VSEPR and Molecular Shapes

Molecules have shape, and that shape governs almost everything about how they behave. VSEPR theory — Valence Shell Electron Pair Repulsion — predicts three-dimensional geometry from a two-dimensional Covalent Bonding and Lewis Structures diagram. It uses one simple idea. Electron pairs around a central atom push each other as far apart as possible. This article builds the electron-domain framework from scratch. It covers how to count domains, and how domains arrange themselves in space. It also shows how lone pairs distort the "ideal" geometry into the shapes chemists actually observe. The same counting logic works even when a Lewis structure has multiple valid Resonance Structures. This is because resonance never changes the number of electron domains at an atom. Molecular geometry is not just a geometric curiosity. It is the doorway to understanding Bond and Molecular Polarity, reactivity, and even biological recognition. For example, the shape of a drug molecule determines whether it fits its receptor. Everything here rests only on Lewis structures and basic geometry. So no prior exposure to orbital theory is needed.

Key takeaways

Electron domains — bonding pairs, lone pairs, or any multiple bond treated as one domain — arrange to minimize repulsion.
Electron-domain geometry depends on the total number of domains (2 through 6); molecular geometry depends on how many of those domains are actually atoms versus lone pairs.
Lone pairs occupy more space than bonding pairs, compressing bond angles below the ideal values.
The five basic domain geometries are linear, trigonal planar, tetrahedral, trigonal bipyramidal, and octahedral.
In trigonal bipyramidal arrangements, lone pairs always occupy equatorial positions first, because those have fewer close neighbors.
Key idea: count the domains, place them symmetrically, then read off the shape traced by the atoms alone.

The core insight

Shape = domains arranged for minimum repulsion, then "erase" the lone pairs and look only at where the atoms sit.

The physical picture

Every central atom in a Lewis structure carries a certain number of electron domains: regions of concentrated electron density. A single bond, a double bond, a triple bond, and a lone pair each count as exactly one domain — multiplicity does not add extra domains because a double or triple bond's extra electron pairs are locked into the same region of space as the sigma bond. Because electron domains are all negatively charged, they repel each other electrostatically and settle into the geometric arrangement that maximizes their mutual separation. This is the entire physical content of VSEPR: no orbitals, no quantum mechanics, just charged regions minimizing repulsion, much like balloons tied together at a point naturally splay outward into symmetric arrangements. Two distinct things then need naming. The electron-domain geometry describes the arrangement of all domains (bonding and lone pairs together). The molecular geometry describes only the positions of the atoms — lone pairs are real, but invisible to an outside observer trying to describe the molecule's shape. When there are no lone pairs, the two geometries coincide. When lone pairs are present, the molecular geometry is a distorted subset of the electron-domain geometry, and bond angles shrink from their ideal values because lone pairs are held only by one nucleus and spread out more than bonding pairs shared between two nuclei.

Figure

Five electron-domain geometries built from repulsion alone

The core relations

The number of electron domains, $n$ , is found directly from a Lewis structure:

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

where:

$\sigma$ -bonded atoms are counted once per attached atom, regardless of bond order (a double or triple bond still counts as one attached atom / one domain);
lone pairs are nonbonding electron pairs residing on the central atom, read directly from the completed Lewis structure.

The ideal domain geometry follows from $n$ alone, independent of what the domains actually are:

n = 2 \Rightarrow \text{linear } (180^\circ), \quad n = 3 \Rightarrow \text{trigonal planar } (120^\circ), \quad n = 4 \Rightarrow \text{tetrahedral } (109.5^\circ)

n = 5 \Rightarrow \text{trigonal bipyramidal } (90^\circ, 120^\circ), \quad n = 6 \Rightarrow \text{octahedral } (90^\circ)

where each angle is the ideal separation between adjacent domains when all domains are identical (all bonding, no lone pairs). The molecular geometry is then read from the notation $AX_mE_k$ :

n = m + k

where:

$A$ is the central atom;
$X_m$ denotes $m$ atoms directly bonded to $A$ ;
$E_k$ denotes $k$ lone pairs on $A$ ;
$n = m+k$ is the same total domain count used above, so the electron-domain geometry is fixed by $n$ , while the molecular geometry is fixed by the pair $(m,k)$ .

The repulsion-strength ordering that explains bond-angle distortions is:

\text{lone pair–lone pair} \;>\; \text{lone pair–bonding pair} \;>\; \text{bonding pair–bonding pair}

where this ordering reflects the fact that a lone pair is held by only one nucleus and so spreads out more diffusely than a bonding pair shared — and pulled inward — by two nuclei.

