- 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:Exercise 3: MOs of homo nuclear moleculesE(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.
In the following use this energetic order:1σg < 1σu < 2σg < 2σu < 1πu < 3σg < 1πg < 3σu< 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?