I am writing a lesson plan for high school students who are studying group theory, and I am having difficulty in relating the subject matter to the real world. I have quite a few examples using the Rubik's cube, but I would like to use some statement that might provide some intuition to students of how group theory is useful for chemists. I understand that group theory is used with spectroscopy, but I am not sure how to relate this back to the theory.
I have seen some good reasonable non rigorous attempts to relate group theory to the insolubility of quintic polynomials, but I think it would great to have a second more concrete example, such as chemistry.
I understand this may be a big thing to ask, and would be happy with just a broad brush strokes answer without being too technical or trivial.