Derivation AFrom Lewis structure to bond angle: the case of a bent AX₂E molecule

Goal. Show explicitly why a molecule with two bonding domains and one lone pair (like a bent triatomic) has a bond angle measurably less than the ideal $109.5^\circ$ tetrahedral angle, rather than staying at $109.5^\circ$ or dropping to $90^\circ$ .

Step 1. Count the domains. Take a central atom with two single bonds and one lone pair. The domain count is

n = m + k = 2 + 1 = 3

Wait — three domains around a central atom that also has a lone pair actually corresponds to a trigonal planar electron-domain geometry only if $k=1$ contributes a third domain alongside two bonds; here we must recompute the actual AX₂E case used for molecules such as SO₂-type or ozone-like bent species: with two bonding atoms and one lone pair, $n=3$ , so the electron-domain geometry is trigonal planar, and the ideal unperturbed angle is $120^\circ$ .

Step 2. Identify the reference (ideal) angle. Since $n=3$ gives trigonal planar geometry, the reference bond angle before any distortion is

\theta_{\text{ideal}} = 120^\circ

This is the angle three identical domains would adopt.

Step 3. Apply the repulsion-strength ordering. One of the three domains is a lone pair, not a bonding pair. From the ordering

\text{LP–BP repulsion} > \text{BP–BP repulsion}

the lone pair pushes the two bonding domains closer to each other than $120^\circ$ , because the lone pair itself demands a larger effective angular "footprint" and crowds the two remaining bonds.

Step 4. Quantify the direction and magnitude of the shift. The bonding pairs must close ranks to compensate for the lone pair's greater spread. Empirically, for a trigonal-planar-derived AX₂E system, the observed angle is compressed to roughly

\theta_{\text{observed}} \approx 119^\circ \text{ to } 120^\circ \text{ (small distortion, since only one of three domains is a lone pair)}

The compression is small here precisely because only one-third of the domains are lone pairs; contrast this with an AX₂E₂ (tetrahedral-derived, bent) system where two of four domains are lone pairs and the compression is much larger, typically down to about $104.5^\circ$ from an ideal $109.5^\circ$ .

Step 5. State the general trend. The more lone pairs present relative to bonding pairs, and the more of them are mutually adjacent, the larger the downward distortion from the ideal domain angle. This is the qualitative rule used throughout VSEPR: count domains for the geometry, then count lone pairs for the distortion direction and rough magnitude.

Worked examples

Example 1 — Sulfur tetrafluoride, SF₄ (asymmetric AX₄E case). Sulfur is the central atom. Sulfur contributes 6 valence electrons; each of 4 fluorines contributes 7, and each S–F bond uses one electron from each atom. Total valence electrons:

6 + 4(7) = 34 \text{ electrons}

Four S–F single bonds use $4 \times 2 = 8$ electrons, leaving

34 - 8 = 26 \text{ electrons} = 13 \text{ lone pairs to distribute}

Each fluorine needs 3 lone pairs to complete its octet ( $4 \times 3 = 12$ lone pairs used), leaving

13 - 12 = 1 \text{ lone pair remaining on sulfur}

So sulfur has 4 bonded atoms and 1 lone pair:

n = m + k = 4 + 1 = 5

Five domains means the electron-domain geometry is trigonal bipyramidal. The lone pair goes to an equatorial position (fewer close 90° neighbors: an equatorial position has only two 90° neighbors, while an axial position has three). The molecular geometry with $AX_4E$ is called a seesaw, and the observed bond angles split into two distinct sets:

\theta_{\text{axial–S–axial}} \approx 173^\circ \quad (\text{slightly less than the ideal } 180^\circ)

\theta_{\text{equatorial–S–equatorial}} \approx 102^\circ \quad (\text{compressed from the ideal } 120^\circ \text{ by the equatorial lone pair})

Both angles are asymmetric and distinct — this is the hallmark of the seesaw shape, distinguishing it clearly from a symmetric tetrahedral or trigonal-bipyramidal molecule with no lone pairs. Limiting case check: if the lone pair were replaced by a fifth bonding atom (hypothetically making it $AX_5$ , i.e. no lone pair at all), the geometry would relax back to a perfectly symmetric trigonal bipyramid with clean $90^\circ$ and $120^\circ$ angles — confirming the lone pair, not some other effect, is the source of the distortion.

Example 2 — Iodine pentafluoride, IF₅ (asymmetric AX₅E case). Iodine contributes 7 valence electrons; five fluorines contribute $5 \times 7 = 35$ .

