should be the same length. So we introduce the concept of Resonance, and the above two structures are actually resonance structures, with the real structure being a mixture of the two (you could say that bond is not single or double, but 1.5).

Fig. 8.3.3: The two resonance structures for ozone. Note the two headed arrow represents resonance structures, and neither of these is the actual molecule, with the real molecule being the mixture of these two structures.

In reality, what we will learn in chapter 9 is that the second bond of the double bond, which is called a \(\pi\) bond, is not between two atoms, but between all three. That is, the failure of the Lewid dot structure is in the concept that a bond is an orbital shared by two atoms, where in this case it is shared by three atoms. This could be expressed by the dotted line in figure 8.3.4

Fig. 8.3.4: Ignoring the lone electrons, this images is showing that the bonding electron on the dotted orbital is actually being shared by all three atoms. Note, here the multiple bonds (line plus dashed line) are a mixture of a single and double bond, and so are like a bond of order 1.5.

Bond Order

Bond order is a way of describing resonance structures that do not always add up to integer bonds.

• Bond Order = 1: Single Bond
• Bond Order = 2: Double Bond
• Bond Order = 3: Triple Bond
• Bond Order = 1.5: Single and Double Bond mixed
• Bond Order = 1.33 Two Single Bonds mixed with a Double Bond

Does a single and a doted line always mean the bond order is 1.5?
No, look at Nitrate in the next example, where it is 1.33

Nitrate Ion

In figure 8.3.5 we see three resonance structures of nitrate ion.

Figure 8.3.5: Three resonance structures of nitrate ion. Note, for ions, we place the Lewis dot structure in brackets and the charge as a superscript on the outside of the bracket. In section 8.3.5 we will learn how to draw Lewis dot structures, but it needs to be noted that you have extra electrons for anions, and fewer for cations.

If we were to merge the Lewis dot structure into one figure like we did in fig. 8.3.4 for ozone

Figure 8.3.6. In this figure we have mixed the three resonance structures in figure 8.3.5 into one structure, where the multiple bond (line plus dashed line) represents one double and 2 single bonds, and so has a bond order of 1.333.

It is important to note that the dashed lines in figure 8.3.4 and 8.3.6 have different meanings, and so the dashed line itself does not indicate the magnitude of the multiple bond, just that it is bigger than a single bond and smaller than a double.

Benzene

Benzene (C₆H₆) is a ring structure that is common in organic compounds known as aromatics. Here, there are electrons in an orbital that covers 6 nuclei, and there are two ways of drawing the Lewis dot structures of benzene.

Fig. 8.3.7: Lewis dot structure of benzene.

Note here we have 3 single and 3 double bonds in the ring. In organic chemistry the carbon and hydrogen atoms are not explicitly drawn as in figure 8.3.7, but implicitly inferred, as in figure 8.3.8. This is done by assuming each line ends with a carbon, and each carbon has 8 electrons around it, and so has 4 bonds.

Fig. 8.3..8: This is the same as figure 8.3.7, except that the carbons and hydrogens are implied.

As each structure has 6 corners with a carbon at each end, there are 6 carbons. As each corner is the junction of a single and a double bond, there are 6 electrons around each carbon, and so we assume there is one additional bond with the remaining two electrons being shared with hydrogen.

It is very common to merge the two electrons into one structure, which is often done with a solid ring.

Fig. 8.3.9: Condensed drawings of benzene resonance structures into a single Lewis dot structure.

Note here, that the second bond represented by the circles represents an orbital that covers 6 nuclei.

Do resonance structures always add up to non-integer bond orders?
No, look at the resonance structures of carbon dioxide in the next example

Carbon Dioxide

Fig. 8.3.10: Resonance structures of carbon dioxide

In the above figure we see the second and third resonance structures average out to the first, and so the average of all the resonance structures is a double bond. That is, if you look at the first, the two structures on the right add up to a total of 4, which when averaged out between the two of them, becomes 2. Thus it is common to write carbon dioxide as having two double bonds, and that resonance structure is the correct structure of carbon dioxide.

Summary

So what we have seen is that one of the shortcoming of Lewis dot structures comes from the concept that a line represents a bond between two nuclei, but that sometimes, the bond is between more than two nuclei. In this case you need to write multiple Lewis dot structures, and use an arrow with two head to indicate that each of the individual structures is a resonance structure, and the true molecule is a combination of them all. If, as in the case of carbon dioxide all the resonance structures average out to one of the resonance structures, that can be treated as the real structure, and you have an integer bond order. If not, the real structure is none of the resonance structures, and the bond order is of non-integer order, often indicated with a dotted line.

It must be emphasized that in resonance structures, the connectivity of the atoms does not change, just where the electrons are placed.