what is orbital hybridization and how does it determine molecular geometry

What is Orbital Hybridization?

Hybridization is the mathematical mixing of atomic orbitals on the same atom to form new orbitals of equal energy and shape, called hybrid orbitals. These hybrid orbitals are better suited for bonding than the original pure atomic orbitals.

Key insight: Hybrid orbitals are a model — a mathematical construct that explains why, for example, carbon forms 4 equal bonds in methane, even though its ground state has only 2 unpaired electrons.

The Pipeline: From Electron Config → Geometry

┌─────────────────────────────────────────────────────────────────────┐ │ HYBRIDIZATION → MOLECULAR GEOMETRY PIPELINE │ └─────────────────────────────────────────────────────────────────────┘

STEP 1: Atomic Orbitals (AOs) ┌──────────────────────────────────────────────────────┐ │ Carbon Ground State: │ │ │ │ 1s² 2s² 2p¹ 2p¹ 2p⁰ │ │ [↑↓] [↑↓] [↑] [↑] [ ] │ │ │ │ Problem: Only 2 unpaired electrons → 2 bonds? │ │ But CH₄ has 4 equal bonds! │ └──────────────────────────────────────────────────────┘ │ │ EXCITATION (promotes one 2s electron) ▼ STEP 2: Excited State ┌──────────────────────────────────────────────────────┐ │ 1s² 2s¹ 2p¹ 2p¹ 2p¹ │ │ [↑↓] [↑] [↑] [↑] [↑] │ │ │ │ Now 4 unpaired electrons — but still not equal! │ │ (one s + three p, different shapes/energies) │ └──────────────────────────────────────────────────────┘ │ │ HYBRIDIZATION (orbitals mix) ▼ STEP 3: Hybrid Orbitals Form ┌──────────────────────────────────────────────────────┐ │ │ │ 1s + 3p ──mix──► 4 × sp³ orbitals │ │ │ │ Each sp³ orbital: │ │ • 25% s-character │ │ • 75% p-character │ │ • Identical energy & shape │ │ • Oriented to MINIMIZE electron repulsion │ └──────────────────────────────────────────────────────┘ │ │ VSEPR (electron pair repulsion) ▼ STEP 4: 3D Geometry Determined ┌──────────────────────────────────────────────────────┐ │ │ │ 4 sp³ orbitals → point to 4 corners of │ │ a tetrahedron → bond angle = 109.5° │ │ │ │ H │ │ \ 109.5° │ │ H - C - H │ │ / │ │ H ← TETRAHEDRAL │ └──────────────────────────────────────────────────────┘

All Major Hybridization Types

┌────────────┬───────────┬────────────┬──────────┬───────────────────┐ │ Hybrid │ AOs Mixed │ # Orbitals │ Geometry │ Bond Angle │ ├────────────┼───────────┼────────────┼──────────┼───────────────────┤ │ sp │ 1s + 1p │ 2 │ Linear │ 180° │ │ sp² │ 1s + 2p │ 3 │ Trigonal │ 120° │ │ │ │ │ Planar │ │ │ sp³ │ 1s + 3p │ 4 │ Tetra- │ 109.5° │ │ │ │ │ hedral │ │ │ sp³d │ 1s+3p+1d │ 5 │ Trigonal │ 90°, 120° │ │ │ │ │ Bipyram. │ │ │ sp³d² │ 1s+3p+2d │ 6 │ Octahed- │ 90° │ │ │ │ │ ral │ │ └────────────┴───────────┴────────────┴──────────┴───────────────────┘

Visual Geometry Reference

sp (Linear) sp² (Trigonal Planar) sp³ (Tetrahedral) 180° 120° 109.5°

A ──── C ──── B B B \ 120° /| 120° C ── A B - C | / \ | B \ | | B

sp³d (Trig. Bipyramid) sp³d² (Octahedral) B B (axial, 90°) | | B -- C -- B B -- C -- B (equatorial, 120°) | | B B (axial, 90°)

How Lone Pairs Distort Geometry

Lone pairs occupy hybrid orbitals but repel more strongly than bonding pairs, compressing bond angles:

MOLECULE HYBRIDIZATION LONE PAIRS SHAPE ANGLE ───────────────────────────────────────────────────────────── CH₄ sp³ 0 Tetrahedral 109.5° NH₃ sp³ 1 Trigonal Pyr. 107° ← compressed H₂O sp³ 2 Bent/V-shape 104.5° ← more compressed BF₃ sp² 0 Trigonal Planar 120° SO₂ sp² 1 Bent ~119°

NH₃ lone pair effect:

:                ← lone pair (takes more space)
 N
/ \

H H Bond angle shrinks from 109.5° → 107° \ / 107°

Quick Determination Rule

COUNT electron groups around central atom: (bonding pairs + lone pairs)

2 groups → sp → Linear 3 groups → sp² → Trigonal Planar (or Bent if 1 lone pair) 4 groups → sp³ → Tetrahedral / Pyramidal / Bent 5 groups → sp³d → Trigonal Bipyramidal / See-saw / T-shape 6 groups → sp³d² → Octahedral / Square Pyramidal / Square Planar

Sigma (σ) and Pi (π) Bonds in Hybridization

sp³ → 4 sigma bonds only (e.g., CH₄, single bonds) sp² → 3 sigma + 1 unhybridized p (e.g., C₂H₄, one π bond → double bond) sp → 2 sigma + 2 unhybridized p (e.g., C₂H₂, two π bonds → triple bond)

Unhybridized p orbitals form π bonds by SIDEWAYS overlap:

   p    p
   |    |

─────|────|───── (σ framework, sp² hybrid) | | p p \ / / ← π bond (above and below plane)

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