SymMath Collection  Curator's Commentary  Author Guidelines  Reviewer Guidelines  About JCE SymMath  Contribute!

Graphing Orbitals in Three Dimensions with Rotatable Density Plots

Abstract
Downloads
Commentary
More Information: Keywords, JCE Citation

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.

Figure 1. 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.

Downloads

Version	Download
Maple 10	DensityPlottingOrbitals.mw

Version	Download
Maple 10	DensityPlottingOrbitals.pdf

 JCE Subscribers only: Institutional IP number access or name and password required

Commentary

Other Information

Keywords

Audience: Upper-Division Undergraduate;

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation