Huckel

# Huckel - Hckel MO Theory Ethylene z E = y x = cA pzA cB...

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Hückel MO Theory Ethylene + = x y z E š š* Ψ = c A p zA + c B p zB α - E β β α - E = 0 E + = α + β E - = α - β α = p z A * H eff p z A d τ Coulomb Integral β = p z A * H eff p z B d τ Resonance Integral S AB = p z A * p z B d τ = 0 Overlap Integral Ψ + = 1 2 ( p zA + p zB ) Ψ - = 1 2 ( p zA p zB ) Butadiene x y z + + + + E α + 1.618β α + 0.618β α - 0.618β α - 1.618β Ψ i = c iA p zA + c iB p zB + c iC p zC + c iD p zD i = 1 ... 4 α - E β 0 0 β α - E β 0 0 β α - E β 0 0 β α - E = 0 Approximations: 1. 2. 3.

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x = ( α - E) β x 1 0 0 1 x 1 0 0 1 x 1 0 0 1 x = 0 x 4 - 3x 2 + 1 = 0 let y = x 2 y 2 -3y + 1 = 0 y = 9-4 2 = 2.618, 0.382 x = y = ±1.618, ±0.618 E = α - x β = α ± 1.618 β or α ± 0.618 β Nodes: + + + + + + + + + + + + + + + + Ψ 4 =0.372p A -0.602p B +0.602p C -0.372p D Ψ 3 =0.602p A -0.372p B -0.372p +0.602p D Ψ 2 =0.602p A +0.372p B -0.372p C -0.602p D Ψ 1 =0.372p A + 0.602p B + 0.602p
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