📊 MO diagrammasi — oktaedrik kompleks
Energiya diagrammasi • SALC • π-ta'sir • Sekulyar tenglama • Δ₀ • HOMO/LUMO • OTM
📋 MO diagrammasi — oktaedrik kompleks
MO diagrammasi — metall va ligand orbitallarining simmetriya bo'yicha o'zaro ta'sirini ko'rsatadi. Oktaedrik (O_h) simmetriyada orbitallar 4 xil simmetriya turiga ajraladi: a₁g, t₁u, e_g, t₂g. MO diagrammasi spektr, magnetizm va Δ₀ ni tushuntiradi.
🎯 Maqsad: MO energiya diagrammasi, simmetriya tahlili, SALC va sekulyar tenglamani o'zlashtirish.
⏱️ Vaqt: ~3 soat
📚 Manba: Cotton — Chemical Applications of Group Theory; Albright — Orbital Interactions
"MO diagrammasi — kompleksning kvant portreti!"
📈 MO energiya diagrammasi — interaktiv Canvas
MO diagrammasi tahlili:
• Bog'lovchi MO: a₁g + e_g + t₁u (6 ta MO, 12 ta e⁻)
• Bog'lamaydigan MO: t₂g (3 ta MO, 6 ta e⁻)
• Bo'shashtiruvchi MO: e_g* + a₁g* + t₁u* (6 ta MO, bo'sh)
• Δ₀ = E(e_g*) − E(t₂g) = normal
Jami: 18 e⁻ | ✅ 18 e⁻ → barqaror!
🔬 Simmetriya bo'yicha MO tahlili
| IRREPS | Metall AO | Ligand SALC | MO | Energiya |
|---|---|---|---|---|
| A₁g | s | σ₁ = (1/√6)(L₁+L₂+L₃+L₄+L₅+L₆) | σ(A₁g) + σ*(A₁g) | Eng past / Yuqori |
| E_g | d_z², d_x²−y² | σ₂ = (1/2)(L₁−L₂), σ₃ = (1/2)(L₃−L₄) | σ(E_g) + σ*(E_g*) | O'rtacha / Yuqori |
| T₁u | p_x, p_y, p_z | σ₄ = (1/√2)(L₅−L₆) va b. | σ(T₁u) + σ*(T₁u) | Past / Yuqori |
| T₂g | d_xy, d_xz, d_yz | — (mos emas) | Faqat n (bog'lamaydigan) | Oraliq |
💡
4 xil simmetriya. t₂g — faqat metall d-orbitallari. Δ₀ = 10 Dq.
📊 MO energiya sathlari — interaktiv tahlil
🔽 Bog'lovchi MO
Metalldan energiyasi past. Ligandlarning σ-elektronlari shu yerga joylashadi. 6 ta σ-bog' hosil qiladi.
MO soni
6 ta
Elektronlar
12 ta e⁻ (ligandlardan)
Simmetriya (a₁g + e_g + t₁u):
• a₁g: s + (L₁+L₂+L₃+L₄+L₅+L₆) — to'liq simmetrik
• e_g: d_z²,d_x²−y² + ligand — 2 ta degenerat MO
• t₁u: p_x,p_y,p_z + ligand — 3 ta degenerat MO
🔄 π-bog'lanishning MO diagrammasiga ta'siri
π-akseptor mexanizmi
Metall t₂g (to'lgan) → ligand π* (bo'sh). Orqaga donorlik t₂g ni stabillashadi → Δ₀ ortadi.
Δ₀ ga ta'siri:
Δ₀ = 25000-36000 cm⁻¹ → kuchli maydon → LS
📐 MO nazariyasining matematik asoslari
Sekulyar tenglama — MO energiyasi:
det|H − E·S| = 0
Ikki atomli sistema (A va B):
H{AA} = H{BB} = α (koulomb integrali, ~AO energiyasi)
H{AB} = H{BA} = β (rezonans integrali, ~qoplanish)
S{AA} = S{BB} = 1, S{AB} = 0 (ortogonal)
Yechim: E = α ± β
E_bog' = α + β (past), E_bo'sh = α − β (yuqori)
α = ∫ ψ_A·H·ψ_A dτ (manfiy, ~−10 eV)
β = ∫ ψ_A·H·ψ_B dτ (manfiy, ~−1 to −3 eV)
💡 |β| qancha katta → qoplanish shuncha kuchli → bog' mustahkam
⚡ Δ₀ — simmetriya asosida izohlash
O_h — d-orbital ajralishi
Tushuntirish:
6 ta ligand. t₂g pastda, e_g* yuqorida. π-akseptor → Δ₀↑, π-donor → Δ₀↓.
⚡ Δ₀ ni o'zgartiruvchi omillar:
1) Geometriya (O_h > T_d) | 2) Ligand (π-akseptor > σ-donor > π-donor) | 3) Metall (3d < 4d < 5d)
🧪 Amaliy misollar — MO diagrammasi bo'yicha tahlil
[Co(NH₃)₆]³⁺ (O_h)
MO tahlili:
18 e⁻. Kuchli maydon (NH₃). d-d o'tish: ¹A₁g → ¹T₁g (sariq rang).
d-d o'tish energiyasi = Δ₀ = 23000 cm⁻¹ → λ = 435 nm
📝 Bilim tekshirish — 1/10
Oktaedrik MO diagrammasida qaysi metall orbitallari bog'lamaydigan (t₂g) bo'lib qoladi?
✅ Asosiy xulosalar
- MO diagrammasi — metall + ligand orbitallarining simmetriya bo'yicha o'zaro ta'siri (O_h: a₁g, e_g, t₁u, t₂g)
- t₂g (d_xy, d_xz, d_yz) — bog'lamaydigan MO, ligand σ bilan mos kelmaydi. Faqat metall d-elektronlarini saqlaydi
- 6 ta bog'lovchi MO (a₁g+e_g+t₁u) = 12 ta e⁻ (ligandlardan). 6 ta bo'shashtiruvchi (e_g*+a₁g*+t₁u*) = odatda bo'sh
- Δ₀ = E(e_g*) − E(t₂g). π-akseptor (CO) → t₂g↓ → Δ₀↑. π-donor (Cl⁻) → t₂g↑ → Δ₀↓
- Sekulyar tenglama: det|H − E·S| = 0 → E = α ± β. α — koulomb, β — rezonans integrali
- SALC: P^Γ = (d_Γ/h)·Σχ_Γ(R)·R. 6 ta σ-SALC → A₁g + E_g + T₁u
- Δ₀ ga ta'sir: Geometriya (O_h > T_d) | Ligand (π-akseptor > σ-donor > π-donor) | Metall (5d > 4d > 3d)
📚 Manba: F.A. Cotton — Chemical Applications of Group Theory; T.A. Albright — Orbital Interactions in Chemistry
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