Molecular Geometry and Hybridization

01 / UNDERSTAND & APPLY

1. A flat formula is not a molecular shape

A structural formula printed on a page is a connectivity map. It does not imply that all atoms lie in the page. Molecular geometry describes the positions of nuclei in three-dimensional space; electron-domain geometry describes the arrangement of bonding directions and lone-pair regions around a chosen central atom. Keeping those two descriptions separate prevents the most common naming error in this chapter.

In VSEPR, regions of valence electron density adopt arrangements that reduce unfavorable crowding. The model is a qualitative structural guide, not a complete calculation of all molecular forces. A bond to one neighboring atom counts as one domain whether it is single, double or triple. A lone pair on the central atom counts as another domain. Lone pairs on terminal atoms are not added to the central atom’s domain count.

Use AX_mE_n notation when helpful: A is the central atom, X represents bonded atoms and E represents lone pairs on A. The domain count is m+n. The notation does not say that all ligands have identical chemical identities; if they differ, angles and dipole cancellation can differ from the highly symmetric ideal example.

Before assigning a shape, construct a valid Lewis picture and check total charge. Forgetting an electron in an anion can remove a lone pair and produce the wrong entire geometry. Multiple bonds should be represented correctly for valence accounting even though they count as one domain for the initial geometric arrangement.

02 / UNDERSTAND & APPLY

2. Two and three domains: linear and planar foundations

Two domains lie on opposite sides of a central atom in the ideal arrangement, giving a linear electron-domain geometry and a 180° separation. CO₂ has two bonding domains around carbon and no carbon lone pairs, so its molecular geometry is linear. A triple bond also counts as one domain: carbon in H–C≡N has two directions, toward H and toward N.

Three domains occupy a trigonal plane with ideal 120° separations. In BF₃, three bonds and no boron lone pair give trigonal-planar molecular geometry. The electron deficiency of boron does not prevent this domain classification. In a three-domain AX₂E species, one position is a lone pair, so the atomic shape is bent rather than trigonal planar.

SO₂ illustrates the distinction: two S–O directions and one sulfur lone pair give three domains in the usual VSEPR description. Its atoms form a bent shape even though the electron-domain arrangement is based on a trigonal plane. Resonance-equivalent bonding should not be interpreted as the molecule alternating between two shapes.

Ideal angles describe a symmetric reference. A multiple-bond domain often occupies more angular space than a single-bond domain, and a lone pair can compress the angle between bonded atoms. VSEPR gives useful trends, but precise angles require experimental or computational information. Writing exactly 120° for every three-domain molecule overstates the model.

03 / UNDERSTAND & APPLY

3. Four domains do not always mean a tetrahedral molecule

Four equivalent directions form a tetrahedron, with ideal angle arccos(−1/3) ≈ 109.5°. CH₄ is AX₄, so both electron-domain and molecular geometry are tetrahedral. A tetrahedron has four vertices, not four atoms arranged in a square around the center. A square planar drawing is a different spatial arrangement with different angles.

NH₃ has three bonds and one lone pair: AX₃E. Its electron-domain arrangement is approximately tetrahedral, while the hydrogen positions define a trigonal pyramid. H₂O has two bonds and two lone pairs: AX₂E₂. Its electron-domain arrangement is likewise approximately tetrahedral, but its molecular shape is bent.

For the familiar CH₄, NH₃ and H₂O comparison, bond angles decrease from about 109.5° to 107° to 104.5°. The qualitative lone-pair crowding model rationalizes that progression. Do not use those exact values as universal angles for every AX₃E or AX₂E₂ species: ligand electronegativity, central-atom size and orbital character also matter.

NH₄⁺ is tetrahedral because it has four N–H bonds and no nitrogen lone pair. Protonation of ammonia uses the lone pair to form a bond, changing the atomic geometry classification from trigonal pyramidal to tetrahedral. The positive charge alone does not dictate the geometry; the resulting electron count does.

