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