Location of muonium and hydrogen in C60 fullerene and associated electronic structure and hyperfine properties

The unrestricted Hartree-Fock (UHF) procedure is used to investigate the locations, associated electronic structures and hyperfine interactions for muonium and hydrogen in C₆₀ fullerene. Our results indicate that from total energy considerations, in keeping with earlier investigations, the exohedral model has the lowest energy. However, the energies of the endohedral model involving the muonium (hydrogen) inside the fullerene and bonded to one of the carbon atoms, and of the muon at the center are found to be almost equal, contrary to earlier results. The hyperfine interaction constant for the endohedral site is in good agreement with that required to explain the lower observed muon spin-rotation (SR) frequency in the C₆₀-muonium system. The same appears to be the case for the exohedral model. However, there seems to be some uncertainty about the theoretical result in the latter case due to significant admixtures of higher spin states in the UHF wave-function. Additionally, in solid fullerene, the calculated location of the muonium for the exohedral model is such that it could be bonded to two fullerene molecules and therefore a muonium attached to a simple fullerene may not be representative of the exohedral state. This feature as well as the difficulty for the exohedral model of explaining the observed equality of the correlation times for relaxation effects associated with both SR and¹³C relaxation times in nuclear magnetic resonance (NMR) experiments suggests that the endohedral model for muonium cannot at present be ruled out as a viable model in favor of the exohedral model. Possible avenues for future investigations to resolve some of the problems for both exohedral and endohedral models are discussed. Results obtained for muonium at the center of fullerene are presented and compared to the features of the observed high frequency SR signal, and possible improvements in theory are discussed.