Formal Charges

In some cases, there are seemingly more than one valid Lewis structures for molecules and polyatomic ions. The concept of formal charges can be used to help predict the most appropriate Lewis structure when more than one reasonable structure exists.

Calculating Formal Charge

The formal charge of an atom in a molecule is the hypothetical charge the atom would have if the electrons in the bonds are evenly distributed between the atoms. Alternatively, formal charge results when from the number of valence electrons of a neutral atom, the nonbonding electrons are first reduced, followed by the subtraction of the number of bonds connected to that atom in the Lewis structure.

Thus, the formal charge is calculated as follows:  

The formal charge calculations can be double-checked by determining the sum of the formal charges for the whole structure. The sum of the formal charges of all atoms in a molecule must be zero; the sum of the formal charges in an ion should equal the charge of the ion. Remember that the formal charge calculated for an atom is not the actual charge of the atom in the molecule. The formal charge is only a useful bookkeeping procedure; it does not indicate the presence of actual charges.

Calculating Formal Charge from Lewis Structures

The following steps are followed to assign formal charges to each atom in the interhalogen ion ICl₄⁻.

Step 1. Divide the bonding electron pairs equally for all I–Cl bonds:

Step 2. Assign lone pairs of electrons to their atoms. Each chlorine atom now has seven electrons assigned to it, and the iodine atom has eight.

Step 3. Subtract this number from the number of valence electrons for the neutral atom:
Iodine: 7 – 8 = –1
Chlorine: 7 – 7 = 0
The sum of the formal charges of all the atoms equals –1, which is identical to the charge of the ion (–1).

Using Formal Charge to Predict Molecular Structure

The arrangement of atoms in a molecule or ion is called its molecular structure. In many cases, following the steps for writing Lewis structures may lead to more than one possible molecular structure — multiple different bonds and lone-pair electron placements or different arrangements of atoms, for instance. A few guidelines involving formal charge can be helpful in deciding which of the possible structures is most likely for a particular molecule or ion:

1. A molecular structure in which all formal charges are zero is preferable to one in which some formal charges are not zero.
2. If the Lewis structure must have non-zero formal charges, the arrangement with the smallest non-zero formal charges is preferable.
3. Lewis structures are preferable when adjacent formal charges are zero or of the opposite sign.
4. When choosing from several Lewis structures with similar distributions of formal charges, the structure with the negative formal charges on the more electronegative atoms is preferable.

To see how these guidelines apply, consider some possible structures for carbon dioxide, CO₂. It is known that the less electronegative atom typically occupies the central position, but formal charges help understand why this occurs. Three possibilities for the structure can be drawn: carbon in the center with two double bonds, the carbon in the center with a single and triple bond, and oxygen in the center with double bonds. 

On comparing the three formal charges, the structure on the left can be identified as preferable because it has only formal charges of zero.

As another example, the thiocyanate ion, an ion formed from a carbon atom, a nitrogen atom, and a sulfur atom, could have three different molecular structures: NCS–, CNS–, or CSN–. The formal charges present in each of these molecular structures can help pick the most likely arrangement of atoms. Possible Lewis structures and the formal charges for each of the three possible structures for the thiocyanate ion are – carbon in the center with double bonds, nitrogen in the center with double bonds, and sulfur in the center with double bonds. 

Note that the sum of the formal charges in each case is equal to the charge of the ion (–1). However, the first arrangement of atoms with carbon in the center is preferred because it has the lowest number of atoms with non-zero formal charges. Also, it places the least electronegative atom in the center and the negative charge on the more electronegative element.

This text is adapted from Openstax, Chemistry 2e, Chapter 7.4 Formal Charges and Resonance.