2.3 Formal Charges

Formal Charges and Molecular Properties

Formal charges tell you how electrons are distributed across atoms in a molecule. They're central to predicting polarity, stability, and reactivity, which makes them one of the most practical tools you'll use throughout organic chemistry.

Formal charge calculation process

Formal charge is the difference between the number of valence electrons a free atom would have and the number of electrons assigned to that atom in a Lewis structure. "Assigned electrons" means all the lone pair (non-bonding) electrons plus half the bonding electrons.

The formula:

$FC = (\text{valence electrons}) - (\text{non-bonding electrons}) - \frac{1}{2}(\text{bonding electrons})$

Here's how to apply it step by step:

1. Draw the Lewis structure of the molecule.
2. For each atom, count its valence electrons (from the periodic table).
3. Count the non-bonding (lone pair) electrons on that atom.
4. Count the total bonding electrons in bonds connected to that atom.
5. Plug into the formula.

Example: Dimethyl sulfoxide (DMSO, $CH_3SOCH_3$)

In the Lewis structure of DMSO, sulfur has three bonds (one to oxygen, two to carbon) and one lone pair. Oxygen has one bond to sulfur and two lone pairs.

1. Sulfur: 6 valence electrons, 2 non-bonding electrons (1 lone pair), 6 bonding electrons (3 bonds)

   • $FC(S) = 6 - 2 - \frac{1}{2}(6) = +1$

2. Oxygen: 6 valence electrons, 4 non-bonding electrons (2 lone pairs), 2 bonding electrons (1 bond)

   • $FC(O) = 6 - 4 - \frac{1}{2}(2) = +1$

Wait, that gives $+1$ on oxygen, which doesn't match what we'd expect. The issue is that DMSO is commonly drawn with a coordinate (dative) bond from sulfur to oxygen, giving sulfur a $+1$ formal charge and oxygen a $-1$ formal charge. Here's the correct breakdown for that structure:

• Sulfur: 6 valence, 2 non-bonding, 6 bonding → $FC = 6 - 2 - 3 = +1$
• Oxygen: 6 valence, 6 non-bonding (3 lone pairs), 2 bonding → $FC = 6 - 6 - 1 = -1$

The carbon and hydrogen atoms each have a formal charge of zero because they share exactly as many electrons as they'd have in isolation.

A quick shortcut: if an atom has its "normal" number of bonds and lone pairs, its formal charge is zero. You only need to calculate when something looks unusual.

Formal charges and molecular properties

Formal charges point to uneven electron distribution within a molecule.

• An atom with a positive formal charge has fewer electrons than its neutral state. It's electron-poor. Carbocations ($R_3C^+$) are a classic example.
• An atom with a negative formal charge has more electrons than its neutral state. It's electron-rich. Carbanions ($R_3C^-$) fit here.

This uneven distribution directly creates polarity. A bond between atoms carrying different formal charges is polar, and if the molecule's geometry is asymmetric, you get a net dipole moment. Acetone is a good example: the carbonyl carbon carries a partial positive character while oxygen is partially negative, and the molecule has an overall dipole.

Formal charges also help you pick the best resonance structure. Two rules to remember:

• Structures with less charge separation (fewer formal charges overall) are more stable.
• When charge separation is unavoidable, the negative charge should sit on the more electronegative atom. A structure with $-1$ on oxygen beats one with $-1$ on carbon.

Molecular structure and geometry

Electron domains around a central atom determine molecular shape. Each lone pair, single bond, double bond, or triple bond counts as one electron domain.

Electron-pair geometry describes how all electron domains arrange themselves (including lone pairs), while molecular geometry describes only the positions of the atoms. These can differ: water has a tetrahedral electron-pair geometry but a bent molecular geometry because two of the four domains are lone pairs.

Hybridization ties into this directly. An atom with four electron domains is $sp^3$ hybridized (tetrahedral), three domains gives $sp^2$ (trigonal planar), and two domains gives $sp$ (linear). Knowing the hybridization tells you bond angles and the types of orbitals available for bonding.

Applications of formal charge concepts

Formal charges predict where reactions happen.

Electrophilic sites carry positive formal charges (or significant partial positive character). These atoms are electron-seeking and attract nucleophiles. The carbonyl carbon in aldehydes and ketones is a textbook electrophile because oxygen's electronegativity pulls electron density away from carbon.

Nucleophilic sites carry negative formal charges. These atoms donate electrons in reactions. Alkoxide ions ($RO^-$) are strong nucleophiles and strong bases precisely because of that concentrated negative charge on oxygen.

Zwitterions are molecules that carry both a positive and a negative formal charge simultaneously. Amino acids at physiological pH are the most important example: the amino group is protonated ($NH_3^+$) and the carboxyl group is deprotonated ($COO^-$). This internal charge separation makes zwitterions highly soluble in water through strong ion-dipole and hydrogen bonding interactions.

Ylides have adjacent atoms bearing opposite formal charges. Phosphonium ylides ($R_3P^+\text{-}^-CR_2$) are key reagents in the Wittig reaction, where they react with carbonyl compounds to form alkenes. The adjacent opposite charges make ylides unusually reactive.