Home work Physical and Theoretical Chemistry IV

- Molecular Spectroscopy -

Discussion  Fr 8.5.2003 at 12:15,  HR30.1 (Hagenring 30)



 
 

Home work 3            The H2-molecule and MOs
 
 
 

Exercise 1:  wavefunction of H2

What is the wavefunction of H2 according to the MO theory ?
Use the LCAO approximation and the MOs of H2+.


Exercise 2:  energy of H2

Using the LCAO approximation C.J. Roothaan [J.Chem.Phys. 46 (1951) 1445] obtained the following analytical expression for H2:

E(H2) = 2 E(H2+) - 1/2R + 5/16 - 1/2R . [1 + 11/8R + 3/4R2 + 1/6R3] . e-2R

where E(H2+) is the energy of H2+ ion and R represents the distance between the nuclei. Draw E(H2) as function of R. Where is the energetic minimum und what is its value, E(H2), at this point? An approximate (rough) value is sufficient.
 

Exercise 3:  MOs of homo nuclear molecules
In the following use this energetic order:

g < 1σu < 2σg < 2σu < 1πu < 3σg < 1πg < u< 4σg< 4σu< 2πu< 5σg< 2πg< 5σu

What is the electronic configuration (the MOs) for Li2 until Ne2?
What is the spectroscopic symbol of the total configuration?