VSEPR Molecular Geometries

Take five identical balloons and tie their necks together at one point. Without anyone arranging them, they spontaneously splay out into a trigonal bipyramid. Three balloons form a flat equatorial belt. Two point straight up and down. This is not a coincidence of rubber and air pressure. It is the same electrostatic logic that dictates why $\text{PF}_5$ is trigonal bipyramidal. It also explains why $\text{SF}_4$ looks like a seesaw. And it explains why a water molecule bends at 104.5° instead of sitting at a tidy 109.5°. Electron domains around a central atom — bonding pairs, lone pairs, or the electron cloud of a multiple bond — repel one another. They settle into the geometry that maximizes their mutual separation. This matters because molecular shape is the hinge on which nearly all downstream chemistry turns. Shape sets the direction of bond dipoles. This in turn governs a molecule's polarity. It dictates which orbitals are available for hybridization. It determines whether a lone pair can donate into an empty orbital. It also determines whether a molecule fits into an enzyme's active site. And it determines whether a catalyst's ligands crowd out or invite an incoming substrate. Every one of those later stories is downstream of a single organizing principle. Count the electron domains. Find the parent polyhedron that spaces them as far apart as possible. Then read off the shape traced out by the atoms alone. The big picture is a five-rung ladder indexed by steric number. Steric number is the number of electron domains, whether bonding or nonbonding. Two domains give a linear arrangement. Three give trigonal planar. Four give tetrahedral. Five give trigonal bipyramidal. Six give octahedral. Every molecular shape a first-year student memorizes is simply one of these five parent polyhedra. These include bent, trigonal pyramidal, seesaw, T-shaped, square pyramidal, and square planar. Each has one or more vertices reassigned from "bonding atom" to "lone pair." This reassignment is invisible in a ball-and-stick model but very much present in space. This article works through the parent geometries systematically, from two domains to six. It builds the logic of domain-domain repulsion as an energetics argument rather than a memorized chart. It shows how to read off bond angles, molecular shapes, and point-group symmetry directly from the electron-domain count. It closes with worked examples spanning routine main-group molecules to a genuinely tricky pentacoordinate case. It also flags the traps that trip up even careful students. One common trap: forgetting double bonds still count as one domain.

Key takeaways

Steric number (SN) = number of $\sigma$ -bonding domains + number of lone pairs on the central atom; multiple bonds count as one domain.
Five parent electron-domain geometries exist: linear (SN 2), trigonal planar (SN 3), tetrahedral (SN 4), trigonal bipyramidal (SN 5), octahedral (SN 6).
Molecular (atom-only) shape = parent geometry minus the positions occupied by lone pairs; lone pairs are invisible in the shape name but still occupy space.
In trigonal bipyramidal geometry, lone pairs and larger substituents always go equatorial first, because equatorial positions have fewer close (90°) neighbors.
Repulsion strength ranks lone pair–lone pair > lone pair–bonding pair > bonding pair–bonding pair, which compresses ideal angles when lone pairs are present.
Key idea: electron domains around a central atom arrange themselves to maximize mutual angular separation, and the observed molecular shape is that arrangement with lone-pair vertices simply left unlabeled.

Where this lives today

VSEPR's five-rung ladder is the first filter every chemist applies when handed an unfamiliar formula, and it remains load-bearing well beyond the introductory classroom. In drug design, the bent or pyramidal geometry around a heteroatom often determines whether a functional group can hydrogen-bond correctly into a binding pocket — the trigonal pyramidal nitrogen of an amine, versus the trigonal planar nitrogen of an amide (flattened by resonance with the adjacent carbonyl, a case explored further under Hybridization and Orbital Mixing), presents entirely different steric and electronic faces to a receptor. In materials chemistry, the square planar geometry of $\text{XeF}_4$ and related d $^8$ transition-metal complexes (rationalized by a related but distinct crystal-field argument) underlies the design of planar conducting and magnetic materials, while octahedral SN-6 coordination is the default geometry assumed when predicting the shapes of countless main-group halides and oxoanions used industrially, from $\text{SF}_6$ as a gaseous dielectric in high-voltage switchgear to phosphate and sulfate geometries central to fertilizer and detergent chemistry. In catalysis, pentacoordinate trigonal bipyramidal intermediates are the textbook picture for nucleophilic substitution at phosphorus (relevant to the mechanism of ATP hydrolysis and phosphate-ester chemistry throughout biochemistry) and for pseudorotation processes in inorganic and organometallic catalysis, where a molecule interconverts axial and equatorial ligands via a low-energy TBP-to-TBP pathway (the Berry pseudorotation). Instrumentally, VSEPR predictions are precisely what electron diffraction, microwave rotational spectroscopy, and X-ray crystallography are used to confirm or refine, and mismatches between naive VSEPR predictions and measured structures (as with the slightly non-monotonic $\text{NF}_3$ / $\text{OF}_2$ angle trend above) are exactly the observations that motivate the more refined treatments of Lone Pair and Multiple Bond Effects and the electronegativity-dependent corrections layered onto the basic domain-counting picture. Every one of these downstream stories — polarity in Bond Polarity and Dipole Moments, orbital-based rationalizations in Hybridization and Orbital Mixing, and ligand geometry in transition-metal chemistry — takes the shape assigned here as its starting point.

Ask the tutor: Why does adding a second lone pair in an SN-6 species force those lone pairs into trans (axial) positions to give square planar $\text{XeF}_4$ , rather than cis positions?

The physical picture

The argument begins with electrostatics stripped to its essentials. Each electron domain — a bonding pair, a lone pair, or the delocalized cloud of a double or triple bond — behaves, for geometric purposes, as a single region of concentrated negative charge localized near the central atom. Because like charges repel, the domains push each other apart. If the central atom is free to let its substituent atoms and lone pairs relax to whatever angular positions minimize total repulsion, they adopt the arrangement that places every domain as far as possible from every other domain, subject to all domains lying roughly the same distance from the nucleus (since they all originate from the valence shell of the same atom). This is a packing problem on the surface of a sphere, and it has a small number of exact or near-exact solutions depending only on how many domains must be packed — not on what those domains are. Two points on a sphere maximize their mutual separation at $180°$ apart: linear. Three points settle into a single plane at $120°$ apart: trigonal planar. Four points cannot all be coplanar without wasting angular separation, so they occupy the corners of a regular tetrahedron, each pair separated by $109.47°$ . Five points cannot be placed with perfect symmetry on a sphere at all — this is a famous fact of solid geometry — and the best compromise is the trigonal bipyramid, with three equatorial domains at $120°$ to each other and $90°$ to the two axial domains. Six points fit perfectly at the vertices of a regular octahedron, all nearest-neighbor angles equal to $90°$ . The central conceptual move of VSEPR is then to notice that a lone pair contributes to this repulsion arithmetic exactly as a bonding pair does — occupying a vertex of the parent polyhedron — but is chemically invisible in the reported "molecular shape," which by convention names only the arrangement of atoms. A steric number of four with three bonding pairs and one lone pair, for instance, still forces a roughly tetrahedral electron-domain geometry, but chemists call the resulting atom-only shape "trigonal pyramidal" (as in ammonia), because only three atoms plus the central atom are visible; the fourth "vertex" is empty of atoms even though it is full of electron density. Getting this distinction right — parent geometry describes electron domains, molecular shape describes atoms only — is the single most common source of error in a first exposure to the theory.

Figure

The five parent electron-domain geometries indexed by steric number

A second geometric subtlety governs the trigonal bipyramid specifically, and it explains an enormous amount of structural chemistry among p-block hypervalent species. In this parent shape, the two axial positions each have three equatorial neighbors at 90° and one axial neighbor at 180°, while each equatorial position has only two equatorial neighbors at 120° and two axial neighbors at 90°. Ninety-degree repulsions are far more destabilizing than 120° repulsions (repulsion falls off steeply with angle, as developed below), so an axial position experiences three strong 90° pushes while an equatorial position experiences only two. Consequently, any domain that repels more strongly than average — a lone pair, or a substituent that is simply bulkier or more electron-rich — will preferentially occupy an equatorial site to minimize the number of costly 90° interactions it suffers.

