Symmetry / Group Theory
Finding Molecular Vibrational Frequencies from HCl to SO2 JCE
Franklin M.C. Chen, University of Wisconsin-Green Bay
Theresa Julia Zielinski, Monmouth University
Students learn about finding molecular vibrational frequencies through normal mode analysis and numerical solutions for simple molecule such as HCl and more complicate molecules such as CO2 and SO2. Topics such as displacement coordinates, internal coordinates, symmetry coordinates, and their relationship are developed.
Learning Molecular Geometry & Symmetry Through Quantum Computations and Mathcad™ Exercises JCE
Franklin M.C. Chen, University of Wisconsin-Green Bay
A Mathcad template to help students learn about molecular geometry and symmetry calculations based on the coordinate datagenerated from quantum computation software such as HyperChem. The molecular coordinate data serve as excellent real-world materials for students to appreciate the applications of linear algebra and to refresh their algebra learning experiences about linear transformations learn about fundamental properties of quantum and symmetry operators.
Using a Computer to Help Understand How Symmetry Principles Reduce Calculations JCE
Louis Kijewski, Monmouth University
This Mathcad document uses symmetry to simplify the evaluation of an eigenvalue problem by reducing a matrix to sparse form. The sparse matrix is then transformed to block diagonal form. Group theory is used to set up the calculations without going through the proofs of the methods. The ability to use symmetry principles to get the vibrational frequencies and other information about molecules with symmetry is an important asset to any chemist.