Complete basis set correlation energies. II. The beryllium isoelectronic series

The convergence of natural orbital expansions of the 1s2 and 2s2 intraorbital pair energies of the beryllium isoelectronic series is examined. The observed convergence of the 1s2 pair energies follows the asymptotic form error (N×N)?(ΣNμ = 1Cμ)2 (−225/4608)N−1 to within ∼3% of the MCSCF error (i.e., the absolute accuracy is ∼0.000 25 hartree for N as small as five configurations). The 2s2 pair energies show the expected interference effect—the large negative coefficients of the 2s2→2p2 excitations give small interference factors (ΣNμ = 1 Cμ)2 and hence the convergence of the 2s2 pairs is relatively rapid. However, the constant in the asymptotic form for the 2s2 pair energies appears to deviate significantly from (−225/4608) and the relative accuracy of the extrapolation is only ∼15% unless variations in the constant are determined by perturbation calculations. Nevertheless, the absolute accuracy for the 2s2 pairs is still ∼0.000 31 hartree for the five-configuration extrapolation. The total correlation energy extrapolated from the best CI and perturbation calculations available agrees with experiment to within 0.000 25 hartree for the entire isoelectronic series from z = 3 through z = 10. This is substantially better than previous results without extrapolations.