Hybrid orbitals are linear combinations of atomic orbitals on the same atom. Three of the hybrid orbitals , , and , commonly used in organic chemistry, are plotted in three dimensions to exhibit their characteristic shapes.
This Demonstration shows the basic characteristics of these hybrid orbitals: the number and type of atomic orbitals involved in the construction, the molecular geometry, examples, and two 3D views (visual style: stripes/points) of the probability density (boundary surface in cartoon form, phase coloring included).
For given values of , an atomic orbital can be described by the values . Angular functions for depend on , , or both and are complex. Two complex spherical harmonics , combined pairwise and linearly, yield real functions. They can be plotted as boundary surfaces.
The Mathematica function pos inside OrbitalModel is shown at this link: "Problem with SphericalPlot3D plotting". It is used to attach signs to the positive or negative parts of the radial wavefunction, so both parts are colored differently.