Getting started

Pick an element in the table at the bottom. After you choose, the table slides away; hover over its bar (or tap it) to bring it back.
Pick an orbital on the left – 1s, 2s, 2p … – or Total for the whole atom.
Drag to rotate and use the mouse wheel to zoom. On a touch screen, drag with one finger and pinch with two.

On a phone the controls live in the tabs at the bottom (Element, Orbital, View, Info); tap a tab to open it and tap it again to close it.

An orbital is the region around the nucleus where an electron is likely to be found. These are neutral atoms in their lowest-energy (ground) state.

Keys and mouse

Drag / one finger	Rotate the view (not in 2D Slice)
Mouse wheel / pinch	Zoom
`Ctrl` + wheel	Move the cutaway plane (the slice in 2D Slice)
`R`	Reset the cutaway to the middle
`C`	Turn the cutaway 90° (not in 2D Slice)
`F1`	Show this help
`Esc`	Close this help

Three ways to look at it

Solid: A surface around the region that holds a chosen share of the electron’s probability (90% by default).
Volumetric: A glowing cloud: the brighter and warmer the colour, the denser the electron. The colour legend is at the top right.
2D Slice: A flat cross-section through the nucleus, seen face-on along the x axis. It cannot be rotated; the slider moves the slice.

What the settings do

Shown region holds: How much of the electron’s probability lies inside what you see – the solid surface, the edge of the cloud and the outline. 99% shows more of the faint outer fringe, 50% only the dense core.
Full subshell (sum over m): p, d and f orbitals normally show one lobed orbital (p_z, d_z², f_z³). Tick this to show the whole subshell instead: a sphere, averaged over all directions. For a partly filled subshell (such as Fe 3d⁶) it is an average weighted by how many electrons it holds.
Total: All occupied orbitals added together: the atom’s total electron density.
Cutaway: Cuts the orbital open so you can see inside. Show cutaway plane draws the cut; Rotate cutaway turns it 90°.
Show outline & Brightness: Volumetric only: a thin line around the Solid surface, and how opaque the cloud is.
Quality: Trades sharpness for speed. The app tests your device on the first visit and picks a level; if dragging feels slow, try Low or Medium.

Reading the numbers

Radial probability (top right): How likely the electron is to be found at each distance r from the nucleus. Dashed lines are radial nodes (distances where it is never found), the dot is the most likely distance, and the blue tick is the radius that holds the chosen share.
Density, e/Å³: Electrons per cubic ångström (1 Å = 100 pm). For a single orbital this is per electron; for a full subshell it is multiplied by the number of electrons, and for Total it is the real electron density.
Scale bar and axes: The scale bar (bottom left) follows your zoom; the XYZ globe (bottom right) follows your view.

About the data

The orbitals come from published non-relativistic Hartree–Fock calculations, so they are an approximation: good for learning about shapes and nodes, not for quantitative research. Elements 104–118 are greyed out because no such data exists for them.

References and sources

Wavefunction data, H–Xe: T. Koga, Y. Kanayama, S. Watanabe and A. J. Thakkar, “Analytical Hartree–Fock wave functions subject to cusp and asymptotic constraints: He to Xe, Li⁺ to Cs⁺, H⁻ to I⁻”, Int. J. Quantum Chem. 71, 491–497 (1999).
Wavefunction data, Cs–Lr: T. Koga, K. Kanayama, T. Watanabe, T. Imai and A. J. Thakkar, “Analytical Hartree–Fock wave functions for the atoms Cs to Lr”, Theor. Chem. Acc. 104, 411–413 (2000).
Data distribution: A. J. Thakkar’s research data downloads, ajit.ext.unb.ca/download.htm; the coefficient tables used here were taken from J. W. Furness, AtomicOrbitals, github.com/JFurness1/AtomicOrbitals.
Slater-type orbitals: J. C. Slater, “Atomic shielding constants”, Phys. Rev. 36, 57 (1930), doi:10.1103/PhysRev.36.57.
Hartree–Fock–Roothaan method: C. C. J. Roothaan, “New developments in molecular orbital theory”, Rev. Mod. Phys. 23, 69 (1951), doi:10.1103/RevModPhys.23.69.
Angular parts (real spherical harmonics): P. Atkins and R. Friedman, Molecular Quantum Mechanics, 5th ed., Oxford University Press (2011).
Bohr radius (length unit): E. Tiesinga, P. J. Mohr, D. B. Newell and B. N. Taylor, “CODATA recommended values of the fundamental physical constants: 2018”, Rev. Mod. Phys. 93, 025010 (2021), doi:10.1103/RevModPhys.93.025010.
Volume rendering: M. Levoy, “Display of surfaces from volume data”, IEEE Comput. Graph. Appl. 8(3), 29–37 (1988), doi:10.1109/38.511; N. Max, “Optical models for direct volume rendering”, IEEE Trans. Vis. Comput. Graph. 1(2), 99–108 (1995), doi:10.1109/2945.468400.
Colour map: inspired by the “inferno” map of S. van der Walt and N. Smith (Matplotlib), bids.github.io/colormap; the version here is a simplified hand-coded approximation.
Element names and table layout: IUPAC Periodic Table of the Elements, iupac.org.
3D library: three.js (r128, MIT licence), threejs.org.

Contact

Questions, corrections or suggestions about this application are welcome.