One question about the projection process

[XinYu73]

In the paper titled "MOLSYM: A Python package for handling symmetry in molecular quantum chemistry", the authors mention that the only thing the user needs to provide is how the basis functions transform under each operation in a group, as the IR matrices are hardcoded in MOLSYM. Since the IR matrix is not unique, is the suite of IR matrices valid for projection onto any basis function?

[sgoodlett]

The irreducible representation matrices are not unique, this is true. However, any set of irreducible representation matrices are equivalent under unitary transformation. For our purposes, we define the molecular orientation very specifically so it matches our matrix definitions. We are currently pursuing a way to operate in an orientation independent way. But for now, it is sufficient to rotate the molecule to our reference frame to obtain SALCs, perform a calculation, and then back-rotate to the original reference frame. We also hope to provide some functions to help do this in the future.

So I believe that if your molecule is in our reference frame, the matrices will provide the correct projection behavior for any basis function.