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

In a recent work [M. Jiang, M. Moeller, M. Berciu, and G. A. Sawatzky, Phys. Rev. B textbf{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 $sim 50$ % 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 %.