We present a theoretical analysis for the band-gap difference among the cubic lead triiodide perovskite materials by using a NH4+ probe molecule. We show the position of A-site cation induces the removal of 3-fold degeneracy of Pb(6px, 6py, 6pz), which are the main part of the conduction band minimum (CBM). The degree of stabilization of CBM depends on the overlap integrals between occupied molecular orbitals of A-site cation and unoccupied 6p orbitals of Pb.