Lewis Structure & VSEPR Molecular Lab

Build molecules by selecting central atoms, adding ligands, and placing lone pairs. Drag to rotate the 3D VSEPR shape and observe how lone pairs distort bond angles.

Worked example — Lewis Structure & VSEPR Molecular Lab

Steric Number (SN)	4
Formal Charge on Central Atom	0
Multi-lone-pair compression:	≈ 104.5°

These are the values the calculator shows when the page opens. Change any input above to recompute them.

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Lone pairs take more room than bonds do 🖖

VSEPR (Valence Shell Electron Pair Repulsion) theory explains molecular shapes by assuming that electron pairs in the valence shell of a central atom repel each other. To minimize electrostatic repulsion, these electron pairs arrange themselves in space to maximize their separation, defining geometries like linear, tetrahedral, and octahedral. A critical detail is that non-bonding lone pairs occupy more space than bonding pairs, because they are held close to a single nucleus rather than shared between two. This pushes adjacent chemical bonds closer together, distorting ideal bond angles. For example, water has a tetrahedral electron geometry, but the repulsion from its two lone pairs squeezes the H-O-H bond angle down from the ideal 109.5° to 104.5°.

From flat dots to real shape 🖖

This lab turns a flat Lewis diagram into the 3D shape a molecule actually takes. The recipe is pure counting: add the atoms bonded to the central atom to its lone pairs to get the steric number, and that single number predicts the geometry. Invisible lone pairs count just as much as visible atoms — methane (CH₄) and ammonia (NH₃) both have a steric number of 4, but ammonia swaps one bond for a lone pair, tipping the flat-looking tetrahedron into a pyramid.

The d-orbital myth of hypervalency 🖖

Build SF₄ or XeF₄ and the lab reports sp³d or sp³d² hybridization — the textbook story for a central atom holding more than eight electrons. Yet computational chemistry has largely debunked it: the d-orbitals of sulfur and xenon sit far too high in energy to contribute meaningfully. These hypervalent molecules are better described by 3-center-4-electron bonds spread across the ligands, so the tidy sp³d label you see is more a useful teaching fiction than physical reality.

VSEPR — COUNT THE ELECTRON DOMAINS, THEN NAME WHAT THE ATOMS MAKE

Which Molecular Shape Does Your Molecule Take?

VSEPR needs two counts. First the electron domains around the central atom — every bond counts once no matter how many pairs it holds, and every lone pair counts once too — and that fixes the electron geometry. Then look only at the atoms: the lone pairs are still there and still pushing, but they are invisible when you name the shape. Six cases cover almost everything you will be asked to predict.

Two domains — linear, 180° AX₂ → 180°

Three domains, no lone pair — trigonal planar, 120° AX₃ → 120°

Four domains, one lone pair — trigonal pyramidal AX₃E → 107.8°

Four domains, two lone pairs — bent AX₂E₂ → 104.5°

Five domains, one lone pair — seesaw AX₄E → 173° / 102°

Six domains, two lone pairs — square planar, 90° AX₄E₂ → 90°

Two domains — linear, 180°

What you know: Two electron domains on the central atom and no lone pairs. A double or triple bond still counts as a single domain.

Domains: AX₂ → 180°

Worked example: CO₂: carbon carries two double bonds and no lone pairs → 2 domains → linear, O=C=O at exactly 180°

Open this case: Carbon Dioxide (CO₂)

Two domains — linear, 180°. Two domains and no lone pairs: the atoms sit on a straight line through the centre. Two electron domains on the central atom and no lone pairs. A double or triple bond still counts as a single domain. — Two domains and no lone pairs: the atoms sit on a straight line through the centre.

Three domains, no lone pair — trigonal planar, 120°

What you know: Three electron domains and no lone pairs. Everything lies flat in a single plane.

Domains: AX₃ → 120°

Worked example: BF₃: boron has three single bonds and no lone pairs → 3 domains → trigonal planar, F–B–F = 120°

Open this case: Boron Trifluoride (BF₃)

Three domains, no lone pair — trigonal planar, 120°. Three bonding domains in a plane: 120° apart, with nothing to distort them. Three electron domains and no lone pairs. Everything lies flat in a single plane. — Three bonding domains in a plane: 120° apart, with nothing to distort them.

Four domains, one lone pair — trigonal pyramidal

What you know: Four electron domains, one of them a lone pair. The electron geometry is tetrahedral; the shape you name counts the three atoms only.

Domains: AX₃E → 107.8°

Worked example: NH₃: nitrogen has three bonds plus one lone pair → 4 domains → trigonal pyramidal, H–N–H = 107.8° instead of 109.5°

Open this case: Ammonia (NH₃)

Four domains, one lone pair — trigonal pyramidal. Tetrahedral electron geometry with one corner invisible: the atoms make a pyramid. Four electron domains, one of them a lone pair. The electron geometry is tetrahedral; the shape you name counts the three atoms only. — Tetrahedral electron geometry with one corner invisible: the atoms make a pyramid.

Four domains, two lone pairs — bent

What you know: Four electron domains with two lone pairs. The electron geometry is still tetrahedral, but only two atoms are attached.