04 / UNDERSTAND & APPLY

4. Five domains have unequal axial and equatorial sites

Five domains adopt a trigonal-bipyramidal reference arrangement: three equatorial positions form a plane at 120° to one another, while two axial positions lie above and below that plane. An axial direction is 90° from all three equatorial directions; an equatorial direction has only two 90° interactions, with the axial pair. The two types of site are therefore not geometrically equivalent.

A lone pair normally prefers an equatorial position in this simple VSEPR setting because it has fewer 90° interactions. For AX₄E, exemplified by SF₄, the remaining atom positions form a seesaw. For AX₃E₂, exemplified by ClF₃, two equatorial lone pairs leave a T-shaped arrangement of atoms. The angles are distorted from the ideal reference by unequal interactions.

For AX₂E₃, the three lone pairs occupy the equatorial plane, leaving the two bonded atoms axial and opposite. XeF₂ is therefore linear despite having five domains around xenon. It should not be called “trigonal bipyramidal” when the question asks for the molecular shape rather than the electron-domain reference.

PCl₅ is a standard gaseous molecular AX₅ example with trigonal-bipyramidal geometry. The axial and equatorial P–Cl bonds occupy different environments. The solid-state structure can be ionic rather than simply an assembly of identical gas-phase PCl₅ molecules, so specify the phase when the question makes it relevant. A molecular-shape rule cannot be transferred blindly across phase-dependent structural changes.

05 / UNDERSTAND & APPLY

5. Six domains give octahedral, pyramidal or square-planar shapes

Six equivalent directions form an octahedral arrangement. Four can be pictured in a square plane with one above and one below, all centered on A. Neighboring directions are 90° apart and opposite directions 180°. SF₆ is AX₆ and has octahedral molecular geometry in the simple isolated-molecule model.

With one lone pair, AX₅E leaves five atoms in a square pyramid, as in BrF₅. With two lone pairs, the preferred simple arrangement puts them opposite, reducing their mutual crowding. The four remaining atoms form a square plane, as in XeF₄. The molecular geometry is square planar while the six-domain reference is octahedral.

Valence counting makes the difference between XeF₂ and XeF₄ clear. XeF₄ has four bonds and two lone pairs on xenon, rather than two bonds and three lone pairs. Both species can be nonpolar by symmetry with identical ligands, but their geometry and domain counts are different. Counting just the number of fluorines without accounting for the remaining electrons misses the reason.

Square-planar transition-metal complexes should not automatically be assigned this main-group AX₄E₂ explanation. Their geometry depends on d-electron configuration, ligand-field effects and bonding. The same geometric label can arise from different electronic models. Use the coordination-compound model for those species rather than force central lone-pair counting to explain them.

06 / UNDERSTAND & APPLY

6. What sp, sp² and sp³ mean in a localized model

Hybridization is a mathematical combination of atomic orbitals on the same atom to produce a useful set of directional orbitals. Combining one s and one p orbital gives two sp hybrids; one s and two p orbitals give three sp² hybrids; one s and three p orbitals give four sp³ hybrids. The number of orbitals is conserved. Hybridization does not create additional electrons or require an atom to physically execute a timed mixing step before bonding.

In the idealized model, sp hybrids are linear with 50% s character; sp² hybrids are trigonal planar with one-third s character; sp³ hybrids are tetrahedral with one-quarter s character. Unused p orbitals remain available for π bonding: two in an sp description, one in sp² and none in sp³. These counts help connect local sigma geometry with multiple bonds.

Each carbon in ethene is approximately sp²: three sigma directions lie in a plane and an unhybridized p orbital participates in the π system. Each carbon in ethyne is approximately sp: two sigma directions are linear and two perpendicular p orbitals form two π components. The methyl carbon in ethane is ordinarily described as sp³ with four sigma directions.

A hybridization label is a model, not a direct synonym for molecular geometry. A lone pair can occupy a directional orbital in the localized description, leaving fewer atom positions than total orbitals. Thus ammonia is commonly described with approximately sp³ nitrogen even though its molecular shape is pyramidal, not tetrahedral. Real orbitals need not contain the exact ideal s:p ratio assumed by a simple label.

