The correspondence between two sets of orbitals can be established by means of SVD of the overlap matrix: the singular values of one reveal the orbitals matching exactly, whereas smaller values would correspond to partial overlap and zeros would correspond to orthogonal subspaces. Thus, SVD of the overlap between the α occupied and β virtual orbitals allows us to identify the orbitals from the singly occupied subspace. In all considered systems, two Assuming that the reference is a high-spin state in which the number of α electrons is larger than the number of β electrons, the algorithm proceeds as follows: