  By combining electron energy-loss spectroscopy and state-of-the-art
computational methods, we were able to provide an extensive picture of the
excitonic processes in $1T$-HfS$_2$. The results differ significantly from the
properties of the more scrutinized group VI semiconducting transition metal
dichalcogenides such as MoS$_2$ and WSe$_2$. The measurements revealed a
parabolic exciton dispersion for finite momentum $\textbf{q}$ parallel to the
$\Gamma$K direction which allowed the determination of the effective exciton
mass. The dispersion decreases monotonically for momentum exchanges parallel to
the $\Gamma$M high symmetry line. To gain further insight into the excitation
mechanisms, we solved the ab-initio Bethe-Salpeter equation for the system. The
results matched the experimental loss spectra closely, thereby confirming the
excitonic nature of the observed transitions, and produced the
momentumdependent binding energies. The simulations also demonstrated that the
excitonic transitions for $\textbf{q}$ || $\Gamma$M occur exactly along that
particular high symmetry line. For $\textbf{q}$ || $\Gamma$K on the other hand,
the excitations traverse the Brillouin zone crossing various high symmetry
lines. A particular interesting aspect of our findings was that the calculation
of the electron probability density revealed that the exciton assumes a
six-pointed star-like shape along the real space crystal planes indicating a
mixed Frenkel-Wannier character.
