Question

General approach to examine irreducible representations of vibrations Example1: Ammonia 1. Determine point group of the molecule 2. Generate the reducible representation for translation (x, y, z) CE 2C 30v A1 1 1 2 x2+y+, z? Az 1 1-1 R E 2 -1 0 (x,y) (R3, Ry) (x2- y?.xy) 2C 3sv E 13 3. Write down the number of atoms which do not change their location during each symmetry operation. 203 35v E 4 # of unmoved atom

confused on how to get these answers

Answer 1

Symmetry elements means rotation through axis or reflection through plane or inversion through point that leaves molecule unchanged. E means 360^o rotation, every molecule has E as symmetry elements.

morud Wh₂ from top view 120° rotation 240° rotation reflection OV reflection symmetry elements in Nha E CC, on 52, JV, 5v2 point group a Car

3. If you do E (360^o) rotation all atom come to its same position so all 4 atom remains unchanged.

C₃ means 120^o degree rotation all hydrogen atom moves, since axis is through nitrogen atom its position does not change. So 1 atom remains unchanged

Sv (sigma V) means vertical plane it passes along one hydrogen and nitrogen so while doing reflection position of these two atoms does not change. So number of atom unchanged is 2.