pchemII.lecture31.Bonding_is_QM

PchemII.lecture31.Bo - Page 1 of 10 31 Bonding is a Quantum Mechanical Phenomenon Suggested Reading Chapters 9-4 to 9-6 of the text Introduction In

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Page 1 of 10 Scott Kirkby Last revised: 13 April 2008 31. Bonding is a Quantum Mechanical Phenomenon Suggested Reading: Chapters 9-4 to 9-6 of the text. Introduction In the previous lecture we set the stage for looking at molecules. We left off looking at overlap integrals for linear combinations of atomic orbitals. Now lets look at (31-1) Using (31-2) ψ + H ˆ ψ + r d 1 s A 1 s B + () H ˆ 1 s A 1 s B + r d = 1 s A 1 s B + 1 2 -- 2 1 r A ----- 1 r B 1 R --- + –1 s A 1 s B + r d = 1 s A 1 s B + 1 2 2 1 r A 1 r B 1 R + s A r d = 1 s A 1 s B + 1 2 2 1 r A 1 r B 1 R + s B r d + H ˆ j 1 2 2 1 r J ---- = H ˆ j 1 s J E 1 s 1 s J =
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Physical Chemistry II Lecture # 31 Page 2 of 10 Scott Kirkby Last revised: 13 April 2008 therefore (31-3) (31-4) The integral (31-5) represents the charge density around nucleus A interacting with nucleus B via the coulomb potential and the internuclear repulsion. This integral is called the Coulomb integral and given the symbol J. (31-6) since R is fixed during the integration over . 1 s A 1 2 -- 2 1 r A ----- –1 s A r d E 1 s = ψ + H ˆ ψ + r d 1 s A 1 s B + () E 1 s 1 r B 1 R --- + s A r d = 1 s A 1 s B + E 1 s 1 r A 1 R + s B r d + 2 E 1 s 1 S + 1 s A 1 r B 1 R + s A r d + = 1 s B 1 r B 1 R + s A r d 1 s A 1 r A 1 R + s B r d ++ 1 s B 1 r A 1 R + s B r d + 1 s A 1 r B 1 R + s A r d J 1 s A 1 r B 1 R + s A r d = 1 s A 1 r B s A r d 1 R + = r
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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.lecture31.Bo - Page 1 of 10 31 Bonding is a Quantum Mechanical Phenomenon Suggested Reading Chapters 9-4 to 9-6 of the text Introduction In

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