8.2 Hybrid Atomic Orbitals

Atomic orbital hybridization explains why molecules form the shapes they do. Standard atomic orbitals (s, p, d) don't point in the right directions to account for observed molecular geometries, so we mix them together into new hybrid orbitals that do. Understanding hybridization connects electron configuration to molecular shape and bond strength.

Atomic Orbital Hybridization

Process of orbital hybridization

When an atom forms covalent bonds, its atomic orbitals can blend together to create new hybrid orbitals with different shapes and energies than the originals. This happens because hybrid orbitals overlap more effectively with neighboring atoms, producing stronger, more stable bonds.

The mixing combines s, p, and sometimes d orbitals:

• s + p orbitals mix to form sp, sp², or sp³ hybrids
• d orbitals can also participate, forming sp³d or sp³d² hybrids

A few key rules govern this process:

• The number of hybrid orbitals formed always equals the number of atomic orbitals that went into the mix. If you combine one s and three p orbitals, you get exactly four sp³ hybrids.
• Hybrid orbitals orient themselves to minimize electron repulsion and maximize bond strength, which is why each type has a characteristic geometry and bond angle.
• Any unhybridized atomic orbitals that remain can form pi ($\pi$) bonds (as in ethene's double bond) or hold lone pairs (as in water).

Prediction of hybrid orbital types

You can figure out the hybridization of a central atom by counting its electron domains, which include both bonding pairs and lone pairs. Each electron domain count maps to a specific hybridization:

Here's the step-by-step approach:

1. Draw the Lewis structure of the molecule.
2. Count the total electron domains (bonding pairs + lone pairs) around the central atom. A double or triple bond counts as one domain.
3. Match the domain count to the hybridization in the table above.

Lone pairs change the molecular shape but not the hybridization. The hybridization depends on the total number of electron domains, while the visible shape depends on where the atoms (not the lone pairs) end up. For example:

• Bent (2 bonding + 1 lone pair): still sp² hybridization ($SO_2$)
• Trigonal pyramidal (3 bonding + 1 lone pair): still sp³ hybridization ($NH_3$)
• Seesaw (4 bonding + 1 lone pair): still sp³d hybridization ($SF_4$)
• T-shaped (3 bonding + 2 lone pairs): still sp³d hybridization ($ClF_3$)
• Square pyramidal (5 bonding + 1 lone pair): still sp³d² hybridization ($BrF_5$)

VSEPR theory is what ties this all together: electron domains arrange themselves to be as far apart as possible, and that arrangement determines both the hybridization and the molecular geometry.

Shapes of hybrid vs. atomic orbitals

Standard atomic orbitals have familiar shapes:

• s orbitals are spherical
• p orbitals are dumbbell-shaped, oriented along the x, y, and z axes
• d orbitals have more complex, multi-lobed shapes

Hybrid orbitals look different. Each hybrid orbital has one large lobe pointing in a specific direction, which makes it very effective at overlapping with another atom's orbital to form a sigma ($\sigma$) bond.

• sp hybrids: formed from one s + one p orbital → 2 orbitals pointing 180° apart (linear). Example: each carbon in ethyne ($C_2H_2$).
• sp² hybrids: formed from one s + two p orbitals → 3 orbitals pointing 120° apart (trigonal planar). Example: each carbon in ethene ($C_2H_4$).
• sp³ hybrids: formed from one s + three p orbitals → 4 orbitals pointing 109.5° apart (tetrahedral). Example: carbon in methane ($CH_4$).

Any p orbitals that don't participate in hybridization keep their original dumbbell shape and orientation. These unhybridized p orbitals are what form $\pi$ bonds through side-by-side overlap. In ethene, for instance, each carbon is sp² hybridized with one leftover p orbital, and those two unhybridized p orbitals overlap to create the second bond in the double bond.

Molecular Structure and Bonding

Hybridization is a useful model, but it has limits. Molecular orbital (MO) theory provides a more complete picture of how electrons behave in molecules by treating orbitals as spread across the entire molecule rather than localized between two atoms. For an intro course, though, hybridization gives you a reliable way to connect Lewis structures → electron domain counts → molecular geometry → bond angles.

Keep in mind that bond angles can deviate slightly from the ideal values. Lone pairs repel more strongly than bonding pairs, which compresses bond angles. That's why $NH_3$ has bond angles of about 107° instead of the ideal 109.5° for sp³.