Investigation of the electronic structure and optical absorption spectra of the icosahedral gold fullerene Au$_{42}$

The electronic structure of the gold fullerene molecule Au$_{42}$ has been studied within the framework of the Hubbard Hamiltonian. Expressions are obtained for the Fourier transforms of the Green's functions, the poles of which determine the energy spectrum of the considered nanocluster. The energy spectrum of Au$_{42}$ is studied in comparison with the spectrum of the icosahedral gold fullerene Au$_{42}$. The energy spectrum indicates the semiconducting state of the gold fullerene Au$_{42}$. The density of electronic states is given, the peaks of which correspond to the Van Hove features. The optical absorption spectra of the neutral and negatively charged fullerene Au$_{42}$ are presented; the energy of the first direct optical transition of the negatively charged ion of the gold fullerene Au $_{42}^-$ is 0.985 eV, and is in the near infrared region. The possibility of using the investigated nanocluster of gold atoms for the diagnosis and treatment of cancer is shown.