Exercices IV_corrige - AIMF2: Symtrie et Thorie des Groupes...

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AIMF2: Symétrie et Théorie des Groupes Exercices Chapitre 4: Les Applications Exercice 4.1 : a) Construisez une représentation réductible en utilisant les coordonnées x , y et z pour chaque atome de la molécule SF 6 . O h E 8C 3 6C 2 6C 4 3C 2 i 6S 4 8S 6 3 σ h 6 σ d Γ 21 0 -1 3 -3 -3 -1 0 5 3 b) Réduisez la représentation et classez chacune des representations irréductibles en mode de translation, rotation, vibration. A 1g = (1/48)[(21)(1)+8(0)(1)+6(-1)(1)+6(3)(1)+3(-3)(1)+(-3)(1) +6(-1)(1)+8(0)(1)+3(5)(1)+6(3)(1)]=(1/48)*48= 1 A 2g =(1/48)[(21)(1)+8(0)(1)+6(-1)(-1)+6(3)(-1)+3(-3)(1)+(-3)(1) +6(-1)(-1)+8(0)(1)+3(5)(1)+6(3)(-1)]=(1/48)*0= 0 E g = (1/48)[(21)(2)+8(0)(-1)+6(-1)(0)+6(3)(0)+3(-3)(2)+(-3)(2) +6(-1)(0)+8(0)(-1)+3(5)(2)+6(3)(0)]=(1/48)*48= 1 T 1g = (1/48)[(21)(3)+8(0)(0)+6(-1)(-1)+6(3)(1)+3(-3)(-1)+(-3)(3) +6(-1)(1)+8(0)(0)+3(5)(-1)+6(3)(-1)]=(1/48)*48= 1 T 2g = (1/48)[(21)(3)+8(0)(0)+6(-1)(1)+6(3)(-1)+3(-3)(-1)+(-3)(3) +6(-1)(-1)+8(0)(0)+3(5)(-1)+6(3)(1)]=(1/48)*48= 1 A 1u
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This note was uploaded on 10/08/2010 for the course CH 3123 taught by Professor -- during the Fall '08 term at Ecole Polytechnique Fédérale de Lausanne.

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Exercices IV_corrige - AIMF2: Symtrie et Thorie des Groupes...

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