The Atomic Explorer (AE) is designed to display the atomic orbitals and densities of elements 1 through 54 (hydrogen through xenon). The displays are based on published data from self-consistent Roothaan-Hartree-Fock computations.

With the Atomic Explorer the user can explore trends in the Periodic Table and become familiar with the shapes of the atomic orbitals in preparation for understanding molecular bonding. Specifically, the Atomic Explorer lends itself to inquiries into the shapes and sizes of atomic orbitals, the role of screening, and ionization trends. The Atomic Explorer also serves as a supporting tool for understanding the diatomic and polyatomic molecules that can be studied with the Diatomic and Polyatomic Explorers, and as a direct link to the activities of the soon-to-be-available Spectrum Explorer.

Here we provide an introduction to the use of the Atomic Explorer. This is a how-to, not a curriculum exercise, intended to acquaint the new user with the tools available from the different menus of the application, and also a few pointers about pitfalls in the use of the tools.

Launch the Atomic Explorer.On launch the Atomic Explorer displays two windows. The window on the left is referred to as the Energy Level Diagram Viewer; the window on the right is the Slice Viewer. By default the Energy Level Diagram for hydrogen is displayed on launch. You should see what appears in Figure 1.

The left-hand window displays the energy levels of hydrogen. A scale for the energies runs along the left margin of the window. Each line segment is labeled by the atomic orbital to which it belongs.

The energy levels are labeled according to the conventional scheme. Each level has principal quantum number n, and an angular momentum quantum number l. The letters s, p,d, and f correspond to the values l = 0, 1, 2, 3. For each value of l there are 2l+1 states corresponding to the component of angular momentum along an axis in an arbitrary direction (conventionally the z-axis). So for l=1, there are three 2p orbitals. [N.B.: In the above all orbitals for H for a specified value of n have the same energy. For example, the 2s and 2p orbitals all have the same energy. Experimentally this is not true. There is a small splitting of the energy levels in each shell. A later edition of the program will offer a toggle to show a more correct energy diagram for expert use.]

For example, the lowest energy state quantum of the H-atom is the 1s state. Its energy is -13.6 eV.

The next highest energy state of H is the n=2 level corresponding to an energy -3.4 eV. There are 4 orbitals for this energy; these are the 2s, 2p_x, 2p_y, and 2p_z orbitals. The subscripts are not included in the orbital labeling because of space limitations.

To display a graphical representation of an orbital, click on an energy level. As an exercise, duplicate Fig. 2 below.

The orbital display window now has the caption Amplitude: 3d_xy. By amplitude we mean that we are plotting the wave function of the orbital (as opposed to the electronic density). We are displaying the real wave functions (as opposed to the real part of the complex wave functions). The purple and green color code indicates the phase of the lobe. Since this is a real valued wave function, the phase is either +1 or -1. It is arbitrary which color is associated with which sign provided that after you choose an assignment you retain it. Other orbitals can be selected by clicking on their energy level representation.

The Orbital Display window is also referred to as the slice viewer. What is plotted in two dimensions is the intersection of a plane (in this case the yz-plane) with the orbital. It is quite possible that the slice of an orbital could produce a blank Orbital Display window. For example, the xy-plane intersecting with 3d_xy is blank, as this is a slice through a node of the wave function.

If you are running the 3d version of the program: To obtain a better feeling for the orbital, view it as a surface in three-dimensions. Select Isosurface from the Display pull-down menu. You should see the following:

The Isosurface window is an interactive window. To orient the isosurface as show in Figure 3, drag on it with your mouse.

To reproduce Figure 4 of the 2p orbital of carbon, first select the Edit pull-down menu and there choose Set Atom. The floating dialog window shown in Figure 5 will appear.

Select Carbon from the pull-down menu of this dialog box, or type in 6 for the Atomic Number. If you type in the Atomic Number, click on Update. Now go to the Display pull-down menu and select Density. Finally, click on the orbital level to be displayed in the Energy Level Window.

The image you are likely to see in the Orbital Display Window is probably much smaller and pixelized than that in Figure 4. To adjust your image, note that the width of the Display Window is 80 A. Decrease this width by selecting in sequence the following:

Preferences pull-down menu

Slice

Zoom In

Repeat this process two more times. Each Zoom In reduces the width by a factor of 2. At the end of the Zoom In process the size of the orbital will be brighter and larger than that in Figure 4. Size is somewhat arbitrary in the current display: it is a function of the selected display intensity. To reduce the intensity, select the Intensity pull-down menu and choose 2. This should reproduce the image in Figure 4.

Suppose we wanted to study the core electrons of iron. Iron does not appear on the pull-down menu of the Set Atom box. However, you can type in 26 for the Atomic Number to select iron. You should obtain what appears in Figure 6.

In the Energy Level window is displayed the valence electron of iron. To observe all electronic energy levels down to the 1s electron follow this sequence:

select the Preferences menu

select the Energy Level Diagram option

select Scale to Screen

You will obtain the windows in Figure 7.

To see the 1s orbital, scroll down in the Energy Level Window. You can now select a series of orbitals to compare in size and geometry. Some of the orbitals may be too tightly packed for easy distinction. A combination of Zoom Ins and Zoom Outs from the Energy Level Diagram option under Preferences will be necessary.

Here we list the function of each of the options from the menus of the Atomic Explorer. Many of these are self-explanatory or have been used in the examples above.

New: Open a new window for either the Atomic Explorer, the Bond Explorer, or the Diatomic Molecule Explorer. You can have multiple windows for any of these Explorers. This allows comparison of displays for different parameters.

Open: Not an active feature at this time. When completed it will allow opening a saved file.

Save: Not an active feature at this time. When completed it will allow saving a file.

Exit: Exit for the Explorer. Only the window with the menu will be closed. Other instances that are active must be shut separately.

Set Atom: Opens a dialog box to specify the atom to be studied. Atoms can be selected by name for elements hydrogen through argon. Atoms can be selected by atomic number for elements from hydrogen through xenon.

Show Energy Level Diagram: When this option is selected the window showing the energy level diagram is visible. If this option is selected a check mark appears in the menu next to it.

Show Orbital Slice: When this option is selected the window showing a planar slice through orbital amplitude or density is displayed. If this option is selected a check mark appears in the menu next to it.

Energy Level Diagram: If this option is selected a pull-down menu is displayed. From this pull-down menu the following options are available:

Slice: If this option is selected a pull-down menu is displayed. From this pull-down menu the following options are available to alter the view in the Orbital Slice Window.

Select a number from 1 to 5 to vary the brightness of the display. The dimmest setting is 1. The brightest is 5. This option is a simplified version of setting the minimum and maximum values for the Color Range in the Orbital Slice Preferences dialog box.

Specify the plane to which the slice through the orbital is parallel. Options are xy, yz, or zx. This option menu is a simplified version of setting the Plane in the Orbital Slice Preferences dialog box.