# Atomic orbitals 4f electron density

This page contains movies depicting the 4fxy, 4fxz, 4fyz, and 4fx2-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.

## 4fz3, 4fx3, and 4fy3 orbital electron density

Movie depicting the 4fz3 electron density function (ψ4fz3)2. The z-axis lies from left to right. The 4fx3 and 4fy3 orbitals are identical in appearance but orientated along the x and y axes respecively. The 4fz3 orbital has two conical nodes.

## 4fxz2 and 4fyz2 orbital electron density

Movie depicting the 4fxz2 electron density function (ψ4fxz2)2. The left image shows a two-dimensional electron dot-density plot of the 4fxz2 orbital (across the x=0 plane). The right image is a plot along the y axis. The 4fyz2 is identical in appearance but rotated by 90° about the y-axis.

## 4fxyz and 4fz(x2-y2) electron density

Movie depicting the 4fxyz electron density function (ψ4fxyz)2. The left image shows a two-dimensional electron dot-density plot of the 4fxyz orbital (across the x=y plane). The right image is along the x=y, z=0 line. The 4fxyz and 4fz(x2-y2) are related to each other by a 45° rotation about the z-axis.

## 4fy(3x2-y2) and 4fx(x2-3y2) electron density

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

The OrbitronTM, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/