# Atomic orbitals: 5g electron "dot-density"

This page shows representations of electron density in two ways. The first is two-dimensional electron "dot-density" diagrams - plots across an appropriate plane of each 5g orbital. These were created using a Monte Carlo computational method. The second page allows you interact (zoom, rotate) with three-dimensional electron "dot-density" models representing electron density of the various 5g atomic orbitals created by the same Monte Carlo computational method. Green represents regions for which the wave functions are positive and white represents where values are negative.

## 5gz4 electron "dot-density"

The 5gz4 orbital is an abbreviation for 5g35z4 - 30z2r2 + 3r4.

The first image shows a two-dimensional electron dot-density plot of the 5gz4 (z-axis is vertical). The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

## 5gz3y and 5gz3x electron "dot-density"

The 5gz3x orbital is an abbreviation for 5gyz(7z2 - 3r2). The 5gz3y orbital is an abbreviation for 5gxz(7z2 - 3r2). These two orbitals are related to each other by a 90° rotation about the z-axis.

The first image shows a two-dimensional plot representing electron density of the 5gz3y orbital (across the x=0 plane) and 5gz3x orbital (across the y=0 plane). The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

## 5gz2xy and 5gz2(x2-y2) electron "dot-density"

The 5gz2xy orbital is an abbreviation for 5gxy(7z2 - r2). The 5gz2(x2 - y2) orbital is an abbreviation for 5g(x2 - y2)(7z2 - r2). These two orbitals are related to each other by a 45° rotation about the z-axis.

The first image shows a two-dimensional electron dot-density plot of the 5gz2(x2 - y2) across the y=0 plane. The electron density plot of the 5gz2xy orbital is identical in appearance but plotted through the x=y plane. The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

## 5gzy3 and 5gzx3 electron "dot-density"

The 5gzy3 is an abbreviation for 5gyz(3x2 - y2). The 5gzx3 orbital is an abbreviation for 5gxz(x2 - 3y2). These two orbitals are related to each other by a 30° rotation about the z-axis.

The first image shows a two-dimensional electron dot-density plot of the 5gzy3 orbital (across the x=0 plane. The 5gzx3 electron density plot is identical when plotted across the y=0 plane. The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

## 5gxy(x2-y2) and 5g(x4+y4) electron "dot-density"

The 5gxy(x2-y2) and 5g(x4+y4) orbitals are related to each other by a 22.5° rotation about the z-axis.

The first image shows a two-dimensional electron dot-density plot of the 5g(x4+y4) orbital across the z=0 plane). The corresponding plot for the 5gxy(x2-y2) orbital is similar but rotated by 22.5° in the plane of your screen. The second image is an interactive (see below for instructions) represention of electron density in three-dimensions for the same orbitals.

### Using JSmol

You can use your mouse to manipulate the "orbital" in the "JSmol" image above. How you do this depends upon how you are viewing this page.

• On a computer, to rotate about the x and y directions, drag mouse around the image
• On a computer, to rotate about the z direction (which comes out of the screen towards you), hold shift and drag mouse horizontally
• To zoom, hold shift key down and drag mouse vertically
• To reset the image, hold down shift key and double click ony part of the image not containing dots
• On a mobile device experiment using one or two fingers to rotate and zoom

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