The linear combination of a single 4s-orbital with all three 4p-orbitals (4p_x, 4p_y, and 4p_z) results in four 4sp³-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 4sp³-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 4sp³-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). Click on the images to enlarge view or see the VRML 3D-model.

90% Probability Contour	90-25% Probability Contours	Nodal Plane
Four 4sp3-Hybrid Orbitals	Four 4sp3-Hybrid Orbitals	Four 4sp3-Hybrid Orbitals

LCAOs:

ψ1  =  1/√4 φ4s  +  1/√4 φ4px  +  1/√4 φ4py  +  1/√4 φ4pz ψ2  =  1/√4 φ4s  +  1/√4 φ4px  -  1/√4 φ4py  -  1/√4 φ4pz ψ3  =  1/√4 φ4s  -  1/√4 φ4px  -  1/√4 φ4py  +  1/√4 φ4pz ψ4  =  1/√4 φ4s  -  1/√4 φ4px  +  1/√4 φ4py  -  1/√4 φ4pz

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 4s- and 4p-orbitals; Cartesian wave functions were taken from The Orbitron Gallery of Atomic Orbitals and Molecular Orbitals.