Formal Charge and Choosing the Best Structure
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You should be comfortable drawing basic Lewis structures, counting valence electrons, and understanding the octet rule as described in the previous lecture.
Why this matters
Formal charge is the bookkeeping tool that tells us which of several valid Lewis structures is the most realistic representation of a molecule.
When drawing Lewis structures for polyatomic ions or molecules with multiple possible connectivity patterns, we often find more than one arrangement that satisfies the octet rule. However, not all valid structures are equally important. Some contribute significantly to the true electronic structure of the molecule, while others are minor contributors. Formal charge allows us to quantitatively assess the stability of each structure by assigning a hypothetical charge to each atom based on an equal sharing of bonding electrons. By minimising the magnitude of these charges and placing negative charges on more electronegative atoms, we can identify the dominant structure that best describes the chemical reality.
The Concept of Formal Charge
Imagine a molecule where two atoms are bonded. In reality, the electrons in that bond are not shared equally; the more electronegative atom pulls them closer. Formal charge is a simplified accounting method that pretends the electrons are shared equally. We calculate it by asking: "If I took my share of the bonding electrons and kept my lone pairs, how many electrons would I have? How does that compare to the number of valence electrons a neutral atom of this element normally has?" The difference is the formal charge. A formal charge of zero means the atom has exactly the number of electrons it expects. A negative formal charge means it has more electrons than a neutral atom, and a positive formal charge means it has fewer. This is not the real partial charge (which depends on electronegativity), but it is a crucial tool for comparing different structural possibilities.
Calculating Formal Charge
The formula for formal charge is derived from the electron count. For any atom in a Lewis structure, the formal charge \(FC\) is calculated as the number of valence electrons in the free, neutral atom (\(V\)), minus the number of non-bonding electrons (lone pairs, \(L\)), minus half the number of bonding electrons (\(B\)). Mathematically, this is expressed as:
Here, \(V\) is the group number for main-group elements. \(L\) is the total number of electrons in lone pairs on that specific atom. \(B\) is the total number of electrons in bonds connected to that atom. Since each bond consists of two electrons, \(\frac{B}{2}\) is simply the number of bonds. This formula allows us to assign a charge to every atom in a proposed structure.
Rules for Selecting the Best Structure
When multiple Lewis structures satisfy the octet rule, we use formal charge to rank them. The primary rule is to minimise the magnitude of the formal charges on individual atoms. A structure with all formal charges equal to zero is generally more stable than one with separated positive and negative charges. If formal charges are unavoidable (as in ions), we prefer the structure where the formal charges are closest to zero. For example, a structure with charges of +1 and -1 is preferred over one with +2 and -2.
The second rule applies when two structures have the same set of formal charge magnitudes. In this case, we place the negative formal charge on the more electronegative atom. Electronegativity reflects an atom's ability to hold onto electrons; therefore, a structure where the more electronegative atom carries the negative charge is energetically more favourable. Conversely, positive formal charges should reside on the less electronegative atoms.
Applying the Rules: Nitrate Ion
Consider the nitrate ion, \(\mathrm{NO_3^-}\). The total number of valence electrons is \(5 + 3(6) + 1 = 24\). Nitrogen is the central atom. If we draw three single bonds to oxygen, nitrogen has a formal charge of \(5 - 0 - 3 = +2\), and each oxygen has a formal charge of \(6 - 6 - 1 = -1\). The sum of formal charges is \(+2 + 3(-1) = -1\), which matches the ion charge. However, the magnitude of the charges is high. By forming one double bond and two single bonds, the formal charges become: Nitrogen \(5 - 0 - 4 = +1\); double-bonded Oxygen \(6 - 4 - 2 = 0\); single-bonded Oxygens \(6 - 6 - 1 = -1\). The sum is \(+1 + 0 + 2(-1) = -1\). This structure has smaller charge magnitudes (max 1 vs 2) and places the negative charge on oxygen, the more electronegative atom. Thus, the structure with one double bond is the preferred major contributor.
