# Atomic orbitals: 6*h* 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 6*h* 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 6*h* atomic orbitals created by the same Monte Carlo computational method. Turquoise (cyan) represents regions for which the wave functions are positive and white represents where values are negative.

## 6*h*_{z5} electron "dot-density"

The 6*h*_{z5} orbital name is an abbreviation for 5*h*_{z(63z4 - 70z2r2 + 15r4)}.

*h*

_{z5}(

*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.

## 6*h*_{yz4} and 6*h*_{xz4} electron "dot-density"

The 6*h*_{yz4} orbital name is an abbreviation for 6*h*_{y(21z4–14z2r2+r4)}. The 6*h*_{xz4} orbital name is an abbreviation for 6*h*_{x(21z4–14z2r2+r4)}. These two orbitals are related to each other by a 90° rotation about the *z*-axis.

*h*

_{yz4}orbital (across the

*x*=0 plane) and 6

*h*

_{xz4}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.

## 6*h*_{z3xy}, 6*h*_{z3(x2–y2)} electron "dot-density"

The 6*h*_{z3xy} orbital is an abbreviation for 6*h*_{(2xy)(3z3–zr2)}. The 6*h*_{z3(x2–y2)} orbital is an abbreviation for 6*h*_{(x2–y3)(3z3–zr2)}. These two orbitals are related to each other by a 45° rotation about the *z*-axis.

*h*

_{z3xy}across the

*y*=0 plane. The electron density plot of the 6

*h*

_{z3(x2–y2)}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.

## 6*h*_{z2y3} and 6*h*_{z2x3} electron "dot-density"

The 6*h*_{z2y3} is an abbreviation for 6*h*_{y(3x2–y2)(9z2–r2)}. The 6*h*_{z2x3} orbital is an abbreviation for 6*h*_{x(x2–3y2)(9z2–r2)}. These two orbitals are related to each other by a 30° rotation about the *z*-axis.

*h*

_{z2y3}orbital (across the

*x*=0 plane. The 6

*h*

_{z2x3}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.

## 6*h*_{z(4x3y–4xy3)} and 6*h*_{z(x4–6x2y2+y4)} electron "dot-density"

The 6*h*_{z(4x3y–4xy3)} and 6*h*_{z(x4–6x2y2+y4)} orbital are related to each other by a 22.5° rotation about the *z*-axis.

*h*

_{(x4+y4)}orbital across the

*z*=0 plane). The corresponding plot for the 6

*h*

_{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.

## 6*h*_{yx4}, and 6*h*_{xy4} electron "dot-density"

The 6*h*_{yx4} is an abbreviation for 6*h*_{y(5x4–10y2x2+y4)} and 6*h*_{xy4} is an abbreviation for 6*h*_{x(x4–10y2x2+5y4)}. They are related to each other by a 18° rotation about the *z*-axis.

*h*

_{yx4}orbital (across the

*z*=0 plane. The 6

*h*

_{xy4}electron density plot is identical but rotated by a 18° rotation about the

*z*-axis. 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 2002-2021 Prof Mark J. Winter [Department of Chemistry, The University of Sheffield]. All rights reserved.