 
Optimization of Geometries by Energy Minimization©  
Tracy P. Hamilton Department of Chemistry University of Alabama at Birmingham Birmingham, AL 352941240 United States mail to: hamilton@uab.edu  
Abstract  
The purpose of this document is to describe the details of using the NewtonRaphson method to minimize the energy of a molecular structure by optimizing the coordinates that define that structure. This is done by exploring the details of a minimization process in detail. This permits students to see beyond the black box usage of commercially available molecular modeling programs. The document is heavily annotated and contains student exercises for each section. Students exercises range from simple to more complex at the end where they are asked to repeat the process by writing a Mathcad document for optimizing the structure of water. Harmonic, anharmonic, forces, and uncoupled and coupled coordinates are included. Students learn how to construct a Hessian matrix and study the consequences of a guessed Hessian matrix on the optimization process. This document can be used profitably by Junior and Senior undergraduates or first year graduate students. Acompanion document that students can use to understand a gradient search on a potential energy surface is Steepest Descents: Finding the Minimumin a Function. A study of the unit analysis of the Morse potential function found in document Exploring the MorsePotential would be a valuable adjunct to the material developed here. Development of this document was made possible by the NSF supported 1997 "Workshop for Integrationof Numerical Methods into the Undergraduate Physical Chemistry Curriculum Using theMathcad Software" at the University of South Alabama, Mobile Alabama.  
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Comments to: Tracy P. Hamilton at hamilton@uab.edu  
©Copyright Tracy P. Hamilton, 1997. 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.  