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Density functional theory computational investigation was performed to study the electronic structures, muon sites, and the associated hyperfine interactions in [Au 25 (SR) 18 ] 0 and [Au 25 (SeR) 18 ] 0 where R is phenylethane. The calculated electronic structures show inhomogeneous spin density distribution and are also affected by different ligands. The two most stable muon sites near Au atoms in the thiolated system are MAu11 and MAu6. When the thiolate ligands were replaced by selenolate ligands, the lowest energy positions of muons moved to MAu6 and MAu5. Muons prefer to stop inside the Au12 icosahedral shell, away from the central Au and the staple motifs region. Muonium states at phenyl ring and S/Se atoms in the ligand were found to be stable and the Fermi contact fields are much larger as compared to the field experienced by muons near Au atoms.

Density functional theory method at the B3LYP/6-31G level was used to determine the structure of 12mer single-strand guanine oligomers. The length and width of the optimized structure are 38.7 and 18.2 Å, respectively, and the observed high-resolution transmission electron microscopy image of the 12mer single-strand guanine sample shows similar oligomer dimensions with the calculated ones. Both HOMO and LUMO are significantly delocalized, and the calculated HOMO-LUMO gap is 3.31 eV. A total of 96 muonium trapping sites at C2, C4, C5, C6, C8, N3, N7, and O6 were investigated. All 12 C8 sites have lower energy than the other 84 sites and are clustered in the energy–muon hyperfine coupling constant scatter plot. The calculated muon hyperfine coupling constant at C8 sites range from 384.6 to 481.1 MHz, and the corresponding estimated ALC-μSR resonance for |ΔM| = 1 range from 1.419 to 1.775 T.