Note: The 3D-models presented here represent the "old style" visualizations, these pages are no longer maintained. A new section using Jmol Models is available on this site, which does not require the installation of additional plugins for your browser.

The following pages provide some 3D-models of hydrogenic atomic orbitals. In order to view these models, an appropriate plugin for viewing VRML (Virtual Reality Modeling Language) files (WRL-file type for plugins such as the CosmoPlayer etc.) must be installed. Please note, that the files for the contour surfaces are rather large (100-1200 KBytes) and, depending on your line speed, may need some time to download. However, for this web-page these representations have been slightly reduced in resolution, and they may not disclose the fine "inner" details of the orbitals appropriately, for high-quality images with enhanced resolution of the different orbitals see the gallery of hydrogenic orbitals and hybrid orbitals. Further informations on how these models were generated and on some background theory is also available from these pages.

• 3D-Models of Atomic Orbitals - Visualizations
• 3D-Models of Hybrid Orbitals - Visualizations

The plot files (all 90% probability contours of the electron density ψ², with different colors blue and yellow corresponding to opposite signs of the wave function ψ, respectively) presented here are not scaled relative to each other, so the size of the orbitals may not be directly compared (for orbitals of "real" atoms see the atomic orbitals derived from DFT calculations). Click on the individual images to obtain the 3D models of the orbitals (a new window will open); the models can be freely rotated after downloading.

The picture on the right gives an illustration on how these 3D models look like when displayed with a VRML plugin. For 3D Models of superior quality see the Jmol Models of atomic and hybrid orbitals.

For more detailed information on these models see the page about hydrogenic orbitals.

3D-Model of an Orbital viewed with a VRML Plugin

Quantum Numbers

angular QN (l)

l = 0

l = 1

l = 2

principal QN (n )

magnetic QN (ml)

ml = 0

ml = -1, 0, +1

ml = -2, -1, 0, +1, +2

n = 1

s- Orbital

1s

n = 2

s- Orbital

p- Orbitals

2s

2px

2py

2pz

n = 3

s- Orbital

p- Orbitals

d- Orbitals

3s

3px

3py

3pz

3dxy

3dxz

3dyz

3dx2-y2

3dz2

n = 4

s- Orbital

p- Orbitals

d- Orbitals

4s

4px

4py

4pz

4dxy

4dxz

4dyz

4dx2-y2

4dz2

l = 3 ml = -3, ... +3 (general set)

f- Orbitals

4fz3

4fxz2

4fyz2

4fy(3x2-y2)

4fx(x2-3y2)

4fz(x2-y2)

4fxyz

l = 3 ml = -3, ... +3 (cubic set)

f- Orbitals

4fz3

4fy3

4fx3

4fx(z2-y2)

4fy(z2-x2)

4fz(x2-y2)

4fxyz

n = 5

s- Orbital

p- Orbitals

d- Orbitals

5s

5px

5py

5pz

5dxy

5dxz

5dyz

5dx2-y2

5dz2

l = 3 ml = -3, ... +3 (general set)

f- Orbitals

5fz3

5fxz2

5fyz2

5fy(3x2-y2)

5fx(x2-3y2)

5fz(x2-y2)

5fxyz

l = 3 ml = -3, ... +3 (cubic set)

f- Orbitals

5fz3

5fy3

5fx3

5fx(z2-y2)

5fy(z2-x2)

5fz(x2-y2)

5fxyz

l = 4 ml = -4, ... +4

g- Orbitals

5gz4

5gz3x

5gz3y

5gz2xy

5gz2(x2-y2)

5gzx3

5gzy3

5gxy(x2-y2)

5gx4+y4

n = 6

s- Orbital

p- Orbitals

d- Orbitals

6s

6px

6py

6pz

6dxy

6dxz

6dyz

6dx2-y2

6dz2

Note: The f-orbitals are special in as much as two different sets of functions are commonly in use, the general and the cubic set. The latter cubic set may be appropriate for describing atoms in an environment of cubic symmetry. Both sets have three orbitals in common (nf_z³, nf_xyz, and nf_z(x²-y²) with n = 4 (4f), 5 (5f), ...).

For more detailed information on the concept of hybrid orbitals and these models see the page about hybrid orbitals.

2sp	2sp2	2sp3		3sp	3sp2	3sp3		4sp	4sp2	4sp3
3sp2d	3sp3d	3sp3d2		4sp2d	4sp3d	4sp3d2

Here, only the most commonly used hybrid orbitals are listed, some examples and more detailed descriptions are available here.