Molecular Orbital Theory (MOT) for Diatomics Why MOT matters (the O2 story) Valence Bond Theory (VBT) explains many bonds but fails for oxygen’s magnetism. Liquid dioxygen (O2, SMILES: O=O) is attracted by a magnet — it is paramagnetic. Molecular Orbital Theory (MOT) nails this because it lets electrons spread over the whole molecule in molecular orbitals (MOs), predicting unpaired electrons in O2. That’s why MOT is a high-yield NEET topic: it predicts bond order, stability, and magnetic nature directly from electron filling. Paramagnetism of liquid O2: unpaired electrons make it attracted to a magnet — a key success of MOT. clinical O2 paramagnetism helps in medical imaging. MRI signals differ for oxygenated vs deoxygenated blood because dissolved O2 has unpaired electrons. Oxygen sensors and hyperbaric oxygen therapy design also lean on this MOT insight. From atomic orbitals to molecular orbitals (LCAO idea) When two atoms approach, their atomic orbitals (AOs) on different atoms combine linearly to form new orbitals that belong to the whole molecule — molecular orbitals (MOs). Think of two water waves overlapping: where crests meet, the wave grows (constructive); where crest meets trough, they cancel (destructive). Similarly, AO overlap can produce a lower-energy bonding MO (electron density between nuclei) and a higher-energy antibonding MO (a node between nuclei). Constructive combination: electron density increases between nuclei. LCAO for bonding MO Destructive combination: a node appears between nuclei (destabilizing). LCAO for antibonding MO LCAO of two 1s AOs: constructive overlap gives σ1s (bonding), destructive overlap gives σ 1s (antibonding). Bonding MO (σ, π): lower energy; electron density between nuclei; stabilizes. Antibonding MO (σ , π ): higher energy; node between nuclei; destabilizes. σ-MO: head-on overlap (s–s, s–p, or p–p along internuclear axis). π-MO: sidewise overlap of p orbitals (above–below or front–back of the axis). Key MOT terms (simple view) Filling electrons and computing bond order Electrons fill MOs in increasing energy (Aufbau), with max two per MO (Pauli), and they occupy degenerate MOs singly before pairing (Hund). The stability of a molecule follows from bond order — how many net bonds are formed. Bond order N b = electrons in bonding MOs; N a = electrons in antibonding MOs. If BO > 0, the species can exist; larger BO means stronger/shorter bond. remember Paramagnetic if any unpaired electrons remain in the MO diagram; diamagnetic if all electrons are paired. Energy ordering of MOs: the s–p mixing rule For homonuclear diatomics, the 1s and 2s pairs come first (σ1s, σ 1s, σ2s, σ 2s). For the 2p set, the order depends on s–p mixing (interaction between σ2s and σ2p). For Li2 through N2, s–p mixing is significant, pushing the σ2p (along the axis) above the π2p pair. For O2 and F2 (and Ne2), s–p mixing is negligible, so σ2p lies below the π2p pair. Li2 to N2 (s–p mixing present) … σ2s, σ 2s, π2p x = π2p y, σ2p z, π 2p x = π 2p y, σ 2p z O2, F2, Ne2 (negligible s–p mixing) … σ2s, σ 2s, σ2p z, π2p x = π2p y, π 2p x = π 2p y, σ 2p z Standard MO energy order (valence shells shown) Set Molecules Order of 2p MOs (lowest → highest) Side-by-side MO energy diagrams: Left for B2–N2 showing π2p below σ2p; Right for O2–F2 showing σ2p below π2p. Include labeled energy axis, σ/π and σ /π levels, thin arrows indicating s–p mixing on left. Clean 2D vector, textbook style, no in-image text beyond σ/π labels and energy. 