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Group Theory and Chemistry
Group theoretical principles are an integral part of modern chemistry. Not only do they help account for a wide variety of chemical phenomena, they simplify quantum chemical calculations. Indeed, knowledge of their application to chemical problems is essential for students of chemistry. This complete, self-contained study, written for advanced undergraduate-level and graduate-level chemistry students, clearly and concisely introduces the subject of group theory and demonstrates its application to chemical problems.
To assist chemistry students with the mathematics involved, Professor Bishop has included the relevant mathematics in some detail in appendixes to each chapter. The book can then be read either as an introduction, dealing with general concepts (ignoring the appendixes), or a fairly comprehensive description of the subject (including the appendixes). In any case, the author assures students that "the mathematics involved in actually applying, as opposed to deriving, group theoretical formulae is quite trivial. It involves little more than adding and multiplying."
To assist chemistry students with the mathematics involved, Professor Bishop has included the relevant mathematics in some detail in appendixes to each chapter. The book can then be read either as an introduction, dealing with general concepts (ignoring the appendixes), or a fairly comprehensive description of the subject (including the appendixes). In any case, the author assures students that "the mathematics involved in actually applying, as opposed to deriving, group theoretical formulae is quite trivial. It involves little more than adding and multiplying."
336 pages, Paperback
First published January 1, 2012
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Displaying 1 - 2 of 2 reviews
September 26, 2026
I read this straight through like a novel and I don't know any chemistry, so probably best not to put any stock into this summary.
It was interesting and challenging and fun to read the character theory through the different perspective of a chemist, for example figuring out Bishop's different notation or being surprised at the mathematical background he would blast through as self-evident versus going into great detail to describe things that, to me, were beyond comment.
Once Bishop got to the applications, it was beyond me. The main point is character theory greatly simplifies the calculations necessary to find solutions to Schrodinger's equations. Reading through the latter half of the book where these techniques are applied to molecular vibrations, the two main things that struck me were how impressively versatile the specialists in this field are at calculation and computation and how much any hope of solving these calculations (especially in the era as automated computation was just beginning to be a viable approach) still required deep understanding of the physical rules so that one could, in effect, bake some simplifications into the operating assumptions. Different approaches would make different assumptions, and, over time, the community would figure out which yielded the most accurate results.
Once last comment on the quotation below. Long ago, someone I admire greatly would tell me that character theory is a beautiful subject, but if one wanted to judge the utility of a field by its ability to prove results beyond its own domain, then character theory cannot really be deemed a success. The point was the jewel results that character theory give to group theory were eventually shown to be provable without recourse to characters. Now, having read through Bishop's book, it would have been nice to respond with the tremendous computational power that comes out of those representations.
my favorite quote: "At first sight, group theory appears so abstract and so unrelated to physical reality that it seems amazing that is should be the powerful practical tool which it is."
It was interesting and challenging and fun to read the character theory through the different perspective of a chemist, for example figuring out Bishop's different notation or being surprised at the mathematical background he would blast through as self-evident versus going into great detail to describe things that, to me, were beyond comment.
Once Bishop got to the applications, it was beyond me. The main point is character theory greatly simplifies the calculations necessary to find solutions to Schrodinger's equations. Reading through the latter half of the book where these techniques are applied to molecular vibrations, the two main things that struck me were how impressively versatile the specialists in this field are at calculation and computation and how much any hope of solving these calculations (especially in the era as automated computation was just beginning to be a viable approach) still required deep understanding of the physical rules so that one could, in effect, bake some simplifications into the operating assumptions. Different approaches would make different assumptions, and, over time, the community would figure out which yielded the most accurate results.
Once last comment on the quotation below. Long ago, someone I admire greatly would tell me that character theory is a beautiful subject, but if one wanted to judge the utility of a field by its ability to prove results beyond its own domain, then character theory cannot really be deemed a success. The point was the jewel results that character theory give to group theory were eventually shown to be provable without recourse to characters. Now, having read through Bishop's book, it would have been nice to respond with the tremendous computational power that comes out of those representations.
my favorite quote: "At first sight, group theory appears so abstract and so unrelated to physical reality that it seems amazing that is should be the powerful practical tool which it is."
November 24, 2012
The kindle version is not the best, but is readable anyway.
Displaying 1 - 2 of 2 reviews