5.2 Hybrid Atomic Orbitals | Chemistry: Atoms First 2e

Learning Objectives

Explain the concept of atomic orbital hybridization
Determine the hybrid orbitals associated with various molecular geometries

Core Concepts & Principles

While simple valence bond theory works well for diatomic molecules, it fails to explain the real-world bond angles of multi-atom molecules. For example, using unhybridized $2p$ orbitals on oxygen predicts a $90^\circ$ bond angle for water ( $H_2O$ ), but experiments show the actual angle is $104.5^\circ$ .

To reconcile theory with reality, we use hybridization: the mathematical combination of atomic wave functions (using linear combinations of atomic orbitals, or LCAO) when atoms form covalent bonds. This creates new hybrid orbitals with shapes and orientations perfectly suited to explain observed molecular shapes.

Rules of Orbital Hybridization

Formation: Hybrid orbitals do not exist in isolated atoms; they form only when atoms undergo covalent bonding.
Conservation of Orbitals: The number of hybrid orbitals produced always equals the total number of atomic orbitals combined.
Equivalence: All orbitals within a specific set of hybrid orbitals are identical in shape and energy.
Geometry Alignment: The type of hybrid orbital formed directly matches the VSEPR electron-pair geometry.

Common Types of Hybridization

The hybridization of a central atom depends entirely on its total number of electron-density regions (electron domains):

sp Hybridization (2 Domains): Mixing one $s$ orbital and one $p$ orbital yields two equivalent $sp$ hybrid orbitals arranged in a linear geometry ( $180^\circ$ apart). Examples: $BeCl_2$ , $CO_2$ , $C_2H_2$ .
sp² Hybridization (3 Domains): Mixing one $s$ orbital and two $p$ orbitals yields three equivalent $sp^2$ hybrid orbitals arranged in a trigonal planar geometry ( $120^\circ$ apart). One unhybridized $p$ orbital remains. Examples: $BH_3$ , $CH_2O$ , $C_2H_4$ .
sp³ Hybridization (4 Domains): Mixing one $s$ orbital and three $p$ orbitals yields four equivalent $sp^3$ hybrid orbitals arranged in a tetrahedral geometry ( $109.5^\circ$ apart). Lone pairs and bonding pairs occupy these spaces, with lone pairs slightly compressing bond angles (e.g., $NH_3$ at $107.3^\circ$ and $H_2O$ at $104.5^\circ$ ). Examples: $CH_4$ , $NH_3$ , $H_2O$ , $CCl_4$ .
sp³d Hybridization (5 Domains): Mixing one $s$ , three $p$ , and one $d$ orbital yields five $sp^3d$ hybrid orbitals in a trigonal bipyramidal geometry. Restricted to atoms in period 3 or lower with available $d$ orbitals. Examples: $PCl_5$ , $SF_4$ .
sp³d² Hybridization (6 Domains): Mixing one $s$ , three $p$ , and two $d$ orbitals yields six $sp^3d^2$ hybrid orbitals in an octahedral geometry. Examples: $SF_6$ , $XeF_4$ .

Problem-Solving Routines & Methods

How to Determine Central Atom Hybridization

1
Draw the correct Lewis structure for the molecule.
2
Count the total number of electron-density regions (electron domains) around the central atom. Treat single bonds, double bonds, triple bonds, radicals, and lone pairs each as a single domain.
3
Match the total domain count to its corresponding VSEPR geometry and hybrid orbital set: 2 domains = sp, 3 domains = sp2, 4 domains = sp3, 5 domains = sp3d, 6 domains = sp3d2.

Pro-Tip: Never count individual bonds within a double or triple bond as separate electron domains. A double bond counts as only 1 region of electron density.

Practice & Concept Checks

Concept Check

What is the hybridization and electron-pair geometry of the carbon atom in carbon dioxide (CO₂)? photochemical context aside.

Concept Check

Why is the bond angle in hydrogen sulfide (H₂S) closer to 90° than the 109.5° tetrahedral angle found in water (H₂O)?

Key Terms & Vocabulary

hybridizationBonding Theory

The mathematical combination of atomic wave functions to form new, specialized hybrid orbitals with tailored shapes and orientations during covalent bonding.

hybrid orbitalsBonding Theory

New, equivalent orbitals formed by combining atomic orbitals on a bonded atom; their shapes and energies match the molecule's spatial geometry.

sp hybrid orbitalsHybridization Types

A set of two equivalent hybrid orbitals oriented linearly at 180° resulting from the mixing of one s and one p orbital.

Example: Found in linear molecules like BeCl2 and CO2.

sp2 hybrid orbitalsHybridization Types

A set of three equivalent hybrid orbitals arranged in a trigonal planar geometry (120°) resulting from the mixing of one s and two p orbitals.

Example: Found in trigonal planar molecules like BH3 and formaldehyde.

sp3 hybrid orbitalsHybridization Types

A set of four equivalent hybrid orbitals arranged in a tetrahedral geometry (109.5°) resulting from the mixing of one s and three p orbitals.

Example: Found in tetrahedral molecules like CH4, NH3, and H2O.

sp3d hybrid orbitalsHybridization Types

A set of five equivalent hybrid orbitals arranged in a trigonal bipyramid resulting from mixing one s, three p, and one d orbital.

Example: Found in expanded octet molecules like PCl5.

sp3d2 hybrid orbitalsHybridization Types

A set of six equivalent hybrid orbitals arranged in an octahedron resulting from mixing one s, three p, and two d orbitals.

Example: Found in octahedral molecules like SF6.