📊 MO diagramma — 3D vizualizatsiya
Three.js | 6 geometriya | IRREPS tahlili | Xarakterlar jadvali | SALC | OTM
📋 MO diagramma — 3D interaktiv model
Three.js (WebGL) asosidagi 3D model 6 xil geometriya (Oₕ, T_d, D₄h, D₃h, C₄v, C₂v) uchun MO energiya diagrammasini interaktiv ko'rsatadi. Model uch qismdan iborat: metall AO (chap), MO sathlari (markaz), ligandlar (o'ng).Sariq strelka = Δ₀ = E(e_g*) − E(t₂g).
🎯 Maqsad: 6 geometriya, IRREPS tahlili va sekulyar tenglama orqali MO nazariyasini mustahkamlash.
⏱ Vaqt: ~3 soat
📚 Manba: F.A. Cotton — Chemical Applications of Group Theory | Three.js
det|H − E·S| = 0 → E = α ± β
🎯 3D MO diagramma — Three.js interaktiv model
Eng yuqori simmetriya. t₂g orbitallari ligand σ bilan mos kelmaydi → bog'lanmaydi.
🔬 Simmetriya va IRREPS tahlili
| IRREPS | dim | Bazis funksiya | Ligand SALC | MO turi | Energiya |
|---|---|---|---|---|---|
| A₁g | 1 | s, x²+y²+z² | σ₁+σ₂+σ₃+σ₄+σ₅+σ₆ | σ bog'lovchi | Eng past |
| A₂g | 1 | — | — | — | — |
| E_g | 2 | (2z²−x²−y², x²−y²) | σ₁−σ₂, σ₃−σ₄ | σ bog'lovchi | O'rtacha |
| T₁g | 3 | (R_x, R_y, R_z) | — | — | — |
| T₂g | 3 | (xy, xz, yz) | — (mos emas) | n (bog'lamaydigan) | Oraliq |
| T₁u | 3 | (x, y, z) | σ₅−σ₆ va b. | σ bog'lovchi | Past |
💡
6 ta σ-SALC: A₁g + E_g + T₁u. t₂g orbitallari (d_xy, d_xz, d_yz) ligand σ bilan mos kelmaydi.
📐 MO matematik asoslari
Sekulyar tenglama (MO energiyasini hisoblash):
det |H − E·S| = 0
Ikki atomli sistema (A va B) uchun 2 × 2 determinant:
| (α − E) β | = (α − E)² − β² = 0
| β (α − E) |
Yechimlar:
E₁ = α + β → bog'lovchi MO (energiya past)
E₂ = α − β → bo'shashtiruvchi MO (energiya yuqori)
α = ∫ ψ_A* · H · ψ_A dτ — koulomb integrali (~−10 eV)
β = ∫ ψ_A* · H · ψ_B dτ — rezonans integrali (~−1 to −3 eV)
|β| ∝ S (qoplanish) — katta β → kuchli bog'
📜 Xarakterlar jadvali
| Oₕ | E | 8C₃ | 6C₂ | 6C₄ | 3C₂′ | i | 6S₄ | 8S₆ | 3σₕ | 6σ_d | Bazis |
|---|---|---|---|---|---|---|---|---|---|---|---|
| A₁g | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | x²+y²+z² |
| A₂g | 1 | 1 | −1 | −1 | 1 | 1 | 1 | −1 | 1 | −1 | — |
| E_g | 2 | −1 | 0 | 0 | 2 | 2 | 0 | −1 | 2 | 0 | (2z²−x²−y², x²−y²) |
| T₁g | 3 | 0 | −1 | 1 | −1 | 3 | 1 | 0 | −1 | −1 | (R_x, R_y, R_z) |
| T₂g | 3 | 0 | 1 | −1 | −1 | 3 | −1 | 0 | −1 | 1 | (xy, xz, yz) |
| T₁u | 3 | 0 | −1 | 1 | −1 | −3 | −1 | 0 | 1 | 1 | (x, y, z) |
💡
Γ_dipol = T₁u (IQ). Γ_qutbl = A₁g + E_g + T₂g (Raman).
📊 Bog' tartibi (BO) va MO konfiguratsiyasi
[Co(NH₃)₆]³⁺ (Oₕ)
MO konfiguratsiyasi:
HOMO: t₂g⁶
Elektron konfiguratsiya: d⁶ LS
Barqarorlik: ✅ Barqaror
📊 Geometriyalarni Δ₀ va d-ajralish bo'yicha taqqoslash
| Geometriya | h | KS | d-ajralish | Δ₀ (cm⁻¹) | Nisbiy |
|---|---|---|---|---|---|
| Oₕ — Oktaedrik | 48 | 6 | t₂g (3) + e_g* (2) | 10400−35000 | 10 Dq |
| T_d — Tetraedrik | 24 | 4 | e (2) + t₂ (3) — teskari | 3000−8000 | 0.44Δ₀(Oh) |
| D₄h — Kv. planar | 16 | 4 | b₂g + e_g + a₁g + b₁g | 15000−25000 | ~1.7Δ₀(Oh) |
| D₃h — Trig. bipir. | 12 | 5 | e′ + e″ (2+2) | 8000−15000 | ~0.7Δ₀(Oh) |
| C₄v — Kv. piramida | 8 | 5 | b₂ + e + a₁ + b₁ | — | — |
| C₂v — Burchakli | 4 | 4 | a₁ + a₂ + b₁ + b₂ | — | — |
🧪 Amaliy misollar — MO bo'yicha kompleks tahlili
[Co(NH₃)₆]³⁺ (Oₕ)
MO tahlili:
¹A₁g → ¹T₁g (λ≈435 nm). NH₃ σ-donor. 18 e⁻. Diamagnit.
3D modelda Oₕ geometriyasini tanlab, MO sathlarini vizual ko'ring.