4.3 VSEPR Theory, Molecular Geometries & Polarity

VSEPR Theory, Molecular Geometries & Polarity

Quick Summary: Valence Shell Electron Pair Repulsion (VSEPR) theory determines three-dimensional molecular shapes by minimizing electrostatic repulsions among electron domains around a central atom. Total domain count defines the electron-pair geometry, while the arrangement of bonded atoms defines the molecular geometry. Diffuse nonbonding lone pairs exert stronger repulsive forces than bonding pairs, systematically compressing bond angles. Molecular polarity arises when individual bond dipole vectors fail to cancel due to asymmetric geometry.

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1. VSEPR Principles & Steric Number

Valence electron pairs—whether localized in bonds or lone pairs—repel each other electrostatically. To minimize potential energy, these domains adopt spatial arrangements maximizing mutual separation.

Steric Number (SN)

$\text{SN} = (\text{Number of Bonded Atoms}) + (\text{Number of Lone Pairs on Central Atom})$

• Multiple Bonds: A single, double, or triple bond each counts as exactly one electron domain.
• Lone Pairs: Each nonbonding pair localized on the central atom counts as one electron domain.
• Electron-Pair vs. Molecular Geometry: Electron-pair geometry describes the spatial arrangement of all domains. Molecular geometry describes the arrangement of bonded nuclei only.

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2. Repulsive Hierarchy & Bond Angle Distortion

Bonding pairs are held electrostatically between two positive nuclei, confining their electron clouds. Nonbonding lone pairs are attracted to only one nucleus, creating broader, more diffuse clouds that occupy greater angular volume.

Repulsion Hierarchy

$\text{Lone Pair - Lone Pair (lp-lp)} > \text{Lone Pair - Bonding Pair (lp-bp)} > \text{Bonding Pair - Bonding Pair (bp-bp)}$

Bond Angle Compression in the Tetrahedral Family (SN = 4)

• Methane ($\text{CH}_4$, 4 bp, 0 lp): Ideal tetrahedral angle of $109.5^\circ$.
• Ammonia ($\text{NH}_3$, 3 bp, 1 lp): Heightened $\text{lp-bp}$ repulsion compresses the $\text{H}-\text{N}-\text{H}$ angle to $107.0^\circ$.
• Water ($\text{H}_2\text{O}$, 2 bp, 2 lp): Intense $\text{lp-lp}$ and $\text{lp-bp}$ repulsion compresses the $\text{H}-\text{O}-\text{H}$ angle to $104.5^\circ$.

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3. Molecular Geometry Catalog (Steric Numbers 2 to 6)

SN = 2 (Linear Electron Geometry, $180^\circ$)

• $\text{AX}_2$ (2 bp, 0 lp): Linear ($180^\circ$). Examples: $\text{BeCl}_2, \text{CO}_2, \text{HCN}$.

SN = 3 (Trigonal Planar Electron Geometry, $120^\circ$)

• $\text{AX}_3$ (3 bp, 0 lp): Trigonal Planar ($120^\circ$). Examples: $\text{BF}_3, \text{SO}_3, \text{CO}_3^{2-}$.
• $\text{AX}_2\text{E}$ (2 bp, 1 lp): Bent ($< 120^\circ \approx 119^\circ$). Examples: $\text{SO}_2, \text{NO}_2^-$.

SN = 4 (Tetrahedral Electron Geometry, $109.5^\circ$)

• $\text{AX}_4$ (4 bp, 0 lp): Tetrahedral ($109.5^\circ$). Examples: $\text{CH}_4, \text{CCl}_4, \text{SO}_4^{2-}$.
• $\text{AX}_3\text{E}$ (3 bp, 1 lp): Trigonal Pyramidal ($< 109.5^\circ \approx 107^\circ$). Examples: $\text{NH}_3, \text{PCl}_3$.
• $\text{AX}_2\text{E}_2$ (2 bp, 2 lp): Bent ($< 109.5^\circ \approx 104.5^\circ$). Examples: $\text{H}_2\text{O}, \text{SCl}_2, \text{OF}_2$.

SN = 5 (Trigonal Bipyramidal Electron Geometry)

Features two distinct positions: equatorial ($120^\circ$ apart, two $90^\circ$ neighbors) and axial ($180^\circ$ apart, three $90^\circ$ neighbors).

