  The electronic structure of the toroid D$_{6h}$-Au$_{42}$ is studied within
the framework of the Hubbard Hamiltonian in the approximation of static
fluctuations. An expression for the Fourier transform of the Green's function,
the poles of which determine the energy spectrum of the nanocluster under
consideration, is obtained. The energy spectrum of the D$_{6h}$-Au$_{42}$
toroid indicates that the nanosystem is in a metallic state. Graphical
representations of the equation for the chemical potential and the density of
state of electrons are presented. The spectrum of optical absorption is shown,
the energies of direct optical transitions D$_{6h}$-Au$_{42}$ are 0.95 eV, 1.24
eV, 1.39 eV, are in the near infrared region. The energy of the ground state is
calculated for the electrically neutral as well as for the positively and
negatively charged ions of the toroid. The possibility of using of the
investigated toroid from Au atoms for the diagnostics and treatment of cancer
is shown.
