VSEPR Theory

Valence Shell Electron Pair Repulsion (VSEPR) theory—also known as the Gillespie–Nyholm theory—is a foundational model in inorganic, organic, and physical chemistry used to predict the three-dimensional molecular geometry of polyatomic molecules and ions from the number of valence electron domains surrounding a central atom. Originally proposed by Nevil Sidgwick and Herbert Powell at the University of Oxford in 1940 and systematically expanded into a quantitative predictive framework by Ronald J. Gillespie and Ronald S. Nyholm at University College London in 1957, VSEPR theory posits that localized regions of high electron density in a valence shell—comprising both covalent bond domains (single, double, or triple bonds) and non-bonding lone pair domains—adopt spatial arrangements on the valence sphere that minimize mutual inter-domain repulsion.

🧪 Interactive Simulation & Curriculum: Explore 3D molecular shapes, lone-pair repulsion, and bond angles in VSEPR Lab and study the companion VSEPR & Orbital Bonding Mechanics learning module.

Beyond Classical Electrostatic Repulsion

Although introductory treatments often describe VSEPR geometries in terms of classical Coulombic repulsion (V ∝ q₁q₂ / r) between negatively charged electron clouds, Ronald Gillespie and István Hargittai demonstrated through quantum mechanical analysis that the Pauli exclusion principle provides the primary physical driving force behind electron-pair domain separation. Because electrons are spin-½ fermions, the total many-electron wavefunction must be antisymmetric with respect to the exchange of any two electrons. Consequently, two electrons possessing identical spin quantum numbers (m_s = +½ or −½) have zero probability of occupying the same point in three-dimensional space—a correlation region termed the Fermi hole.

In a closed-shell molecule, opposite-spin electrons can share the same spatial region only when paired within a localized orbital hybridization domain or molecular orbital. Opposite-spin pairs belonging to different domains still experience same-spin Pauli exclusion against one member of each neighboring pair. Mapping the Laplacian of the electron density (−∇²ρ(r)) within Richard Bader's Quantum Theory of Atoms in Molecules (QTAIM) or computing the Electron Localization Function (ELF) reveals discrete local maxima of valence shell charge concentration (VSCC) around the central core that match the geometric vertices predicted by the AX_nE_m VSEPR notation.

The AX_nE_m Steric Number Notation

In Gillespie–Nyholm AX_nE_m nomenclature:

• A denotes the central polyvalent atom (such as carbon, nitrogen, oxygen, phosphorus, sulfur, or xenon).
• X_n denotes the number (n) of covalently bonded peripheral atoms (ligands) attached to A. A single σ bond, a double bond (σ + π), a triple bond (σ + 2π), or a resonance-delocalized fractional bond targeting a single peripheral nucleus counts as one bonding domain, because all shared electron pairs between A and X are confined along the same internuclear axis.
• E_m denotes the number (m) of localized non-bonding lone pair domains residing on the valence shell of A.
• Steric Number (SN = n + m): The sum of bonding domains and lone-pair domains defines the electron-domain geometry (parent coordination polyhedron), whereas the spatial coordinates of the atomic nuclei (A and X_n alone) define the experimentally observable molecular geometry measured by X-ray crystallography, gas-phase electron diffraction, or rotational microwave spectroscopy.

When all n peripheral ligands around a central atom A are identical and no lone pairs are present (m = 0), the bonding domains distribute symmetrically onto the vertices of regular polyhedra (or the axial-equatorial trigonal bipyramid for SN = 5). Replacing one or more peripheral ligands with non-bonding lone pairs preserves the parent electron-domain polyhedron while reducing the symmetry of the nuclear framework:

Rule 1: The Repulsion Hierarchy (LP–LP > LP–BP > BP–BP)

A bonding electron pair (BP) is attracted simultaneously by two positively charged atomic nuclei (A and X), which confines its charge distribution into a narrow cylindrical volume along the A–X internuclear vector. By contrast, a non-bonding lone pair (LP) is attracted solely by the single core of central atom A; lacking a second confining nucleus, its electron density spreads out laterally across a wider solid angle on the valence sphere of A. This angular expansion yields the Gillespie–Nyholm repulsion hierarchy:

Lone Pair–Lone Pair (LP–LP) > Lone Pair–Bonding Pair (LP–BP) > Bonding Pair–Bonding Pair (BP–BP)

Across the isoelectronic 10-valence-electron second-row hydride series (SN = 4), progressive replacement of bonding pairs by lone pairs compresses the interbond angle steadily below the ideal tetrahedral angle (arccos(−⅓) = 109.47°):

• Methane (CH₄, AX₄E₀): Zero lone pairs; four symmetric C–H bonding domains meet at 109.47°.
• Ammonia (NH₃, AX₃E₁): One lone pair compresses the three N–H bonding domains to 107.8°.
• Water (H₂O, AX₂E₂): Two lone pairs exert combined LP–LP and LP–BP repulsion, compressing the H–O–H bond angle to 104.45°.

