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.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZbib_uzidfDZZWmh6SU8saJ8VukZLrOyQDnYBmrHs4ryBfcgcriRl4fDa_tSJG-A3NYT2d1LYQIVjn55fO8ign3ojYKtCQBmUQIx329waP8dgem2f57j7wJdqx0SvpIy9k1ZQN0MKaTWTBw_L2A7bgPUC5X8N4zeRfSW3emGNSYf-Iy2yro6jx3ramw8/w414-h258/hatom.jpg)
- 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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiqbI4i3psyYxJtVBIlHCQbS-swJwg0ZBRwycCZ6V_h8inb5eiRO8oymr2ByAtRn8fgNFlbHhYjsuvfBXWnpG-Oi8G3ZWEGXh56Zr3PqkHR7nB3OO6L71uNMZjzOLTEiOfgFLNapV39zTYTffJbAfMASZjwhtlFgSbmHYI799ZdF4MlMnO9UxoDqVD3ZzI/s320/he1.jpg)
- Now Hamiltonion Of System (H2 Molecule)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhNwGoEaizpPVP2RXbmhNdlYYvUfq3BQxu8nk8etrsvXDb6UUFM_Rdeg6h-3kd7fn1u5N698aov4CS10xXUf6CwF32mt0KU6Y4YQeihME0OAwCm3SrBk8i7XTC0bfDGTCA-obi3BMBPBbkQW9pYzHMNLetVSEnm5xtniRYqAwO1nl3ObSnoxvtkKPjFoPA/w415-h92/he4.jpg)
- Possible Wave Fuction
1e⁻ = ψ1
2e⁻ = ψ2
- Trial Wave Fuction
ψ = ψ1 + A ψ2
- Expectation Value Of Hamiltonion
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEha7sRFRTTEm5EF2wkmzKQw4Jc_85tQ958vb-8gQqV1eRg8QWlXQivpb_3ovoIVmwFtMVr2tkl1Oh99fWWTjISyEINfPncYkG9wJG8bDwDsP88qWjv8-yYRrxONQXDVCePb8QibfhrpASSPqTWxbzCHzEh0BP7A1CNOjPP2V3pGbYgclXvjHH2FYbyUEmk/s320/he2.jpg)
- <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
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhjauGv5Q5OHYqPosfoVxLtto7hkPynE2ZhDl4i3q4eOqCUVYAKy23k7f0ki7vrpvLwE_YzhsJYl3ZFUXsU2p-5xm0ULbvgVUWfse0n2ObwWgMQ-cX568wg6JbVj3UHcOHfd-KM-eVt2bMQkkomDEPCCvOHQrd3h83-bOlLt26-jisx-WqieEIyuJRVCXA/w567-h235/he5.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie2I46SqblSWfKNl99XcWCBtQZJo2wBitZBIx3fiTwSD7ZE6Zhu6T5TZEZ0smJPvyTUy5qLm4MYfg8fSchqWtjre9bO55gCDw9FLR51aOIhHDOoZA95D3p_9H9oMVdEjQuy6u1nR3mQruiDm2C38-pRBHBdVXleE4SyGP-tbbrtrp_QC-famfrrM3jXg8/w572-h203/he6.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhh-Xc2MNY4Rnk6VR73UWwoBV06wR5fGU4IUO-Lsp7xXMnhoLgYrgQCftLLl5EP17jampDse_IZE7hLDmnxFz_IsMYvCwxr0sHj1qVtAELhfh3oGOpgLA2EOnx94WFva1frYGXZcKAUErtKvSK1cP5W_ezHs_A2dmZTdOG-nvyJKBLB0WO4j-MMhQcHpmE/w552-h208/he7.jpg)
- Using Approximaion
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDoYEeIijpUEzfk2K9dDPNYeciPwyoXC-iuUKbDOo_D_7KGqsfuVYoPXOuzpC9GefZGatUMNN6Qyfwjt9X36GW5Wm_eeblIhYW8JEij3TXml9oQm4MyaJTy1BvMdbg04woEBkFMfptCrYmehsBPCYOsRVD7pC9-zscUGVYOyJUd569gCL3EyafvMDkIJw/w570-h169/he8.jpg)
- Ther Are Two Value Of Ground State Enegy Which Are
Repesnting Ortho And Para State Of H2 Molecule.
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