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.

High accuracy ab initio studies of electron-densities for the ground state of Be-like atomic systems.

Benchmark results for electron densities in the ground states of Li(-), Be, C(2+), Ne(6+), and Ar(14+) have been generated from very accurate variational wave functions represented in terms of extensive basis sets of exponentially correlated Gaussian functions. For Ne(6+), and Ar(14+), the upper bounds to the energies improve over previous results known from the literature. For the remaining systems our bounds are from 0.1 to 1.1 µhartree higher than the most accurate ones. We present in graphical and, partially, numerical form results both for the radial electron densities and for the difference radial density distributions (DRD) (defined with respect to the Hartree-Fock radial density) that highlight the impact of correlation effects on electron densities. Next, we have employed these DRD distributions in studies of the performance of several broadly used orbital-based quantum-chemical methods in accounting for correlation effects on the density. Our computed benchmark densities for Be have been also applied for testing the possibility of using the mathematically strict result concerning exact atomic electron densities, obtained by Ahlrichs et al. [Phys. Rev. A 23, 2106 (1981)], for the determination of the reliability range of computed densities in the long-range asymptotic region. The results obtained for Be are encouraging.

Towards benchmark second-order correlation energies for large atoms. II. Angular extrapolation problems.

We have studied the use of the asymptotic expansions (AEs) for the angular momentum extrapolation (to l --> infinity) of atomic second-order Moller-Plesset (MP2) correlation energies of symmetry-adapted pairs (SAPs). The AEs have been defined in terms of partial wave (PW) increments to the SAP correlation energies obtained with the finite element MP2 method (FEM-MP2), as well as with the variational perturbation method in a Slater-type orbital basis. The method employed to obtain AEs from PW increments is general in the sense that it can be applied to methods other than MP2 and, if modified, to molecular systems. Optimal AEs have been determined for all types of SAPs possible in large atoms using very accurate FEM PW increments up to lmax = 45. The impact of the error of the PW increments on the coefficients of the AEs is computed and taken into account in our procedure. The first AE coefficient is determined to a very high accuracy, whereas the second involves much larger errors. The optimum l values (lopt) for starting the extrapolation procedures are determined and their properties, interesting from the practical point of view, are discussed. It is found that the values of the first AE coefficients obey expressions of the type derived by Kutzelnigg and Morgan [J. Chem. Phys. 96, 4484 (1992); 97, 8821(E) (1992)] for He-type systems in the bare-nucleus case provided they are modified by fractional factors in the case of triplet and unnatural singlet SAPs. These expressions give extremely accurate values for the first AE coefficient both for the STO and the FEM Hartree-Fock orbitals. We have compared the performance of our angular momentum extrapolations with those of some of the principal expansion extrapolations performed with correlation consistent basis sets employed in the literature and indicated the main sources of inaccuracy.

Towards benchmark second-order correlation energies for large atoms: Zn2+ revisited.

To provide very accurate reference results for the second-order Møller-Plesset (MP2) energy and its various components for Zn(2+), which plays for 3d-electron systems a similar role as Ne for smaller atoms and molecules, we have performed extensive calculation by two completely different implementations of the MP2 method: the finite element method (FEM) and the variation-perturbation (VP) method. The FEM and VP calculations yield partial wave contributions up to l(max)=45 and 12, respectively. Detailed comparison of all FEM and VP energy components for l(max)=12 has disclosed an extraordinary similarity, which justifies using the present results as benchmarks. The present correlation energies are compared with other works. The dependability of an earlier version of FEM, already applied to very large closed-shell atoms, is confirmed. It has been found that for larger atoms the accuracy of the analytical Hartree-Fock results has an impact on the accuracy of the MP2 energies greater than for smaller atoms. Fields of applications of the present results in studies of various electron correlation effects in 3d-electron atoms and molecules are indicated.