TUD Organische Chemie  Immel  Tutorials  Orbitals  Atomic  View or Print (this frame only) 
Although the Schrödinger equation may not be explicitly solved for many electron systems, DFT and ab initio calculations can be used to numerically
and iteraviely solve the problem. Using this methodology, atomic and molecular orbitals can be computed, and the values of the wave functions or electron densities
can be generated on three dimensional grids around atoms or molecules. This page gives an overview on some atomic orbitals calculated for "real" atoms. Orbitals were
generated for the corresponding noble gases (n = 1: He, n = 1: Ne, n = 3: Ar, n = 4: Kr), with exception
of the forbitals that were generated for the Luthetium (Lu). For more information on the Quantum numbers, and other orbitals of higher states (from the 1s up to the 6d level),
see the hydrogenic orbitals generated for single electron systems (H, He^{+}, Li^{2+}, ...).
The following table provides an overview on the different types and shapes of orbitals from the 1s up to the 4f level. The orbitals are usually visualized as isocontour surfaces on the electron density, thus a 90% probability surface displays the threedimensional volume in which an electron is to be found with a 90% chance. Yellow and blue colors indicate regions of opposite sign of the wave function ψ (the electron density is proportional to ψ^{2}); and the "nodal" planes indicate spatial areas (actually planes, spheres, and cones) were the wave function passes through zero and changes sign. 


In contrast to the hydrogenic orbitals generated from pure Cartesian wave functions, these images are for the "real" atoms,
and all graphics were generated at a constant scale factor. Therefore, the size of the orbitals may be compared to each other for the different atoms (He, Ne, Ar, Kr, and Lu).
Click on the individual images to obtain enlarged visualizations of the orbitals, respectively.


Note: The forbitals displayed correspond to the general set of ffunctions listed for the hydrogenic atomic orbitals. 