Group Theory Applied to Chemistry

The second edition of this textbook provides a more elaborate explanation of several important group-theoretical concepts in quantum chemistry, such as: the bra-ket conjugation relation, the connection between point groups and isometries, the practical use of subduction tables, the eigenvalues of Cayley graphs, and the symmetry of Slater determinants. A new chapter introduces the application of line and plane groups to the properties of nanostructured low-dimensional molecular systems. In addition, several extra study problems are inserted to illustrate group theory at work in molecular science. The book is of great interest to advanced undergraduate and graduate students, enabling them to put the tools of group theory into practice when studying chemical problems of their own research. More experienced researchers will find in this book useful leads to the mathematical aspects of their subject.

Operations.- Function Spaces and Matrices.- Groups.- Representations.- What has Quantum Chemistry Got to Do with It?.- Interactions.- Spherical Symmetry and Spins.-  Line Groups and Plane Groups.

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).