Bonding

• Bonding happens in the outermost e⁻ shell.
• First 3 quantum numbers (n, l, mₗ) describe size, shape, number, and orientation of atomic orbitals.

Principal Quantum Number (n)

• Corresponds to energy level of an e⁻ → basically the size of the orbital.
• Smaller n → closer to nucleus → lower energy.
• $n = 1 \text{ to } \infty$ (MCAT: up to 7)

Azimuthal Quantum Number (l)

• Describes subshell shape.
• $l = 0 \text{ to } n - 1$
• Subshells:
  • $l = 0 → s$
  • $l = 1 → p$
  • $l = 2 → d$
  • $l = 3 → f$
• Higher l = higher energy.

Magnetic Quantum Number (mₗ)

• Ranges from $-l \text{ to } +l$.
• For l = 2 (d subshell) → $m_l = -2, -1, 0, +1, +2$ (each with ± spin → 10 combinations)

Orbital Shapes

• s orbital: spherical + symmetric around nucleus.
• p orbitals: two-lobed dumbbells; node at nucleus; oriented along x, y, z.
  • 3 total: $m_l = -1, 0, +1$
• d orbitals: 4 clover-shaped + 1 donut-shaped.

Spin Quantum Number (mₛ)

• Values: $+ \tfrac{1}{2} \text{ or } - \tfrac{1}{2}$.
• Each orbital holds 2 e⁻.

• Molecular orbitals form by adding or subtracting atomic orbital wave functions.
• Bonding orbital: formed when signs match → low energy.
• Antibonding orbital: signs opposite → high energy.

Sigma (σ) Bonds

• Formed from head-to-head or tail-to-tail overlap.
• All single bonds are σ bonds.

Pi (π) Bonds

• Formed from side-by-side overlap of p orbitals.
• A double bond = 1 σ + 1 π.
• A triple bond = 1 σ + 2 π.

Bond Rotation + Length

• π bonds restrict rotation.
• More bonds = shorter + stronger overall bond.
• σ bonds stronger than individual π bonds because s orbitals overlap more effectively.
• Breaking π bonds (but keeping σ) is common in orgo.

Extra notes

• Proteins have limited rotation due to resonance in amide bonds.
• π bond cannot exist alone—needs σ bond to align p orbitals.

sp³ Hybridization

• 1 s + 3 p orbitals.
• Tetrahedral geometry.
• No unhybridized p orbitals → no π bonds.
• Character: 25% s / 75% p.

  

sp² Hybridization

• 1 s + 2 p orbitals.
• Seen in alkenes.
• 120° spacing (trigonal planar).
• In ethene: 2 orbitals → C–H, 1 orbital → C=C σ bond.

  

sp Hybridization

• 1 s + 1 p → 2 sp orbitals; 2 p orbitals remain for π bonds.
• Linear geometry (180°).
• Used for triple bonds or 2 double bonds.
• Example: BeH₂ is sp-hybridized.

  

Resonance

• Delocalization of e⁻ in conjugated systems (alternating single/multiple bonds).
• Needs unhybridized p orbitals aligned in backbone.
• Resonance hybrid = real structure.
• More stable structures contribute more to hybrid.