Quantum Chemistry

Vakinformatie

TBA

Examenvragen

Monday 13th January 2020 (8:30 am)

You get 4 hours to make the exam. You write everything down and then you go to the professor for oral examination.

Question 1 (8 of 20 points)

1. Obtain all atomic terms and levels of a d9 configuration.
2. Rank them in order of energy and give their relative energies in terms of the one-electron spin-orbit coupling constants.

Question 2 (4 of 20 points)

1. Show that the 2px and the 2pz functions of hydrogenlike atoms are orthogonal. (Given: real wave function of the 2px and 2pz hydrogenlike orbitals)
2. For the ground state of a hydrogenlike atom, show that <R> = 3a/2Z. (Given: value of some difficult integral that you will need to calculate <R>)

Question 3 (4 of 20 points)

Given: all atomic states of the ground state configuration of a carbon atom and their energies, and all atomic states of the 1s22s2p3 configuration and their relative energies.

1. Comment on the order of the atomic states. (He expects that you talk about Hund’s rules, when are these valid, when not, talk about order of atomic states with different J values but from the same term…)
2. From the given energy values, estimate the value for ζ2p.
3. What spectral transitions are allowed between the ground state and the given excited state? Give the energies of these transitions.

Question 4 (4 of 20 points)

By using second-order perturbation theory, obtain the second-order energy correction due to interaction of the 1S0 and 3P0 states of a p2 configuration. (You should find the wave functions for both states in form of Slater determinants and calculate the matrix elements of ĤSO using the Condon-Slater rules)