The total Hartree-Fock energy-eigenvalue sum relationship in atoms

Using the well known relationships for the isoelectronic changes in the total Hartree-Fock energy, nucleus-electron attraction energy and electron-electron repulsion energy in atoms a simple polynomial expansion in Z is obtained for the sum of eigenvalues which can be used to calculate the total Hartree-Fock energy. Numerical results are presented for 2-10 electron series to show that the present relationship is a better approximation than the other available energy-eigenvalue relationships