Resonance Structures, Delocalization, and Formal Charge

Principles of Resonance and Electron Delocalization

• Definition of Resonance: Resonance structures are employed when a single classical Lewis formula fails to adequately depict the bonding present between adjacent atoms relative to empirical data, specifically experimental bond lengths and bond energies.

• Probabilistic Nature of Electrons: Electrons do not occupy fixed, static spatial positions within atoms, molecules, or polyatomic ions. Instead, electrons are distributed across regions defined by probability densities, known as atomic and molecular orbitals.

• Electron Clouds and Probability Densities:

  • Resonance structures model the regions within a chemical species exhibiting higher electron probabilities (electron densities).

  • The electron cloud encompasses bonding regions and nonbonding domains without confinement to localized positions between two nuclei.

• Electron Delocalization:

  • Delocalization is the phenomenon wherein valence electrons (primarily $\pi$ electrons and nonbonding lone pairs) are free to disperse across three or more adjacent, overlapping atomic orbitals.

  • This spreading of electron density reduces electrostatic repulsion between electrons, increases attraction toward multiple positive nuclei, and significantly stabilizes the molecule or ion thermodynamically.

Rules for Formulating Valid Resonance Structures

• Rule 1: Conservation of Total Valence Electrons:

  • All resonance structures for a given species must possess the exact same total number of electrons.

  • No electrons may be created, added, or removed; the total electron count is verified by summing all bonding and nonbonding electrons.

• Rule 2: Adherence to Standard Lewis Rules:

  • Every resonance contributor must obey the fundamental rules of Lewis structures.

  • Second-row elements ($\text{C}$, $\text{N}$, $\text{O}$, $\text{F}$) must strictly adhere to the octet rule and cannot accommodate an expanded valence shell.

• Rule 3: Invariance of Hybridization:

  • The orbital hybridization state of each constituent atom must remain uniform across all resonance structures.

• Rule 4: Invariance of Nuclear Skeleton:

  • The atomic framework and connectivity (the structural skeleton) must remain completely invariant.

  • Only electrons ($\pi$ electrons and nonbonding pairs) shift positions; nuclei do not move.

• Rule 5: Constant Total Number of Lone Pairs:

  • The total quantity of nonbonding electron lone pairs across the species must remain constant, even though individual lone pairs may convert into $\pi$ bonds and vice versa.

Resonance Hybrids and Empirical Bond Length Metrics

• Nature of the Resonance Hybrid:

  • An actual chemical species does not rapidly alternate, oscillate, or flip between distinct resonance forms.

  • The true physical species is a static quantum mechanical average known as the resonance hybrid.

• Structural Components in a Resonance Hybrid:

  • Solid Lines: Represent localized $\sigma$ bonds that are present in every contributing resonance structure.

  • Dashed Lines: Represent delocalized partial $\pi$ bonds that exist in at least one, but not all, contributing resonance structures.

  • Localized Lone Pairs: Electron pairs residing on the same atom across all resonance contributors.

• Average Bond Lengths Reference Data:

  • Carbon–Carbon Bonds:

  • Single bond ($\text{C}-\text{C}$): $1.54\,\text{Å}$

  • Double bond ($\text{C}=\text{C}$): $1.34\,\text{Å}$

  • Triple bond ($\text{C}\equiv\text{C}$): $1.20\,\text{Å}$

  • Carbon–Nitrogen Bonds:

  • Single bond ($\text{C}-\text{N}$): $1.43\,\text{Å}$

  • Double bond ($\text{C}=\text{N}$): $1.38\,\text{Å}$

  • Triple bond ($\text{C}\equiv\text{N}$): $1.16\,\text{Å}$

  • Carbon–Oxygen Bonds:

  • Single bond ($\text{C}-\text{O}$): $1.43\,\text{Å}$

  • Double bond ($\text{C}=\text{O}$): $1.23\,\text{Å}$

  • Triple bond ($\text{C}\equiv\text{O}$): $1.13\,\text{Å}$

  • Nitrogen–Nitrogen Bonds:

  • Single bond ($\text{N}-\text{N}$): $1.47\,\text{Å}$

  • Double bond ($\text{N}=\text{N}$): $1.24\,\text{Å}$

  • Triple bond ($\text{N}\equiv\text{N}$): $1.10\,\text{Å}$

  • Nitrogen–Oxygen Bonds:

  • Single bond ($\text{N}-\text{O}$): $1.36\,\text{Å}$

  • Double bond ($\text{N}=\text{O}$): $1.22\,\text{Å}$

  • Oxygen–Oxygen Bonds:

  • Single bond ($\text{O}-\text{O}$): $1.48\,\text{Å}$

  • Double bond ($\text{O}=\text{O}$): $1.21\,\text{Å}$

• Empirical Validation in Nitrate ($\text{NO}_3^-$):

  • A standard localized Lewis structure predicts two long $\text{N}-\text{O}$ single bonds ($1.36\,\text{Å}$) and one short $\text{N}=\text{O}$ double bond ($1.22\,\text{Å}$).

  • Experimental measurement reveals that all three nitrogen-oxygen bonds are strictly identical in length at $1.29\,\text{Å}$.

  • The bond order is calculated as:

$\text{Bond Order} = \frac{\text{Total Number of Shared Pairs}}{\text{Total Number of Bonding Positions}} = \frac{4}{3} \approx 1.33$

• The measured length of $1.29\,\text{Å}$ is intermediate between a pure single bond ($1.36\,\text{Å}$) and a pure double bond ($1.22\,\text{Å}$), confirming that the nitrate anion exists as an averaged hybrid.

Case Studies of Prototypical Resonance Systems

• Carbonate Ion ($\text{CO}_3^{2-}$):

  • Features three equivalent resonance contributors separated by double-headed arrows ($\longleftrightarrow$).

  • In each structure, carbon forms one double bond to an oxygen and single bonds to two other oxygens, with each singly bonded oxygen bearing a formal charge of $-1$.

  • Delocalization distributes the $-2$ overall charge evenly across the three oxygen atoms ($-\frac{2}{3}$ charge per oxygen).

• Ozone ($\text{O}_3$):

  • Composed of 18 valence electrons.

  • Has two equivalent major resonance contributors.

  • The central oxygen atom forms a single bond with one terminal oxygen atom and a double bond with the opposite terminal oxygen atom, shifting symmetrically.

• Nitrate Ion ($\text{NO}_3^-$):

  • Possesses 24 valence electrons.

  • Has three equivalent resonance forms with trigonal planar geometry.

  • The single double bond alternates among the three nitrogen-oxygen positions, establishing three equivalent bonds with a bond order of $1.33$.

• Benzene ($\text{C}_6\text{H}_6$):

  • A planar hexagonal ring containing 6 carbon atoms and 6 hydrogen atoms.

  • Represented by two equivalent Kekulé structures with alternating single and double carbon–carbon bonds.

  • The true hybrid displays complete carbon–carbon equivalence, typically drawn as a hexagon containing an inscribed circle representing delocalized $\pi$ electron density.

Formal Charge Calculation and Principles

• Definition of Formal Charge:

  • Formal charge ($\text{FC}$) is a bookkeeping tool that assigns a theoretical charge to an individual atom within a molecule or polyatomic ion, assuming equal sharing of electrons in all covalent bonds regardless of electronegativity differences.

  • Formal charges assist in predicting the most probable and stable Lewis structures among nonequivalent alternatives.

• Mathematical Formula for Formal Charge:

$\text{FC} = (\text{Valence } e^- \text{ in Free Atom}) - (\text{Total Nonbonding } e^-) - \frac{\text{Total Bonding } e^-}{2}$

• Operational Formula Based on Bonds:

$\text{FC} = (\text{Valence } e^- \text{ in Free Atom}) - (\text{Total Nonbonding } e^-) - (\text{Number of Bonds})$

• Formal Charge Verification via Carbon Dioxide ($\text{CO}_2$):

  • For the Lewis structure $\ddot{\text{O}}=\text{C}=\ddot{\text{O}}$, total valence electrons equal $16$.

