4.2 Lewis Structures, Formal Charge, VSEPR Geometry & Molecular Polarity

4.2 Lewis Structures, Formal Charge, VSEPR Geometry & Molecular Polarity

4. Lewis Dot Structures, Resonance, and Formal Charge

Lewis structures depict valence electrons as dots or bonding dashes. Covalent bonding typically aims to satisfy the octet rule (8 valence electrons, matching noble gas configurations).

Octet Rule Exceptions

1. Incomplete Octets: Stable with fewer than 8 electrons (Hydrogen: 2; Helium: 2; Beryllium: 4; Boron: 6 in $BF_3$).
2. Expanded Octets: Elements in Period 3 and below possess available low-lying $d$-orbitals and can accommodate 10, 12, or more valence electrons (e.g., $PCl_5, SF_6, SO_4^{2-}, XeF_4$).
3. Odd-Electron Molecules (Radicals): Contain an odd total count of valence electrons (e.g., nitric oxide, $NO$, with 11 valence electrons).

Formal Charge Equation

Formal charge evaluates the theoretical electrical charge assigned to an individual atom within a molecule, assuming all shared bonding electrons are split equally:

$$\text{Formal Charge (FC)} = V - N_{\text{nonbonding}} - \frac{1}{2} N_{\text{bonding}}$$

Where:

• $V$ is the number of valence electrons of the neutral free atom.
• $N_{\text{nonbonding}}$ is the total number of nonbonding electrons (lone pair dots).
• $N_{\text{bonding}}$ is the total number of shared bonding electrons (2 electrons per single bond line).

Resonance Hybrids and Stability Criteria

When multiple valid Lewis structures can be drawn for a molecule by redistributing delocalized $\pi$ electrons and lone pairs without altering nuclear positions, the true molecule is a resonance hybrid. The hybrid is a weighted average that is more stable (lower in potential energy) than any individual contributing canonical structure.

Criteria for Major Resonance Contributors:

1. Structures in which all atoms fulfill full octets (most dominant factor).
2. Structures with the smallest formal charge magnitudes (closest to zero).
3. Structures that place negative formal charges on the more electronegative elements.
4. Structures that minimize separation between opposite formal charges.

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5. VSEPR Theory, Molecular Geometry, and Dipole Moments

Valence Shell Electron Pair Repulsion (VSEPR) theory models molecular geometry based on the principle that electron domains (bonding pairs and nonbonding lone pairs) repel each other electrostatically and orient as far apart as possible in three dimensions.

Electron-Domain Geometry versus Molecular Geometry

• Electron-Domain Geometry: The spatial arrangement of all electron pairs (both bonding domains and nonbonding lone pairs) surrounding the central atom.
• Molecular Geometry: The spatial arrangement of the nuclei (atoms) only. Lone pairs are invisible in structural crystallography, but their presence strongly alters bond angles.
• Repulsion Hierarchy: Lone Pair-Lone Pair Repulsion > Lone Pair-Bonding Pair Repulsion > Bonding Pair-Bonding Pair Repulsion. Nonbonding lone pairs are held closer to the central nucleus, occupying larger steric volumes and compressing adjacent bonding angles.

Molecular Polarity and Net Dipole Moments

A chemical bond between atoms with an electronegativity difference ($\Delta \text{EN} > 0.4$) possesses a bond dipole moment ($\vec{\mu} = q \vec{r}$, directed from partial positive to partial negative). However, whether an entire molecule is polar depends on the vector sum of its individual bond dipoles:

$$\vec{\mu}_{\text{net}} = \sum_{i} \vec{\mu}_i$$

• Nonpolar Symmetrical Geometries: If polar bonds are arranged with high spatial symmetry, their vector components cancel completely ($\vec{\mu}_{\text{net}} = 0$). Examples: $\text{CO}_2$ (linear), $\text{BF}_3$ (trigonal planar), $\text{CCl}_4$ (tetrahedral), $\text{PCl}_5$ (trigonal bipyramidal), $\text{SF}_6$ (octahedral), and $\text{XeF}_4$ (square planar).
• Polar Asymmetric Geometries: If lone pairs introduce asymmetry or if peripheral atoms differ in electronegativity, vector dipoles do not cancel, producing a permanent molecular dipole. Examples: $\text{H}_2\text{O}$ (bent, $\mu = 1.85\text{ D}$), $\text{NH}_3$ (trigonal pyramidal, $\mu = 1.47\text{ D}$), $\text{SO}_2$ (bent), $\text{CHCl}_3$ (tetrahedral, asymmetric).

