LARGE-Z AND LARGE-N DEPENDENCE OF ATOMIC ENERGIES FROM RENORMALIZATION OF THE LARGE-DIMENSION LIMIT

By combining Hartree-Fock results for nonrelativistic ground-state energies of N-electron atoms with analytic expressions for the large-dimension limit, we have obtained a simple renormalization procedure. For neutral atoms, this yields energies typically threefold more accurate than the Hartree-Fock approximation. Here, we examine the dependence on Z and N of the renormalized energies E(N, Z) for atoms and cations over the range Z, N = 2 --> 290. We find that this gives for large Z = N an expansion of the same form as the Thomas-Fermi statistical model, E --> Z(7/3)(Co + C(1)Z(-1/3) + C(2)Z(-2/3) + C(3)Z(-3/3) + ...), with similar values of the coefficients for the three leading terms. Use of the renormalized large-D limit enables us to derive three further terms. This provides an analogous expansion for the correlation energy of the for Delta E --> Z(4/3)(Delta C-3 + Delta C(5)Z(-2/3) + Delta C(6)Z(-3/3) + ...); comparison with accurate values of Delta E available for the range Z less than or equal to 36 indicates the mean error is only about 10%. Oscillatory terms in E and Delta E are also evaluated. (C) 1994 John Wiley gr Sons, Inc.