Ionization energy based Fermi-Dirac statistics
  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. 
Andrew Das Arulsamy