I am a bit worried about the basisMatching function here: https://github.com/gkclab/libdmet_preview/blob/main/libdmet/dmet/HubPhSymm.py#L37
To my understanding, the issue is that the DMET baths of the two spin sectors are constructed independently from each other in the unrestricted spin case, leading to some nontrivial overlap matrix S_αβ between the spin sectors in the embedding basis. However, pyscf does not support nontrivial overlaps between the spin sectors (in general, the overlap matrix has no spin dependency in all the solvers), so this is a severe issue, in principle. Thus, the basisMatching function tries to circumvent this by matching the alpha and beta bases as closely as possible in order to optimize the overlap (and the error/deviation from the optimal overlap gets logged). But this seems like a patchwork solution to the deeper issue at hand to me. If the logged value of np.min(gamma) is not equal to 1, then the solver will not return the correct solution. Isn't this a large issue? Or has it been proven empirically that this can be neglected in most systems?
I am a bit worried about the basisMatching function here: https://github.com/gkclab/libdmet_preview/blob/main/libdmet/dmet/HubPhSymm.py#L37
To my understanding, the issue is that the DMET baths of the two spin sectors are constructed independently from each other in the unrestricted spin case, leading to some nontrivial overlap matrix S_αβ between the spin sectors in the embedding basis. However, pyscf does not support nontrivial overlaps between the spin sectors (in general, the overlap matrix has no spin dependency in all the solvers), so this is a severe issue, in principle. Thus, the basisMatching function tries to circumvent this by matching the alpha and beta bases as closely as possible in order to optimize the overlap (and the error/deviation from the optimal overlap gets logged). But this seems like a patchwork solution to the deeper issue at hand to me. If the logged value of
np.min(gamma)is not equal to 1, then the solver will not return the correct solution. Isn't this a large issue? Or has it been proven empirically that this can be neglected in most systems?