Molecular shapes and bond angles Knowledge-Based Study

Study notes

1. Valence Shell Electron Pair Repulsion (VSEPR) Theory

   The three-dimensional geometry of a covalent molecule is primarily determined by electrostatic repulsions between valence electron pairs surrounding the central atom. According to VSEPR theory, electron domains (bonding pairs and non-bonding or lone pairs) arrange themselves in space to minimize mutual repulsion, maximizing the distance between them.

   Key Definitions

   • Electron Domain (Steric Number): Any region of electron density around a central atom. A single bond, double bond, triple bond, or lone pair each counts as one electron domain.
   • Electron Domain Geometry: The spatial arrangement of all electron domains around the central atom, regardless of whether they are bonding pairs or lone pairs.
   • Molecular Geometry (Shape): The actual spatial arrangement of only the bonded atoms around the central atom. Lone pairs influence this shape by exerting repulsive forces, but they are not directly observed as vertices of the molecular shape.

   Basic Molecular Shapes with No Lone Pairs

   When the central atom possesses only bonding electron pairs, the molecular geometry is identical to the electron domain geometry. Under these conditions, bond angles achieve their ideal, symmetric values.

   • Linear (Steric Number = 2): Two electron domains point in opposite directions. The ideal bond angle is exactly 180°. Typical example: $\text{BeCl}_2$ or $\text{CO}_2$.
   • Trigonal Planar (Steric Number = 3): Three electron domains lie in a single plane, directed toward the corners of an equilateral triangle. The ideal bond angle is 120°. Typical example: $\text{BF}_3$.
   • Tetrahedral (Steric Number = 4): Four electron domains point toward the vertices of a regular tetrahedron. The ideal bond angle is 109.5°. Typical example: $\text{CH}_4$.
   • Trigonal Bipyramidal (Steric Number = 5): Five electron domains split into axial and equatorial positions. Equatorial–equatorial angles are 120°, while axial–equatorial angles are 90°. Typical example: $\text{PCl}_5$.
   • Octahedral (Steric Number = 6): Six electron domains point toward the vertices of an octahedron. All adjacent bond angles are 90°. Typical example: $\text{SF}_6$.

   Repulsion Hierarchy and Angular Distortion

   Non-bonding electron pairs (lone pairs) are held by only one atomic nucleus, whereas bonding pairs are shared between two nuclei. Consequently, lone pairs occupy a larger spatial volume and exert greater repulsive force than bonding pairs.

   Order of Repulsive Strength

   Lone Pair – Lone Pair > Lone Pair – Bonding Pair > Bonding Pair – Bonding Pair

   Case Study: Four Electron Domains (Steric Number = 4)

   Comparing molecules with a steric number of 4 illustrates how lone pairs systematically compress adjacent bond angles below the ideal tetrahedral angle of $109.5^\circ$:

   • Methane ($\text{CH}_4$): 4 bonding pairs, 0 lone pairs.
     Shape: Tetrahedral
     Bond angle: 109.5°
   • Ammonia ($\text{NH}_3$): 3 bonding pairs, 1 lone pair.
     Shape: Trigonal Pyramidal
     Bond angle: approximately 107° (the lone pair repels the three $\text{N–H}$ bonds downward).
   • Water ($\text{H}_2\text{O}$): 2 bonding pairs, 2 lone pairs.
     Shape: Bent (or V-shaped)
     Bond angle: approximately 104.5° (two lone pairs cause even stronger compression).

   Shapes Derived from Expanded Valence Shells

   Central atoms from Period 3 or below can accommodate more than eight valence electrons. In these systems, lone pairs preferentially occupy positions that minimize strong $90^\circ$ repulsions:

   • Steric Number 5 (Trigonal Bipyramidal Base): Lone pairs always occupy equatorial positions because they encounter fewer $90^\circ$ interactions (only two) compared to axial positions (three).
     • 1 lone pair: Seesaw (e.g., $\text{SF}_4$, bond angles < $120^\circ$ and < $90^\circ$)
     • 2 lone pairs: T-shaped (e.g., $\text{ClF}_3$, bond angles < $90^\circ$)
     • 3 lone pairs: Linear (e.g., $\text{XeF}_2$, bond angle = $180^\circ$)
   • Steric Number 6 (Octahedral Base): All six positions are initially equivalent. However, a second lone pair will locate $180^\circ$ opposite the first to minimize lone pair–lone pair repulsion.
     • 1 lone pair: Square Pyramidal (e.g., $\text{BrF}_5$, bond angles < $90^\circ$)
     • 2 lone pairs: Square Planar (e.g., $\text{XeF}_4$, bond angles = $90^\circ$)

   Step-by-Step Method to Determine Molecular Geometry

   1. Draw the valid Lewis structure of the molecule.
   2. Count the total number of electron domains (bonding groups + lone pairs) on the central atom to find the steric number.
   3. Identify the corresponding electron domain geometry.
   4. Account for the positions of lone pairs to determine the final molecular shape and deduce any compression of the ideal bond angles.