Molecular Orbital Theory (MOT), developed by Hund and Mulliken, treats electrons as belonging to the entire molecule rather than individual atoms. Atomic orbitals combine to form molecular orbitals (MOs). Linear Combination of Atomic Orbitals (LCAO): when two AOs overlap, they form two MOs — a bonding MO (lower energy, constructive interference) and an antibonding MO (higher energy, destructive interference, marked with *). Rules for filling MOs: (1) Aufbau principle: fill lowest energy MO first. (2) Pauli exclusion: max 2 electrons per MO. (3) Hund rule: in degenerate MOs, fill one electron each before pairing. The energy order of MOs for diatomic molecules from Li₂ to N₂: σ1s < σ*1s < σ2s < σ*2s < π2p = π2p < σ2p < π*2p = π*2p < σ*2p. For O₂ and beyond: σ2p comes before π2p.

Bond order (BO) = (number of electrons in bonding MOs − number in antibonding MOs) / 2. Bond order indicates: (1) Stability: BO > 0 → stable molecule. BO = 0 → molecule does not exist. BO < 0 is not possible in practice. (2) Bond length: BO ↑ → bond length ↓. More bonding electrons pull nuclei together more tightly. (3) Bond energy: BO ↑ → bond energy ↑. Triple bonds are stronger than double bonds, which are stronger than single bonds. (4) Magnetic properties: molecules with unpaired electrons are paramagnetic; those with all electrons paired are diamagnetic. Examples: H₂ (BO=1, diamagnetic), O₂ (BO=2, paramagnetic — 2 unpaired π* electrons), N₂ (BO=3, diamagnetic), He₂ (BO=0, does not exist), He₂⁺ (BO=0.5, exists briefly).

H₂: σ1s² — BO=1, diamagnetic, stable. He₂: σ1s²σ*1s² — BO=0, does not exist. Li₂: σ1s²σ*1s²σ2s² — BO=1, diamagnetic. B₂: ...π2p¹π2p¹ — BO=1, paramagnetic (2 unpaired). C₂: ...π2p²π2p² — BO=2, diamagnetic. N₂: ...σ2p² — BO=3, diamagnetic, very stable (triple bond, 945 kJ/mol). O₂: ...π*2p¹π*2p¹ — BO=2, paramagnetic (2 unpaired electrons — explains why O₂ is attracted to a magnet). F₂: ...π*2p²π*2p² — BO=1, diamagnetic. Ne₂: BO=0, does not exist. Ions: O₂⁺ (BO=2.5), O₂⁻ (BO=1.5), N₂⁺ (BO=2.5), NO (BO=2.5). The prediction of paramagnetism of O₂ was a great triumph of MOT over VBT which incorrectly predicts O₂ to be diamagnetic.

VBT: bond forms when half-filled orbitals of two atoms overlap. Electron pair is localised between two bonded atoms. Hybridisation explains molecular geometry. Simple and intuitive. Limitation: cannot explain paramagnetism of O₂ (VBT predicts all electrons paired = diamagnetic), cannot explain fractional bond orders, fails for molecules like H₂⁺. MOT: electrons delocalized over entire molecule. Explains magnetic properties correctly. Explains bond orders including fractional ones. Predicts stability of molecular ions. Limitation: more complex, molecular orbital diagrams required. NEET requires both: VBT + hybridisation for structure/geometry; MOT for magnetic properties, bond order, stability of species. Resonance structures in VBT are an approximation of what MOT describes as electron delocalization.

VSEPR (Valence Shell Electron Pair Repulsion): electron pairs in valence shell repel each other and adopt geometry that minimises repulsion. Order of repulsion: lone pair-lone pair > lone pair-bond pair > bond pair-bond pair. This ordering explains why actual bond angles deviate from ideal. Examples: CH₄ (4 BP, 0 LP): tetrahedral, 109.5°. NH₃ (3 BP, 1 LP): trigonal pyramidal, 107° (one LP compresses angle). H₂O (2 BP, 2 LP): bent, 104.5° (two LPs compress further). PCl₅ (5 BP, 0 LP): trigonal bipyramidal. SF₆ (6 BP): octahedral. XeF₂ (2 BP, 3 LP): linear (3 LPs occupy equatorial positions in trigonal bipyramidal arrangement). XeF₄ (4 BP, 2 LP): square planar. The VSEPR model is remarkably successful at predicting geometry from Lewis structures alone, without complex quantum mechanical calculations.

sp: linear, 180°. Examples: BeCl₂, CO₂, C₂H₂ (acetylene). sp²: trigonal planar, 120°. Examples: BF₃, SO₃, C₂H₄ (ethylene), benzene. sp³: tetrahedral, 109.5°. Examples: CH₄, NH₄⁺, CCl₄, SiF₄. sp³d: trigonal bipyramidal, 90°/120°. Examples: PCl₅, SF₄, ClF₃. sp³d²: octahedral, 90°. Examples: SF₆, [Co(NH₃)₆]³⁺. sp³d³: pentagonal bipyramidal. Examples: IF₇. Hybridisation determines: molecular geometry, bond angles, existence of isomers (cis-trans), reactivity (sp³ less reactive toward electrophiles than sp²). In benzene: each C is sp² hybridised, unhybridised p orbitals form the π system (6 electrons delocalised in two ring-shaped MOs above and below the ring).

Hydrogen bond forms when H is covalently bonded to a highly electronegative atom (F, O, N) — the H becomes partially positive and is attracted to a lone pair on another electronegative atom. Intermolecular H-bonding: between different molecules. Increases boiling point, melting point, viscosity, surface tension. Examples: H₂O (boiling point 100°C vs H₂S which has higher MW but no H-bonding at −60°C), HF (boiling point 20°C), NH₃, alcohols, carboxylic acids. Intramolecular H-bonding: within same molecule. Decreases boiling point. Examples: o-nitrophenol (lower bp than p-nitrophenol), o-chlorophenol, salicylaldehyde. Special case: water has 4 H-bonds per molecule (2 as donor, 2 as acceptor) → tetrahedral network → explains anomalous expansion on freezing (ice less dense than water), high specific heat, high surface tension.

Weak intermolecular forces that hold non-polar molecules together. Three types: (1) London dispersion (induced dipole-induced dipole): present in ALL molecules. Increases with molecular size (more electrons → larger temporary dipoles). Explains why larger noble gases (Xe, Kr) have higher boiling points than smaller ones (He, Ne). (2) Dipole-dipole: between polar molecules (HCl, SO₂). Stronger than London forces at same molecular size. (3) Dipole-induced dipole (Debye forces): permanent dipole of one molecule induces dipole in another. Weakest of the three directed forces. The total van der Waals force = London + dipole-dipole + dipole-induced. In addition: hydrogen bonding is much stronger (~20 kJ/mol) compared to van der Waals (~1-5 kJ/mol) and is responsible for many unique properties of water and biological molecules (DNA double helix, protein secondary structure).