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A Rigorous Proof of the Symmetry-Based Molecular Orbital Method

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Tags: group-theoryrepresentation-theorychemistry

A thorough walkthrough, and a rigorous formulation, of the process of finding the molecular orbitals of a molecule using nothing but its symmetry. For chemists/physicists with a linear algebra background.

https://minerharry.github.io/some4.html

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6.4

I’m not sure it’s that obvious that a group representation on a invariant subspace is unique up to basis change. This can be highlighted and left as an exercise for the reader, although it should be mentioned.

There are equations which I think should be separated out in another row, especially if they are important.

When describing the group action on the Hamiltoninan, it’s not immediately clear what group action this represents and in which space.

A few illustrations here can also help to understand and make the point clearer, but I think the author is aware of this. Overall, I think they did a good job to condense quite a dense subject into a slightly shorter paper that encapsulates the idea on how symmetries really help to reduce the search space and make the answers easier to find.

I would have liked to see an example. This is a topic with great potential to show pictures of the orbitals. Although I have significant experience working with multidimensional integrals, eigenvalues and eigenvectors, I’m not convinced I can generate an orbital of a molecule based on your description.