Large‐Z and ‐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^7/2(C₀ + C₁Z^−1/3 + C₂Z^−2/3 + C₃Z^−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 form δE δZ^4/3(δC₃ + δC₅Z^−2/3 + δC₆Z^−3/3 + ⃛); comparison with accurate values of δE available for the range Z ⩽ 36 indicates the mean error is only about 10%. Oscillatory terms in E and δE are also evaluated. © 1994 John Wiley & Sons, Inc.