Optimization of Geometries by Energy Minimization©
Tracy P. Hamilton
Department of Chemistry
University of Alabama at Birmingham
Birmingham, AL 35294-1240
United States
mail to: hamilton@uab.edu

The purpose of this document is to describe the details of using the Newton-Raphson 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.
Audiences: Upper-Division Undergraduate, Graduate Education / Research
Pedagogies: Computer-Based Learning
Domains: Physical Chemistry
Topics: Chemometrics, Mathematics / Symbolic Mathematics, Molecular Mechanics / Dynamics, Theoretical Chemistry
File NameDescriptionSoftware TypeSoftware Version
molmech.mcd Computational Mathcad Document Mathcad
molmech.pdf Read-Only Document
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.