  Transition metal dichalcogenide materials $MX_2 (M=Mo,W;X=S,Se)$ are being
thoroughly studied due to their novel two-dimensional structure, that is
associated with exceptional optical and transport properties. From a
computational point of view, Density Functional Theory simulations perform very
well in these systems and are an indispensable tool to predict and complement
experimental results. However, due to the time and length scales where even the
most efficient DFT implementations can reach today, this methodology suffers of
stringent limitations to deal with finite temperature simulations or
electron-lattice coupling when studying excitation states: the unit cells
required to study, for instance, systems with thermal fluctuations or large
polarons would require a large computational power. Multi-scale techniques,
like the recently proposed Second Principles Density Functional Theory, can go
beyond these limitations but require the construction of tight-binding models
for the systems under investigation. In this work, we compare two such methods
to construct the bands of WSe$_2$. In particular, we compare the result of (i)
Wannier-based model construction with (ii) the band fitting method of Liu and
co-workers where the top of the valence band and the bottom of the conduction
band are modeled by three bands symmetrized to have mainly Tungsten $d_{z^2}$,
$d_{xy}$ and $d_{x^2-y^2}$ character. Our results emphasize the differences
between these two approaches and how band-fitting model construction leads to
an overestimation of the localization of the real-space basis in a
tight-binding representation.
