2.3.12
Intuition Bada picture (MOT kyun exist karta hai)Valence Bond Theory kehti hai ki ek bond do atoms hain jo apne khud ke atomic orbitals mein electrons share karte hain.
Ye kaam karta hai, lekin ye fail ho jaata hai simple facts explain karne mein jaise: O₂ paramagnetic kyun hai (usmein unpaired electrons hain)?
MOT isse fix karta hai ye kehke: jab atoms paas aate hain, unke atomic orbitals apni personal property rehna band kar dete hain aur
naye orbitals mein merge ho jaate hain jo poore molecule ki property hote hain. Electrons phir in molecular orbitals ko fill karte hain
bilkul waisi tarah jaise atomic orbitals fill hote hain (Aufbau, Pauli, Hund). Molecule ko ek "bade atom" ki tarah treat kiya jaata hai.
Definition LCAO (Linear Combination of Atomic Orbitals)Ek molecular orbital bonding atoms ke atomic orbital wavefunctions ko add aur subtract karke banaya jaata hai.
Do atoms A aur B ke saath atomic orbitals ψ A ψ B ψ M O = c A ψ A ± c B ψ B
Add aur subtract kyun? Ek wavefunction ek wave hai. Do waves in phase milke milti hain (crests add ho jaate hain → constructive)
ya out of phase (crest trough se milti hai → destructive). Nature tumhe dono combinations deta hai, isliye N atomic orbitals
hamesha N molecular orbitals produce karte hain (kuch kho nahi jaata, orbitals sirf re-mix ho jaate hain).
Intuition Bonding lower kyun hai aur antibonding higher kyun hai (Feynman-level)Electrons do positive nuclei ke beech mein baithna chahte hain — wahan ye dono taraf se pull feel karte hain → stable, low energy.
Antibonding orbital mein electrons ko beech se door rakha jaata hai (node), isliye bare nuclei ek doosre ko repel karte hain → unstable, high energy.
Key symmetry: antibonding orbital utna thoda zyada raise hota hai jitna bonding wala lower hota hai.
Atomic orbitals ke acchi tarah combine karne ke liye unhe chahiye:
Comparable energies Significant overlap Molecular (internuclear) axis ke baare mein same symmetry
Worked example Symmetry kyun matter karti haiEk 2 p z along point kar raha hai doosre 2 p z σ bond banata hai.
Ek 2 p x 2 p x sideways overlap karta hai → ek π bond banata hai.
Lekin 2 p z 2 p x net zero overlap → no bond .
Ye step kyun? Overlap integral S = ∫ ψ A ψ B d τ
σ (sigma) orbital:z z z π (pi) orbital:x x y y
Antibonding versions par ek star lagaya jaata hai: σ ∗ π ∗
Worked example H₂ (2 electrons)Fill: σ 1 s 2 N b = 2 , N a = 0 ⇒ B.O. = 2 2 − 0 = 1 Kyun? Dono electrons bonding mein → stable single bond. Diamagnetic (sab paired). ✅ reality se match karta hai.
Worked example He₂ (4 electrons)Fill: σ 1 s 2 σ 1 s ∗ 2 N b = 2 , N a = 2 ⇒ B.O. = 2 2 − 2 = 0 Ye step kyun? Antibonding pair bonding pair ko cancel kar deta hai → koi net bond nahi → He₂ exist nahi karta . ✅ Ye MOT ki triumph hai — VBT yahan struggle karta hai.
Worked example O₂ (16 electrons) — star resultOrder (O, F ke liye): σ 1 s 2 σ 1 s ∗ 2 σ 2 s 2 σ 2 s ∗ 2 σ 2 p z 2 π 2 p x 2 π 2 p y 2 π 2 p x ∗ 1 π 2 p y ∗ 1 N b = 10 , N a = 6 ⇒ B.O. = 2 10 − 6 = 2 Ye step kyun? Last 2 electrons do degenerate π ∗ ek ek jaate hain (Hund's rule) → 2 unpaired electrons → paramagnetic! ✅ MOT ye predict karta hai; VBT (O=O) galat tarah diamagnetic predict karta hai.
Common mistake Steel-man: "O₂ aur aage ke liye, σ2p ko π2p ke neeche rakho, toh sab kuch ek hi order mein hai."Ye sahi kyun lagta hai: σ overlap (head-on) dikhta hai π (sideways) se stronger, isliye aap expect karte ho ki σ 2 p z Fix: B₂, C₂, N₂ (Z ≤ 7) ke liye, 2s aur 2p orbitals energy mein close hote hain → ye mix karte hain (s-p mixing) , jo σ 2 p z π 2 p
B₂, C₂, N₂: π 2 p < σ 2 p z O₂, F₂, Ne₂: σ 2 p z < π 2 p paramagnetic hain.