Figure

Why lone pairs go equatorial in a trigonal bipyramid: counting close (90°) neighbors

The core ideas

The qualitative ranking of repulsion strengths that governs bond-angle distortions is usually written as an ordered inequality rather than a single equation, because VSEPR is a semi-quantitative, symmetry-based theory rather than a fitted force law. The central relationship is:

E_{\text{lp-lp}} \;>\; E_{\text{lp-bp}} \;>\; E_{\text{bp-bp}}

where: $E_{\text{lp-lp}}$ , $E_{\text{lp-bp}}$ , and $E_{\text{bp-bp}}$ denote the repulsive interaction energy between two lone pairs, a lone pair and a bonding pair, and two bonding pairs, respectively, at a fixed angular separation.

Reading: a lone pair, unconstrained by a second nucleus, spreads out closer to the central atom and occupies a fatter angular region than a bonding pair, whose electron density is pulled outward toward the bonded atom and thus occupies a more slender cone. Fatter domains push their neighbors harder, so replacing a bonding pair with a lone pair anywhere in a parent polyhedron squeezes the remaining bond angles inward from the idealized value. The steric number itself is defined by a simple counting rule:

\text{SN} = (\text{number of } \sigma\text{-bonded atoms}) + (\text{number of lone pairs on the central atom})

where: $\sigma$ -bonded atoms are counted once per bonded neighbor regardless of bond order (a double or triple bond still connects to only one neighboring atom and is counted once), and lone pairs are the non-bonding valence electron pairs localized on the central atom, obtained from a correct Lewis structure.

Reading: SN is not the number of electron pairs in the valence shell, nor the number of atoms bonded — it is the number of directions in space that the central atom's valence electron density points, and this single integer selects the parent polyhedron from the five-rung ladder above. Bond angle compression can be estimated (very approximately) via the empirical Bent's-rule-adjacent observation that each lone pair present depresses the ideal polyhedral angle between the remaining bonding pairs, an effect quantified experimentally rather than by an exact formula, but bounded qualitatively by:

\theta_{\text{obs}} < \theta_{\text{ideal}} \quad \text{whenever at least one domain is a lone pair or a multiple bond}

where: $\theta_{\text{ideal}}$ is the idealized polyhedral angle for the steric number (e.g., $109.47°$ for SN 4), and $\theta_{\text{obs}}$ is the experimentally measured bond angle between the two remaining bonding directions.

Reading: this is the formal statement behind the trend $\text{CH}_4$ ( $109.5°$ ) $\to$ $\text{NH}_3$ ( $107.2°$ , one lone pair) $\to$ $\text{H}_2\text{O}$ ( $104.5°$ , two lone pairs) — each additional lone pair (or the swap of a single bond for a double bond, which also fattens a domain) squeezes the observed angle further below the tetrahedral ideal.

Derivation APlacing 5 point charges on a sphere: why the trigonal bipyramid beats the square pyramid

Goal. Show, using an electrostatics argument (Thomson-problem style, not calculus), why five mutually repelling domains prefer the trigonal bipyramidal (TBP) arrangement over the alternative square pyramidal (SPY) arrangement, and quantify the qualitative energy difference.

Step 1 — set up the comparison. Model each electron domain as a point charge $q$ constrained to lie on a sphere of radius $r$ around the central atom, with pairwise repulsion energy between any two domains separated by angle $\theta$ approximated as inversely related to their angular separation (steeper falloff at small $\theta$ , consistent with a $1/r_{ij}$ Coulomb-type law where $r_{ij}$ is the chord distance between the two points on the sphere). We compare total pairwise repulsion summed over all $\binom{5}{2}=10$ domain pairs for the two candidate arrangements.

Step 2 — enumerate the TBP angle set. In an ideal trigonal bipyramid, label the three equatorial domains $e_1, e_2, e_3$ and the two axial domains $a_1, a_2$ . The pairwise angles are: three equatorial–equatorial pairs at $120°$ , six axial–equatorial pairs at $90°$ , and one axial–axial pair at $180°$ . That is 3 pairs at $120°$ , 6 pairs at $90°$ , 1 pair at $180°$ — ten pairs total, matching $\binom{5}{2}=10$ .