Equatorial Rule: Because $90^\circ$ repulsions are severely destabilizing, nonbonding lone pairs always occupy equatorial positions.

• $\text{AX}_5$ (5 bp, 0 lp): Trigonal Bipyramidal ($90^\circ, 120^\circ, 180^\circ$). Example: $\text{PCl}_5$.
• $\text{AX}_4\text{E}$ (4 bp, 1 lp): Seesaw (axial-eq $< 90^\circ \approx 87^\circ$, eq-eq $< 120^\circ \approx 102^\circ$). Example: $\text{SF}_4$.
• $\text{AX}_3\text{E}_2$ (3 bp, 2 lp): T-Shaped ($< 90^\circ \approx 87.5^\circ, < 180^\circ$). Examples: $\text{ClF}_3, \text{BrF}_3$.
• $\text{AX}_2\text{E}_3$ (2 bp, 3 lp): Linear ($180^\circ$). Three equatorial lone pairs cancel; axial atoms form a straight line. Examples: $\text{XeF}_2, \text{I}_3^-$.

SN = 6 (Octahedral Electron Geometry, $90^\circ, 180^\circ$)

• $\text{AX}_6$ (6 bp, 0 lp): Octahedral ($90^\circ$). Examples: $\text{SF}_6, \text{PF}_6^-$.
• $\text{AX}_5\text{E}$ (5 bp, 1 lp): Square Pyramidal ($< 90^\circ \approx 85^\circ$). Examples: $\text{BrF}_5, \text{IF}_5$.
• $\text{AX}_4\text{E}_2$ (4 bp, 2 lp): Square Planar ($90^\circ, 180^\circ$). Lone pairs occupy opposite trans positions ($180^\circ$) to minimize mutual repulsion. Examples: $\text{XeF}_4, \text{ICl}_4^-$.

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4. Master VSEPR Geometry Reference Table

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5. Molecular Polarity & Vector Dipole Moments

Molecular polarity requires polar bonds in an asymmetric shape preventing vector cancellation ($\vec{\mu}_{\text{net}} = \sum \vec{\mu}_i \ne 0$).

• Nonpolar via Symmetry ($\vec{\mu} = 0$): In symmetric molecules with identical terminal atoms, equal dipoles cancel: $\text{CO}_2$ (linear), $\text{BF}_3$ (trigonal planar), $\text{CCl}_4$ (tetrahedral), $\text{PCl}_5$ (trigonal bipyramidal), $\text{XeF}_2$ (linear), $\text{SF}_6$ (octahedral), and $\text{XeF}_4$ (square planar).
• Polar Molecules ($\vec{\mu} > 0$): Asymmetry yields net dipole reinforcement: $\text{H}_2\text{O}$ (bent, $\mu = 1.85\text{ D}$), $\text{NH}_3$ (pyramidal, $\mu = 1.47\text{ D}$), $\text{CHCl}_3$ (broken symmetry), $\text{SF}_4$ (seesaw), $\text{ClF}_3$ (T-shaped).
• Geometric Isomers: In cis-1,2-dichloroethene, dipoles reinforce (polar); in trans-1,2-dichloroethene, dipoles cancel across the inversion center (nonpolar).

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6. Coordination Complexes Geometry Overview

Transition metal complexes adopt shapes dictated by coordination number (CN) and metal $d$-electron count:

• CN = 2: Linear ($180^\circ$). Formed by $d^{10}$ ions: $[\text{Ag}(\text{NH}_3)_2]^+$, $[\text{Au}(\text{CN})_2]^-$.
• CN = 4: Competing tetrahedral and square planar:
  • Tetrahedral ($109.5^\circ$): Favored by $d^{10}$ ions ($[\text{Zn}(\text{NH}_3)_4]^{2+}$) and high-spin complexes ($[\text{CoCl}_4]^{2-}$).
  • Square Planar ($90^\circ, 180^\circ$): Favored by $d^8$ metals ($\text{Pt}^{2+}, \text{Pd}^{2+}$). Clinically exemplified by antitumor drug cisplatin (cis-$[\text{PtCl}_2(\text{NH}_3)_2]$).
• CN = 6: Universally octahedral ($90^\circ, 180^\circ$), e.g., $[\text{Fe}(\text{CN})_6]^{4-}, [\text{Co}(\text{NH}_3)_6]^{3+}$.