Comment on "Two-component density functional theory study of quantized muons in solids"

TL;DR

This paper critically evaluates a proposed electron-muon correlation functional within two-component density functional theory, revealing its limitations in accurately predicting key properties of muonic systems and discussing theoretical challenges in its development.

Contribution

It provides a benchmark assessment of Deng et al.'s functional, highlighting its shortcomings and offering insights into the theoretical complexities of defining electron-muon correlation energy.

Findings

The functional fails to reproduce correct one-muon densities.

It does not accurately predict muon's kinetic energy and total energies.

The hyperfine coupling constants are coincidentally reproduced due to error cancellations.

Abstract

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.