Visualizing Atomic Orbitals
Atomic orbitals are the
wavefunctions which are solutions of the Schrödinger equation for the
hydrogen atom. The subset of atomic orbitals 
, 
, 
and 
are plotted in three dimensions to exhibit their characteristic shapes.
Contributed by: Guenther Gsaller (June 2007)
(Institute of Organic Chemistry, Johannes Kepler University, Linz, Austria, http://www.jku.at/orc/)
Open content licensed under CC BY-NC-SA
Snapshots
Details
In chemistry
orbitals can be classified according to their orientation in a
rectangular coordinate system. The set of shapes in the snapshots is
given for 
and for combinations of 
.
The three 
-orbitals for a given value of 
are described by the values 
; gives the 
orbital. The angular functions for 
are complex and depend on 
, 
, or both. Pairwise linear combinations of complex spherical harmonics 
yield real functions, which can be plotted as boundary surfaces.
For 
and 
, for example, we have
and 
.
The function pos inside OrbitalModel is shown at the link Problem with SphericalPlot3D plotting. It is used to attach signs to the positive or negative parts of the radial wavefunction. Then both parts are colored differently.
Alternative representations for the seven 
orbitals can be written. In this Demonstration, the most commonly used convention was chosen [3].
References
[1] P. Atkins, R. Friedman, Molecular Quantum Mechanics, Oxford: Oxford University Press, 2011.
[2] R. King, "Atomic orbitals, symmetry, and coordination polyhedra," Coordination Chemistry Reviews, 197, 2000 pp. 141–168.
[3] M. Winter. "The Orbitron: a gallery of atomic orbitals and molecular orbitals on the WWW." (Jan 2013) http://winter.group.shef.ac.uk/orbitron/AOs/4f/index-gen.html.
Permanent Citation
https://demonstrations.wolfram.com/VisualizingAtomicOrbitals/
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