1. Consider the transition dipole matrix element for the vibrational part of a ro-vibrational transition of a polyatomic molecule.
From a group theory point of view, what is the selection rule expressed through this integral?
(A) Levels j and k must belong to the same irrep.
(B) Levels j and k must belong to different irreps.
(C) The direct product of the symmetries of levels j and k must
transform like x, y or z.
(D) The direct product of the symmetries of levels j and k must contain the totally symmetric irrep of the point group.
(E) Level j or level k must be totally symmetric.

2. Consider the transition dipole matrix element for the vibrational part of a ro-vibrational transition of a polyatomic molecule.
From a group theory point of view, what is the selection rule expressed through this integral?
(A) Levels j and k must belong to the same irrep.
(B) Levels j and k must belong to different irreps.
(C) The direct product of the symmetries of levels j and k must
transform like x, y or z.
(D) The direct product of the symmetries of levels j and k must contain the totally symmetric irrep of the point group.
(E) Level j or level k must be totally symmetric.

3. Consider the situations sketched below, where the electric dipole moment and the polarizability are plotted as a function of the normal coordinate for three different vibrations. Which ones are IR/Raman active?
(A) IR: II and III; Raman: II and III
(B) IR: I and II; Raman: II and III
(C) IR: I; Raman: II and III
(D) IR: II and III; Raman: I
(E) IR: none; Raman: all
I II III

4. Consider the situations sketched below, where the electric dipole moment and the polarizability are plotted as a function of the normal coordinate for three different vibrations. Which ones are IR/Raman active?
(A) IR: II and III; Raman: II and III
(B) IR: I and II; Raman: II and III
(C) IR: I; Raman: II and III
(D) IR: II and III; Raman: I
it’s CO2 explanations on right
(E) IR: none; Raman: all
I II III