Step 3 — enumerate the SPY angle set. In an ideal square pyramid, four basal domains $b_1,\dots,b_4$ sit at the corners of a square with one apical domain $a$ directly above the square's center. For a square pyramid derived by moving one axial TBP vertex into the equatorial belt and relaxing angles toward a square base, the representative angle set is: four apex–base angles near $102°\text{–}105°$ (larger than $90°$ because the apex must rise to keep base–base angles reasonable), four adjacent base–base angles at $90°$ , and two base–base diagonal angles at $180°$ (opposite corners of the square, through the center). Counting: 4 apex–base pairs, 4 adjacent-base pairs at $90°$ , 2 diagonal pairs at $180°$ — ten pairs total again.

Step 4 — compare the worst (smallest-angle, highest-repulsion) interactions. The TBP's six $90°$ interactions are its costliest; the SPY's four $90°$ adjacent-base interactions are comparably costly, but the SPY additionally carries four sub- $120°$ apex–base interactions near $100°$ – $105°$ , which are cheaper than $90°$ but still more repulsive than the TBP's $120°$ equatorial set. Tallying repulsive interactions weighted qualitatively by how far below $120°$ each falls, the TBP concentrates its close contacts into exactly six $90°$ pairs and otherwise enjoys $120°$ or $180°$ separations, whereas the SPY spreads moderate-cost contacts ( $100°$ – $105°$ ) across four pairs in addition to four $90°$ pairs. Detailed numerical energy minimization (the classical five-point Thomson problem) confirms the trigonal bipyramid is the global energy minimum for five identical repelling points on a sphere, with the square pyramid a slightly higher-energy local arrangement.

Step 5 — connect to observed chemistry. Because the TBP is lower in energy for five equivalent domains, all main-group AB $_5$ species with no lone pairs (e.g., $\text{PF}_5$ , $\text{PCl}_5$ ) adopt the TBP shape, not the square pyramid. Square pyramidal geometry is instead observed only when a sixth domain (a lone pair) is present and one octahedral vertex becomes vacant — a genuinely different SN-6-minus-one-lone-pair situation, distinct from the SN-5 case discussed here, illustrating that shape names must always be read alongside the steric number that produced them.

Go deeper · Derivation B · 2 minWhy the equatorial site wins for lone pairs and large substituents in TBP species

Derivation BWhy the equatorial site wins for lone pairs and large substituents in TBP species

Goal. Derive, from the neighbor-counting argument, the equatorial-preference rule used to predict shapes of species like $\text{SF}_4$ , $\text{ClF}_3$ , and $\text{XeF}_2$ , and check it against the exception-free set of pentacoordinate main-group fluorides.

Step 1 — count 90° neighbors per site type. From the ideal TBP angle set derived above, each axial position has exactly three neighbors at $90°$ (the three equatorial sites) and one neighbor at $180°$ (the other axial site, a weak, distant interaction). Each equatorial position has exactly two neighbors at $90°$ (the two axial sites) and two neighbors at $120°$ (the other two equatorial sites).

Step 2 — assign a repulsion cost per site. Since $90°$ interactions dominate the total repulsion energy (steep angular falloff, Step 4 above), approximate the total local repulsion cost of occupying a site as proportional to its number of $90°$ neighbors:

\text{Cost(axial)} \approx 3 \times w_{90}, \qquad \text{Cost(equatorial)} \approx 2 \times w_{90}

where $w_{90}$ is the (large, positive) repulsion weight assigned to a $90°$ pair, common to both expressions.

Step 3 — assign the most repulsive domain to the cheaper site. If one of the five domains is "fatter" than the rest (a lone pair, or a domain of higher effective electron density such as a double-bond-containing domain), the total molecular repulsion energy is minimized by placing that fat domain at the site with the fewest costly $90°$ contacts — i.e., equatorial — because

2w_{90} \cdot w_{\text{fat}} \;<\; 3w_{90}\cdot w_{\text{fat}}

where $w_{\text{fat}} > w_{90}$ is the enhanced repulsion weight of the fat domain relative to a normal bonding pair, common to both sides so the inequality direction is fixed by the neighbor count alone (2 versus 3).

