Heitler Londone Theory of H2 Molecules
[1] Heitler Londone Theory Of H2 Molecules
(Hydrogen Molecule Or Valence Bond
Theory)
- The Valance Band Theory Is Also An Approximation Method For
Explaining Between H Atome In H2 molecule
- The Intrection Between Atom Valance e⁻ Give Rise To Bounding
Force Between Atome Which Hold The Atom Togather In
Molecule.
- Heitler London Theory Of H Molecule Which Help To Devolop Of
Picture Of Chemical Bond.
- Let Us Suppose That The Spinnig Of e⁻ Is Negleated & The
System Consistes Of Two Hydrogen Atome 'A' And 'B' And Two
Electron.
- rab = Distence Between Both Nucles a & b
- r12 = Distence Between Both Electron
- r1b = Distence Of 1st e⁻ From The Centre Of Nucleus Of
Atom 'b'
- r2b = Distence Of 2nd e⁻ From The Centre Of Nucleus Of Atom
'b'
- r2a = Distance Of 2nd e⁻ Center Of 'a'
- r1a = Distance Of 1st e⁻ From The Center Of 'a'
- The Potential Energy Of Two Nuclei Of H Atom
- Now Hamiltonion Of System (H2 Molecule)
- Possible Wave Fuction
1e⁻ = ψ1
2e⁻ = ψ2
- Trial Wave Fuction
ψ = ψ1 + A ψ2
- Expectation Value Of Hamiltonion
- <ψ|ψ> = <ψ1 + A ψ2|ψ1 + A ψ2>
= <ψ1|ψ1> + A <ψ1|ψ2> + A* <ψ2|ψ1> + A*A <ψ2|ψ2>
- now put
<ψ1|ψ1> =
<ψ2|ψ2> = 1
<ψ1|ψ2> =
<ψ2|ψ1> = v
- <ψ|ψ> = 1 + AV + AV +A^2
= 1 + 2AV +
A^2.......(A)
- <ψ|H|ψ> = <ψ1 + A ψ2|H|ψ1 + A ψ2>
= <ψ1|H|ψ1> + A <ψ1|H|ψ2> + A <ψ2|H|ψ1> +
A^2 <ψ2|H|ψ2>
= H11 + A H12 + A H21 + A^2 H22
- ( H12 = H21 )
- <ψ|H|ψ> = H11 + 2A H12 + A^2 H22.....(B)
- put value in eq (1) from (a) & (b)
- Accroding To Variation Method
dE/dA = 0
vdu-udv/v^2
- Using Approximaion
- Ther Are Two Value Of Ground State Enegy Which Are
Repesnting Ortho And Para State Of H2 Molecule.
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