Ab initiostudies of electron correlation effects in heavier closed-shell atoms: Structure of the all-electron correlation energies of Zn2+and Zn

Abstract

To provide reliable reference results for various components of the electron correlation energies of Zn${}^{2+}$ and Zn, which play a similar role for $3d$-electron systems as Ne and Mg do for lighter atoms, we have performed extensive calculations of the all-electron correlation energy and of its various components with several state-of-the-art ab initio techniques. Two pairs of basis-set sequences that systematically converge to the complete basis set (CBS) limit have been employed in the calculations. One pair [cc-pV$n$Z and aug-cc-pV$n$Z (correlation consistent polarized valence $n$-zeta and augmented cc-pV$n$Z with $n=$ D, T, Q, 5, $6(\ensuremath{-}k)$)] is oriented towards the description of valence electron correlation. The second pair of sequences [cc-pCCV$n$Z and aug-cc-pCCV$n$Z (core core-valence $n$-zeta, with $n$ = D, T, Q, 5, $6(\ensuremath{-}k)$)] is developed for the description of all-electron correlation effects. The correlation energies have been determined with second-order M\o{}ller-Plesset perturbation theory (MP2) and several single-reference coupled-cluster (CC) methods. The present correlation energies represent accurate post-MP2 correlation energies for closed-shell atoms including 3$d$ electrons both at the all-electron and subshell levels and should be useful benchmark results for various transitions. We have also employed the present results for assessments of the focal-point approximation (FPA), broadly used in approximations of difference correlation effects for molecular interaction problems, in applications aiming at estimating correlation effects in heavier atoms. Our results indicate that for the systems considered, the magnitudes of the MP2 correlation energies overestimate the magnitudes of the CC values for all electrons correlated as well as of their various subsets. For the all-electron correlation energies of the Zn atom, our result confirms the finding of S. P. McCarthy and A. J. Thakkar [J. Chem. Phys. 134, 044102 (2011)] obtained by means of non--ab initio approaches for all heavy closed-shell atoms from Zn to Rn. We have shown that for both Zn${}^{2+}$ and Zn this overestimation is directly caused by the presence of the $3{d}^{10}$ electron configuration.