Rule 2: Equatorial Placement in Trigonal Bipyramidal (SN = 5) Systems

Unlike the regular Platonic solids of SN = 3, 4, and 6, a trigonal bipyramid (SN = 5) possesses two geometrically inequivalent vertex sets: two axial sites colinear at 180° (each having three nearest neighbors at 90°) and three equatorial sites lying in a horizontal plane at 120° (each having only two 90° axial neighbors and two 120° equatorial neighbors). Because domain-domain repulsion falls off steeply with angular separation (1/rⁿ with effective n ≈ 6 to 12), interactions at 90° dominate over those at 120° or 180°.

Consequently, larger electron domains—including all lone pairs and covalent double bonds—preferentially occupy the less crowded equatorial positions in SN = 5 molecules:

• In SF₄ (AX₄E₁, seesaw), placing the single lone pair at an equatorial vertex creates only two 90° LP–BP interactions (with the two axial fluorines), whereas axial placement would create three 90° LP–BP interactions. The equatorial lone pair pushes the axial S–F bonds back to an F_ax–S–F_ax angle of 173.1° (86.5° from the equatorial plane) and narrows the equatorial F_eq–S–F_eq angle from 120° to 101.6°.
• In ClF₃ (AX₃E₂, T-shaped), two equatorial lone pairs leave two axial fluorines and one equatorial fluorine at an F_ax–Cl–F_eq angle of 87.5°.
• In XeF₂ and I₃⁻ (AX₂E₃, linear), all three lone pairs occupy the equatorial triangle at 120°, leaving the two peripheral atoms colinear along the vertical axis at 180°.

By contrast, in octahedral SN = 6 systems, all six vertices are equivalent; the first lone pair in BrF₅ (AX₅E₁) occupies any vertex to give a square pyramidal geometry (F_ax–Br–F_eq = 84.8°), while the second lone pair in XeF₄ (AX₄E₂) adopts the trans (180°) position opposite the first to minimize LP–LP repulsion, yielding a planar square planar molecule with 90° F–Xe–F angles.

Rule 3: Ligand Electronegativity, Bent's Rule, and Heavy p-Block Hydrides

When peripheral ligands differ in Pauling electronegativity (χ), a more electronegative ligand draws bonding electron density away from the central atom A toward the periphery, shrinking the angular volume of that bonding domain on the valence shell of A. Thus, F–A–F bond angles are systematically smaller than H–A–H or Cl–A–Cl angles around the same central atom:

• OF₂ (103.1°) < H₂O (104.45°) < Cl₂O (110.9°) (where steric ligand-ligand crowding between large chlorine atoms widens the angle).
• NF₃ (102.3°) < NH₃ (107.8°).
• In mixed trigonal bipyramidal molecules such as PCl₂F₃ and CH₃PF₄, the most electronegative ligands (fluorine) occupy the axial sites while less electronegative ligands (–Cl, –CH₃) and lone pairs occupy the equatorial sites. Known as Bent's rule (formulated by Henry A. Bent in 1961), atomic s-character concentrates in hybrid orbitals directed toward electropositive substituents and lone pairs (the equatorial sp² set), whereas more electronegative substituents draw p-rich orbitals (or three-center four-electron bond axial orbitals).

When descending Group 15 and Group 16 from Period 2 (NH₃, H₂O) to Period 3 and below (PH₃, AsH₃, SbH₃; H₂S, H₂Se, H₂Te), bond angles drop abruptly toward 90° (PH₃ = 93.5°, AsH₃ = 91.8°, SbH₃ = 91.7°; H₂S = 92.1°, H₂Se = 90.6°, H₂Te = 90.3°). In heavier main-group elements, the radial separation and energy gap between the valence ns and np subshells widen, making s–p orbital hybridization energetically unfavorable; the lone pair remains primarily in the spherical ns² orbital while the three orthogonal np_x, np_y, and np_z orbitals form covalent σ bonds at nearly 90°.

