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 0 r 1 B e 2 4 0 r 2 A e 2 4 0 r 2 B e 2 4 0 r 12 e 2 4 0 R ---------------- ++
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Physical Chemistry II Lecture # 30 Page 2 of 8 Scott Kirkby Last revised: 13 April 2008 r 2A is the separation distance between electron two and nucleus A. r 1B is the separation distance between electron one and nucleus B. r 2B is the separation distance between electron two and nucleus B. r 12 is the separation distance between electron one and electron two. R is the separation distance between nucleus A and nucleus B. (Historical convention is to label electrons with numerals and nuclei with uppercase letters.) Figure 30-1: Sketch of the distance vectors for the hydrogen molecule problem. The nuclei are ~1000 times heavier than the electrons and thus their motion is significantly slower than the electronic motion. We may use this to help solve the problem.
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Physical Chemistry II Lecture # 30 Page 3 of 8
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This note was uploaded on 04/19/2008 for the course CHEM PCHEM taught by Professor Kirkby during the Spring '08 term at East Tennessee State University.

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

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