Molecular Geometry and the Lone Pair Effect Note

Lewis theory serves as the primary tool to describe the arrangement of electrons around a molecule and to predict molecular shapes, specifically when the central atom possesses lone pairs.
Lone pair groups occupy more physical space on the central atom compared to bonding pairs. This occurs because their electron density is localized exclusively on the central atom rather than being shared between two nuclei like bonding electron groups.
The relative magnitude of repulsive force interactions determines molecular stability and shape distortion. The hierarchy of repulsion is as follows:
- \text{Lone Pair -- Lone Pair} > \text{Lone Pair -- Bonding Pair} > \text{Bonding Pair -- Bonding Pair}
This hierarchy of repulsion significantly impacts bond angles, causing them to compress and become smaller than the ideal angles predicted by basic molecular geometries.

Bonding electrons are shared between two atoms. Consequently, a portion of the negative charge is removed from the vicinity of the central atom to reside between the nuclei.
Nonbonding electrons (lone pairs) are localized entirely on the central atom. Because they are not stretched toward a second nucleus, the area of negative charge they occupy takes up significantly more volume around the central atom.

A molecule will exhibit one of the basic molecular geometries if all electron groups around the central atom are bonding groups and all those bonds are equivalent.
Molecules containing lone pairs will exhibit derivative shapes. These shapes feature distorted bond angles and varying bond lengths compared to the idealized parent geometries.

When a central atom has 3 electron groups and 1 of those groups is a lone pair (2 bonding groups total), the resulting molecular geometry is labeled as a trigonal planar-bent shape.
The presence of the lone pair causes the bond angle between the bonding groups to be less than the ideal value of $120^\circ$ (< 120^\circ).

When a central atom has 4 electron groups and 1 of those is a lone pair (3 bonding groups total), the resulting molecular geometry is called Trigonal pyramidal.
- This is characterized as a triangular-base pyramid with the central atom positioned at the apex.
- The bond angle in a trigonal pyramidal shape is less than the ideal tetrahedral angle (< 109.5^\circ). For example, ammonia ( $NH_3$ ) has an actual bond angle of $107^\circ$ .
When a central atom has 4 electron groups and 2 of those are lone pairs (2 bonding groups total), the resulting molecular geometry is called a tetrahedral-bent shape.
- Although the electron geometry is tetrahedral, the molecular geometry is planar in appearance.
- This shape is similar to the trigonal planar-bent shape, but the bond angles are significantly smaller because of the increased repulsion from two lone pairs.
- The bond angle is less than the ideal $109.5^\circ$ . For example, water ( $H_2O$ ) has an actual bond angle of $104.5^\circ$ .

Distorted Tetrahedron (or Seesaw): Occurs when there are 5 electron groups and 1 of them is a lone pair.
T-shape: Occurs when there are 5 electron groups and 2 of them are lone pairs.

When 6 electron groups exist around a central atom and multiple lone pairs are present, each even-numbered lone pair will occupy a position directly opposite the previously placed lone pair to minimize repulsion.
Square Pyramidal Shape: This occurs when there are 6 electron groups and 1 is a lone pair (5 bonding groups).
- In this geometry, the bond angles between the axial and equatorial positions are less than $90^\circ$ (< 90^\circ).
Square Planar Shape: This occurs when there are 6 electron groups and 2 are lone pairs (4 bonding groups).
- The two lone pairs sit opposite each other, which allows the bonding groups to remain in a single plane.
- The bond angles between the equatorial bonding positions remain at exactly $90^\circ$ .

Total Groups: 2
- Bonding Groups: 2
- Lone Pairs: 0
- Electron Geometry: Linear
- Molecular Geometry: Linear
- Approximate Bond Angle: $180^\circ$
- Example: $CO_2$ (represented as $:O=C=O:$ )
Total Groups: 3
- Bonding Groups: 3 | Lone Pairs: 0 | Electron Geometry: Trigonal planar | Molecular Geometry: Trigonal planar | Angle: $120^\circ$ | Example: $BF_3$
- Bonding Groups: 2 | Lone Pairs: 1 | Electron Geometry: Trigonal planar | Molecular Geometry: Bent | Angle: < 120^\circ | Example: $SO_2$
Total Groups: 4
- Bonding Groups: 4 | Lone Pairs: 0 | Electron Geometry: Tetrahedral | Molecular Geometry: Tetrahedral | Angle: $109.5^\circ$ | Example: $CH_4$
- Bonding Groups: 3 | Lone Pairs: 1 | Electron Geometry: Tetrahedral | Molecular Geometry: Trigonal pyramidal | Angle: < 109.5^\circ | Example: $NH_3$
- Bonding Groups: 2 | Lone Pairs: 2 | Electron Geometry: Tetrahedral | Molecular Geometry: Bent | Angle: < 109.5^\circ | Example: $H_2O$

Draw the Lewis Structure: Determine the arrangement of atoms and valence electrons.
Determine Electron Groups: Count the total number of electron groups around the central atom.
Classify Groups: Categorize each electron group as either a bonding group or a lone pair.
- Note: Multiple bonds (double or triple) count as a single electron group.
Assign Geometry: Use the counts of bonding and nonbonding groups to identify the molecular shape and bond angles based on standardized geometry tables.

Step 1: Valence Electron Calculation
- $Cl = 7\,e^-$
- $O_2 = 2 \times 6\,e^- = 12\,e^-$
- $F = 7\,e^-$
- Total Valence Electrons = $26\,e^-$
Step 2: Identify Central Atom
- Chlorine ( $Cl$ ) is the central atom as it is the least electronegative element in the molecule.
Step 3: Electron Group Analysis
- Number of Electron Groups on Chlorine: 4
- Number of Bonding Groups: 3
- Number of Lone Pairs: 1
Step 4: Determine Geometry and Angles
- Molecular Shape: Trigonal Pyramidal
- Bond Angles: O-Cl-O < 109.5^\circ and O-Cl-F < 109.5^\circ