Calculating Formal Charges on Atoms

Formal charge is the charge an atom would have in a Lewis structure if all bonding electrons were shared equally between the bonded atoms, and it is calculated as formal charge = (valence electrons) − (nonbonding electrons) − ½ (bonding electrons). In brief: in the ammonium ion, nitrogen has 5 valence electrons, 0 nonbonding electrons and 8 bonding electrons, so its formal charge is 5 − 0 − 4 = +1; the best Lewis structure usually has the smallest formal charges, with any negative charge on the most electronegative atom.

When more than one Lewis structure can be written for a species, formal charges help to decide which one is the most likely. They are a bookkeeping tool, not the true charges on atoms. This article gives the formula and a quick rule, shows how to use formal charges to choose between structures, compares them with oxidation numbers, includes tables of typical bonding patterns, works through examples including expanded octets and gives some history.

How do you calculate formal charge?

For each atom in a Lewis structure:

formal charge = V − N − B ÷ 2

where V is the number of valence electrons in the free atom, N is the number of nonbonding (lone pair) electrons on the atom and B is the number of electrons in the bonds to the atom, that is, 2 for each bond. Because B ÷ 2 is just the number of bonds, an alternative formula is formal charge = V − (lone pair electrons) − (number of bonds). The sum of the formal charges of all atoms must equal the overall charge of the molecule or ion.

Which bonding patterns give zero formal charge?

This table is a quick way to check: if an atom has its usual number of bonds, its formal charge is zero.

How do you choose the best Lewis structure?

1. The structure in which all formal charges are zero is preferred.
2. If it is not possible, choose the one with the smallest formal charges (+1 and −1 are better than +2 and −2).
3. Formal charges of the same sign on adjacent atoms are unfavorable.
4. When there are formal charges, the negative charge should be on the most electronegative atom.
5. The sum of the formal charges equals the overall charge.

Worked examples

1. Ammonium, NH₄⁺. Nitrogen: V = 5, N = 0, bonds = 4. FC = 5 − 0 − 4 = +1. Each hydrogen: 1 − 0 − 1 = 0. The sum is +1, which equals the ion’s charge.
2. Carbon monoxide, CO (triple bond). Carbon has 1 lone pair (2 electrons) and 3 bonds: FC = 4 − 2 − 3 = −1. Oxygen has 1 lone pair and 3 bonds: FC = 6 − 2 − 3 = +1. The sum is 0. The formal charges suggest that the negative charge is on carbon, the less electronegative atom, which is an unusual situation that is reflected in the chemistry of CO.
3. Carbon dioxide, two possible structures. O=C=O: carbon 4 − 0 − 4 = 0; each oxygen 6 − 4 − 2 = 0. All zero. The alternative [O≡C–O] with a triple and a single bond gives O (triple): 6 − 2 − 3 = +1 and O (single): 6 − 6 − 1 = −1. The structure with two double bonds is better because all formal charges are zero.
4. Nitrate, NO₃⁻. The structure has one N=O and two N–O⁻. Nitrogen: 5 − 0 − 4 = +1. Double-bonded O: 6 − 4 − 2 = 0. Each single-bonded O: 6 − 6 − 1 = −1. The sum is +1 + 0 − 1 − 1 = −1, as required for the ion.
5. Hydronium, H₃O⁺. Oxygen has 3 bonds and 1 lone pair: FC = 6 − 2 − 3 = +1. Each hydrogen has 0. The sum is +1.
6. Thiocyanate, SCN⁻: which atom carries the negative charge? The structure S–C≡N has S: 6 − 6 − 1 = −1; C: 4 − 0 − 4 = 0; N: 5 − 2 − 3 = 0. The structure S=C=N has S: 6 − 4 − 2 = 0; C: 0; N: 5 − 4 − 2 = −1. The first puts −1 on sulfur (electronegativity 2.58), and the second on nitrogen (3.04), so the second is preferred according to the electronegativity rule, but the real ion is a hybrid of these and other forms, and it can bond through either S or N.

What about expanded octets?

For ions such as sulfate, SO₄²⁻, two Lewis structures are possible. In the first, sulfur has four single bonds and obeys the octet: S: 6 − 0 − 4 = +2, and each O: 6 − 6 − 1 = −1, so the sum is +2 − 4 = −2. In the second, sulfur has two double bonds and two single bonds (12 electrons): S: 6 − 0 − 6 = 0, two double-bonded O: 0 each, and two single-bonded O: −1 each, so the sum is −2. The second has smaller formal charges, and is often drawn in textbooks. However, calculations show that the d orbitals contribute little to the bonding, and the best description is one in which the bonds are highly polar and the S–O bonds have order of about 1.5, so chemists now often prefer the structure with all single bonds and formal charges for explanations of the electron distribution. Both are accepted at the introductory level, and it is useful to know the reasons.

Formal charge versus oxidation number

The true distribution of charge lies between the two models. In CO, for instance, the electrons are shared unequally, but the molecule has a very small dipole moment (0.11 D).

How did the concept develop?

The use of formal charge developed in the 1930s and 1940s as part of the application of Lewis structures to inorganic ions and organic reaction mechanisms. Linus Pauling’s electroneutrality principle, formulated in 1948, suggested that the actual charges on atoms in stable molecules tend to be small, which helps to explain why structures with minimal formal charges are favored. Today, formal charge is used in introductory teaching and also to track charges in curved-arrow mechanisms in organic chemistry.

Which mistakes are common?

Mistake 1: Counting lone pairs as pairs instead of electrons

A lone pair is 2 nonbonding electrons. Use the electron count in the formula.

Mistake 2: Dividing bonding electrons incorrectly

Use half of the bonding electrons, which is the number of bonds, not all of them.

Mistake 3: Thinking that formal charge is the real atomic charge

It is a model. Real charges are usually smaller and spread out.

Mistake 4: Confusing formal charge with oxidation state

They are calculated with different assumptions and are usually different numbers.