Electronic structure and optical absorption spectra of gold fullerenes Au$_{16}$ and Au$_{20}$

The electronic and optical properties of gold fullerenes are studied in the framework of the Hubbard model. The expressions of the Fourier transforms of anticommutator Green functions have been obtained for gold fullerenes Au$_{16}$ and Au$_{20}$, the poles of which determine the energy spectrum of the system under consideration. The calculations are performed for the thermodynamic means that characterize jumps of electrons from a nanosystem site to a neighboring site, the correlation functions demonstrating the possibility of existing two d electrons with oppositely oriented spin projections on the same site of the fullerenes consisting of gold atoms. The optical absorption spectra are presented. The optical absorption peaks of ions Au$_{20}^{-}$ and Au$_{16}^{-}$ correspond to a near-infrared spectral region, where the light absorption by blood or a soft tissue is vanishingly small; thus, these ions can be used as a new class of contrast improvements and phototherapeutic means for diagnostics and treatment of cancer.