  • Central Carbon Atom:

$\text{FC}_\text{C} = 4 - 0 - 4 = 0$

• Terminal Oxygen Atoms (each):

$\text{FC}_\text{O} = 6 - 4 - 2 = 0$

• All atoms carry a formal charge of zero, yielding an optimal, uncharged, highly stable structure.

Stability Criteria for Evaluating Resonance Contributors

• Primary Principles for Evaluating Resonance Contributions:

  • Goal #1 (Charge Minimization): Structures with formal charges closest to zero are preferred over structures with larger magnitudes of charge.

  • Goal #2 (Electronegativity Alignment): Any unavoidable negative formal charges must reside on the most electronegative atom(s).

• Six Rules for Estimating Resonance Stability:

  1. Maximum Number of Covalent Bonds: The contributor with the greatest number of covalent bonds possesses the greatest stability because more atoms attain complete valence octets.

  2. Minimum Number of Formal Charges: The structure displaying the least number of formal charges is more stable.

  3. Minimal Charge Separation: Structures that minimize the distance and magnitude of formal charge separation are more stable.

  4. wNegative Charge Placement: A structure that places negative formal charges on the more electronegative atom(s) is more stable.

  5. Positive Charge Placement: A structure that places positive formal charges on the least electronegative (most electropositive) atom(s) is more stable.

  6. Equivalent Forms: Resonance contributors that are chemically and structurally equivalent possess equal stability and contribute equally to the resonance hybrid (e.g., benzene, carbonate, nitrate).

Comparative Analysis of Thiocyanate Resonance Contributors

• Valence Electron Count: The thiocyanate ion ($[\text{SCN}]^-$) contains $16$ valence electrons ($6$ from $\text{S}$, $4$ from $\text{C}$, $5$ from $\text{N}$, and $1$ from the negative ionic charge).

• Evaluation of the Three Contributing Structures:

  • Structure 1: Double bond between sulfur and carbon, double bond between carbon and nitrogen:

$[:\ddot{\text{S}}=\text{C}=\ddot{\text{N}}:]^- controls:$

- Sulfur formal charge:

$\text{FC}_\text{S} = 6 - 4 - 2 = 0$

- Carbon formal charge:

$\text{FC}_\text{C} = 4 - 0 - 4 = 0$

- Nitrogen formal charge:

$\text{FC}_\text{N} = 5 - 4 - 2 = -1$

• Structure 2: Triple bond between sulfur and carbon, single bond between carbon and nitrogen:

$[:\text{S}\equiv\text{C}-\ddot{\text{N}}:]^- controls:$

- Sulfur formal charge:

$\text{FC}_\text{S} = 6 - 2 - 3 = +1$

- Carbon formal charge:

$\text{FC}_\text{C} = 4 - 0 - 4 = 0$

- Nitrogen formal charge:

$\text{FC}_\text{N} = 5 - 6 - 1 = -2$

• Structure 3: Single bond between sulfur and carbon, triple bond between carbon and nitrogen:

$[:\ddot{\text{S}}-\text{C}\equiv\text{N}:]^- controls:$

- Sulfur formal charge:

$\text{FC}_\text{S} = 6 - 6 - 1 = -1$

- Carbon formal charge:

$\text{FC}_\text{C} = 4 - 0 - 4 = 0$

- Nitrogen formal charge:

$\text{FC}_\text{N} = 5 - 2 - 3 = 0$

• Determination of the Major Contributor:

  • Structure 2 possesses high charge magnitudes ($+1$ and $-2$) and significant charge separation, making it the least stable and a negligible contributor.

  • Both Structure 1 and Structure 3 feature minimal formal charges ($0, 0, -1$).

  • Electronegativity values dictate stability: nitrogen has an electronegativity of approximately $3.0$, whereas sulfur has an electronegativity of approximately $2.5$.

  • Because nitrogen is more electronegative than sulfur, the negative formal charge is more stably situated on the nitrogen atom.

  • Therefore, Structure 1 ($[:\ddot{\text{S}}=\text{C}=\ddot{\text{N}}:]^-$) represents the most stable resonance contributor and best describes the ground-state bonding of the thiocyanate ion.