Atomic orbital simulator using a sphere-array discretization to depict wavefunctions in 3D. Focuses on orbital geometry, internal structure, and symmetry with numerical sampling.
BY CHRIS GUDMUNDSEN
DEC. 2024
This program is meant to calculate and display the probability density functions of an electron in the hydrogen atom. Once the user enters their desired quantum numbers, a window is created with 3 axes and hundreds of spheres arranged in a cube. The electron probability density at several points in 3D space is represented by the radius of the sphere at that location. The origin of the axis represents the nucleus of the hydrogen atom. The maximum radius for each orbital is arbitrary - it has been manually fitted to be visually appealing and clear (this means that it is not recommended to draw conclusions from radius size when comparing orbitals stemming from different combinations of quantum numbers). In addition, the scale of the axes change from orbital to orbital. They have been manually set to display the most interesting parts of each orbital clearly. The scale of the axes for each orbital is printed to terminal for the viewer's reference. The viewer can assume that the probability density decreases to 0 outside of the axis volume.
How is this simulation different from the rest? Most depictions of the orbitals of the hydrogen atom depict a surface called an isosurface, where points of constant probability are bridged to form a surface However, this misplaces a lot of information; the viewer cannot visualize the probability densities within the surface. A naive viewer may be led to believe that the probability density is thus uniform within the surface. This is not the case. This program is meant to prove it.
W : move forwards into the plane of the screen
S : move backwards away from the plane of the screen
A : move left upon the plane of the screen
D : move right upon the plane of the screen
CNTRL : down (-y)
SPACE : up (+y)
Mouse : click and drag to change camera angle
Quantum numbers: n = 1, l = 0, ml = 0
Quantum numbers: n = 2, l = 1, ml = 1
Quantum numbers: n = 3, l = 1, ml = 0
Quantum numbers: n = 3, l = 2, ml = 0
Quantum numbers: n = 3, l = 2, ml = 1
OpenGL single sphere indices and vertices generation from "OpenGL Sphere Tutorial" by Song Ho Ahn
https://www.songho.ca/opengl/gl_sphere.html
Texture, Camera, EBO, VAO, VBO, and shaderClass .cpp and .h (basic OpenGL 3D display and movement)
from Youtube "OpenGL Course - Create 3D and 2D Graphics With C++" by freeCodeCamp.org
(Github VictorGordan/opengl-tutorials)
https://www.youtube.com/watch?v=45MIykWJ-C4
https://github.com/VictorGordan/opengl-tutorials
Glad library