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Symmetry and Group Theory in Chemistry

Symmetry and Group Theory in Chemistry
•Grades will be based on the homework
(roughly 50%), midterm and final exams

Required Books, etc.
•Chemical Applications of Group Theory,”
by Cotton, Wiley, 1990.
•Symmetry and Spectroscopy; An Introduction...”,
by Harris & Bertolucci, Dover, 1989.

•Undergraduate chemistry courses, especially
inorganic and physical chemistry.
•Usual math courses for scientists, especially linear algebra.
•If you have not had linear algebra, then familiarity with vectors and matrices acquired elsewhere may suffice
—don’t wait to review these topics, do so this week! –Minimum background: Appendix in Cotton’s text.

Symmetry and Group Theory in Chemistry

Objectives: The incentives of the course are promote in-depth understanding of principles of symmetry and group theory; demonstrate the extensive and powerful applications of group theory in various problems; and demonstrate how real complex cases are solved with the aid of group theory and the combination of multiple approaches.

As a result, students who complete this course are expected to:
1. understand the basics of group theory and their mathematical and physical origins;
2. be able to identify the problem and find the correct information from appropriate tables; and
3. be able to apply the principles to address a variety of research topics, especially those involving vibrationalspectroscopy and crystallography.

Why is Group Theory Important??

Chapter 1: Symmetry Elements or Operations
≺Symmetry Operations (or Elements):
identity –Inversion –Rotation –Reflections -Improper Rotations
≺Relations Between Symmetry Elements
≺Optical Activity
≺Qualitative Symmetry Element Classifications

Chapter 2 -Point Groups
≺Specific sub-and superscript notations for symmetry elements
≺Process for identifying the symmetry of an object

Chapter 3 -Group Theory
≺Terms and definitions
≺Group Multiplication Table (matrix operations)
≺Matrix Operations
≺Group Representations
≺Character Tables
≺The Great OrthogonalityTheorem
≺Five “Rules”about Irreducible Representations:

Chapter 4 -Applications: Molecular Vibrations
≺Molecular vibrations
≺Infrared Selection Rules
≺Metal Carbonyls

Chapter 5 -X-Ray Structure Analysis
≺Trans Effects
≺p-Acceptor TransEffects
≺Some Structural Examples:
≺Moving to the Later Transition Metals:
≺Second Row “Anomaly”Effect?
≺Bond Length vs. Bond Strength??