  Quantitative differences of Lagrange multipliers between standard Fermi-Dirac
statistics (FDS) and Ionization energy ($E_I$) based FDS (iFDS) are analyzed in
detail. It is shown here that iFDS is degenerate and its total energy remains
the same with the standard FDS. The total energy can be obtained by recasting
the $E_I$ in quantized form, as required by the restrictive condition.
