Explicitly correlated calculation of the second-order Moeller-Plesset correlation energies of Zn2+ and Zn

Accurate second-order Moeller-Plesset correlation energies are reported for the closed-shell atomic systems Zn2+ and Zn. We demonstrate that submillihartree accuracy can be obtained from explicitly correlated second-order Moeller-Plesset perturbation theory (MP2-R12) by employing one-electron basis sets which consist of orbitals with angular momentum l ≤ 7. To obtain the same level of accuracy, much higher l-values are needed in calculations with standard orbital-product wavefunctions, also when radial and angular extrapolations are employed. Our MP2-R12 calculations were carried out not only in the conventional manner using four-index integrals, but also with a newly developed code that uses only three-index integrals by virtue of a resolution-of-identity (RI) approximation (RI-MP2-R12)