Hybridization & MO Theory

the idea

Atomic orbitals don't point the right way for bonding, so atoms remix them.

Carbon's valence orbitals are one round 2s and three 2p orbitals at 90°. But methane's bonds sit at 109.5°, not 90°. Valence bond theory fixes this with hybridization: mix the s and p orbitals into new, identical orbitals aimed exactly where VSEPR says the electron domains go.

Plant version: it's like reformulating a blend. One part of ingredient s and three parts of ingredient p get mixed into four identical portions of "sp³". Each portion is 25% s and 75% p, and they're interchangeable. You don't lose any material. You just get four uniform units that fit the packaging (the tetrahedral geometry) better than the raw ingredients did.

The shortcut: count electron domains on the atom (bonds + lone pairs, a double or triple bond counts once). 2 → sp, 3 → sp², 4 → sp³, 5 → sp³d, 6 → sp³d². Hybridization is the same domain count you already used for VSEPR, under a different name.

try it

Domains → hybrid orbitals

sigma and pi

Every bond has one σ. Extra bonds are π.

A σ bond is head-on overlap along the line between nuclei. A π bond is side-by-side overlap of leftover unhybridized p orbitals, above and below that line. Single = 1σ. Double = 1σ + 1π. Triple = 1σ + 2π. π bonds lock rotation, which is why cis and trans fats are different molecules.

molecular orbital theory

Electrons belong to the whole molecule.

MO theory combines atomic orbitals into bonding MOs (lower energy, electron density between the nuclei) and antibonding MOs (marked *, higher energy, a node between the nuclei). Fill them like atomic orbitals: lowest first, Hund's rule, two per orbital. Then bond order = (bonding e⁻ − antibonding e⁻) ÷ 2.

remove or add an electron to make ions

	B₂	C₂	N₂	O₂	F₂
Bond order	1	2	3	2	1
Bond length (pm)	159	131	110	121	143
Bond enthalpy (kJ/mol)	290	620	941	495	155
Magnetism	para	dia	dia	para	dia

B₂ through N₂ have the π₂ₚ below the σ₂ₚ, because 2s–2p mixing pushes σ₂ₚ up in the lighter atoms. O₂ onward switch back. That ordering is why B₂ comes out paramagnetic.

practice

Hybridization and σ/π

practice

MO bond order and magnetism

engineering version

Oxygen's two unpaired electrons and light-struck milk

Lewis structures say O₂ has every electron paired. MO theory says it has two unpaired electrons in the π* orbitals, and it's right: liquid oxygen sticks between magnet poles. That unusual "triplet" state also makes ground-state O₂ slow to react directly with most organic molecules.

Light changes that. Riboflavin in milk absorbs visible light and passes the energy to O₂, flipping it into the far more reactive singlet oxygen. That oxidizes proteins and lipids into the "light-struck" or cardboard off-flavor. It's why milk and yogurt packaging blocks light, and why clear containers in a lit dairy case are a shelf-life risk.

exam traps

Common mistakes

Forgetting lone pairs when assigning hybridization. The O in water is sp³ (2 bonds + 2 lone pairs), not sp.
Counting a double bond as 2 σ. It's 1 σ + 1 π.
Not counting C–H bonds in σ totals. Every bond to H is σ.
Using the O₂ MO ordering for N₂. B₂, C₂, and N₂ use the π-below-σ order.
Getting the bond-order trend in ions backwards. Removing an antibonding electron (O₂ → O₂⁺) raises the bond order, so the bond gets shorter and stronger.