1. Formal Charge & Lewis Dot Structure Exceptions

Formal Charge (FC) on an atom in a Lewis structure: FC = [Total valence electrons in free atom, V] - [Total non-bonding lone pair electrons, L] - (1/2)[Total bonding/shared electrons, S]. Structures with lowest formal charges are most stable. Octet Rule Exceptions: (1) Incomplete Octet (electron deficient): BF3 (6 electrons around B), BeCl2 (4 electrons around Be), AlCl3 monomer; (2) Expanded Octet (hypervalent molecules with d-orbital participation): PCl5 (10 electrons around P), SF6 (12 electrons around S), IF7 (14 electrons around I); (3) Odd-Electron Molecules: NO (11 valence electrons) and NO2 (17 valence electrons).

2. Universal Hybridization State Shortcut Formula

Calculate Steric Number (H) to find hybridization in 5 seconds: H = (1/2) [V + M - C + A], where V = number of valence electrons of central atom; M = number of monovalent surrounding atoms (H, F, Cl, Br, I; divalent atoms like O and S count as 0); C = positive cationic charge; A = negative anionic charge. Hybridization mapping: H = 2 -> sp (Linear, 180°, e.g., BeCl2, CO2); H = 3 -> sp² (Trigonal planar, 120°, e.g., BF3); H = 4 -> sp³ (Tetrahedral, 109°28', e.g., CH4, NH4+); H = 5 -> sp³d (Trigonal bipyramidal, 120° & 90°, e.g., PCl5); H = 6 -> sp³d² (Octahedral, 90°, e.g., SF6); H = 7 -> sp³d³ (Pentagonal bipyramidal, 72° & 90°, e.g., IF7).

3. VSEPR Molecular Geometry & Lone Pair Distortions

Valence Shell Electron Pair Repulsion Theory: Repulsion order: Lone Pair - Lone Pair (lp-lp) > Lone Pair - Bond Pair (lp-bp) > Bond Pair - Bond Pair (bp-bp). As lone pairs increase, bond angles contract: (1) Steric 4: 0 lp -> Tetrahedral (109.5°, CH4); 1 lp -> Trigonal Pyramidal (107°, NH3); 2 lp -> Bent / V-shaped (104.5°, H2O). (2) Steric 5 (sp³d, lone pairs ALWAYS occupy equatorial positions to minimize 90° repulsions): 0 lp -> Trigonal Bipyramidal (PCl5); 1 lp -> See-Saw (SF4); 2 lp -> T-shaped (ClF3); 3 lp -> Linear (XeF2, I3-). (3) Steric 6 (sp³d²): 0 lp -> Octahedral (SF6); 1 lp -> Square Pyramidal (BrF5); 2 lp -> Square Planar (XeF4, 180° lp-lp opposition).

4. Molecular Orbital Theory (MOT) & Bond Order Calculations

Bond Order (BO): BO = (1/2) [N_b - N_a], where N_b is number of electrons in bonding molecular orbitals and N_a is in anti-bonding orbitals (*). Physical meaning: BO = 1 (single bond), BO = 2 (double bond), BO = 3 (triple bond); BO = 0 means the diatomic molecule cannot exist (e.g., He2, Be2). Greater bond order implies greater bond dissociation energy and shorter bond length. Energy Level Order: (1) For molecules with ≤ 14 electrons (B2, C2, N2): σ1s < σ*1s < σ2s < σ*2s < (π2px = π2py) < σ2pz < (π*2px = π*2py) < σ*2pz (note: π2p is lower than σ2p due to sp-mixing); (2) For molecules with > 14 electrons (O2, F2): σ1s < σ*1s < σ2s < σ*2s < σ2pz < (π2px = π2py) < (π*2px = π*2py) < σ*2pz. Magnetic property: O2 has 16 electrons, resulting in 2 unpaired electrons in degenerate π*2px and π*2py orbitals, proving its PARAMAGNETISM.

5. Dipole Moment & Molecular Polarity

Dipole Moment (μ): Measure of bond polarity: μ = charge (q) × separation distance (d). SI unit: Coulomb-meter (C·m); Practical unit: Debye (1 D ≈ 3.33564 × 10^-30 C·m). Dipole moment is a vector pointing from positive to negative center. Symmetric molecules with zero dipole moment (non-polar): CO2 (linear), BF3 (trigonal planar), CCl4 and CH4 (tetrahedral), SF6 (octahedral), XeF4 (square planar). High-frequency comparison: NH3 vs NF3: Both have trigonal pyramidal shape with 1 lone pair, but dipole moment of NH3 (1.47 D) is MUCH GREATER than NF3 (0.23 D). In NH3, orbital dipole of lone pair points in same direction as resultant N-H bond dipoles; in NF3, highly electronegative F atoms pull electron density downward, opposing the lone pair dipole.

6. Hydrogen Bonding Conditions & Anomalies

Hydrogen bond forms when hydrogen is covalently attached to small, highly electronegative elements (specifically F, O, N). Types: (1) Intermolecular H-bonding: Between different molecules (e.g., H2O, HF, NH3, p-nitrophenol), leading to anomalously high boiling points, high viscosity, and water solubility. High boiling point of H2O (100 °C) vs H2S (-60 °C) is due to extensive 3D intermolecular H-bonding; (2) Intramolecular H-bonding: Within same molecule forming a 5- or 6-membered chelate ring (e.g., o-nitrophenol, salicylaldehyde), leading to lower boiling point, lower water solubility, and high steam-volatility compared to para-isomer.