Author Profile

Dr. Anne Baranger is a prominent chemist, award-winning educator. She earned her B.S. in Chemistry from the Massachusetts Institute of Technology (MIT) before completing her Ph.D. in Inorganic Chemistry at UC Berkeley. Following a prestigious postdoctoral fellowship in Chemical Biology at Yale University, Dr. Baranger built a distinguished career holding faculty positions at Wesleyan University and the University of Illinois at Urbana-Champaign. With decades of experience teaching rigorous chemical content and pioneering evidence-based educational practice, Dr. Baranger is nationally recognized for her work in chemical education and inclusive excellence in STEM. In Molecular Symmetry and Group Theory, she channels her extensive background in inorganic structure and student-centered pedagogy to make the mathematical and physical foundations of molecular symmetry accessible, engaging, and profoundly

About The Book

Molecular Symmetry and Group Theory is the definitive guide to mastering one of the most elegant, powerful, and essential mathematical frameworks in modern chemistry. Often perceived as abstract or daunting, molecular symmetry is actually the master key to predicting how molecules behave, vibrate, and interact with light. This book transforms complex mathematical principles into an intuitive, visually rich, and highly actionable tool for chemists. Designed for advanced undergraduates, graduate students, and researchers alike, this text bridges the gap between pure mathematics and chemical reality. It demonstrates how the foundational laws of group theory directly dictate the physical properties of matter, from the structural geometries of simple inorganic complexes to the intricate electronic spectra of advanced materials.

Table of Contents

Preface
1. SYMMETRY ELEMENTS AND SYMMETRY OPERATIONS: MOLECULAR SYMMETRY
Introduction
Molecular Symmetry: In Non-mathematical and Geometrical Sense
Symmetry operations and symmetry elements
Naming systems of notation for symmetry operations/elements
Proper axis of symmetry
Plane of symmetry
Center of symmetry/inversion center
Rotation–reflection axis or axis of improper rotations
2. APPLICATION OF GROUP THEORY TO ELECTRONIC SPECTROSCOPY
Introduction
Electronic spectroscopy
Effect of Jahn-Teller distortion on electronic spectra of complexes
Correlation diagram: ordering of energy states
Correlation diagram and Hole formalism
Tanabe-Sugano correlation diagram
Variation in Racah parameter B: nephelauxetic series
3. MOLECULAR SYMMETRY AND GROUP THEORY TO VIBRATIONAL SPECTROSCOPY
Introduction
Generation of reducible representation
Symmetry selection rules for IR and Raman spectroscopy: Identification of IR and Raman active vibrations
Complementary nature of IR and Raman spectra
The mutual exclusion principle/rule
Polarization of Raman lines
Prediction of IR and Raman active modes in some molecules of different point Groups


Complications in IR and Raman spectra and difficulties in assignments
Ascent-descent or group–subgroup in symmetry: interpretation of spectral data
IR and Raman spectra of linear molecules
4. CHEMICAL REACTIONS: ORBITAL SYMMETRY RULES
Introduction
Chemical reactions: symmetry rules
Inorganic/organic reactions: symmetry considerations
Nucleophilic displacement reactions
Berry’s pseudorotation: orbital symmetry control
Correlation diagrams: prediction of orbital symmetry allowedness for Berry’s pseudorotation
Stable shape of the molecules: symmetry rules
Symmetry controlled pericyclic reactions
Classes of pericyclic reactions
Interpretation of pericyclic reactions: different approaches
Woodward–Hoffmann approach
Mechanistic interpretation of some pericyclic reactions with symmetry property
Frontier molecular orbital approach: Interpretation of pericyclic reactions
5. APPENDIX I: Character tables for Chemically important Symmetry groups
6. APPENDIX II: Correlation table for Oh and Td groups
7. APPENDIX II: Some Useful Trigonometric Relations Used in Text

Bibliography
Index