[REQUEST] Utility for computing AO <-> MO transformation matrices

[wilhadams]

Is your feature request related to a problem? Please describe. In the docs, we mention that the user can use the transform key to perform linear transformations of basis functions. Later on in the notes, we show that it's possible to use AO to MO and MO to AO transformations for all of our high-level functions. It would be useful if we actually provided the functionality to generate these transformations, instead of leaving that up to the user to generate.

[PaulWAyers]

The key code is https://github.com/theochem/gbasis/blob/c57de8f1cfbe1dbaac8941c7cb9993797c76fca6/gbasis/integrals/electron_repulsion.py#L204

We should provide good examples and easier functionality for supporting this. @msricher

[marco-2023]

I am sorry, I am a little confused about this, as I understood it what is needed is the matrix transformation from AO to MO, this is the transpose of the MO coefficients matrix (see PR #147 for examples of use). Is this what is needed?

[PaulWAyers]

I think the idea was to provide a utility function that allows one to pass an arbitrary matrix/tensor in one basis, together with a transformation matrix, and return it in another basis. It's a trivial operation, but one that if you do it (incredibly) naively is problematic.