 
Approximate Molecular Orbital Calculations for H_{2}^{+}©  
George M. Shalhoub Department of Chemistry La Salle University Philadelphia, PA 191411199 United States mail to: shalhoub@lasalle.edu  
Abstract  
The H_{2}^{+} is the prototype molecule and is the basis for our understanding of molecular orbital theory. Although H_{2}^{+} can be solved exactly in elliptical coordinates, the exact solution cannot be applied to other diatomic molecules and is therefore limited. It is more important for the understanding of molecular orbital concepts to approximate the solution to H_{2}^{+}. Such approximations can be compared to the exact theoretical values and the effectiveness of the approximations can be evaluated. These approximations can then be applied to more complicate molecular systems. This document presents a solution to the H_{2}^{+} ion Schrodinger equation using the Variational Method. All intermediate steps are shown with many plots of functions presented to enhance understanding the concepts. Exercises are embedded through out the document to focus student learning. The document concludes with the plots of the molecular orbitals and the probability density functions. This document is appropriate for undergraduate physical chemistry and first year graduate quantum chemistry courses and independent study courses.  
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Comments to: George M. Shalhoub at shalhoub@lasalle.edu  
©Copyright George M. Shalhoub, 2003. All rights reserved. You are welcome to use this document in your own classes but commercial use is not allowed without the permission of the author.  