Quantum Atomica Features

Quantum Atomica allows the user to experience visualisation of the complete set of hydrogen orbitals up to and including those for which the quantum number n is equal to 4.

In Quantum Atomica, these can either be selected by name as listed above, or by specifying the quantum numbers n, l & m. The selection process is exceptionally easy; for example the orbital 4Dx²-y² is being selected in the screenshot below:

Moments after pressing calculate, you are able to use the visualisations that Quantum Atomica was really designed for. The current types of visualisation include transects, weighted dot distributions and raytraced images.

Transects

Plotting transects is the most 'traditional' way of viewing the structure of the hydrogen orbitals. Quantum Atomica is capable of performing transects perpendicular to all 3 of the Cartesian co-ordinate axes. The probability density function corresponding to the orbital is sampled in the plane of the transect, and this data is used to plot a colour map, such as the following transects through 1S and 4Fz³ respectively (the brighter areas indicate regions of higher probability):

It is possible to change the position of the plane along its current axis smoothly in real-time, so animations of how the internal structure of the orbital function varies across an axis can readily be generated.

Weighted Dot Distributions

Plotting weighted dot distributions allows the users to experience the hydrogen orbitals in all three dimensions. The orbital functions, which are inherently continuous across space, are first converted into discrete distributions of points across space, using the continuous function as a basis to decide how to weight the placement of these points - areas which have a higher density of points correspond to areas of higher probability. Probability variation can also be depicted using colour; bright green is associated with the maximum probability, which then fades to red and finally transparency for very low probability. The following pair of images, showing 4Fxyz and 4Dxy respectively, illustrate these concepts:

Furthermore, users have the luxury of being able to actually make these images seem 3D through the magic of stereoscopic anaglyphs. Instead of the computer using one camera, such as when generating the images above, two slightly separated cameras are used - one which sees only in green, and one which sees only in red. When this is done, images such as the following are produced:

If these images are viewed with the appropriate colour filters (a red filter covering the right eye and a green filter covering the left eye), then the orbital pops into sharp relief and users are able to see it floating in space some way in front of the screen. Combining this facility with the fact that all the weighted dot distributions are readily rotated in real-time provides the user with a fully spatial understanding of the structures of the orbital functions.

Raytraced Images (Volumetric Images)

Raytraced images, referred to in Quantum Atomica as Volumetric Images, are the closest Quantum Atomica actually gets to drawing the oft cited 'electron probability cloud.' Hypothetical rays of light are passed through the orbital functions, and the total amount of probability it encounters during this brief journey gives an indication of how opaque this section of the volumetric image is. Volumetric images are extremely useful for assaying the internal structure of an orbital function as they will pick up details that the weighted dot distribution visualisation will miss:

As can be seen on the above images of the 3Dz² orbital, the volumetric image has picked up a channel of very low probability which goes through the centre of the torus and the two external lobes. The volumetric images can also be rotated in real-time, so that it is possible to view them from all angles.

As of version 2 of Quantum Atomica, volumetric images can be rendered using orthographic, perspective or anaglyph modes. This allows even better visualisation - particularly with volumetric anaglyphs where the probability "cloud" can be viewed truly in 3D. The following picture shows 4Fz³ rendered as a volumetric anaglyph.

Summary

Typically, all three methods are used together - for example, the following screenshot shows a transect being taken through a weighted dot distribution image of 4Dz²: