The linear combination of a 4s-orbital with three 4p-orbitals (4p_x, 4p_y, and 4p_z) and two 3d-orbitals (3d_x²-y² and 3d_z²) results in six sp³d²-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 planes of a sp³d²-orbital (actually not "planar" planes; ψ = 0), where different colors indicate regions of opposite sign in ψ.

In the bottom row, all six sp³d²-orbitals and their octahedral 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.

90% Probability Contour	90-25% Probability Contours	Nodal Planes
Six sp3d2-Hybrid Orbitals	Six sp3d2-Hybrid Orbitals	Six sp3d2-Hybrid Orbitals

LCAOs:

ψ1  =  1/√6 φ4s  -  1/√2 φ4px  -  1/√12 φ3dz2  +  1/√4 φ3dx2-y2 ψ2  =  1/√6 φ4s  +  1/√2 φ4px  -  1/√12 φ3dz2  +  1/√4 φ3dx2-y2 ψ3  =  1/√6 φ4s  -  1/√2 φ4py  -  1/√12 φ3dz2  -  1/√4 φ3dx2-y2 ψ4  =  1/√6 φ4s  +  1/√2 φ4py  -  1/√12 φ3dz2  -  1/√4 φ3dx2-y2 ψ5  =  1/√6 φ4s  -  1/√2 φ4pz  +  1/√3 φ3dz2 ψ6  =  1/√6 φ4s  +  1/√2 φ4pz  +  1/√3 φ3dz2

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.