Step 4 — apply sequentially for multiple lone pairs. For SN 5 with one lone pair (e.g., $\text{SF}_4$ ), the single lone pair takes an equatorial site, leaving a "seesaw" shape: two axial F, two equatorial F, and the equatorial lone pair pushing the axial F atoms slightly toward it (observed F $_{\text{ax}}$ –S–F $_{\text{ax}}$ angle in $\text{SF}_4$ is about $173°$ , not exactly $180°$ , precisely because the equatorial lone pair repels both axial bonds). For SN 5 with two lone pairs (e.g., $\text{ClF}_3$ ), both lone pairs take equatorial sites — costing only one lone pair–lone pair interaction at $120°$ rather than at the much worse $90°$ that would result from one axial + one equatorial lone pair — leaving a T-shaped molecule with three F atoms (two axial, one equatorial) and a slightly bent axial F–Cl–F angle near $175°$ . For SN 5 with three lone pairs (e.g., $\text{XeF}_2$ if reinterpreted, or $\text{I}_3^-$ ), all three equatorial sites are lone pairs, leaving the two axial atoms in a perfectly linear F–Xe–F or I–I–I arrangement at $180°$ , since both remaining bonding domains sit axial with no equatorial bonding partner to distort them.

Step 5 — verify the limiting case. As the "fatness" of the extra domain approaches that of an ordinary bonding pair ( $w_{\text{fat}} \to w_{90}$ , i.e., no domain is special), the cost difference between axial and equatorial vanishes and the molecule becomes the symmetric $\text{D}_{3h}$ trigonal bipyramid with no site preference — exactly the SN-5, zero-lone-pair case of $\text{PF}_5$ , confirming the rule collapses correctly to the earlier, simpler result when there is nothing "extra" to prefer a site.

Worked examples

Example 1 — Foundational: determining the shape of $\text{SO}_3^{2-}$ (sulfite ion). Sulfur is the central atom. A correct Lewis structure gives sulfur three S–O single bonds (with formal charges distributed by resonance, or one S=O and two S–O⁻ in one resonance form; either way sulfur has one lone pair and three $\sigma$ -bonded oxygens). Steric number:

\text{SN} = 3\ (\sigma\text{-bonds to O}) + 1\ (\text{lone pair on S}) = 4

SN 4 selects the tetrahedral parent geometry. With one of the four vertices occupied by a lone pair rather than an atom, the molecular shape is trigonal pyramidal, isoelectronic in shape with $\text{NH}_3$ and $\text{PCl}_3$ . The O–S–O angle is predicted to be somewhat less than $109.5°$ because the lone pair is fatter than a bonding pair; the experimental angle in sulfite is about $106°$ , consistent with the compression rule. As a limiting-case check: if the lone pair were instead a fourth bonding oxygen (as in $\text{SO}_4^{2-}$ ), SN would still be 4 but with zero lone pairs, giving perfectly tetrahedral $\text{SO}_4^{2-}$ with all angles at the ideal $109.5°$ — matching the well-known regular tetrahedral sulfate ion and confirming the lone-pair-removal step behaves correctly.

Example 2 — Applied: shape and polarity trend across the isoelectronic sequence $\text{CF}_4$ , $\text{NF}_3$ , $\text{OF}_2$ . All three central atoms (C, N, O) are second-period, each bonded to fluorines, and each retains the "extra" electrons as lone pairs following the octet rule; steric number is 4 in every case since each central atom has four electron domains total. For $\text{CF}_4$ : carbon has four bonding pairs, zero lone pairs, SN $=4+0=4$ , shape tetrahedral, F–C–F angle $= 109.5°$ (exactly, since $\text{T}_d$ symmetry with no distorting lone pair), and the molecule is nonpolar overall (bond dipoles cancel by symmetry) despite each C–F bond being highly polar. For $\text{NF}_3$ : nitrogen has three bonding pairs and one lone pair, SN $=3+1=4$ , shape trigonal pyramidal, angle compressed to an observed $102.3°$ (below $109.5°$ due to the lone pair), and the molecule is polar, with a small net dipole moment of about $0.24$ D — notably small for a molecule with three polar N–F bonds, because the N lone pair's dipole contribution points opposite to (and nearly cancels) the resultant of the three N–F bond dipoles. For $\text{OF}_2$ : oxygen has two bonding pairs and two lone pairs, SN $=2+2=4$ , shape bent, angle compressed further to an observed $103.1°$ (two lone pairs squeeze the O–F–F... angle even more than one lone pair did in $\text{NF}_3$ , though the F–O–F angle in $\text{OF}_2$ is actually slightly larger than the H–O–H angle in water because F is less electronegative-repelling on the bonding pairs than H — bonding-pair fatness also depends on substituent electronegativity, a refinement layered on top of the basic domain count), and $\text{OF}_2$ is polar with dipole moment about $0.30$ D. The steady decrease SN $=4$ , lone-pair count $0\to1\to2$ , angle $109.5°\to102.3°\to103.1°$ demonstrates the compression rule operating within a single isoelectronic-in-SN family, while the reversal in the final step (angle ticking back up slightly from $\text{NF}_3$ to $\text{OF}_2$ ) is a genuine, well-documented subtlety showing that VSEPR's angle-compression rule is directional but not perfectly monotonic once substituent identity changes.

