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Orbital Graphing

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Abstract

The goal of this document is to help students become familiar with preparing and viewing three-dimensional graphs of the angular parts of hydrogen-like atomic orbitals. The students plot the angular part of an s (l = 0, m = 0) orbital and a p_z (l = 1, m = 0) orbital. However, the atomic orbitals p₁ (l = 1, m = 1) and p_–1 (l = 1, m = –1) are graphed but look nothing like the familiar shape of a p orbital. Linear combinations of these orbitals are graphed, and the combinations result in the familiar p_x and p_y orbitals. The process is repeated for some of the d orbitals. In the second part of the document, the students use linear combinations of s and p orbitals to construct hybrid sp, sp², and sp³ orbitals.

Figure 1. The angular part of an f_z3 eigenfunction for a hydrogen-like ion. Screen from Orbital Graphing.

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Version	Student	Instructor
Mathcad 2001i	OrbitalGraphingStdnt2001i.mcd	OrbitalGraphing2001i.mcd

Version	Student	Instructor
Mathcad	OrbitalGraphingStdnt2001i.pdf	OrbitalGraphing2001i.pdf

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Keywords

Domain: Physical Chemistry;

Pedagogy: Computer-Based Learning;

Topics: Atomic Properties / Structure; Computational Chemistry; Mathematics / Symbolic Mathematics; Quantum Chemistry;

JCE Citation