Chem120A+Notes+10-17-08

Chem120A+Notes+10-17-08 - Chem120A Notes 10/17/08...

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Unformatted text preview: Chem120A Notes 10/17/08 Perturbation Theory 1 st order correction ) , ( ) , ( 2 1 ) ( ) 1 ( 2 1 * ) ( 2 1 ) 1 ( r r H r r r d r d E v v v v v v = ( 1 ) to do 1 st order correction, use 0 th order wavefunctions with 1 st order Hamiltonian. For the 2 electron system, we have (in atomic units) 12 ) 1 ( 1 r H = ( 2 ) And the 0 th order wavefunctions are approximated by the Hydrogen 1s wavefunctions: 2 , 1 , ) ( 2 1 3 1 = = j e Z r j Zr j s v ( 3 ) Substitution (2) and (3) into (1) gives 2 1 2 1 2 1 3 2 1 3 12 2 1 3 2 1 3 2 1 ) 1 ( 1 Zr Zr Zr Zr e Z e Z r e Z e Z dr dr E = Z r e e dr dr Z E Zr Zr 8 5 12 2 2 2 1 2 6 ) 1 ( 2 1 = = Hartrees (4) eV-74.83 Hartrees 750 . 2 8 10 4 8 5 2 ) 1 ( )...
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Chem120A+Notes+10-17-08 - Chem120A Notes 10/17/08...

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