  We study a 4-orbital tight-binding (TB) model for ZrSiS from the square
sublattice generated by the Si atoms. After studying three other alternatives,
we endow such model with a new effective spin-orbit coupling (SOC) consistent
with {\em ab initio} dispersions around the Fermi energy ($E_F$) in four
systematic steps: (1) We calculate the electronic dispersion of bulk ZrSiS
using an implementation of density-functional theory (DFT) based on numeric
atomic orbitals [{\em J. Phys.: Condens. Matter} {\bf 14}, 2745 (2002)] in
which on-site and off-site SOC can be told apart. As a result, we determine
that local SOC-induced band gaps around $E_F$ are predominantly created by the
on-site contribution. (2) Gradually reducing the atomic basis set size, we then
create an electronic band structure with 16 orbitals per unit cell (u.c.) which
retains the qualitative features of the dispersion around $E_F$, including
SOC-induced band gaps. (3) Zr is the heaviest element on this compound and it
has a non-negligible contribution to the electronic dispersion around $E_F$; we
show that it provides the strongest contribution to the SOC-induced band gap.
(4) Using L\"{o}wdin partitioning approach, we project the effect of SOC onto
the 4-orbital Hamiltonian. This way, we facilitate an effective SOC interaction
that was explicitly informed by {\em ab initio} input.
