On the (N, Z) dependence of the second-order Møller-Plesset correlation energies for closed-shell atomic systems

Accurate Møller-Plesset (MP2) correlation energies calculated by means of the variational-perturbation and the finite-element methods are presented for several members of the Cu(+) isoelectronic series (N = 28), which represent closed-shell systems containing for the first time the 3d(10)-electron configuration and, consequently, closed M-shell. Total MP2 energies as well as their inner- and inter-shell components are reported for Cu(+), Zn(2+), Ge(4+), Kr(8+), Sr(10+), and Cd(20+). We found that for these ions the Z-dependence of the total MP2 energies is significantly weaker than for the members of the Ar-like series. The origin of this fact is rationalized by a detailed analysis performed at the levels of the shell- and inter-shell contributions to the MP2 energies. To get, for the first time, more general information about the (N, Z) characteristics of the MP2 energies for closed-shell atomic systems, we compare the Z-dependence of the Cu(+)-like systems with the MP2 energies calculated for other isoelectronic series. The weak Z-dependence is found for the He-, Ne-, and Cu(+)-like series, which consist of atoms having perfectly closed-shell K-, KL-, and KLM-electronic structures, respectively. In turn, for the Be-, Mg-, and Ar-series, the Z-dependence is considerably stronger.