Properties of f-orbitals

Question

I am not a Chemist, but I took enough undergraduate Chemistry classes to understand the basic properties of s, p and d orbitals and how the behaviour of electrons contributes to different kinds of chemical bonds and elemental/molecular properties.

I stopped before we got to actual quantum mechanics - my maths wouldn't have been good enough to stand it. It still isn't.

However, I was always fascinated as to why none of the lecturers would ever tell us about f-orbitals. When asked, they muttered dark hints that they were significantly different from lower electron shells, and that explaining why was not only a waste of time but might spoil our existing understanding.

I left university 20 years ago, but I was suddenly blindsided by remembering this question out of nowhere. And now I want to know the answer. Google searches reveal a lot of maths that I can't follow. So can someone explain:

• What are some of the basic properties of elements with electrons in f-orbitals, and how do they differ from lower orbital positions?
• I assume this is related to the fact that most (all?) elements with f-orbitals manifest as metals, so how and why? And why do some elements without f-orbitals display metallic properties?
• Why were my tutors so unwilling to try and explain this to non-Chemists who were supposed to stop at their appreciation of lower orbitals and basic covalent bonds?

Answer 1

I think there are multiple reasons contributing.

First of all, the atomic orbitals of the f-block and their properties and interactions are complicated. You have a lot of electrons, and they are far away from the nucleus, on many differently oriented orbital lobes. (well, that is the visualisation at least, in reality atomic orbitals are described by quantum mechanical wavefunctions, and those get more complicated as well for the f orbitals)
Since you have a lot of electrons repelling each other, and on top of that there are relativistic effects coming into play, it is rather difficult to do quantum chemical calculations with these elements to determine their energy levels, etc. A lot of "rules" (and approximations) valid for low atomic number elements stop working.
Overall, heavy elements have special properties, that cannot be explained by the simple rules and approximations used for light elements. As you have said there is a lot of difficult math in the background. The rules and visualisations are just there to be an easy to grasp abstraction of the underlying physics. The side effect of this is that you need more and more exceptions as the system gets more complicated.

Second, they are usually rare and expensive elements.(actinides are also radioactive) They have no known biological role, and usually only have few significant uses. So usually one does not encounter them unless one is working in some niche field.