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  Home > JCE Print > Journal of Chemical Education > Issues > 2007  > November  >
Information • Textbooks • Media • Resources
JCE SymMath: Symbolic Mathematics in Chemistry
Graphing Orbitals in Three Dimensions with Rotatable Density Plots
Louis Kijewski
Department of Chemistry, Medical Technology, and Physics, Monmouth University, West Long Branch, NJ 07764
Cover
November 2007
Vol. 84 No. 11
p. 1887
Abstract
Maple may be used to make three dimensional plots that may be rotated to view at any orientation. The procedures for making density plots of the probability density Ψ* Ψ of wave functions for 1s, 2p, and 3d hydrogen orbitals are explained. Density plots show many points per volume element where the probably density is large and few points per volume element where the probability density is small. The density plot of a cross section of a 2s orbital’s probability density shows a spherical node. Plots for sp, sp2, and sp3 hybrids are also produced and the procedure explained. A plot of a surface that contains 95% of the probability for the 2s2p hybrid is produced to compare to its density plot. Instructors can use this document in class discussions of density plots. Opportunities exist for instructors or students to create other density plots as mastery exercises.

A 3-D density plot for a 3d orbital with quantum numbers l = 2 and m = 0. Points are generated by using the probability of finding an electron in a shell of radius r and thickness dr, where r is measured in Bohr radii.
Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
More Information
*
Citation
Kijewski, Louis. J. Chem. Educ. 2007, 84, 1887.
*
Keywords
Computer-Based Learning; Mathematics / Symbolic Mathematics; Physical Chemistry; Quantum Chemistry; Upper-Division Undergraduate
*
History
Created:
Last Updated:
9/19/2007
9/27/2007
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