VSEPR theory Knowledge-Based Study

Study notes

1. Foundations of VSEPR Theory

   Valence Shell Electron Pair Repulsion (VSEPR) theory provides a straightforward model for predicting the three-dimensional shapes of covalent molecules and polyatomic ions. The fundamental premise of the theory rests on electrostatic repulsion: valence electron pairs surrounding a central atom repel each other and consequently arrange themselves in space as far apart as possible to minimize repulsive forces and achieve electrostatic stability.

   Electron Domains and the Steric Number

   An electron domain (or region of high electron density) corresponds to either a bond or a nonbonding lone pair on the central atom. When determining electron domains, single, double, and triple bonds each count as one single electron domain.

   The steric number (SN) of the central atom is defined as:

   Steric Number = (Number of bonded atoms) + (Number of lone pairs on the central atom)

   Electron-Domain Geometry vs. Molecular Geometry

   It is vital to distinguish between two distinct concepts:

   • Electron-Domain Geometry: The spatial arrangement of all electron domains (both bonding pairs and nonbonding lone pairs) around the central atom.
   • Molecular Geometry: The spatial arrangement of the bonded nuclei only. Nonbonding lone pairs are not directly observed as vertices of the shape, but they dictate the overall geometry by exerting repulsive forces on bonding pairs.

   Geometries with No Lone Pairs

   When the central atom possesses no nonbonding lone pairs, the molecular geometry is identical to the electron-domain geometry. The five ideal arrangements corresponding to steric numbers 2 through 6 are:

   • Steric Number 2 — Linear: Two electron domains orient in opposite directions to produce a bond angle of $180^\circ$. Typical examples include $BeCl_2$ and $CO_2$.
   • Steric Number 3 — Trigonal Planar: Three domains lie in a single plane directed toward the corners of an equilateral triangle, yielding bond angles of $120^\circ$. An example is $BF_3$.
   • Steric Number 4 — Tetrahedral: Four domains project into three-dimensional space toward the vertices of a regular tetrahedron, yielding ideal bond angles of $109.5^\circ$. An example is $CH_4$.
   • Steric Number 5 — Trigonal Bipyramidal: Five domains arrange with three in an equatorial plane ($120^\circ$ separations) and two along an axial axis perpendicular to the plane ($90^\circ$ to equatorial domains, $180^\circ$ to each other). An example is $PCl_5$.
   • Steric Number 6 — Octahedral: Six domains point toward the vertices of a regular octahedron, with all adjacent positions separated by $90^\circ$. An example is $SF_6$.

   Order of Repulsive Strength

   Electrons in nonbonding lone pairs are attracted to only one atomic nucleus, making their electron clouds broader and more spatially diffuse than bonding pairs, which are localized between two positive nuclei. Consequently, electron-pair repulsions decrease in the following hierarchy:

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

   Angular Compression in Tetrahedral-Based Systems

   The asymmetric repulsion of lone pairs causes deviations from ideal bond angles:

   • Methane ($CH_4$): 4 bonding pairs, 0 lone pairs. Perfect tetrahedral shape; bond angle is $109.5^\circ$.
   • Ammonia ($NH_3$): 3 bonding pairs, 1 lone pair. Trigonal pyramidal shape; the lone pair compresses the $H-N-H$ bond angles to approximately $107^\circ$.
   • Water ($H_2O$): 2 bonding pairs, 2 lone pairs. Bent (angular) shape; the two lone pairs compress the $H-O-H$ bond angle further to approximately $104.5^\circ$.

   Equatorial Preference in Trigonal Bipyramidal Systems

   In a trigonal bipyramidal electron-domain geometry (steric number 5), lone pairs selectively occupy equatorial rather than axial sites. An equatorial lone pair experiences only two unfavorable $90^\circ$ repulsions with axial bonding pairs, whereas an axial lone pair would encounter three $90^\circ$ repulsions with equatorial bonding pairs. This site preference produces distinct shapes:

   • 1 Lone Pair: Seesaw shape (e.g., $SF_4$)
   • 2 Lone Pairs: T-shaped (e.g., $ClF_3$)
   • 3 Lone Pairs: Linear shape (e.g., $XeF_2$, $I_3^-$)

   Step-by-Step Procedure

   To determine the molecular geometry of any central atom unambiguously, follow this standardized sequence:

   1. Draw the Lewis Structure: Count total valence electrons, establish single bonds between the central atom and terminal atoms, satisfy terminal octets (or duets for hydrogen), and assign remaining electrons as lone pairs to the central atom. Ensure formal charges are minimized where applicable.
   2. Determine the Steric Number: Count the total number of bonded atoms and lone pairs on the central atom. Multiple bonds (double or triple) count as one bonding domain.
   3. Assign the Electron-Domain Geometry: Correlate the steric number to its parent geometry (2 = linear, 3 = trigonal planar, 4 = tetrahedral, 5 = trigonal bipyramidal, 6 = octahedral).
   4. Deduce the Molecular Shape: Position any lone pairs in the locations that minimize high-energy $90^\circ$ repulsions (particularly equatorial sites in steric number 5). Name the shape using only the spatial arrangement of the atomic nuclei.
   5. Estimate Bond Angles: Adjust the ideal bond angles downward where nonbonding lone pairs exert greater repulsive pressure on adjacent bonding pairs.