The \(\mathrm{NH}_{3}\) molecule is described in Problem 4. Here is its character table.

Its nontrivial normal modes are basis functions for the irreducible representations \(2 A_{1}+2 E\).

(a) How many nontrivial normal modes are there?

(b) Which of the normal modes are IR active?

(c) How many different IR frequencies does \(\mathrm{NH}_{3}\) exhibit?

Data from Problem 4

Ammonia, \(\mathrm{NH}_{3}\), is tetrahedral, with the three hydrogens in an equilateral triangle base plane and with the nitrogen at the top of the tetrahedron.
What are its symmetry operations (including mirrors/inversions)?
For each symmetry operation, which atoms stay at home?

Transcribed Image Text:

basis functions z, x + y, z Lz x, y, x2 y2, xy, xz, yz, Lx, Ly - 1 3z mx A 1 1 1 A2 1 1 -1 E 2 -1 0