Home work Physical and Theoretical Chemistry IV
- Molecular Spectroscopy -

Discussion  Fr 20.6.2003 at 12:15,  HR30.1 (Hagenring 30)



Home work 8       electronic configuration and transition dipole moment

Exercise 1
a)  Determine the ground state configuration X of NH2. Draw the symmetry adopted orbitals and qualitatively the MO energies as function of the bond angle (Walsh diagram).
b)  Is NH2 linear or bent?
c)  What is the spectroscopic term symbol for the ground state X?
d)  The first excited state A is reached by promoting a 3a1 elektron to the 1b1 orbital. Is this A state more or less bent compared to the ground state X?
e)  What is the spectroscopic term symbol for the excited state A?
f)  What is the direction of the transition dipole moment A ← X ?
g) Draw qualitatively the potential energy for the X and A states as function of the bond angle between 0° and 360°.
h)  What is the symmetry and the term symbol for 180°?
i)   For an asymmetric change of the N-H bond lengths NH2 belongs to the Cs symmetry. What is the electronic configuration and the spectroscopic term symbol for both the X and the A state?
j)   What is now the direction of the transition dipole moment A ← X ?

Excercise 2
a)  What are the symmetry elements of ethylene?
b)  What is the symmetry point group of ethylene?
c)  Determine the symmetry symbols for the following symmetry adopted hydrogen orbitals:
        h1 = s1+s2+s3+s4
        h2 = s1+s2-s3-s4
        h3 = s1-s2+s3-s4
d)  Determine the symmetry of the product B1gx B1u  and of the product B1g  x B2u. Use the table below for this multiplication.
e)  Is the transition from B1g to B1u or from B1g  to B2u  dipole allowed or forbidden and (if allowed) what is the location of the transition dipole moment?
Use the character table of the corresponding symmetry point group:

E C2(z) C2(y) C2(x)   i  σ(xy) σ(xz) σ(yz)    
Ag 1 1 1 1 1 1 1 1   x2, y2, z2
B1g 1 1 -1 -1 1 1 -1 -1 Rz xy
B2g 1 -1 1 -1 1 -1 1 -1 Ry xz
B3g 1 -1 -1 1 1 -1 -1 1 Rx yz
Au 1 1 1 1 -1 -1 -1 -1    
B1u 1 1 -1 -1 -1 -1 1 1 z  
B2u 1 -1 1 -1 -1 1 -1 1 y  
B3u 1 -1 -1 1 -1 1 1 -1 x