Visualization of Wavefunctions of the Ionized Hydrogen Molecule
John L. Johnson
Department of Engineering Science and Mechanics,The Pennsylvania State University, University Park, PA 16802
Abstract
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Commentary
More Information: Keywords, JCE Citation
Abstract
Using Mathcad and the Shooting Method, students can numerically solve the Schrödinger equation for the ionized hydrogen molecule. The solutions to the angular portions of the wavefunctions are the spheroidal harmonics, which students can plot to visualize the shapes of molecular orbitals. These exact solutions are compared with those obtained from the linear combination of atomic orbital (LCAO) method, using hydrogenic orbitals as basis functions. From the products of the angular and radial wavefunctions, students can also plot the electronic charge densities to see the concentration of charge that distinguishes bonding and anti-bonding states. The bonding properties are confirmed by plotting the energies of the wavefunctions as a function of internuclear distance for the eight lowest molecular energy states.
Mathcad plot of the 3sg orbital for the ionized hydrogen molecule as given by the spheroidal harmonic with a degree of 2 and an order of 0.
Downloads
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Document link |
Document type |
Download Info |
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IonizedHydrogen.zip |
.ZIP archive |
828 KB |
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ZIP archive contains: HMI.mcd, Oblate spheroidal coordinates.mcd, Prolate spheroidal coordinates.mcd, Spherical coordinates.mcd
Fully interactive with Mathcad 11 or higher
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IonizedHydrogen.pdf |
Acrobat.pdf |
214 KB |
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Non-interactive derived from Mathcad 11 files above. |
JCE Subscribers only: Institutional IP number access or name and password required
Commentary
Editor's Commentary
Other Information
Keywords
Computer-Based Learning; Physical Chemistry; Quantum Chemistry; MO Theory; Mathematics;/Symbolic Mathematics; Upper Division Undergraduate
JCE Citation
Johnson, John L. J. Chem. Educ. 2004, 81, 1535.
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