  Density-functional Theory (DFT) approaches have recently been used to judge
the topological order of various materials despite its well-known band gap
underestimation. Use of the more accurate quasi-particle GW approach reveals
here few cases where DFT identifications are false-positive, possibly
misguiding experimental searches of materials that are topological insulators
(TI) in DFT but not expected to be TI in reality. We also present the case of
false-positive due to the incorrect choice of crystal structures and adress the
relevancy of such choice of crystal structure with respect to the ground state
one and thermodynamical instability with respect to binary competing phases. We
conclude that it is then necessary to consider both the correct ground state
crystal structure and the correct Hamiltonian in order to predict new TI.
