Local scaling transformation function and atomic shell structure in density functional theory

The method of local scaling transformation in density functional theory calculates a transformation function (TRF) in order to generate an optimized atomic N-electron wave function from a trial density and a reference density/wave function. The TRFsf(r) for several atomic systems are studied and it is observed that the number of minima in df(r)/drequals the number of atomic shells, except whenρ=ρ0andf=r.