Common mistake Steel-man: "Antibonding electrons matter nahi karte, sirf bonding wale count karo."Ye sahi kyun lagta hai: "Antibonding" sunne mein lagta hai "kuch nahi karta."
Fix: Antibonding electrons actively destabilise karte hain — isliye hi ye B.O. mein subtract hote hain. Inhe ignore karne se predict hota hai ki He₂ exist karta hai. Hamesha inhe subtract karo.
Recall 12-saal ke bacche ko explain karo (click to reveal)Socho do speakers ek hi note baja rahe hain. Unhe ek doosre ki taraf point karo:
agar sound waves line up kar jaayein (in phase), toh awaaz bilkul beech mein loud ho jaati hai — wo "loud middle" bonding orbital hai, ye do speakers ko saath pakde rehne wale glue jaisi hai.
Agar waves ulti ho jaayein (out of phase), ye beech mein cancel ho jaati hain aur wahan silent ho jaati hain — wo dead-zone antibonding orbital hai, aur ab speakers actually alag ho jaate hain.
Electrons loud, glued spot prefer karte hain. "Bond order" sirf count karta hai ki kitna zyada glue hai push ke comparison mein, phir 2 se divide karta hai kyunki ek bond electrons ki ek pair hai.
Mnemonic Sab kuch yaad rakhna"BOND = Between; ANTI = Away."
Bonding → density nuclei ke B eech mein (koi node nahi). Antibonding → density A way push ho jaati hai (ek node hai ★).
Orbital order ke liye: "Nitrogen aur neeche flip karo" → N₂ tak, π pehle aata hai; O₂ se aage, σ pehle aata hai.
LCAO ka full form kya hai? Linear Combination of Atomic Orbitals — MOs atomic orbital wavefunctions ko add/subtract karke banate hain.
LCAO mein N atomic orbitals N molecular orbitals kyun dete hain? Kyunki tum dono in-phase (add) aur out-of-phase (subtract) combinations lete ho; orbitals conserved hote hain, sirf recombine hote hain.
Bonding MO kaun sa combination deta hai? In-phase, additive combination ψ_A + ψ_B (constructive interference, nuclei ke beech density).
Bonding MO energy mein lower kyun hota hai? +2ψ_Aψ_B term electron density ko nuclei ke beech concentrate karta hai, toh electrons dono nuclei se attraction feel karte hain → stabilised.
Antibonding MO ki defining physical feature kya hai? Nuclei ke beech ek node (zero electron density), −2ψ_Aψ_B destructive term se.
Bond order formula do. B.O. = (N_b − N_a)/2, jahaan N_b/N_a = bonding/antibonding MOs mein electrons.
Bond order mein 2 se divide kyun karte hain? Kyunki ek full covalent bond ek electron pair ke corresponding hota hai.
He₂ exist kyun nahi karta (MOT ke zariye)? Config σ1s² σ1s²; N_b=2, N_a=2, toh B.O.=0 → koi net bonding nahi.
O₂ paramagnetic kyun hai? ::: Iske do highest electrons do degenerate π 2p orbitals mein singly occupy karte hain (Hund's rule) → 2 unpaired electrons.
B₂, C₂, N₂ ke liye MO energy order kya hai? σ1s < σ1s < σ2s < σ 2s < π2p (x,y) < σ2pz < π2p < σ 2pz (s-p mixing ki wajah se π, σ2pz ke neeche).
O₂, F₂ ke liye MO order kya hai? Same hai lekin σ2pz π2p ke NEECHE aa jaata hai (significant s-p mixing nahi hoti).
Effective LCAO overlap ke liye teen conditions? Comparable orbital energies, significant spatial overlap, aur internuclear axis ke baare mein same symmetry.
σ aur π MOs mein kya difference hai? σ = internuclear axis ke baare mein symmetric (head-on overlap); π = axis containing ek nodal plane hai (sideways overlap).
Antibonding raise hota hai ya bonding lower? Antibonding MO thoda zyada raise hota hai jitna bonding MO lower hota hai.
Valence Bond Theory — MOT ka rival; VBT O₂ paramagnetism par fail karta hai jise MOT explain karta hai.Atomic Orbitals and Quantum Numbers — LCAO mein ψ_A, ψ_B inputs.Aufbau Principle, Pauli Exclusion, Hund's Rule — MOs fill karne ke liye use hote hain.Sigma and Pi Bonds — overlap geometry jo σ vs π MOs determine karti hai.Bond Order, Bond Length and Bond Energy — B.O. length se inversely aur strength se directly correlate karta hai.Paramagnetism and Diamagnetism — MOs mein unpaired electrons se decide hota hai.
O2 paramagnetism explain karne mein fail
+2 psiA psiB piles density between nuclei
comparable energy, overlap, same symmetry
electrons fill via Aufbau, Pauli, Hund