Domains: AX₂E₂ → 104.5°

Worked example: H₂O: oxygen has two bonds plus two lone pairs → 4 domains → bent, H–O–H = 104.5°

Open this case: Water (H₂O)

Four domains, two lone pairs — bent. Two bonds and two lone pairs: the atoms trace a bend, not a line. Four electron domains with two lone pairs. The electron geometry is still tetrahedral, but only two atoms are attached. — Two bonds and two lone pairs: the atoms trace a bend, not a line.

Five domains, one lone pair — seesaw

What you know: Five electron domains, one a lone pair. The electron geometry is trigonal bipyramidal, which is the first one with two different kinds of site.

Domains: AX₄E → 173° / 102°

Worked example: SF₄: sulfur has four bonds plus one lone pair → 5 domains → seesaw, the axial F–S–F squeezed to 173° and the equatorial pair at 102°

Open this case: Sulfur Tetrafluoride (SF₄)

Five domains, one lone pair — seesaw. Trigonal bipyramidal with the lone pair equatorial: the atoms make a seesaw. Five electron domains, one a lone pair. The electron geometry is trigonal bipyramidal, which is the first one with two different kinds of site. — Trigonal bipyramidal with the lone pair equatorial: the atoms make a seesaw.

Six domains, two lone pairs — square planar, 90°

What you know: Six electron domains with two lone pairs. The electron geometry is octahedral, and all six sites are equivalent.

Domains: AX₄E₂ → 90°

Worked example: XeF₄: xenon has four bonds plus two lone pairs → 6 domains → square planar, F–Xe–F = 90°

Open this case: Xenon Tetrafluoride (XeF₄)

Six domains, two lone pairs — square planar, 90°. Octahedral electron geometry with the lone pairs opposite: the atoms form a flat square. Six electron domains with two lone pairs. The electron geometry is octahedral, and all six sites are equivalent. — Octahedral electron geometry with the lone pairs opposite: the atoms form a flat square.

References (2)

Insight block 3 — the calculation that took the d orbitals away: E. Magnusson, "Hypercoordinate molecules of second-row elements: d functions or d orbitals?" Journal of the American Chemical Society 112(22), 7940–7951, 1990.
And the model the tool actually applies: R. J. Gillespie and R. S. Nyholm, "Inorganic stereochemistry." Quarterly Reviews, Chemical Society 11(4), 339–380, 1957 — where VSEPR was set out, including lone pairs occupying more space than bonding pairs.

Problem solved in full

Water built from its electron count and the 104.5° bond angle 5 steps
Build water from its electron count alone: steric number, formal charge, shape, and bond angle. Then explain why the angle is 104.5° and not the 109.5° the shape predicts.
1. Count valence electrons and pair them up. Oxygen brings six, each hydrogen one, and eight electrons are four pairs.
  
  $valence = 6 (O) + 2 \times 1 (H) = 8 e^{-} = 4 pairs$
2. Two pairs are doing the bonding, so the rest are lone pairs. The steric number counts both kinds, because both take up room — that is the one idea VSEPR contains.
  
  $bonding pairs = 2 \Rightarrow lone pairs = 4 - 2 = 2 \Rightarrow SN = 2 + 2 = 4 (A X_{2} E_{2})$
3. Formal charge tests whether the structure is the sensible one: valence electrons, minus the lone-pair electrons, minus half the bonding electrons. Zero means no better arrangement is waiting.
  
  $FC = V - N - \frac{1}{2} B = 6 - 4 - \frac{1}{2} (4) = 0$
4. A steric number of 4 means the four pairs arrange tetrahedrally, which would be 109.5° if all four were alike. They are not, and the compression scales with the number of lone pairs.
  
  $SN = 4 \Rightarrow tetrahedral 109. 5^{\circ}; C H_{4} 109. 5^{\circ} \to N H_{3} 10 7^{\circ} \to H_{2} O 104. 5^{\circ}$
5. The consequence is a dipole. Two O–H bond moments at 104.5° add vectorially to 1.85 D; straighten the molecule to 180° and they cancel exactly.
  
  $μ = 2 μ_{OH} cos \frac{104. 5 ^{\circ}}{2} = 2 (1.51) (0.611) = 1.85 D; 18 0^{\circ} \Rightarrow μ = 0$
Answer

AX₂E₂, steric number 4, formal charge 0, bent at 104.5°. The 5° shortfall is the lone pairs: they belong to one nucleus rather than being shared between two, so they spread wider and squeeze the bonding pairs together — about 2.5° per lone pair, which is why the series runs 109.5° for methane, 107° for ammonia and 104.5° for water. That residual bend is not a detail. A linear molecule with two identical bonds has no net dipole; water's 104.5° leaves it 1.85 D, and essentially everything water does as a solvent — dissolving salts, forming hydrogen bonds, boiling 160 K above the heavier H₂S when the group trend says it should boil lower — is downstream of those five degrees.

$A X_{2} E_{2}, SN = 4, FC = 0, bent at 104. 5^{\circ}$

By the 42Math team · Updated 2026-07-27

Reviewed against published sources. Corrections welcome. Editorial policy · Corrections

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