We present finite-size scaling and phenomenological renormalization eq
uations for calculations of the critical points of the electronic stru
cture of atoms and molecules. Results show that the method is efficien
t and very accurate for estimating the critical screening length for o
ne-electron screened Coulomb potentials and the critical nuclear charg
e for two-electron atoms. The method has potential applicability for m
any-body quantum systems. [S0031-9007(97)04408-6].