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1. Walton Section 2 - W hat use is group theory Thereis no...

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What use is group theory? There is no doubt that group theory is of pivotal importance in chemistry.In most undergraduate chemistry courses, the group theory course comes about halfway through the wholeof the chemistry course. By this time the basic concepts used in chemistry will have been covered-especially the ideas of atomic orbitals, bonding theories, molecular vibrations, molecular shape and electronic configurations. To take these ideas further it becomes necessary to understand something about group theory. Indeed, courses which follow the group theory course are likely to buildon the concepts (and terminology) ofgroup theory quite extensively. Unfortunately, it is true that some students can find their first encounter with group theory an uncomfortable one. In manycases this can be traced backto a lack of familiarity with the mathematical concepts that group theory uses, and in other cases it is related to the difficulty in 'seeing' the symmetry operations involved in examining a molecule's overall symmetry. Even for the students who are familiar with the mathematics and can perform three-dimensional manipulations in their head with little difficulty, thewhole reason for group theory can be unclear. Whatever your starting point when it comes to understanding group theory, it is important that you can at least use group theory to solve some chemical problems, and that you are familiar with the terminology, which pops up again and agarn in other areas of chemistry. Hopefully this book can help anychemistry student studying group theory for the first time. If you areone who findsgroup theory unpalatable because of the mathematics, then you should know that using group theory in chemistry onlyrequires simple arithmetic: no more! (Of course, a fuller understanding of group theory requires mathematics.) In fact, the exercises in this book can be completed without having to read the'mathematical'bit (Section 4) at all. If you areone of those who findsit difflcult to 'see' thesymmetry properties of a molecule, then realise that 'practice makes perfect'. The worked exercises in this book are designed exactly for this pufpose, to make you more confident in handling the three-dimensional shape of molecules. And, finally, if you are one who just cannot see where group theory hts in and where it all leads, Lhen some of the simple explanations in this book-particularly those in Section S-will hopefully helpto make things clearer. Certainly, doing the workedexercises will help you to see the use of group theory in chemisUy. This book is meant to be written in. Doing the exercises is an important part of completing the book,and 1'ou should have a pencilat hand. There are spaces for you to write yoru answers to the problems.The full answers are ihen given immediately below. Try to resist the temptation to look at the answer before you attempt the problem; it might help to cover'up theanswer with a piece of paper.
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