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
•chem673.html
Required Books, etc.
•Chemical Applications of Group Theory,”
by Cotton, Wiley, 1990.
•Symmetry and Spectroscopy; An Introduction...”,
by Harris & Bertolucci, Dover, 1989.
•Handouts
Prerequisites
•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
1.to promote in-depth understanding of principles of symmetry and group theory;
2.to demonstrate the extensive and powerful applications of group theory in
various problems; and
3.to 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.
Syllabus
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)
≺SubGroups
≺Classes
≺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??