chem104alecture16 - Chem 104A, UC, Berkeley Chem 104A, UC,...

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1 Chem 104A, UC, Berkeley Projection Operator Method 1. Construct a reducible rep. Using ligand orbitals as a basis. (any basis function that moves contribute nothing). 2. Apply reduction formula: 3. Apply projection operator: to the basis orbitals to generate LGOs ) ( 1 # R iR N h χ × × = Γ Γ Γ = R R h l c P i i i ) ( i l Γ Dimension of i Γ i R Γ ) ( Character for operator R in i Γ Cotton, Chemical Applications of Group Theory , Wiley, 1990, chapt 6, 8 Chem 104A, UC, Berkeley Construct a reducible rep. Using ligand orbitals as a basis. (any basis function that moves contribute nothing). S a S b S c Γ 3h 3 0 1 3 0 1 Apply reduction formula: ' ' 1 3 E A h + = Γ (xz, yz) (R x , R y ) 0 1 -2 0 -1 2 E’’ z 1 -1 -1 -1 1 1 A’’ 2 -1 -1 1 1 2 S 3 1 0 -1 1 3 C 2 -1 -1 1 1 A’’ 1 (x 2 -y 2 , xy) x 2 + y 2 , z 2 (x,y) R z 0 2 -1 2 E’ -1 1 1 1 A’ 2 1 1 1 1 A’ 1 3 σ v σ h 2 C 3 E D 3h Chem 104A, UC, Berkeley Apply projection operator : Γ Γ Γ = R R h l c P i i i ) ( to the basis orbitals to generate LGOs S a S b S c (xz, yz) (R x , R y ) 0 1 -2 0 -1 2 E’’
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This note was uploaded on 04/12/2008 for the course CHEM 104 taught by Professor Yang during the Spring '04 term at University of California, Berkeley.

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chem104alecture16 - Chem 104A, UC, Berkeley Chem 104A, UC,...

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