2026-05-26T17:04:20.317Z Visual comparison of MO energy ordering with and without s–p mixing. gpt-image-2 Before O, π wins; After O, σ wins. (Up to N2: π2p below σ2p. From O2 onward: σ2p below π2p.) Quick wins: H2 and He2 Dihydrogen (H2, SMILES: [H][H]) forms by σ 1s 2 : N b = 2, N a = 0 → BO = 1 (stable, diamagnetic). For He2, two He atoms bring 4 electrons into 1s MOs: σ 1s 2 σ 1s 2 , so N b = N a = 2 → BO = 0 (does not exist as a stable molecule). H2 σ 1s 2 Diamagnetic Exists (strong single bond) He2 σ 1s 2 σ 1s 2 Diamagnetic Does not exist (BO = 0) Species MO configuration BO Magnetism Stability H2 vs He2 (1s-only picture) s-block diatomics: Li2 and Be2 For heavier diatomics, 1s AOs are core and do not contribute to bonding. In Li2, the two valence electrons fill σ 2s 2 → BO = 1 (exists). In Be2, four valence electrons give σ 2s 2 σ 2s 2 → BO = 0 (does not exist). Li2: σ 2s 2 → BO = 1 → diamagnetic → exists. Be2: σ 2s 2 σ 2s 2 → BO = 0 → diamagnetic → does not exist. The s–p mixing zone up to N2 Dinitrogen (N2, SMILES: N N) follows the Li2–N2 order with π2p x = π2p y below σ2p z. Valence filling: σ 2s 2 σ 2s 2 (π2p x) 2 (π2p y) 2 σ2p z 2. Bonding electrons = 8; antibonding = 2 → BO = 3. All electrons are paired → diamagnetic. This matches its very strong, short N≡N triple bond. MO diagram for N2 showing π2p below σ2p (all electrons paired; BO = 3). gpt-image-2 2026-05-26T17:04:20.370Z Clean MO diagram for N2: show σ2s, σ 2s, π2p x=π2p y (filled pairs), σ2p z (filled pair). Indicate energy axis and pairing dots. Vector, black/blue lines, red arrows for electron spins, no extra text. neet-alert Ordering trap: Up to N2, π2p comes before σ2p; from O2 onward, σ2p comes before π2p. Examiners love flipping this. O2, F2, Ne2 — MOT explains magnetism and stability MO energy-level diagram for O2: two unpaired electrons in π orbitals → paramagnetism; BO = 2. For dioxygen (O2, O=O), negligible s–p mixing places σ2p z below π2p. Electron filling leaves two unpaired electrons in π 2p, so O2 is paramagnetic with BO = 2. Difluorine (F2, SMILES: F-F) fills both π 2p orbitals, giving BO = 1 and diamagnetism. Dineon (Ne2) would have equal bonding and antibonding electrons in valence MOs → BO = 0, so it does not exist as a stable molecule. Paramagnetic O2 is visibly attracted by a magnet — a classic demonstration in labs and industry. H2 (dihydrogen, [H][H]) σ 1s 2 Diamagnetic Exists He2 (dihelium, [He][He]) σ 1s 2 σ 1s 2 Diamagnetic Does not exist Li2 (dilithium) σ 2s 2 Diamagnetic Exists Be2 (beryllium dimer) σ 2s 2 σ 2s 2 Diamagnetic Does not exist N2 (dinitrogen, N N) σ 2s 2 σ 2s 2 (π2p x) 2 (π2p y) 2 σ2p z 2 Diamagnetic Exists (very strong bond) O2 (dioxygen, O=O) σ 2s 2 σ 2s 2 σ2p z 2 (π2p x) 2 (π2p y) 2 (π 2p x) 1 (π 2p y) 1 Paramagnetic Exists F2 (difluorine, F-F) σ 2s 2 σ 2s 2 σ2p z 2 (π2p x) 2 (π2p y) 2 (π 2p x) 2 (π 2p y) 2 Diamagnetic Exists Ne2 (dineon) … plus σ 2p z 2 (all filled) Diamagnetic Does not exist Molecule MO configuration (valence) Bond order Magnetic nature Stability Homonuclear diatomics (valence MO picture; 1s cores omitted except H2/He2) High-yield ions: H2+, He2+, O2−, O2²− Exam alerts love charged species. Add or remove electrons carefully in the MO diagram and recompute BO. H2+ (σ 1s 1 ): BO = (1−0)/2 = 0.5 → paramagnetic → exists (gas-phase). He2+ (σ 1s 2 σ 1s 1 ): BO = (2−1)/2 = 0.5 → paramagnetic → detectable (mass spectrometry). O2− (superoxide): add 1 e− to O2 → one π becomes paired; still 1 unpaired → BO = 1.5 → paramagnetic. O2²− (peroxide): add 2 e− to O2 → both π fully paired → BO = 1 → diamagnetic. tip Count only valence electrons for