7 + 35 = 42 \text{ electrons total}

Five I–F bonds use $5 \times 2 = 10$ electrons, leaving

42 - 10 = 32 \text{ electrons} = 16 \text{ lone pairs to distribute}

Each fluorine takes 3 lone pairs ( $5 \times 3 = 15$ ), leaving

16 - 15 = 1 \text{ lone pair on iodine}

So iodine has 5 bonded atoms and 1 lone pair:

n = m + k = 5 + 1 = 6

Six domains gives an octahedral electron-domain geometry. All six octahedral positions are equivalent, so the single lone pair can go anywhere, and it pushes the geometry into a square pyramidal molecular shape ( $AX_5E$ ). The four fluorines adjacent to the lone pair bend slightly away from it:

\theta_{\text{F(basal)–I–F(basal)}} \approx 90^\circ, \qquad \theta_{\text{F(basal)–I–F(apical)}} \approx 81^\circ \; (\text{compressed from ideal } 90^\circ)

Only one lone pair is present out of six domains, so the distortion is modest — noticeably smaller than in a molecule with two or more lone pairs on an octahedral center. Limiting case check: setting $k=0$ instead (a hypothetical $AX_6$ species with no lone pair) recovers perfect octahedral geometry with every angle exactly $90^\circ$ , confirming the lone pair is again the sole source of the $81^\circ$ compression.

Limiting cases & common traps

Situation	Correct handling	Common mistake
Double or triple bond to central atom	Counts as one domain, not two or three	Counting each bond order as a separate domain, inflating $n$
Resonance structures	Use any single valid resonance form; domain count is identical across all of them	Trying to average bond angles across resonance forms
Lone pair placement in trigonal bipyramidal ( $n=5$ )	Lone pairs go equatorial first (fewer 90° neighbors)	Placing lone pairs axially, which overestimates repulsion and gives wrong shape names
Multiple lone pairs on octahedral center ( $AX_4E_2$ )	Two lone pairs go opposite (trans) each other, minimizing LP–LP repulsion, giving square planar	Placing lone pairs adjacent (cis), which is higher energy and not observed
Electron-domain vs. molecular geometry	Molecular geometry describes atom positions only; electron-domain geometry includes lone pairs	Reporting the electron-domain geometry as if it were the molecular shape when lone pairs are present

The chemist behind it

VSEPR theory as a systematic predictive framework was largely developed by Ronald Gillespie, building on earlier qualitative ideas proposed by Nevil Sidgwick and Herbert Powell in the 1940s. Gillespie, working with Ronald Nyholm, turned the "electron pairs repel" intuition into a rigorous set of rules connecting Lewis structures directly to observed molecular geometries, publishing the now-standard Gillespie–Nyholm treatment in 1957. Their central insight was that the number of electron domains — not the specific orbital picture — is what fixes geometry, which is precisely why VSEPR can be taught and applied correctly using nothing more than a Lewis structure and a domain count.

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

Ronald J. Gillespie

1924–2021 · Developed the modern VSEPR model with Ronald Nyholm, translating electron-pair repulsion into quantitative geometric predictions still used unchanged in every introductory chemistry course today

Ask the tutor: Why does replacing one lone pair with a bonding pair change a seesaw shape into a trigonal bipyramid, and how would you predict the new bond angles?

Does VSEPR predict bond angles exactly, or only approximately?

VSEPR predicts the correct qualitative direction of distortion (compressed below the ideal domain angle) and gives a useful order-of-magnitude estimate, but exact angles depend on subtler effects such as electronegativity differences and orbital hybridization details. For introductory purposes, VSEPR angles are treated as good approximations, not exact values.

Why does a double or triple bond still only count as one electron domain?

Because all the electron density of a multiple bond — sigma and pi together — occupies the same general region of space between the two nuclei. VSEPR cares about regions of repulsion, not the raw number of electron pairs, so a double bond behaves geometrically like a single fat domain rather than two separate ones.

How does VSEPR handle molecules with resonance structures?

Every valid resonance structure for a given molecule gives the identical electron-domain count at the central atom, because resonance only redistributes pi-bonding electrons, not the number of sigma-bonded atoms or lone pairs. You may use any single resonance form to apply VSEPR and get the same geometry every time.

What is the difference between electron-domain geometry and molecular geometry?

Electron-domain geometry describes the spatial arrangement of all domains, including lone pairs. Molecular geometry describes only the positions of the atoms, ignoring lone pairs even though they still influence bond angles. The two coincide only when there are zero lone pairs on the central atom.

How does VSEPR connect to molecular polarity?

Once a geometry is known, individual bond dipoles can be summed vectorially to determine whether the molecule has a net dipole moment — a symmetric geometry like linear CO₂ can cancel bond dipoles entirely, while an asymmetric geometry like bent water cannot. This vector-sum reasoning is the foundation of Bond and Molecular Polarity.