# Atomic orbitals 7*f* wave functions

This page contains movies depicting the 7*f* wave functions and their nodal structures. In all cases the green zones are where the 7*f* wave function has positive values and the white zones denote negative values. See the 7*f* electron density page for movies depicting the 7*f* electron_density and nodal structures.

In each case the graph on the left is a surface plot of ψ_{7f} 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 7*f* orbitals has three planar nodes or conical nodes. The 7*f* orbitals have three spherical nodes but the higher *f*-orbitals (8*f*, 9*f*, ...
) have more while the lower orbitals (
4*f*,
5*f*, and
6*f*) have fewer.

## 7*f*_{z3}, 7*f*_{x3}, and 7*f*_{y3} orbital wave functions

**Movie depicting the 7 f_{z3} wave functions (ψ_{7fz3})^{2}.** The z-axis lies from left to right. The 7

*f*

_{x3}and 7

*f*

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

*x*and

*y*axes respecively. The 7

*f*

_{z3}orbital has one planar and two conical nodes. The 7

*f*orbitals have three spherical nodes but the higher

*f*-orbitals (8

*f*, 9

*f*, ... ) have more while the lower orbitals ( 4

*f*, 5

*f*, and 6

*f*) have fewer.

## 7*f*_{xz2} and 7*f*_{yz2} orbital wave functions

The first image shows a two-dimensional wave function plot of the 7*f*

_{xz2}orbital (across the

*x*=0 plane). The 7

*f*

_{yz2}wave function is identical in appearance but the orbital is related by a rotation by 90° about the

*y*-axis.

## 7*f*_{xyz} and 7*f*_{z(x2-y2)} wave functions

**Movie depicting the 7 f_{xyz} wave function (ψ_{7fxyz})^{2}**. The left image shows a two-dimensional wave function plot of the 7

*f*

_{xyz}orbital (across the

*x*=y plane). The right image is along the x=y, z=0 line. The 7

*f*

_{xyz}and 7

*f*

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

*z*-axis.

## 7*f*_{y(3x2-y2)} and 7*f*_{x(x2-3y2)} wave functions

**The first image shows a two-dimensional wave function plot of the 7 f_{x(x2-3y2)} orbital (across the z=0 plane, x axis pointing right).** The 7

*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.