second-period diatomics (omit 1s cores). Use the correct 2p order: up to N2 use π before σ; from O2 onward, σ before π. Heteronuclear diatomics: CO and NO When atoms differ, their AO energies differ. The lower-energy AO (more electronegative atom) contributes more to the lower-energy MOs; the higher-energy AO contributes more to higher-energy MOs. Still, we can fill MOs and use BO as usual. • Carbon monoxide (CO, SMILES: [C-] [O+]) has 10 valence electrons overall and is diamagnetic with BO = 3 (very strong bond). • Nitric oxide (NO, SMILES: [N]=O) has 11 valence electrons; one unpaired electron remains → paramagnetic with BO = 2.5 (half-integer values are possible). Schematic heteronuclear MO diagram: unequal AO energies mix to form polarized MOs (example: CO/NO). gpt-image-2 Generic heteronuclear MO energy diagram: left atom lower (O), right atom higher (C/N). Show bonding MOs skewed toward the lower-energy side. Indicate HOMO and LUMO. Minimalist vector, clear σ/π labels, no text paragraphs inside the image. 2026-05-26T17:04:20.409Z HOMO–LUMO: the highest occupied MO and the lowest unoccupied MO. Many photochemical and UV–Vis transitions are HOMO → LUMO jumps. remember Putting it together — expected NEET tasks Sketch/follow an MO diagram and fill electrons using Aufbau + Hund + Pauli. Compute bond order quickly with BO = ( N b − N a )/2. Predict stability (BO > 0) and magnetic behavior (unpaired → paramagnetic). Use the correct 2p ordering set (s–p mixing rule). Handle ions (add/remove electrons) and heteronuclear pairs (CO, NO). Molecular orbitals are just atomic orbitals drawn on top of each other. MOs are new orbitals formed by linear combination of AOs; electron density redistributes over the entire molecule (delocalized), not a simple superposition picture. Overlap creates both bonding and antibonding MOs. Electrons in antibonding MOs reduce bond order and can prevent bonding (e.g., He2 with σ 1s 2 ). Antibonding occupancy also affects magnetism. Any AO overlap makes bonding; antibonding MOs are basically empty so they don’t matter. neet-alert O2 paramagnetism is the classic MOT–VBT comparison. VBT cannot explain it; MOT does via two unpaired electrons in π orbitals. Molecular orbital (MO) Orbital that belongs to the entire molecule, formed by linear combination of atomic orbitals (LCAO). Delocalized electron density. MO Lower-energy MO with electron density between nuclei; occupancy increases stability. Bonding orbital Higher-energy MO with a node between nuclei (marked with ); occupancy decreases stability. Antibonding orbital MO formed by head-on overlap along internuclear axis; electron density symmetric about the axis. Sigma MO (σ) MO formed by sidewise overlap of p orbitals; electron density above–below or front–back of axis. Pi MO (π) Linear Combination of Atomic Orbitals — the method to construct MOs from AOs. LCAO Half the difference between electrons in bonding and antibonding MOs: ( N b − N a )/2. Bond order (BO) Attracted by magnetic field; arises from one or more unpaired electrons. Paramagnetic Weakly repelled by magnetic field; all electrons paired. Diamagnetic Interaction of σ2s and σ2p that alters 2p-level ordering (π2p below σ2p up to N2). s–p mixing Highest Occupied Molecular Orbital; electrons here are most easily excited. HOMO Lowest Unoccupied Molecular Orbital; primary target of electronic excitation. LUMO Glossary — MOT essentials remember Industry connect: Liquid O2 is paramagnetic — it’s trapped by strong magnets during liquefaction and handling. MOT explains this cleanly.