Conjugation can favor an approximately planar arrangement and alter the simple isolated-atom domain picture. An amide nitrogen is approximately planar because its lone pair participates in conjugation with the carbonyl, often described using a p orbital and sp² sigma framework. Blindly counting three bonds plus one lone pair and assigning a strongly pyramidal sp³ geometry would miss this electronic effect.

07 / UNDERSTAND & APPLY

7. Treat conventional d-hybrid labels as limited bookkeeping

Some introductory and examination conventions label five-domain geometries sp³d and six-domain geometries sp³d². If a question explicitly asks for that conventional hybridization assignment, trigonal-bipyramidal and octahedral reference arrangements correspond to those labels in that scheme. Recognizing the convention is useful, but it should not be confused with a modern demonstration of strong d-orbital participation.

For main-group hypervalent molecules such as PF₅, SF₆ or XeF₂, modern bonding descriptions can explain the structure through molecular orbitals and multicenter interactions without requiring the central atom’s d orbitals to form the literal equivalent hybrids of the older picture. The VSEPR shape prediction and the claimed orbital explanation are separate statements; accepting the former does not force the latter.

VSEPR also has limits for transition-metal complexes, some radicals, strongly delocalized systems and stereochemically inactive lone pairs. The domain method is most useful for the common main-group closed-shell cases taught here. If a problem gives measured geometry or a more specific electronic model, use that information rather than override it with an overgeneralized steric-number rule.

Bond angle is influenced by more than lone-pair count. Differences in central atom, ligand electronegativity, multiple bonding, steric crowding and conjugation can all matter. Use broad lone-pair repulsion trends within comparable examples, and avoid claiming an exact numerical angle from domain count alone.

08 / UNDERSTAND & APPLY

8. Symmetry decides whether bond dipoles cancel

After finding geometry, compare the bond-dipole vectors. Equal vectors arranged symmetrically can cancel: linear CO₂, trigonal-planar BF₃, tetrahedral CF₄, trigonal-bipyramidal PF₅ and octahedral SF₆ have symmetry-enforced cancellation in their ideal isolated structures. The existence of polar bonds alone does not make the molecule polar.

Lone pairs often reduce atomic symmetry and prevent complete cancellation, as in bent H₂O or pyramidal NH₃, but “has a lone pair” is not a universal polarity test. Linear XeF₂ and square-planar XeF₄ have central lone pairs while their equivalent bond dipoles cancel by symmetry. Always inspect the actual atom arrangement rather than stop at the lone-pair count.

For an AX₄ tetrahedron with unequal substituents, such as CH₃Cl, the four contributions are not equivalent, so tetrahedral geometry alone does not imply zero dipole. Likewise, a linear heteronuclear triatomic molecule need not be nonpolar: cancellation requires equal opposing contributions. Symmetry is a sufficient reason in the standard examples; accidental numerical cancellation in unsymmetrical cases cannot be assumed.

For two equal bond dipoles of magnitude μ_b separated by angle θ, the vector-sum magnitude is 2μ_b cos(θ/2). It vanishes at 180° but not at a typical bent angle. This simple vector model provides intuition, although an actual molecular dipole includes the full electron distribution and need not be exactly the sum of transferable isolated bond-dipole values.

09 / UNDERSTAND & APPLY

9. Original shape and orbital practice

These original problems refer to isolated molecular species in the stated elementary models unless a phase is specified. Count valence electrons first for an unfamiliar ion or noble-gas compound. Then report electron-domain geometry and molecular geometry separately when both are requested.

For a multiple-center molecule, assign geometry locally. For a polarity question, add a symmetry argument after the shape. For a hybridization question, state whether you are using a conventional introductory label or a more detailed bonding interpretation. This prevents a correct geometric result from carrying an unjustified orbital claim.