Molecular Shapes (VSEPR) predicts that methane's bonds point to the corners of a tetrahedron, $109.5^\circ$ apart. But carbon's valence orbitals, one 2s and three 2p (Quantum Numbers), point in quite different directions: the p orbitals are $90^\circ$ apart. Valence bond theory resolves this by mixing them into new hybrid orbitals.
Key idea
The hybridization matches the number of electron groups (bonded atoms plus lone pairs) on an atom: 2 groups, sp ($180^\circ$); 3 groups, sp² ($120^\circ$); 4 groups, sp³ ($109.5^\circ$). A single bond is one $\sigma$ bond. A double bond is one $\sigma$ and one $\pi$ bond; a triple bond is one $\sigma$ and two $\pi$ bonds.
Why it works
Mixing one s orbital with three p orbitals gives four equal sp³ orbitals aimed at the corners of a tetrahedron, each able to overlap end-on with another atom's orbital: a $\sigma$ bond, with its electron density on the line between the nuclei. Mixing s with only two p orbitals gives three sp² orbitals in a plane and leaves one p orbital standing up, perpendicular to it. Two such leftover p orbitals on neighboring atoms overlap side by side, above and below the bond axis: a $\pi$ bond. That is why a double bond is one $\sigma$ plus one $\pi$, why the atoms around it lie in one plane, and why it can't twist without breaking the $\pi$ overlap.
Worked example: Hybridization from electron groups
Give the hybridization of the central atom in $\mathrm{NH_3}$, $\mathrm{BF_3}$ and $\mathrm{CO_2}$.
- $\mathrm{NH_3}$: 3 bonds + 1 lone pair = 4 groups: sp³.
- $\mathrm{BF_3}$: 3 bonds, no lone pairs = 3 groups: sp².
- $\mathrm{CO_2}$: two double bonds = 2 groups (a double bond counts once): sp.
Answer: sp³, sp² and sp.
Worked example: Counting σ and π bonds
Acrylonitrile is $\mathrm{H_2C{=}CH{-}C{\equiv}N}$. Count its σ and π bonds, and give each carbon's hybridization.
- Bonds: two C–H on the first carbon, one C–H on the second, C=C, C–C and C≡N.
- σ: every bond has exactly one: $2 + 1 + 1 + 1 + 1 = 6$. π: one in C=C and two in C≡N: 3.
- First carbon: 3 groups, sp². Second carbon: 3 groups, sp². Third carbon (C≡N): 2 groups, sp.
Answer: 6 σ and 3 π; sp², sp², sp.
Common mistake
Two traps. First, counting a double bond as two σ bonds: only one bond between two atoms can lie on the axis, so a double bond is one σ plus one π. Second, matching hybridization to the number of atoms attached instead of the number of electron groups. Water's oxygen has only 2 atoms attached but 4 groups (2 bonds, 2 lone pairs), so it is sp³, with a bond angle near $104.5^\circ$, not $180^\circ$. Check: count lone pairs as groups and count a multiple bond as one group.
For five and six electron groups, older books use "sp³d" and "sp³d²". Modern bonding theory describes those molecules differently, and AP Chemistry does not assess those labels; the shapes from VSEPR are what matter.