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pchemII.lecture30.Chemical_Bonding

pchemII.lecture30.Chemical_Bonding - Page 1 of 8 30 The...

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Page 1 of 8 Scott Kirkby Last revised: 13 April 2008 30. The Born Oppenheimer Approximation and the Chemical Bond Suggested Reading: Chapters 9-1 to 9-3 of the text. Introduction We will now move from our study of atoms and begin our look at molecules. The simplest neutral molecule is H 2 . The Hamiltonian for H 2 is: (30-1) where M is the mass of the hydrogen nucleus. m e is the mass of the electron. r 1A is the separation distance between electron one and nucleus A. H ˆ h 2 2 M ------- A 2 B 2 + ( ) h 2 2 m e --------- 1 2 2 2 + ( ) = e 2 4 πε 0 r 1 A -------------------- e 2 4 πε 0 r 1 B -------------------- e 2 4 πε 0 r 2 A -------------------- e 2 4 πε 0 r 2 B -------------------- e 2 4 πε 0 r 12 -------------------- e 2 4 πε 0 R ---------------- + +
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