WHY add and subtract? A wavefunction is a wave. Two waves can meet in phase (crests add → constructive)
or out of phase (crest meets trough → destructive). Nature gives you both combinations, so N atomic orbitals
always produce N molecular orbitals (nothing is lost, orbitals are just re-mixed).
Imagine two speakers playing the same note. Point them at each other:
if the sound waves line up (in phase), the sound gets loud right in the middle — that "loud middle" is the bonding orbital, it's like glue holding the two speakers together.
If the waves are flipped (out of phase), they cancel in the middle and go silent there — that dead-zone is the antibonding orbital, and now the speakers actually push apart.
Electrons prefer the loud, glued spot. "Bond order" just counts how much more glue than push you have, then divides by 2 because a bond is a pair of electrons.
Linear Combination of Atomic Orbitals — MOs made by adding/subtracting atomic orbital wavefunctions.
In LCAO, why do N atomic orbitals give N molecular orbitals?
Because you take both the in-phase (add) and out-of-phase (subtract) combinations; orbitals are conserved, just recombined.
Which combination gives the bonding MO?
The in-phase, additive combination ψ_A + ψ_B (constructive interference, density between nuclei).
Why is a bonding MO lower in energy?
The +2ψ_Aψ_B term concentrates electron density between the nuclei, so electrons feel attraction from both nuclei → stabilised.
What physical feature defines an antibonding MO?
A node (zero electron density) between the nuclei, from the −2ψ_Aψ_B destructive term.
Give the bond order formula.
B.O. = (N_b − N_a)/2, where N_b/N_a = electrons in bonding/antibonding MOs.
Why divide by 2 in bond order?
Because one full covalent bond corresponds to one electron pair.
Why does He₂ not exist (via MOT)?
Config σ1s² σ1s²; N_b=2, N_a=2, so B.O.=0 → no net bonding.
Why is O₂ paramagnetic? ::: Its two highest electrons occupy the two degenerate π2p orbitals singly (Hund's rule) → 2 unpaired electrons.
Dekho, Molecular Orbital Theory ka basic funda ye hai: jab do atoms paas aate hain, toh unke atomic orbitals apni-apni "personal property" nahi rehte — wo mil ke naye orbitals bana lete hain jo poore molecule ke hote hain. Isko banate kaise hain? LCAO se, matlab atomic orbital ke wavefunctions ko jodh (add) bhi karte hain aur ghata (subtract) bhi. Add karne se bonding orbital banta hai — yaha electron density dono nuclei ke beech mein ikattha ho jaati hai, jo gum ki tarah dono ko jodh ke rakhti hai, isliye energy kam (stable). Subtract karne se antibonding orbital banta hai — yaha beech mein ek node (zero density) aa jaata hai, nuclei ek dusre ko dhakelte hain, energy zyada (unstable), star ke saath likhte hain (σ*, π*).
Bond order nikalna simple hai: B.O.=(Nb−Na)/2. Nb matlab bonding mein electrons, Na matlab antibonding mein. 2 se divide isliye karte hain kyunki ek bond = ek electron pair. Agar B.O. = 0 aaye (jaise He₂ mein) toh molecule exist hi nahi karta — ye MOT ki sabse badi jeet hai, kyunki VBT isko theek se explain nahi kar paata.
Sabse important yaad rakhne wali baat: orbital ka order har jagah same nahi hota. B₂, C₂, N₂ (Z ≤ 7) tak s-p mixing hoti hai, isliye π2p, σ2pz se neeche aa jaata hai. Lekin O₂, F₂ mein σ2pz neeche aa jaata hai. Isi wajah se O₂ ke last do electrons alag-alag π* orbitals mein single-single baithte hain (Hund's rule) — do unpaired electrons — isliye O₂ paramagnetic hai. Exam mein ye O₂ wala point aur B₂/C₂ paramagnetic hona bahut poochha jaata hai, toh order flip zaroor yaad rakhna!
