OPOpenPithMake curiosity visibleChemistry lab / Molecular shape

About this lab

Eight experiments, one thread: electron pairs push each other apart, and the shape of a molecule is how they get out of each other’s way.

The valence electron pairs around a central atom, bonding pairs and lone pairs, repel each other and stay as far apart as they can. The first three experiments look at this rule itself: how the pairs spread out, what shape is left when the lone pairs are hidden, and why lone pairs squeeze the bond angles. The fourth switches to orbitals: s and p mix into hybrid orbitals that point the same way as the pairs. The last four use shape to answer questions: is the molecule polar, where do lone pairs go when the centre holds more than eight electrons, why a mirror image cannot be superimposed, and a shape table of 24 molecules.

Every electron pair on screen is placed by the same repulsion model, solved numerically. The angles are measured, not copied from a table. Drag a pair and let go: the spring-back you see is the model searching for the lowest-energy arrangement.

What the eight experiments show

What the eight experiments show

01 Pair repulsion: “the pairs can sit anywhere”

Four pairs start from scrambled positions; the energy falls all the way until every angle is 109.5°, a regular tetrahedron. Drag one pair elsewhere and let go: it returns to the same arrangement. Five pairs settle into a trigonal bipyramid, six into an octahedron.

02 Hide the lone pairs: “NH₃ has four pairs, so it is tetrahedral”

NH₃ has a tetrahedral pair geometry, but no atom sits on the lone pair. Hide it and the three H atoms with N form a trigonal pyramid; hide the two lone pairs of H₂O and it is bent. Pair geometry counts all pairs; molecular shape looks only at atoms.

03 Bond angles: “every tetrahedral molecule has 109.5° angles”

Lone pairs sit closer to the nucleus and repel harder, pushing the bonding pairs together. After relaxing, the model measures CH₄ 109.5°, NH₃ 106.4° and H₂O 104.2°; the measured values are 109.5°, 107° and 104.5°. More lone pairs, smaller angle. Even with the lone-pair factor set to 1.00, NH₃ and H₂O reach only 107.5° and 106.0°: a lone pair closer to the nucleus already takes more room.

04 Hybrid orbitals: “hybrid orbitals are extra orbitals out of nowhere”

One s orbital and n − 1 p orbitals recombine into n hybrid orbitals; the number of orbitals does not change. An sp³ orbital is 25.0 % s, and any two are 109.47° apart; only fully mixed are they orthogonal to each other. The p orbitals left over in sp and sp² stand perpendicular to the hybrids, and their side-by-side overlap forms the π bonds of ethyne and ethene.

05 Molecular polarity: “a molecule with polar bonds is always polar”

Both C=O bonds in CO₂ are polar, but they point opposite ways: the total dipole is 0.00, a nonpolar molecule. H₂O is bent, so its two bond dipoles do not cancel: total 1.52 (in electronegativity units). Among tetrahedral molecules, CH₄ and CCl₄ cancel while CH₃Cl does not, with a total of 0.96.

06 Expanded octets: “it makes no difference where lone pairs go”

With five pairs the lone pairs always take equatorial sites: SF₄ is a seesaw, ClF₃ is T-shaped, XeF₂ and I₃⁻ are linear, because an equatorial site has only two neighbours at 90°. With six pairs the two lone pairs of XeF₄ are 180.0° apart and the molecule is square planar.

07 Chiral molecules: “turn the mirror image enough and it will match”

Try all 12 rotations of a tetrahedron on CHFClBr’s mirror image: at most 2 groups match at once, never all 4. Replace F with H and CH₂BrCl has a plane of symmetry: its mirror image matches all 4, so it is not chiral. Lactic acid’s four groups, H, OH, CH₃ and COOH, are all different, so it too has a pair of mirror-image isomers.

08 Molecule library: “just memorise the shape table”

The library puts 24 molecules through one model: count pairs and lone pairs from valence electrons, relax the shape, measure the angles and add up the dipole. Every row of the table is computed by the model.

Model and sources

Model and sources

  • Pair counting: lone pairs on the central atom = ½(a − xb), where a is the central atom’s valence electrons minus the ion’s charge, x is the number of attached atoms, and b is the most electrons each attached atom can accept (1 for H, otherwise 8 minus its valence electrons). Electron pairs = x + lone pairs.
  • Repulsion model: each pair is a point, and each pair of points has repulsion U = qᵢqⱼ / d². Bonding pairs sit on a sphere of radius 1; lone pairs sit closer, on a sphere of radius 0.8, with q = 1.1; bonding pairs have q = 1. So at the same angle, lone–lone > lone–bond > bond–bond.
  • Relaxation: gradient descent along the sphere for a fixed 480 steps, from 6 random starts with fixed seeds, keeping the lowest-energy run. After you drag, it starts from where you left the pairs.
  • Hybrid orbitals: hᵢ = a·s + b·(dᵢ·p), a = 1/√n, b = √(1 − 1/n). Orthogonality requires cos θ = −1/(n − 1), which gives 180°, 120° and 109.47°.
  • Polarity: bond dipole = electronegativity difference × bond direction, pointing to the more electronegative end; the molecular dipole is their vector sum. Electronegativities are Pauling values.
  • Chirality: the mirror image is a reflection in the plane x = 0; superposition uses rotations only, all 12 rotations of a tetrahedron. R / S follows the groups’ priorities.

The exponent 2, lone-pair radius 0.8 and q = 1.1 are teaching assumptions chosen to reproduce the trend CH₄ > NH₃ > H₂O; this is not a quantum-chemical calculation. The model treats single and double bonds alike, so SO₂ comes out too narrow (model 113.7°, measured about 119°) and the equatorial angle of SF₄ too wide. Bond dipoles use electronegativity differences only, without lone pairs or bond lengths, so no debye values are given. The sp³d and sp³d² labels for five and six pairs are disputed in modern bonding theory; this page describes those molecules by pair geometry only.

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