4.2 Lewis Structures, Formal Charges & Resonance

Lewis Structures, Formal Charges & Resonance

Quick Summary: Lewis dot structures represent valence electrons organized into shared covalent bonds and nonbonding lone pairs. Formal charge calculations identify dominant electronic configurations by assessing deviations from neutral atomic valences. Delocalized $\pi$ electron systems are described through resonance hybrids exhibiting fractional bond orders. Key exceptions to the octet rule include odd-electron free radicals, electron-deficient Group 2 and 13 molecules, and hypervalent Period 3+ elements with expanded valence shells.

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1. Protocol for Constructing Lewis Structures

Constructing a valid Lewis formula follows a systematic six-step procedure:

1. Tabulate Total Valence Electrons ($N_{\text{val}}$): Sum the valence electrons from all neutral atoms. Add one electron for each negative ionic charge; subtract one electron for each positive ionic charge.
2. Identify the Central Atom: Place the least electronegative element at the center (excluding hydrogen, which is always terminal). Carbon is virtually always central; halogens are typically terminal.
3. Form Single ($\sigma$) Bonds: Connect each terminal atom to the central atom using a single covalent bond, subtracting $2$ electrons per bond from $N_{\text{val}}$.
4. Satisfy Terminal Octets: Distribute remaining electrons as lone pairs to give terminal atoms an octet (duet for hydrogen).
5. Assign Remaining Electrons to the Central Atom: Place any surplus electrons on the central atom as nonbonding pairs.
6. Form Multiple Bonds to Complete Octets: If the central atom lacks an octet, convert nonbonding lone pairs from terminal atoms into double or triple bonds.

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2. Formal Charge Calculation & Structure Evaluation

Formal charge (FC) evaluates electron allocation assuming equal sharing across all covalent bonds:

$\text{FC} = V - N - \frac{1}{2}B = V - \text{lone pair electrons} - \text{number of bonds}$

where $V$ is valence electrons in the isolated atom, $N$ is nonbonding electrons, and $B$ is shared bonding electrons. The sum of all formal charges equals the overall species charge ($\sum \text{FC}_i = Q_{\text{net}}$).

Formal Charge Criteria for Dominant Structures

1. Structures minimizing formal charge magnitudes ($0$ preferred over $\pm 1$, $\pm 2$ disfavored) dominate.
2. Negative formal charges must reside on the most electronegative atoms.
3. Like formal charges on adjacent bonded atoms indicate electrostatic destabilization.

Diagnostic Comparison: The Cyanate Ion ($\text{OCN}^-$, 16 Valence Electrons)

Because oxygen (EN 3.44) is more electronegative than nitrogen (EN 3.04), Structure III is the dominant contributor.

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3. Resonance Structures & the Resonance Hybrid

When a species can be represented by multiple valid Lewis structures differing solely in electron positions, these representations are resonance structures.

• The Resonance Hybrid: The molecule does not oscillate among forms; it exists as a single, static resonance hybrid with delocalized $\pi$ electrons, lowering potential energy by the resonance stabilization energy.
• Carbonate Ion ($\text{CO}_3^{2-}$, 24 $e^-$): Three equivalent resonance structures distribute one double bond and two single bonds across three oxygen atoms. All three $\text{C}-\text{O}$ bonds are identical in length ($128\text{ pm}$, between single $143\text{ pm}$ and double $122\text{ pm}$). The calculated bond order is: $\text{Bond Order} = \frac{\text{Total Bonding Pairs in Linkage}}{\text{Resonance Positions}} = \frac{1 + 1 + 2}{3} = \frac{4}{3} \approx 1.33$ Each oxygen bears an effective formal charge of $-\frac{2}{3}$.
• Nitrate ($\text{NO}_3^-$) and Ozone ($\text{O}_3$): Exhibit fractional bond orders of $1.33$ and $1.5$, respectively.

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4. Exceptions to the Octet Rule

Three systematic classes of stable molecules depart from the octet rule:

1. Odd-Electron Molecules (Free Radicals)

Species with an odd total number of valence electrons possess an unpaired electron, imparting paramagnetism and high reactivity:

• Nitric Oxide ($\text{NO}$, 11 $e^-$): $:\dot{\text{N}}=\ddot{\text{O}}:$, with the unpaired electron localized on nitrogen (less electronegative than oxygen).
• Nitrogen Dioxide ($\text{NO}_2$, 17 $e^-$): Paramagnetic brown gas that readily dimerizes to diamagnetic $\text{N}_2\text{O}_4$.

2. Incomplete Octets (Electron-Deficient Compounds)

Compounds of Group 2 ($\text{Be}$) and Group 13 ($\text{B}, \text{Al}$) are stable with fewer than eight valence electrons:

• $\text{BeCl}_2$ (vapor): Beryllium forms two single bonds ($4$ valence electrons).
• $\text{BF}_3$: Boron forms three single bonds ($6$ valence electrons). Forming a $\text{B}=\text{F}$ double bond would place an unfavorable $+1$ formal charge on fluorine.
• Lewis Acid Behavior: Electron-deficient centers act as strong Lewis acids, reacting with Lewis bases like $\text{NH}_3$ to form adducts via coordinate covalent bonds ($\text{F}_3\text{B}\leftarrow\text{NH}_3$).

3. Expanded Octets (Hypervalent Molecules)

Central atoms from Period 3 and below ($\text{P}, \text{S}, \text{Cl}, \text{Br}, \text{I}, \text{Xe}$) accommodate $10$, $12$, or $14$ valence electrons:

• $\text{PCl}_5$: 5 single bonds ($10$ valence electrons).
• $\text{SF}_6$: 6 single bonds ($12$ valence electrons).
• $\text{XeF}_4$: 4 single bonds + 2 lone pairs ($12$ valence electrons).
• $\text{I}_3^-$: 2 single bonds + 3 lone pairs ($10$ valence electrons).

Why Period 2 Elements NEVER Expand Their Octets

Second-period elements ($\text{C}, \text{N}, \text{O}, \text{F}$) cannot expand their octets because their valence shell ($n=2$) contains only $2s$ and $2p$ subshells (maximum 8 electrons). The $3d$ subshell is separated by an enormous quantum energy gap, and their small atomic radii make coordinating five or six ligands sterically impossible.