Orbitron
Since I am dealing with crystal-electric fields I’ve been seeing a lot of nice pictures of electron orbitals, but today, I have encountered a completely new quality on the Internet.
Take a look at the Orbitron webpage and admire beautifully rendered images. You will find pictures of standard orbitals, but also some truly weird stuff like the \( 7i \) orbital.
Apart from the 3D depiction, subtabs for each orbital contain much more information in form of animations, graphs and equations. There seems to be enough knowledge to reproduce those calculations and play around with the orbitals on your own!
Resources
I wonder how far I could go implementing proper formulas for the orbitals in python and exporting the mto POV-ray code.
Steps to make pictures of atomic orbitals
- Understand the phase convention in orbital wavefunctions that allows to use real atomic orbitals. Apparently this convention makes for nicer pictures but the depicted functions are not eigenstates of the \( \hat{L}_z \) operator. Now, these real atomic orbitals seem to me like the tesseral harmonics used in McPhase?
- Implement the function that computes the wavefunction \( \psi_{n,l,m} \) for arbitrary quantum numbers. It consists of the radial part as a Laguerre polynomial and spherical part, as spherical harmonic.
- On the POV-ray side there is an interesting function to plot closed surface of arbitrary shape