Correlation energies for many-electron atoms with explicitly correlated Slater functions

Abstract

In this work we propose a composite method for accurate calculation of the energies of many-electron atoms. The dominant contribution to the energy (pair energies) are calculated by using explicitly correlated factorizable coupled cluster theory. Instead of the usual Gaussian-type geminals for the expansion of the pair functions, we employ a two-electron Hylleraas basis set and discuss the advantages of the latter approach, e.g., a small number of nonlinear parameters that need to be optimized. The remaining contributions to the energy are calculated within the algebraic approximation by using large one-electron basis sets composed of Slater-type orbitals. The method is tested for the beryllium atom where an accuracy better than $1\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ is obtained. We discuss in detail possible sources of the error and estimate the uncertainty in each energy component. Finally, we consider possible strategies to improve the accuracy of the method by 1--2 orders of magnitude and apply it to larger atoms.