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6. Worked Numerical and Conceptual Examples

Example 1: Quantum Numbers, Configurations, and Magnetism

Determine the ground-state electron configuration, total number of unpaired electrons, and magnetic character for:

1. Neutral Manganese ($\text{Mn}, Z = 25$)
2. The Manganese(II) cation ($\text{Mn}^{2+}$)

Solution:

1. For neutral $\text{Mn}$ ($Z = 25$):
   • Argon core accounts for 18 electrons: $[\text{Ar}]$.
   • Next, $4s$ fills with 2 electrons, then $3d$ receives the remaining 5 electrons.
   • Configuration: $[\text{Ar}] 4s^2 3d^5$.
   • By Hund's rule, the five $3d$ electrons occupy the five degenerate $d$-orbitals singly ($m_l = -2, -1, 0, +1, +2$) with parallel spins ($m_s = +\frac{1}{2}$). The $4s$ electrons are paired.
   • Unpaired electrons: Exactly 5. Neutral $\text{Mn}$ is strongly paramagnetic.
2. For the $\text{Mn}^{2+}$ cation:
   • Two electrons are removed from the outermost valence shell, which is the $4s$ subshell (NOT $3d$).
   • Configuration: $[\text{Ar}] 3d^5$.
   • The five $3d$ orbitals remain singly occupied by 5 unpaired electrons.
   • Unpaired electrons: Exactly 5. $\text{Mn}^{2+}$ is strongly paramagnetic.

Example 2: Formal Charge Analysis of the Thiocyanate Ion

The thiocyanate anion ($\text{SCN}^-$) contains 16 valence electrons ($S = 6, C = 4, N = 5$, plus $1$ for the negative charge). Three resonance structures can be written with carbon as the central atom:

• Structure A: $[:\ddot{\text{S}}-\text{C}\equiv\text{N}:]^-$ (single bond S-C, triple bond C-N)
• Structure B: $[:\ddot{\text{S}}=\text{C}=\ddot{\text{N}}:]^-$ (double bond S-C, double bond C-N)
• Structure C: $[:\text{S}\equiv\text{C}-\ddot{\text{N}}:]^-$ (triple bond S-C, single bond C-N)

Evaluate the formal charges for each structure and identify the major resonance contributor.

Solution: Using $\text{FC} = V - N_{\text{nonbonding}} - \frac{1}{2} N_{\text{bonding}}$:

• Structure A:
  • $\text{FC}(\text{S}) = 6 - 6 - \frac{1}{2}(2) = -1$
  • $\text{FC}(\text{C}) = 4 - 0 - \frac{1}{2}(8) = 0$
  • $\text{FC}(\text{N}) = 5 - 2 - \frac{1}{2}(6) = 0$
• Structure B:
  • $\text{FC}(\text{S}) = 6 - 4 - \frac{1}{2}(4) = 0$
  • $\text{FC}(\text{C}) = 4 - 0 - \frac{1}{2}(8) = 0$
  • $\text{FC}(\text{N}) = 5 - 4 - \frac{1}{2}(4) = -1$
• Structure C:
  • $\text{FC}(\text{S}) = 6 - 2 - \frac{1}{2}(6) = +1$
  • $\text{FC}(\text{C}) = 4 - 0 - \frac{1}{2}(8) = 0$
  • $\text{FC}(\text{N}) = 5 - 6 - \frac{1}{2}(2) = -2$

Conclusion: Structure C is a minor contributor due to high charge magnitude ($-2$ on N and $+1$ on S). Structures A and B both minimize formal charges (single $-1$). Comparing electronegativities, Nitrogen ($\text{EN} = 3.0$) is significantly more electronegative than Sulfur ($\text{EN} = 2.5$). Therefore, Structure B, which places the negative formal charge on the more electronegative nitrogen atom, is the major resonance contributor.