Atomic orbitals 4f electron density

This page contains movies depicting the 4f_xy, 4f_xz, 4f_yz, and 4f_x²-y² wave functions. In all cases the greenzones are where the 4f wave function has positive values and the white zones denote negative values. See the 4f wave function page for movies depicting the 4f the wave functions and nodal structures.

The "surface" of the three-dimensional orbital at the top centre of each movie represents points for which the electron density for that orbital is the same - an isosurface. By choosing different values of electron density, denoted by the bar moving up and down on the line plot or by the moving plane on the surface plot, then the size of the three-dimensional plot changes. All values of electron density are of necessity not negative since the square of any real number cannot be less than zero.

4f_z³, 4f_x³, and 4f_y³ orbital electron density

Movie depicting the 4f_z³ electron density function (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.

4f_xz² and 4f_yz² orbital electron density

Movie depicting the 4f_xz² electron density function (ψ_4fxz²)². The left image shows a two-dimensional electron dot-density plot of the 4f_xz² orbital (across the x=0 plane). The right image is a plot along the y axis. The 4f_yz² is identical in appearance but rotated by 90° about the y-axis.

4f_xyz and 4f_z(x²-y²) electron density

Movie depicting the 4f_xyz electron density function (ψ_4fxyz)². The left image shows a two-dimensional electron dot-density 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) electron density

The first image shows a two-dimensional electron dot-density 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.