  In [Phys. Rev. B 107, 094433 (2023)], Deng et al. have proposed an
electron-muon correlation functional within the context of the two-component
density functional theory (TC-DFT) for crystals/molecules containing positively
charged muons. In order to verify its performance, we applied the functional in
conjunction with the B3LYP, as a hybrid electronic exchange-correlation
functional, to a benchmark set of molecules. The results demonstrate that the
proposed functional is not capable of reproducing the correct one-muon
densities as well as some other key properties like muon's kinetic energy, the
total energies and the mean muonic bond lengths. Using the muonium atom in a
double-harmonic trap as a model we also demonstrate that the successful
reproduction of the electron-muon contact hyperfine coupling constants by Deng
et al. is probably the result of error cancellations. We also discuss some
theoretical intricacies with the very definition of the electron-muon
correlation energy within the context of the TC-DFT that must be taken into
account in future efforts to design electron-muon correlation functionals.
