Atomic orbitals 4f wave functions

This page contains movies depicting the 4f wave functions and their nodal structures. In all cases the green zones are where the 4f wave function has positive values and the white zones denote negative values. See the 4f electron density page for movies depicting the 4f electron_density and nodal structures.

In each case the graph on the left is a surface plot of ψ_4f on a slice drawn through the nucleus. They show the wave function collapsing on to the plane so as to show the nodal struction on the plane. The plot on the right shows values along a single line drawn through the nucleus. The points on the line plot or the surface plot where the colour changes from one to the other represent the points at which the orbital nodal spheres crosses the line or surface.

Each of the 4f orbitals has three planar nodes or conical nodes. The 4f orbitals have no spherical nodes but the higher f-orbitals ( 5f, 6f, and 7f) have one or more.

4f_z³, 4f_x³, and 4f_y³ orbital wave functions

Movie depicting the 4f_z³ wave functions (ψ_4fz³)². The z-axis lies from left to right. The 4f_x³ and 4f_y³ orbitals are identical in appearance but orientated along the x and y axes respecively. The 4f_z³ orbital has two conical nodes but no spherical nodes while the higher f-orbitals ( 5f, 6f, and 7f) have one or more.

4f_xz² and 4f_yz² orbital wave functions

4f_xyz and 4f_z(x²-y²) wave functions

Movie depicting the 4f_xyz wave function (ψ_4fxyz)². The left image shows a two-dimensional wave function plot of the 4f_xyz orbital (across the x=y plane). The right image is along the x=y, z=0 line. The 4f_xyz and 4f_z(x²-y²) are related to each other by a 45° rotation about the z-axis.

4f_y(3x²-y²) and 4f_x(x²-3y²) wave functions

The first image shows a two-dimensional wave function plot of the 4f_x(x²-3y²) orbital (across the z=0 plane, x axis pointing right). The 4f_y(3x²-y²) orbital is identical in appearance but rotated by 90° about the vertical z-axis.