Ligand Field Theory

These questions deal in part with concepts presented in today's assigned reading, so please make sure to read the paper by Cotton as well as today's lecture notes before working out your answers.

1. All other things being equal, what is the magnitude of Δ_t relative to that of Δ_o?
2. Who was the great physicist who first applied symmetry and group theory ideas to the splitting of d-orbital energy levels in crystals?
3. What is the relative probability of finding an electron in d_z² at a fixed distance from a metal ion in (a) the xy plane, versus (b) along the z axis?
4. Consult the recent paper by Guy Ashkenazi to learn the relationship between d orbital labels and the angular part of the d orbital wavefunctions.
5. What is the analytical value of the angle θ of the d_z² orbital's nodal cone? Hint: the angular part of the d_z² orbital wavefunction is given in the short paper referenced in the preceding problem.
6. Which is larger, Δ_o or P (the pairing energy), for the d⁵ case when all five electrons are unpaired in an octahedral complex?
7. How is the electron configuration written in the case of the previous question? Is this a high-spin case or a low-spin case?
8. For which dⁿ counts is it not necessary to consider the question of high- versus low-spin configurations?
9. Why is it the case that tetrahedral complexes are almost never found to exhibit a low-spin configuration?
10. Will any given 3d metal complex having the formula [M(NH₃)₆]ⁿ⁺ be high spin as long as the charge is such that the d-electron count comes out to be d⁶?
11. Find all the states that arise from a gas phase d² ion.  Show your work.