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.
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
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
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