Ground-state energy of any atom

Abstract

An extremely simplified version of the atomic shell model is used to obtain an explicit parameter-free approximation to the ground-state energy E_tot(Z) of any atom. The resultant values of E_tot(Z) agree to within a few per cent with those obtained from Hartree-Fock calculations for any Z in the interval Z=2 to Z=102, the agreement being of the order of 0.5% or better for Z>45. This is an order of magnitude better than Thomas-Fermi (TF) theory in this range. For Z to infinity , where TF theory becomes exact (Lieb-Simon theorem), we find (r_ij^-1)/(r_j^-1) to ²/₇, which is the exact TF value, and E_tot approximately -CZ^7/3 with C=0.74, which is within 4% or C_exact=0.77.