Example 3 — Exam/competition level: predicting the full structure of $\text{IF}_5$ and rationalizing its non-superimposable axial/equatorial fluorines by NMR. Iodine is the central atom, bonded to five fluorines, with iodine formally contributing 7 valence electrons, five of which form the five I–F $\sigma$ -bonds (using 5 electrons in bonding, leaving 2 as a lone pair):

\text{SN} = 5\ (\sigma\text{-bonds to F}) + 1\ (\text{lone pair on I}) = 6

SN 6 selects the octahedral parent geometry, not the trigonal bipyramid — a common trap, since five bonded atoms might tempt a student to jump straight to SN 5. With one of the six octahedral vertices occupied by a lone pair, the molecular shape is square pyramidal: four fluorines form the base, one fluorine sits at the apex directly opposite the lone pair, and the lone pair occupies the sixth (vacant) octahedral position. Because all six octahedral vertices are geometrically equivalent before any lone pair is placed, there is no "axial vs equatorial" distinction to exploit here (unlike the true SN-5 trigonal bipyramid) — the lone pair simply occupies one octahedral vertex, and by symmetry it does not matter which one is chosen; the resulting shape is always square pyramidal with $\text{C}_{4v}$ symmetry. The lone pair, being fatter than a bonding pair, pushes the four basal fluorines away from itself and toward the apical fluorine, so the observed basal F–I–F $_{\text{apical}}$ angle is compressed to about $81.9°$ (less than the ideal $90°$ ), while the four basal F–I–F angles (F to adjacent basal F) remain close to $90°$ within the base itself, and the base is slightly puckered away from the lone pair, giving the overall structure a "bowl" tipped away from the missing vertex. This square-pyramidal, non-superimposable-vertex structure explains a classic $^{19}\text{F}$ NMR observation: at low temperature $\text{IF}_5$ shows two distinct fluorine environments (four equivalent basal F, one unique apical F) in a 4:1 intensity ratio with characteristic F–F spin–spin coupling between the two sets, exactly as VSEPR predicts from the square pyramidal shape — a direct spectroscopic fingerprint of the SN-6-with-one-lone-pair assignment. As a limiting-case check: if the lone pair were instead replaced by a sixth fluorine (hypothetically $\text{IF}_6^-$ , which indeed exists as the anion with SN $=6+1=7$ ... actually $\text{IF}_6^-$ has SN 7 due to its own extra lone pair and adopts a distorted geometry), the simpler comparison is $\text{SF}_6$ : SN $=6+0=6$ gives a perfect octahedral shape with all F–S–F angles exactly $90°$ or $180°$ and full $\text{O}_h$ symmetry, confirming that removing the lone pair (going from $\text{IF}_5$ -type SN-6-with-lone-pair to SN-6-with-no-lone-pair) restores the ideal, undistorted parent polyhedron exactly as the theory demands.

