# Atomic orbitals 5*f* electron density

This page contains movies depicting the 5*f*_{xy}, 5*f*_{xz}, 5*f*_{yz}, and 5*f*_{x2-y2} wave functions. In all cases the greenzones are where the 5*f* wave function has positive values and the white zones denote negative values. See the 5*f* wave function page for movies depicting the 5*f* 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.

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

## 5*f*_{z3}, 5*f*_{x3}, and 5*f*_{y3} orbital electron density

**Movie depicting the 5 f_{z3} electron density function (ψ_{5fz3})^{2}.** The z-axis lies from left to right. The 5

*f*

_{x3}and 5

*f*

_{y3}orbitals are identical in appearance but orientated along the

*x*and

*y*axes respecively. The 5

*f*

_{z3}orbital has two conical nodes.

## 5*f*_{xz2} and 5*f*_{yz2} orbital electron density

**Movie depicting the 5 f_{xz2} electron density function (ψ_{5fxz2)2}**. The left image shows a two-dimensional electron dot-density plot of the 5

*f*

_{xz2}orbital (across the

*x*=0 plane). The right image is a plot along the

*y*axis. The 5

*f*

_{yz2}is identical in appearance but rotated by 90° about the

*y*-axis.

## 5*f*_{xyz} and 5*f*_{z(x2-y2)} electron density

**Movie depicting the 5 f_{xyz} electron density function (ψ_{5fxyz})^{2}**. The left image shows a two-dimensional electron dot-density plot of the 5

*f*

_{xyz}orbital (across the

*x*=y plane). The right image is along the x=y, z=0 line. The 5

*f*

_{xyz}and 5

*f*

_{z(x2-y2)}are related to each other by a 45° rotation about the

*z*-axis.

## 5*f*_{y(3x2-y2)} and 5*f*_{x(x2-3y2)} electron density

**The first image shows a two-dimensional electron dot-density plot of the 5 f_{x(x2-3y2)} orbital (across the z=0 plane, x axis pointing right).** The 5

*f*

_{y(3x2-y2)}orbital is identical in appearance but rotated by 90° about the vertical

*z*-axis.

The Orbitron

^{TM}, a gallery of orbitals on the WWW: https://winter.group.shef.ac.uk/orbitron/

Copyright 2002-2021 Prof. Mark Winter [The University of Sheffield]. All rights reserved.