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  Home > JCE Print > Journal of Chemical Education > Issues > 2004  > October  >
Information, Textbooks, Media, Resources
JCE SymMath: Symbolic Mathematics in Chemistry
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
Cover
October 2004
Vol. 81 No. 10
p. 1535
Full Text
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.


Figure 1. 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.
Supplement
Fully interactive computer algebra files are available in the JCE SymMath collection of the JCE Digital Library Only@JCE Online.
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*  Citation
 Johnson, John L. J. Chem. Educ. 2004 81 1535.
*  Keywords
 MO Theory; Numerical Methods; Quantum Chemistry
*  History
 Created:
Last Updated:		 August 31, 2004
September 9, 2004
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