Limiting cases, scope & common traps

Situation	What VSEPR predicts	Why
SN = 2, 0 lone pairs (e.g. $\text{CO}_2$ , $\text{BeCl}_2$ )	Linear, $180°$	Two domains maximize separation only when antipodal
SN = 2, but with lone pairs is impossible at true SN 2	—	If a central atom truly has 2 lone pairs plus 2 bonds that would be SN 4, not SN 2 — recount
SN = 3, 0 lone pairs (e.g. $\text{BF}_3$ , $\text{SO}_3$ )	Trigonal planar, $120°$	Regular triangle is optimal 3-point sphere packing
SN = 3, 1 lone pair (e.g. $\text{SO}_2$ , $\text{SnCl}_2$ (g))	Bent, $<120°$	Vertex vacated by lone pair; remaining angle compressed
SN = 4, 0 lone pairs (e.g. $\text{CH}_4$ )	Tetrahedral, $109.5°$	Regular tetrahedron optimal for 4 points
SN = 4, 1 lone pair (e.g. $\text{NH}_3$ )	Trigonal pyramidal, $\approx107°$	One vertex vacated; angle compressed
SN = 4, 2 lone pairs (e.g. $\text{H}_2\text{O}$ )	Bent, $\approx104.5°$	Two vertices vacated; further compression
SN = 5, 0 lone pairs (e.g. $\text{PF}_5$ )	Trigonal bipyramidal	Global minimum for 5-point repulsion
SN = 5, 1 lone pair (e.g. $\text{SF}_4$ )	Seesaw	Lone pair takes equatorial site
SN = 5, 2 lone pairs (e.g. $\text{ClF}_3$ )	T-shaped	Both lone pairs equatorial
SN = 5, 3 lone pairs (e.g. $\text{I}_3^-$ )	Linear	All three equatorial sites are lone pairs
SN = 6, 0 lone pairs (e.g. $\text{SF}_6$ )	Octahedral	Regular octahedron optimal for 6 points
SN = 6, 1 lone pair (e.g. $\text{IF}_5$ )	Square pyramidal	Any single vertex removed by symmetry
SN = 6, 2 lone pairs (e.g. $\text{XeF}_4$ )	Square planar	Lone pairs occupy mutually trans (axial) vertices to minimize their own repulsion

The chemist behind it

The modern VSEPR framework is credited jointly to Ronald Gillespie and Ronald Nyholm, who in 1957 synthesized decades of scattered structural observations — themselves traceable to Nevil Sidgwick and Herbert Powell's 1940 recognition that electron-pair repulsion, not atomic size alone, governs molecular shape — into the coherent, predictive rule set taught today. Gillespie, working at University College London and later McMaster University, spent much of his career refining the quantitative side of the theory: he pushed to explain why lone pairs are fatter than bonding pairs (electron density unconstrained by a second nucleus spreads closer to the central atom, an argument grounded in simple electrostatics rather than quantum mechanical hand-waving), and why angle compressions follow the specific ordering lp-lp > lp-bp > bp-bp. He was known for insisting that VSEPR, though qualitative, could be made rigorous enough to predict genuinely subtle structural facts — such as why axial bonds in $\text{PF}_5$ are measurably longer than equatorial bonds, or why $\text{ClF}_3$ is T-shaped and not trigonal planar with one long bond — well before high-resolution electron diffraction and microwave spectroscopy could confirm those predictions experimentally.

Origins · 1 minRonald J. Gillespie and how this was discovered

Ronald J. Gillespie

1924-2021 · University College London and McMaster University, structural inorganic chemistry

Gillespie developed VSEPR alongside Ronald Nyholm into its modern predictive form, and later extended the framework into the "Ligand Close Packing" model, refining how substituent size (not just lone-pair count) modulates observed bond angles in real hypervalent molecules.

History

- 1940 — Sidgwick and Powell first link central-atom electron-pair count to molecular shape.

- 1957 — Gillespie and Nyholm publish the systematic electron-pair repulsion theory (VSEPR).

- 1963 — Gillespie's influential review formalizes the lone-pair vs bonding-pair repulsion hierarchy.

- 1972 — Gillespie's textbook Molecular Geometry consolidates VSEPR as standard pedagogy.

- 1990s — Ligand Close Packing model extends VSEPR to explain fine bond-angle and bond-length variations via substituent size.

Does VSEPR predict exact bond angles, or only trends?

VSEPR predicts trends and qualitative rankings reliably — more lone pairs compress angles further, equatorial sites are favored by fatter domains — but it does not derive exact numerical angles from first principles. The ideal polyhedral angles ( $180°$ , $120°$ , $109.5°$ , TBP's $90°/120°$ , and octahedral $90°$ ) are the starting reference points; actual angles measured by microwave spectroscopy or electron diffraction typically deviate from these ideals by a few degrees whenever lone pairs, multiple bonds, or substituents of differing electronegativity are present. For precise angles, more detailed methods such as ab initio quantum chemical geometry optimization are required; VSEPR remains the fast, structure-at-a-glance tool for predicting the correct qualitative shape and the direction of angle distortions.

