The linear combination of a single 2s-orbital with all three 2p-orbitals (2p_x, 2p_y, and 2p_z) results in four 2sp³-orbitals of identical shape, but different orientation in space. The images below provide an illustration of the probability contours (90-25% probability level of the electron density, i.e. ψ²) and the nodal plane of a 2sp³-orbital (actually not a "planar" plane; ψ = 0), where different colors indicate regions of opposite sign in ψ. The nucleus is located at the origin of the coordinate system as indicated by the orange axes, and thus is embedded not between the lobes on the nodal plane, but within the minor (blue) lobe of the hybrid orbital.

In the bottom row, all four 2sp³-orbitals and their tetrahedral relative arrangement are displayed, but note that the orbitals have been moved away from the center towards the outside to facilitate visualization (the orange spheres represent the original location of the nucleus). This arrangement of orbitals is suitable to describe the geometry of molecules such as CH₄ or other alkanes (tetrahedral geometry of H₃C-fragments with bond angles of ≅109°). Click on the images to enlarge view or see the VRML 3D-model.

90% Probability Contour	90-25% Probability Contours	Nodal Plane
Four 2sp3-Hybrid Orbitals	Four 2sp3-Hybrid Orbitals	Four 2sp3-Hybrid Orbitals

LCAOs:

ψ1  =  1/√4 φ2s  +  1/√4 φ2px  +  1/√4 φ2py  +  1/√4 φ2pz ψ2  =  1/√4 φ2s  +  1/√4 φ2px  -  1/√4 φ2py  -  1/√4 φ2pz ψ3  =  1/√4 φ2s  -  1/√4 φ2px  -  1/√4 φ2py  +  1/√4 φ2pz ψ4  =  1/√4 φ2s  -  1/√4 φ2px  +  1/√4 φ2py  -  1/√4 φ2pz

All graphics shown on this page were created using the MolArch⁺ program and POVRAY Persistence of Vision Raytracer. Hybrid Orbitals were generated from the pure hydrogenic wave functions of 2s- and 2p-orbitals; Cartesian wave functions were taken from The Orbitron Gallery of Atomic Orbitals and Molecular Orbitals.