VSEPR: Valence Shell Electron Pair Repulsion and Molecular Geometry

Foundations of Molecular Shape and VSEPR Theory

Lewis structures show how valence electrons are distributed among atoms within a molecule but do not represent the 3D structure.
Predictions about molecular shape can be made based on Lewis structures.
Understanding molecular shape is crucial for determining the chemical and physical properties of compounds.
Examples of physical and chemical property differences related to shape include:
- The behavior of water.
- The mechanism by which drugs bind to receptors.
- The state of matter at room temperature: $\text{CO}_2$ is a gas with a molar mass of $44.01\,g\,mol^{-1}$ , while $\text{H}_2\text{O}$ is a liquid with a molar mass of $18.02\,g\,mol^{-1}$ .
Valence Shell Electron Pair Repulsion (VSEPR) is a simple and powerful method for determining molecular structure.
The fundamental principle of VSEPR is that molecular geometry is determined by the repulsion between pairs of electrons.
Valence electron pairs, including both bonding pairs and lone pairs, arrange themselves to be as far apart as possible to minimize repulsion.
The theory is based on the electrostatic idea that "like charges repel."

Determining Molecular Geometry and Shape

Determine and draw the Lewis structure of the molecule.
Count the number of pairs (regions) of electrons around the central atom.
- Count each bond as one set. VSEPR does not distinguish between single, double, or triple bonds; they all count as one region of electron density.
- Count each set of lone pairs as one region.
- Count a single radical (unpaired electron) as one region.
Determine the Electron Pair Geometry (EPG) based on the total number of electron regions.

Electron Pair Geometry (EPG) Classifications

Orientations are determined by achieving the minimum repulsion energy. The geometry and bond angles vary according to the number of electron regions around the central atom:

2 Electron Pairs:
- Geometry: Linear
- Bond Angle: $180^\circ$
- Examples: $\text{BeF}_2$ and $\text{CO}_2$
3 Electron Pairs:
- Geometry: Trigonal Planar
- Bond Angle: $120^\circ$
- Examples: $\text{BF}_3$ and $\text{NO}_2^-$
4 Electron Pairs:
- Geometry: Tetrahedral
- Bond Angle: $109.5^\circ$
- Examples: $\text{CH}_4$ and $\text{H}_2\text{O}$
5 Electron Pairs:
- Geometry: Trigonal bipyramidal
- Bond Angles: $90^\circ$ and $120^\circ$
- Examples: $\text{PF}_5$ and $\text{I}_3^-$
6 Electron Pairs:
- Geometry: Octahedral
- Bond Angle: $90^\circ$
- Examples: $\text{SF}_6$ and $\text{XeF}_4$

Two Sets of Electron Pairs: Linear Geometry

$\text{BeF}_2$ :
- Valence electrons: $2 + (7 \times 2) = 16$
- Number of electron sets around central atom: 2
- EPG: Linear
$\text{CO}_2$ :
- Valence electrons: $4 + (6 \times 2) = 16$
- Number of electron sets around central atom: 2 (each double bond counts as one set)
- EPG: Linear
$\text{C}_2\text{H}_2$ :
- Valence electrons: $(4 \times 2) + (1 \times 2) = 10$
- Number of electron sets around each carbon atom: 2
- EPG around both carbon atoms: Linear

Three Sets of Electron Pairs: Trigonal Planar Geometry

$\text{BF}_3$ :
- Valence electrons: $2 + (7 \times 3) = 24$
- Number of electron sets around central atom: 3
- EPG: Trigonal planar
- Bond angle: $120^\circ$
$\text{NO}_2^-$ :
- Valence electrons: $5 + (6 \times 2) + 1 = 18$
- Number of electron sets around central atom: 3 (two bonds and one lone pair)
- EPG: Trigonal planar

The Impact of Lone Pairs on Molecular Geometry

Lone pairs occupy more space than bonding pairs.
In a bonding pair, electrons are shared between two nuclei.
In a non-bonding (lone) pair, electrons are associated with only one nucleus, causing them to spread out more and take up more volume around the atom.
Lone pairs have a larger "angular volume" than bonding pairs.
Repulsion Strength Hierarchy: $\text{LP-LP repulsion} > \text{BP-LP repulsion} > \text{BP-BP repulsion}$ .
Because repulsions are not equal, bond angles are often compressed when lone pairs are present.
Molecular Shape vs. EPG:
- EPG describes the arrangement of all electron regions (bonds and lone pairs).
- Molecular Shape describes the arrangement of only the atoms (nuclei positions).
- When the central atom has one or more lone pairs, the EPG and the molecular shape will differ.

Four Sets of Electron Pairs: Tetrahedral Geometry

All molecules with 4 electron regions have a Tetrahedral EPG, but their shapes vary based on lone pairs:

Methane ( $\text{CH}_4$ ):
- 4 bonding pairs, 0 lone pairs.
- Molecular Shape: Tetrahedral
- Bond Angle: $109.5^\circ$
Ammonia ( $\text{NH}_3$ ):
- 3 bonding pairs, 1 lone pair.
- Molecular Shape: Trigonal Pyramidal
- Bond Angle: $107.5^\circ$ (compression due to lone pair)
Water ( $\text{H}_2\text{O}$ ):
- 2 bonding pairs, 2 lone pairs.
- Molecular Shape: Bent or V-shaped
- Bond Angle: $104.5^\circ$ (greater compression due to two lone pairs)

Five Sets of Electron Pairs: Trigonal Bipyramidal Geometry

All molecules with 5 electron regions have a Trigonal Bipyramidal EPG. Lone pairs always occupy equatorial positions to minimize repulsion:

$\text{PCl}_5$ :
- 0 lone pairs.
- Molecular Shape: Trigonal bipyramidal
$\text{SF}_4$ :
- 1 lone pair.
- Molecular Shape: Seesaw
$\text{ClF}_3$ :
- 2 lone pairs.
- Molecular Shape: T-shaped
$\text{I}_3^-$ :
- 3 lone pairs.
- Molecular Shape: Linear

Six Sets of Electron Pairs: Octahedral Geometry

All molecules with 6 electron regions have an Octahedral EPG. Lone pairs are positioned to be as far apart as possible (typically $180^\circ$ from each other):

$\text{SF}_6$ :
- 0 lone pairs.
- Molecular Shape: Octahedral
$\text{ClF}_5$ :
- 1 lone pair.
- Molecular Shape: Square Pyramidal
$\text{XeF}_4$ :
- 2 lone pairs.
- Molecular Shape: Square Planar (Lone pairs are $180^\circ$ apart to minimize repulsion)

Effects of Multiple Bonds on Geometry

While VSEPR treats double and triple bonds as single regions for determining basic geometry, they take up more space than single bonds due to increased electron density.
Example: Formaldehyde ( $\text{CH}_2\text{O}$ )
- The $\text{C=O}$ double bond exerts more repulsion than the $\text{C-H}$ single bonds.
- This results in an $\text{H-C-H}$ bond angle of $118^\circ$ and $\text{H-C-O}$ bond angles of $121^\circ$ (rather than a perfect $120^\circ$ for trigonal planar).

Recommended Resources and Practice

Textbook: "Chemistry 5th Ed" by Blackman, Bottle, Schmid, Mocerino & Wille.
Reading: Sections 5.4 and 5.5.
Practice Questions: 5.17, 5.18, 5.20, 5.22, 5.23 (excluding ball and stick models), 5.24, 5.25, 5.42, 5.44, 5.45, 5.48, 5.49.
Interactive Simulations: PHET simulations on Molecule Shapes and Molecule Shapes Basics (available at phet.colorado.edu).