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2.3.13Chemical Bonding

MO diagrams of H₂, He₂, N₂, O₂, F₂, NO, CO — bond order, magnetism

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WHY molecular orbitals at all?

WHAT an MO is: a molecule-wide electron wavefunction built by combining atomic wavefunctions — a Linear Combination of Atomic Orbitals (LCAO).

WHY two AOs give two MOs: waves can add in phase (constructive → electron density piles up between nuclei → stabilizing) or out of phase (destructive → a node between nuclei → destabilizing). Two combinations from two inputs.

ψbonding=ψA+ψBψantibonding=ψA−ψB\psi_{\text{bonding}} = \psi_A + \psi_B \qquad \psi_{\text{antibonding}} = \psi_A - \psi_B

HOW to build any 2nd-period diagram

Order of MOs from AOs 1s,2s,2p1s, 2s, 2p:

For B₂, C₂, N₂ (Z ≤ 7) — s–p mixing pushes σ2p above π2p: σ1s<σ1s∗<σ2s<σ2s∗<π2px=π2py<σ2pz<π2px∗=π2py∗<σ2pz∗\sigma_{1s} < \sigma^*_{1s} < \sigma_{2s} < \sigma^*_{2s} < \pi_{2p_x}=\pi_{2p_y} < \sigma_{2p_z} < \pi^*_{2p_x}=\pi^*_{2p_y} < \sigma^*_{2p_z}

For O₂, F₂ (Z ≥ 8) — no significant mixing, σ2p below π2p: ⋯<σ2pz<π2px=π2py<π2px∗=π2py∗<σ2pz∗\dots < \sigma_{2p_z} < \pi_{2p_x}=\pi_{2p_y} < \pi^*_{2p_x}=\pi^*_{2p_y} < \sigma^*_{2p_z}

Figure — MO diagrams of H₂, He₂, N₂, O₂, F₂, NO, CO — bond order, magnetism

Worked cases (fill the MOs, count, decide magnetism)

Recall Feynman: explain to a 12-year-old

Imagine two magnets-on-springs (atoms) coming together. Their "clouds" can join into a shape that hugs between them (glue = bonding) or a shape with a gap in the middle that shoves them apart (anti-glue = antibonding). You have a bunch of tiny people (electrons) and you seat them lowest-chair-first, two per chair, and if two equal-height chairs are open you put one person in each before doubling up. Count how many sit in "glue" chairs minus "anti-glue" chairs, divide by two — that's how many bonds. If anyone is sitting alone (unpaired), the molecule feels a magnet.

Flashcards

Formula for bond order in MO theory?
BO=Nb−Na2BO=\dfrac{N_b-N_a}{2} (bonding minus antibonding electrons, over 2).
Why does O₂ show paramagnetism?
Its last 2 electrons singly occupy the two degenerate π*2p orbitals (Hund's rule) → 2 unpaired electrons.
Bond order and magnetism of O₂?
BO = 2; paramagnetic (2 unpaired).
Bond order of N₂ and why diamagnetic?
BO = 3; all electrons paired (π2p⁴ σ2p² full) → diamagnetic.
For which molecules is σ2p ABOVE π2p?
B₂, C₂, N₂ (Z ≤ 7) — due to s–p mixing.
For which molecules is σ2p BELOW π2p?
O₂, F₂ (Z ≥ 8) — negligible s–p mixing.
Bond order of NO and its magnetism?
BO = 2.5; paramagnetic (1 unpaired electron in π*).
Why does He₂ not exist?
Config σ1s² σ*1s²; BO = (2−2)/2 = 0, no net bond.
Bond order of F₂?
1 (single bond), diamagnetic.
CO is isoelectronic with which molecule; its BO?
With N₂ (14 e⁻); BO = 3, diamagnetic.
Bond order comparison N₂ vs O₂ vs F₂?
3 > 2 > 1 (extra electrons go into antibonding MOs, weakening the bond).
What happens to bond order going NO → NO⁺?
Increases from 2.5 to 3 (remove one antibonding π* electron).
Meaning of the asterisk (*) on an MO?
Antibonding orbital: has a node between nuclei, higher energy, destabilizing.

Connections

Concept Map

LCAO combine

in phase

out of phase

density between nuclei

node between nuclei

Z below 8 s-p mixing

Z 8 and up no mixing

Nb electrons

Na electrons

net bonds

unpaired e gives

all paired gives

Atomic Orbitals

Molecular Orbitals

Bonding MO sigma pi

Antibonding MO star

Stabilizing

Destabilizing

MO Energy Order

sigma2p above pi2p

sigma2p below pi2p

Bond Order = Nb minus Na over 2

Bond Strength

Paramagnetic

Diamagnetic

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, jab do atoms paas aate hain to unke atomic orbitals aapas me overlap karte hain. Do orbitals milke do naye molecular orbitals banate hain — ek neeche wala (bonding, jo atoms ko jodta hai) aur ek upar wala (antibonding, star wala, jo atoms ko door karta hai). Bas electrons ko lowest energy se bharo, do-do karke, aur agar do equal energy wale orbital khaali hain to Hund ke rule se pehle ek-ek karke bharo.

Do cheezein nikaalni hain. Pehli — bond order = (bonding electrons − antibonding electrons)/2. N₂ ka 3 aata hai (bahut strong triple bond), O₂ ka 2, F₂ ka sirf 1. Dhyaan rakho: jitne zyada electrons antibonding me jayenge, bond utna kamzor. Doosri — magnetism. Agar koi bhi electron akela (unpaired) baitha hai to molecule paramagnetic (magnet ki taraf khinchega), warna diamagnetic.

Sabse important trick: MO ka order sabke liye same nahi hota. B₂, C₂, N₂ (chhote atoms, Z ≤ 7) me s–p mixing ki wajah se π2p neeche, σ2p upar aata hai. Lekin O₂ aur F₂ me mixing kam ho jaati hai, to σ2p neeche, π2p upar — normal order. Galat order use kiya to O₂ ka magnetism galat aa jayega.

O₂ wala case sabse famous hai. Lewis structure batata hai sab electrons paired hain, par asal me last do electrons do alag π* orbitals me akele baithte hain (Hund) — isliye O₂ paramagnetic hai, aur liquid oxygen magnet se chipak jaata hai. Yehi MO theory ki sabse badi jeet hai. NO me 15 (odd) electrons, isliye BO = 2.5 aur ek unpaired electron — paramagnetic. CO aur N₂ isoelectronic hain (14 e⁻), dono ka BO = 3, dono diamagnetic. Exam me yahi cheezein baar-baar poochi jaati hain.

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Connections

Molecular Orbital Theory (MOT) — LCAO, bonding - antibonding orbitalsChemistry · 2.3.12Valence Bond Theory (VBT) — hybridization (sp, sp², sp³, sp³d, sp³d²)Chemistry · 2.3.10