The result
Lewis structures and the octet rule
A molecule's total valence electrons can be distributed as bonding pairs (shared between two atoms) and lone pairs (localised on one atom) so that, wherever possible, every main-group atom is surrounded by eight electrons (two, for hydrogen). Where more than one such distribution is possible, the formal charge \(FC=V-L-\tfrac{B}{2}\) (valence electrons \(V\), lone-pair electrons \(L\), bonding electrons \(B\)) on each atom selects the best structure: minimise the magnitude of formal charges, and place any necessary negative formal charge on the more electronegative atom.
A common misconception is that formal charge represents the actual physical charge on an atom. It does not. Formal charge is a bookkeeping device based on equal sharing of electrons. The actual partial charge (\(\delta\)) is determined by electronegativity differences and is often different from the formal charge. For instance, in a C–O bond, oxygen has a partial negative charge due to electronegativity, but its formal charge might be zero if it has two bonds and two lone pairs. Always distinguish between formal charge (structural bookkeeping) and partial charge (electronic distribution). C
Worked example
Problem. Determine the best Lewis structure for the cyanate ion, \(\mathrm{OCN^-}\), by calculating formal charges for the two possible connectivity arrangements: \(\mathrm{O-C-N}\) and \(\mathrm{N-C-O}\). Assume carbon is always the central atom in these linear triatomic ions. Total valence electrons: \(6 (\mathrm{O}) + 4 (\mathrm{C}) + 5 (\mathrm{N}) + 1 (\text{charge}) = 16\).
- Consider the structure \(\mathrm{O=C=N^-}\). Calculate formal charges: Oxygen (2 bonds, 2 lone pairs): \(FC = 6 - 4 - 2 = 0\). Carbon (4 bonds, 0 lone pairs): \(FC = 4 - 0 - 4 = 0\). Nitrogen (2 bonds, 2 lone pairs): \(FC = 5 - 4 - 2 = -1\). Sum: \(-1\).
- Consider the structure \(\mathrm{^-O-C\equiv N}\). Calculate formal charges: Oxygen (1 bond, 3 lone pairs): \(FC = 6 - 6 - 1 = -1\). Carbon (4 bonds, 0 lone pairs): \(FC = 4 - 0 - 4 = 0\). Nitrogen (3 bonds, 1 lone pair): \(FC = 5 - 2 - 3 = 0\). Sum: \(-1\).
- Compare the structures. Both have the same magnitude of formal charges (one -1, two 0s). We must apply the electronegativity rule. Oxygen is more electronegative than nitrogen. Therefore, the structure where the negative formal charge resides on oxygen is more stable.
- Identify the best structure. The structure \(\mathrm{^-O-C\equiv N}\) places the negative charge on oxygen, which is preferred over \(\mathrm{O=C=N^-}\) where the negative charge is on nitrogen.
Units check. Formal charge is a dimensionless quantity, so no units are required, but the sum of formal charges must equal the overall ion charge (-1).
Three quick tests
- What is the formal charge on nitrogen in \(\mathrm{NH_4^+}\)?
Answer
+1: \(FC = 5 - 0 - 8/2 = +1\) (no lone pairs, four bonds). The ion's charge sits formally on N. - What are the formal charges in \(\mathrm{H{-}C{\equiv}N}\)?
Answer
All zero: H \(1-0-1\), C \(4-0-4\), N \(5-2-3\). - In carbon monoxide, drawn as \(\mathrm{C{\equiv}O}\) with one lone pair on each atom, what are the formal charges?
Answer
C: \(4-2-3 = -1\); O: \(6-2-3 = +1\). This is a reminder that formal charge is bookkeeping: the real dipole of CO is small.
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Every lecture and every result in this unit, with prerequisites and threads.
Lecture notes drafted with a local model and checked line by line by the editor; every number in the worked example was recomputed.