Comment on "Relevance of Cu-3d multiplet structure in models of high-Tc cuprates"

In a recent work [Jiang et al., Phys. Rev. B 101, 035151 (2020)], the authors solved a model with a Cu impurity in an O-2p band as an approximation to the local electronic structure of a hole doped cuprate. One of their conclusions is that the ground state has only approximate to 50% overlap with a Zhang-Rice singlet (ZRS). This claim is based on the definition of the ZRS in a different representation, in which the charge fluctuations at the Cu site have been eliminated by a canonical transformation. The correct interpretation of the results, based on known low-energy reduction procedures for a multiband model including 3d(8) and 3d(10) configurations of Cu, indicates that this overlap is near 94%.