3. Borane (BH3) belongs to D3h point group. Consider the vibrational (stretching) modes possible for B-H bonds under D3h symmetry. Using the methods we used in class, construct the reducible representation I, and break it down into irreducible representations using the character table provided. Sketch those modes, indicate whether they are IR-active. (6 points) D3h E 2C3 3C2 σh 283 30% A₁' 1 1 1 1 1 1 x² + y², z² 1 -1 1 1 -1 R₂ E' 2 0 2 0 (x, y) (x² - y², xy) " A₁" 1 1 -1 A2" 1 -1 -1 1 Z E" 2 -1 0 -2 1 0 (Ry, Ry) (xz, yz)

3. Borane (BH3) belongs to D3h point group. Consider the vibrational (stretching) modes possible for B-H bonds under D3h symmetry. Using the methods we used in class, construct the reducible representation I, and break it down into irreducible representations using the character table provided. Sketch those modes, indicate whether they are IR-active. (6 points) D3h E 2C3 3C2 σh 283 30% A₁' 1 1 1 1 1 1 x² + y², z² 1 -1 1 1 -1 R₂ E' 2 0 2 0 (x, y) (x² - y², xy) " A₁" 1 1 -1 A2" 1 -1 -1 1 Z E" 2 -1 0 -2 1 0 (Ry, Ry) (xz, yz)

Physical Chemistry

2nd Edition

ISBN:9781133958437

Author:Ball, David W. (david Warren), BAER, Tomas

Publisher:Ball, David W. (david Warren), BAER, Tomas

Chapter13: Introduction To Symmetry In Quantum Mechanics

Section: Chapter Questions

Problem 13.27E: Determine the point group of the following molecules. a cis1,2 Dichloroethylene b trans1,2...

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