This book helps readers acquire the skills to make use of the mathematical tools of group theory for whatever chemical problems they are confronted with in the course of their own research. Includes exercises.

Chemists are used to the operational definition of symmetry, which crystallographers introduced long before the advent of quantum mechanics. The ball-and-stick models of molecules naturally exhibit the symmetrical properties of macroscopic objects. However, the practitioner of quantum chemistry and molecular modeling is not concerned with balls and sticks, but with subatomic particles: nuclei and electrons.

This textbook introduces the subtle metaphors which relate our macroscopic understanding of symmetry to the molecular world. It gradually explains how bodily rotations and reflections, which leave all inter-particle distances unaltered, affect the study of molecular phenomena that depend only on these internal distances. It helps readers to acquire the skills to make use of the mathematical tools of group theory for whatever chemical problems they are confronted with in the course of their own research.

Takes a mathematical approach to understanding group theory Includes exercises Goes back to basics Takes a didactic approach Written for advanced undergraduates and Masters students Includes supplementary material: sn.pub/extras

Autorentext

Arnout Ceulemans is emeritus professor of theoretical chemistry at KULeuven. His research is devoted to the development and application of group theory and topology to chemistry. He has published three books on this topic. In 2013 appeared the first edition of a textbook on group theory applied to chemistry (Springer, 2013). Together with Dr. Pieter Thyssen he authored a book on continuous symmetry groups, entitled 'Shattered Symmetry, group theory from the eightfold way to the periodic table' (2017). His latest contribution is a monograph on the 'Theory of the Jahn-Teller effect, when a boson meets a fermion' (Springer 2022).

Inhalt
Operations.- Function spaces and matrices.- Groups.- Representations.- What has quantum chemistry got to do with it?.- Interactions.- Spherical symmetry and spins.