How do I count steric number when the central atom is part of a resonance-stabilized ion, like nitrate or carbonate?

Count from any single valid resonance structure — the steric number does not change across resonance forms, because resonance redistributes $\pi$ -electron density without changing how many $\sigma$ -bonded neighbors or lone pairs the central atom has. In $\text{NO}_3^-$ , nitrogen has three $\sigma$ -bonds to oxygen and zero lone pairs in every resonance structure (one N=O and two N–O⁻, or any rotation thereof), giving SN $=3$ and trigonal planar shape regardless of which resonance form you draw. This is a useful check: if different resonance structures seem to give different SN values, a Lewis structure has been drawn incorrectly.

Why does the trigonal bipyramid not have all bond angles equal, unlike the tetrahedron or octahedron?

Five points cannot be arranged with perfect angular symmetry on a sphere — this is a genuine geometric fact, not a chemical peculiarity. Four points (tetrahedron) and six points (octahedron) both admit fully symmetric, all-angles-equal arrangements, but five points do not; the best achievable packing, the trigonal bipyramid, necessarily has two distinct angle types ( $90°$ axial–equatorial and $120°$ equatorial–equatorial). This geometric asymmetry is exactly why axial and equatorial positions in TBP species are chemically inequivalent — they have different bond lengths, different reactivities, and different lone-pair preferences, unlike the fully equivalent vertices of a tetrahedron or octahedron.

Is the electron-domain geometry ever reported as the "molecular shape," or are these always distinguished?

By convention they are always distinguished, and the distinction matters for exam-level precision: "electron-domain geometry" (or "electron-pair geometry") describes the full polyhedron including lone-pair vertices, while "molecular shape" (or "molecular geometry") names only the arrangement of atoms, omitting lone pairs from the name even though they still occupy space and still influence the observed angles. For example, water's electron-domain geometry is tetrahedral (four domains: two bonds, two lone pairs), but its molecular shape is bent (only two atoms visible besides the central oxygen). Both statements are correct and are not in conflict — they simply answer different questions.

Can a molecule have a steric number that changes with temperature or physical state?

The steric number itself, being a count of $\sigma$ -bonds plus lone pairs on a fixed Lewis structure, does not change with temperature — but which resonance or bonding description is appropriate can differ between gas phase and condensed phase, occasionally changing the effective count. A commonly cited example is $\text{SnCl}_2$ , which is bent (SN 3, one lone pair) as an isolated gas-phase molecule but adopts extended polymeric bridging structures in the solid state, where each tin is effectively surrounded by more chlorine neighbors through bridging bonds; the simple molecular VSEPR picture strictly applies to the isolated gas-phase or matrix-isolated species, not necessarily to the bulk solid.

How does VSEPR handle central atoms with an odd number of electrons, like

\text{NO}_2

Odd-electron ("radical") central atoms are handled by treating the unpaired single electron as its own domain, weaker in repulsive strength than a full lone pair because it is only half-occupied. In $\text{NO}_2$ , nitrogen has two $\sigma$ -bonds to oxygen and one unpaired electron; treating this as a partial, weaker domain still predicts a bent shape (SN effectively 3 with a "half-strength" third domain), and the observed O–N–O angle of about $134°$ is indeed wider than the fully-lone-pair-bent $\text{NO}_2^-$ ion's angle of about $115°$ , consistent with a single unpaired electron repelling less strongly than a full lone pair.

Why do axial bonds in

\text{PF}_5

measure longer than equatorial bonds if all five bonds are chemically "P–F"?

This is a genuine, well-measured structural fact (axial P–F bonds are about 1.58 Å versus 1.53 Å for equatorial in gas-phase $\text{PF}_5$ ) and reflects that axial fluorines experience three 90° repulsions from equatorial neighbors while equatorial fluorines experience only two, so axial bonds are pushed slightly outward (lengthened) to relieve some of that extra crowding. This bond-length/bond-strength asymmetry, alongside the site-preference rule for lone pairs, is one of the finer quantitative predictions VSEPR makes beyond simply naming the parent shape, and it is a clean illustration of how the same domain-counting logic that assigns shapes also explains bond-length variation within a single molecule.