Chemical Bonding and Molecular Geometry

Formal Charges and Resonance

Molecules can have more than one valid Lewis structure. Formal charge can be used to determine which form is found in nature. Resonance occurs when two or more Lewis structures have equivalent formal charges.
A molecular structure is the three-dimensional shape of a molecule that takes into account bonding and nonbonding electron pairs and molecular rotations to minimize their interactions. Molecular structure plays an important role in determining the properties of a substance. Lewis structures can be used to predict the molecular structure of a compound. It is possible to draw two different Lewis structures for carbon dioxide (CO2). The first structure has two double bonds. The second structure has a single bond and a triple bond. Both of these structures satisfy the octet rule. One of these structures is a better representation of the molecule, as found in nature.

Two Possible Structures for Carbon Dioxide

Carbon dioxide has two possible resonance structures, each satisfying the octet rule that atoms tend to bond in a way that provides each a valence shell with eight electrons.
A formal charge is a hypothetical charge assigned to an atom in a molecule with the assumption that bonding electrons are shared equally. Formal charges can be used to determine which of two or more possible Lewis representations is better—that is, more likely to exist most of the time. To calculate formal charge, follow these steps:

1. Distribute all shared electrons to the atoms equally between bonded atoms.

2. All nonbonding electrons stay with the atom they are attached to.

3. Count how many electrons are on each atom.

4. Compare with the normal number of valence electrons on the neutral atom.

Formal Charge Calculation for CO2 Structure with a Triple Bond (CO{\rm{C{\equiv}O}})

Step First Oxygen Atom Carbon Atom Second Oxygen Atom
Count the electrons. 7 4 5
Write the number of electrons in an uncharged atom. 6 4 6
Subtract to get the formal charge. 1– 0 1+

If the electrons are arranged in a carbon dioxide molecule so that there is one triple bond, the total charge is zero, but one oxygen atom has a 1– charge and another has a 1+ charge.

Formal Charge Calculation for CO2 Structure with Only Double Bonds (C=O{\rm{C{=}O}})

Step First Oxygen Atom Carbon Atom Second Oxygen Atom
Count the electrons. 6 4 6
Write the number of electrons in an uncharged atom. 6 4 6
Subtract to get the formal charge. 0 0 0

If the electrons are arranged in a carbon dioxide molecule so that there are only double bonds, the total charge is zero, and the formal charge on each atom is zero.

Generally, the structure with the lowest formal charge is a better model. In the two calculations of carbon dioxide, the structure with a triple bond has 1–, 0, and 1+ formal charges, and the total charge is zero. The sum of the formal charges must equal the overall charge of the molecule or ion. In the carbon dioxide structure with only double bonds, each oxygen atom and the carbon atom all have a formal charge of zero, and the total is also zero. The formal charges of all atoms in the double-bond representation is zero. Formal charges predict this is the form of carbon dioxide molecule found in nature. Experimentally, this is proven correct. Carbon dioxide molecules have two double bonds, not a single bond and a triple bond.

In some molecules different Lewis representations have the same formal charge. Consider the ozone (O3) molecule. According to the octet rule, ozone has a double bond and a single bond. Ozone has two possible Lewis structures, one with the double bond on the right and the other with the double bond on the left.

Possible Lewis Structures for Ozone

The Lewis structure of an ozone (O3) molecule can be drawn with a double bond on the right or a double bond on the left.

Formal Charge Calculation for Ozone with Double Bond on the Right (OO=O\rm{O{-}O{=}O})

Step Left Oxygen Atom Center Oxygen Atom Right Oxygen Atom
Count the electrons. 7 5 6
Write the number of electrons in an uncharged atom. 6 6 6
Subtract to get the formal charge. 1– 1+ 0

If the electrons are arranged in an ozone molecule so that the double bond is on the right, the formal charge is 1– for the left oxygen atom and 1+ for the center oxygen atom. The total charge is zero.

Formal Charge Calculation for Ozone with Double Bond on the Left (O=OO\rm{O{=}O{-}O})

Step Left Oxygen Atom Center Oxygen Atom Right Oxygen Atom
Count the electrons. 6 5 7
Write the number of electrons in an uncharged atom. 6 6 6
Subtract to get the formal charge. 0 1+ 1–

If the electrons are arranged in an ozone molecule so that the double bond is on the left, the formal charge is 1– for the right oxygen atom and 1+ for the center oxygen atom. The total charge is zero.

The formal charges for the two possible structures of ozone are 1–, 1+, 0 and 0, 1+, 1–. There is no difference between these, and both forms are equally valid. One of two or more Lewis structures with multiple equivalent representations is called a resonance structure. When resonance structures exist, they are used at the same time to represent the molecule. They are related by rotation and thus are the same. A double-sided arrow is used between the structures to show they are resonance structures.
Ozone has two resonance structures.
Resonance does not mean the molecule switches back and forth between two forms. In fact, ozone has two equal bonds with the same length. The electrons are shared evenly between the bonds. It does not have a single bond and a double bond, as the models might suggest. Resonance structures are a refinement of two energetically identical Lewis structures. However, they are still not completely accurate representations.