  The electronic and optical properties of single-layer (SL) tungsten disulfide
(WS$_2$) in the presence of substitutional Holmium impurities (Ho$_{\rm W}$)
are studied. Although Ho is much larger than W, density functional theory (DFT)
including spin-orbit coupling is used to show that Ho:SL WS$_2$ is stable. The
magnetic moment of the Ho impurity is found to be 4.75$\mu_B$ using
spin-dependent DFT. The optical selection rules identified in the optical
spectrum match exactly the optical selection rules derived by means of group
theory. The presence of neutral Ho$_W$ impurities gives rise to localized
impurity states (LIS) with f-orbital character in the band structure. Using the
Kubo-Greenwood formula and Kohn-Sham orbitals we obtain atom-like sharp
transitions in the in-plane and out-of-plane components of the susceptibility
tensor, Im$\chi_{\parallel}$ and Im$\chi_{\perp}$. The optical resonances are
in good agreement with experimental data.
