This book is based on a one-semester course for advanced undergraduates specializing in physical chemistry. I am aware that the mathematical training of most science majors is more heavily weighted towards analysis – typ- ally calculus and differential equations – than towards algebra. But it remains my conviction that the basic ideas and applications of group theory are not only vital, but not dif?cult to learn, even though a formal mathematical setting with emphasis on rigor and completeness is not the place where most chemists would feel most comfortable in learning them. The presentation here is short, and limited to those aspects of symmetry and group theory that are directly useful in interpreting molecular structure and spectroscopy. Nevertheless I hope that the reader will begin to sense some of the beauty of the subject. Symmetry is at the heart of our understanding of the physical laws of nature. If a reader is happy with what appears in this book, I must count this a success. But if the book motivates a reader to move deeper into the subject, I shall be grati?ed.
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This book presents students of introductory physical chemistry the basic principles of symmetry and group theory, and their use in describing and predicting molecular structure and spectra. Symmetry is a crucial determinant of many chemical phenomena, and group theory is the grammar of the language of symmetry. In many cases, simple calculations suffice to explain why certain triatomic molecules are linear and others bent, or why certain transitions do not appear in molecular spectra. In this book, the aim is understanding the ideas, and skills in application of the principles, rather than mathematical rigour. The book is intended as a supplement for students who want to follow up an interest in and recognition of the importance of group theory, and who seek a short and mathematically relatively undemanding introduction. Exercises appearing throughout the text are integrated with the presentation to give readers confidence in their assimilation of the material.
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