  We present a comparative study of different modeling approaches to the
electronic properties of the
$\textrm{Hf}_{0.05}\textrm{Nb}_{0.05}\textrm{Ta}_{0.8}\textrm{Ti}_{0.05}\textrm{Zr}_{0.05}$
high entropy alloy. Common to our modeling is the methodology to compute the
one-particle Green's function in the framework of density functional theory. We
demonstrate that the special quasi-random structures modeling and the
supercell, i.e. the locally self-consistent multiple-scatering methods provide
very similar results for the ground state properties such as the spectral
function (density of states) and the equilibrium lattice parameter. To
reconcile the multiple-scattering single-site coherent potential approximation
with the real space supercell methods, we included the effect of screening of
the net charges of the alloy components. Based on the analysis of the total
energy and spectral functions computed within the density functional theory, we
found no signature for the long-range or local magnetic moments formation in
the
$\textrm{Hf}_{0.05}\textrm{Nb}_{0.05}\textrm{Ta}_{0.8}\textrm{Ti}_{0.05}\textrm{Zr}_{0.05}$
high entropy alloy, instead we find possible superconductivity below $\sim 9$K.
