The linear combination of a single 3s-orbital with all three 3p-orbitals (3p_x, 3p_y, and 3p_z) results in four 3sp³-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 3sp³-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 3sp³-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 3sp3-Hybrid Orbitals	Four 3sp3-Hybrid Orbitals	Four 3sp3-Hybrid Orbitals

LCAOs:

ψ1  =  1/√4 φ3s  +  1/√4 φ3px  +  1/√4 φ3py  +  1/√4 φ3pz ψ2  =  1/√4 φ3s  +  1/√4 φ3px  -  1/√4 φ3py  -  1/√4 φ3pz ψ3  =  1/√4 φ3s  -  1/√4 φ3px  -  1/√4 φ3py  +  1/√4 φ3pz ψ4  =  1/√4 φ3s  -  1/√4 φ3px  +  1/√4 φ3py  -  1/√4 φ3pz

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 3s- and 3p-orbitals; Cartesian wave functions were taken from The Orbitron Gallery of Atomic Orbitals and Molecular Orbitals.