While VSEPR theory accurately predicts the geometry of thousands of main-group molecules, three physical regimes require explicit quantum-mechanical extensions:

1. Open-Shell Transition Metal Complexes (d¹–d⁹): VSEPR treats non-bonding valence shells as spherical cores or stereochemically active lone pairs, which works for d⁰ ([TiCl₄], MnO₄⁻), d⁵ high-spin ([FeCl₄]⁻), and d¹⁰ ([ZnCl₄]²⁻) complexes. However, partially filled d subshells are governed by Ligand Field Stabilization Energy (LFSE) and the Jahn–Teller effect: d⁸ complexes ([PtCl₄]²⁻, [Ni(CN)₄]²⁻) adopt square planar (D_4h) rather than tetrahedral geometries without having two lone pairs, and d⁹ Cu²⁺ complexes undergo tetragonal elongation.
2. Stereochemically Inert ns² Lone Pairs in Heavy Octahedra: In 14-valence-electron AX₆E₁ anions with steric number 7—such as [XeF₆] (in the solid state or specific conformers), [SeCl₆]²⁻, [TeCl₆]²⁻, and [SbBr₆]³⁻—steric ligand-ligand repulsion among six bulky halide ligands forces the seven-domain system into a regular octahedron (O_h) with 90° bond angles, confining the seventh pair (E₁) to a centrosymmetric a_1g (ns²) orbital that is stereochemically inert.
3. Heavy Alkaline Earth Dihalides (Floppy Bent AX₂): Gas-phase BaF₂ (r_Ba–F = 2.32 Å, angle ~115°), SrF₂ (~120°), and CaF₂ (~145°) are bent rather than linear in the gas phase due to core-shell polarization and covalent mixing of low-lying (n − 1)*d* orbitals on the heavy Group 2 cation.

Why is the H–O–H bond angle in water (104.45°) smaller than the H–N–H bond angle in ammonia (107.8°)?

Both water (H₂O, AX₂E₂) and ammonia (NH₃, AX₃E₁) have a steric number of 4 and a tetrahedral parent electron-domain geometry (ideal angle 109.47°). However, nitrogen in NH₃ carries a single non-bonding lone pair that exerts three LP–BP repulsions against the N–H bonds, compressing them to 107.8°. Oxygen in H₂O carries two lone pairs, introducing a strong LP–LP repulsion alongside four LP–BP repulsions, which widens the angle between the two lone-pair centroids above 115° and compresses the remaining H–O–H bonding angle to 104.45°.

Why do double bonds widen adjacent bond angles while compressing the angle opposite them?

A covalent double bond (σ + π, such as C=O in formaldehyde H₂C=O or phosgene Cl₂C=O) places four shared electrons (two spin pairs) inside a single spatial domain between the central carbon and oxygen nuclei. Because this four-electron domain occupies a wider angular cross-section on the central atom's valence sphere than a two-electron single-bond domain, double-bond–single-bond repulsion exceeds single-bond–single-bond repulsion. In formaldehyde (H₂C=O, SN = 3), the C=O domain pushes the two C–H bonds together so that the H–C=O angles expand to 121.8° while the H–C–H angle narrows from the ideal 120° to 116.5°.

How does VSEPR explain why xenon tetrafluoride (XeF₄) is nonpolar despite having four polar Xe–F bonds?

Fluorine (χ = 3.98) is much more electronegative than xenon (χ = 2.60), making each individual Xe–F covalent bond strongly polar. However, XeF₄ has 8 + 4(7) = 36 valence electrons: four Xe–F bonding pairs and two lone pairs (SN = 6, AX₄E₂). Within an octahedral parent geometry, the two lone pairs occupy opposite (trans, 180°) axial positions to minimize LP–LP repulsion, leaving the four fluorine atoms in a flat square planar (D_4h) arrangement at 90° intervals. Because the two pairs of colinear 180° Xe–F bond dipoles point in exactly opposite directions and the two axial lone pairs also cancel, the vector sum of all bond and lone-pair dipoles is zero (net electric dipole moment μ = 0 D).

1. Gillespie, R. J., & Nyholm, R. S. (1957). "Inorganic stereochemistry." Quarterly Reviews, Chemical Society, 11(4), 339–380. https://doi.org/10.1039/QR9571100339
2. Gillespie, R. J., & Hargittai, I. (2012). The VSEPR Model of Molecular Geometry. Dover Publications / Allyn & Bacon. ISBN 978-0486486154
3. Gillespie, R. J. (2008). "Fifty years of the VSEPR model." Coordination Chemistry Reviews, 252(12–14), 1315–1327. https://doi.org/10.1016/j.ccr.2007.07.007
4. Bent, H. A. (1961). "An appraisal of valence-bond structures and hybridization in compounds of the first-row elements." Chemical Reviews, 61(3), 275–311. https://doi.org/10.1021/cr60211a005