Solving electron density function for Hydrogen and drawing in 3D

Question

I recently stumbled upon interesting site that has interactive 3D representation of radial electron distribution (atomic orbital).

here is the url: http://winter.group.shef.ac.uk/orbitron/AOs/1s/e-density-dots.html (java is needed) clicking on the "equations" or this link http://winter.group.shef.ac.uk/orbitron/AOs/1s/equations.html gives equations needed for these calculations.

I tried to somehow get the coordinates in 3D to plot the electron cloud but couldn't manage to do it and I need some help over this.

Any idea how I would use this functions to get the 3d electron cloud? Any help appreciated!

Answer 1

I took a crack at this this morning, but I didn't get as far I as I would have liked, if you want you can look into using MathGL$^{[1]}$ in C++ to try to implement my following suggestion (which my be difficult due to there not being much support for MathGL), but this same thing could very easily be done in either python, octave, or matlab. The general treatment of this problem would be to make a 3D grid over x, y, and z, (each of x, y, and z would be an N by N by N matrix) and then solve $\Psi(x,y,z)^2$ at each point, which is explicitly written for each quantum number on the website you provided. The next thing to do is normalize $\Psi(x,y,z)^2$ to make the color of each point correspond to the value of $\Psi(x,y,z)^2$ there (for example, 0 to 1, representing white to grey to black), so $\Psi(x,y,z)^2$ close to 0 is white, $\Psi(x,y,z)^2$ ~ .5 is grey, and $\Psi(x,y,z)^2$ ~ .9 is black. In other languages (such as python, octave, or matlab) this can easily be accomplished with the 'scatter'/'scatter3' functions and setting the point transparency with the 'alpha' value.

$^{[1]}$ http://uni-smr.ac.ru/archive/science/visualization/MathGL/mathgl-2.0.eng.pdf