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Understanding group theory easily and quickly

The figures below show you how to navigate your way round point group tables. The irreducible representations (irreps) are shown as the row of characters. A reducible representation is a collection of ...
• 30.3k
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What is the mathematical basis behind the Jahn-Teller effect?

1. Perturbations As already mentioned, the Jahn–Teller effect has its roots in group theory. The essence of the argument is that the energy of the compound is stabilised upon distortion to a lower-...
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Why is the letter J omitted in the spdf... sequence?

Omitting j when alphabetically enumerating things has a long tradition. First of all, the alphabet did not always exist in the form we know it today. Quoting Wikipedia: After [...] the 1st century ...
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Why is the letter J omitted in the spdf... sequence?

For the azimuthal quantum number (l) of an atom, there is no "j" because some languages do not distinguish between the letters "i" and "j". L is the total orbital quantum number in spectroscopic ...
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Why do we need the identity operator, E

It is not that we need the identity operator. It is just that things (character tables, irreducible representations, etc.) work the way they do. As to why they do so, I refer you to any decent ...
• 31.1k
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Why do we need the identity operator, E

What you are asking arises as a fundamental consequence of the definition of vector spaces and the operations defined for them and, specifically, symmetry groups. The identity operator does not do "...
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Group theoretical condition for an integral to be zero

By Maschke's Theorem, every direct product of representations is decomposable into a direct sum of representations, that is, the function you are integrating can be rewritten as a sum of functions ...
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How do I determine the molecular vibrations of linear molecules?

As Tyberius noted, the projection formula does not work for infinite order groups (this is because the Hermitian form on characters is defined to be G-invariant by averaging over all elements in a ...
• 3,070
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What are point groups and the benefits of using them?

Point groups are a very valuable tool for analysing molecules without knowing much about them. They rely on analysing a molecule’s symmetry and deducing both physical parameters and the shape of ...
• 67.8k
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Using group theory to make molecular orbital diagrams

Group theory really just formalises the process that you're going through when you construct molecular orbital diagrams by inspection (though as the molecules get bigger it gets significantly harder ...
• 17.1k
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• 17.4k

Group theoretical condition for an integral to be zero

I consulted my coworker who has a Ph.D. in algebraic topology. The guidance I received was pretty helpful, so here's the new way I understand the problem. There are a few steps that I might not be ...
• 17.4k