# Atomic orbitals: 7*g* 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 7*g* 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 7*g* atomic orbitals created by the same Monte Carlo computational method. Purple represents regions for which the wave functions are positive and white represents where values are negative.

## 7*g*_{z4} electron "dot-density"

The 7*g*_{z4} orbital is an abbreviation for 7*g*_{35z4 - 30z2r2 + 3r4}.

*g*

_{z4}(

*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.

## 7*g*_{z3y} and 7*g*_{z3x} electron "dot-density"

The 7*g*_{z3x} orbital is an abbreviation for 7*g*_{yz(7z2 - 3r2)}. The 7*g*_{z3y} orbital is an abbreviation for 7*g*_{xz(7z2 - 3r2)}. These two orbitals are related to each other by a 90° rotation about the *z*-axis.

*g*

_{z3y}orbital (across the

*x*=0 plane) and 7

*g*

_{z3x}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.

## 7*g*_{z2xy} and 7*g*_{z2(x2-y2)} electron "dot-density"

The 7*g*_{z2xy} orbital is an abbreviation for 7*g*_{xy(7z2 - r2)}. The 7*g*_{z2(x2 - y2)} orbital is an abbreviation for 7*g*_{(x2 - y2)(7z2 - r2)}. These two orbitals are related to each other by a 45° rotation about the *z*-axis.

*g*

_{z2(x2 - y2)}across the

*y*=0 plane. The electron density plot of the 7

*g*

_{z2xy}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.

## 7*g*_{zy3} and 7*g*_{zx3} electron "dot-density"

The 7*g*_{zy3} is an abbreviation for 7*g*_{yz(3x2 - y2)}. The 7*g*_{zx3} orbital is an abbreviation for 7*g*_{xz(x2 - 3y2)}. These two orbitals are related to each other by a 30° rotation about the *z*-axis.

*g*

_{zy3}orbital (across the

*x*=0 plane. The 7

*g*

_{zx3}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.

## 7*g*_{xy(x2-y2)} and 7*g*_{(x4+y4)} electron "dot-density"

The 7*g*_{xy(x2-y2)} and 7*g*_{(x4+y4)} orbitals are related to each other by a 22.5° rotation about the *z*-axis.

*g*

_{(x4+y4)}orbital across the

*z*=0 plane). The corresponding plot for the 7

*g*

_{xy(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 Orbitron

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

Copyright 2002-2023 Prof. Mark Winter [The University of Sheffield]. All rights reserved.