Hydrogenic atomic orbital derived from the cartesian wave function ψ (see below). Contour surfaces are given at the 90, 80, 70, 60, 50, 40, and 25% probability level of the electron density, describing the spatial volume around a nucleus in which an electron may be found with the corresponding probability. Yellow and blue colors indicate regions of opposite sign in ψ, (the electron density is proportional to ψ²). Slices through the surfaces indicate the "inner" structure of the orbitals, and the nodal planes display areas were the waves functions passes through zero.

Click on the images to enlarge view; Jmol 3D models of this orbital are also available.

90% Probability Contour	90-25% Probability Contours
75% Probability & Nodal Planes	Slices Through Probability Contour

Angular Wave Function	Y4fx(x2-3y2) = (1 / 4π)1/2 × √(70/16) × x ( x2 - 3y2 ) / r3
Radial Wave Function	R4fx(x2-3y2) = (1 / 96√35 ) × ρ3 × Zeff3/2 × e-ρ/2
The total wave function is ψ = Y × R with r = radius in Bohrs (atomic unit 1 Bohr ≅ 0.529 Å); Zeff is the effective nuclear charge; and ρ = 2 Zeff × r / n (principal quantum number n with n = 4 for this orbital). The electron density is ψ2; and the radial distribution function is r2 × R2.

All graphics shown on this page were created using the MolArch⁺ program and POVRAY Persistence of Vision Raytracer. Cartesian wave functions were taken from The Orbitron Gallery of Atomic Orbitals and Molecular Orbitals.