It is well-known experimentally that the positively charged muon and the muonium atom may bind to molecules and solids, and through muon's magnetic interaction with unpaired electrons, valuable information on the local environment surrounding the muon is deduced. Theoretical understanding of the structures and properties of the resulting muonic species requires accurate and efficient quantum mechanical computational methodologies. In this talk, the two-component density functional theory (TC-DFT) will be introduced as a possible candidate for the proper treatment of muonic systems. This approach is capable of treating the electrons and positive muon on an equal footing as quantum particles, which is beyond the domain of the purely electronic DFT framework. In addition, a novel electron-positive muon correlation functional will be offered for the first time, which serves as the main ingredient of the muonic TC-DFT methodology. The computational application of the developed method to a benchmark set of muonic organic molecules will also demonstrate its capability to elucidate the intricate interactions of the positive muon in complex molecular systems.
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