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

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 $1{\mathrm{cm}}^{-1}$ 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.

Figure 1

Convergence of the MP2 (red pluses) and FCCD (blue crosses) correlation energy with $\mathrm{\Omega }$ for the $\mathrm{SCF}(3,7)$ basis set.

Figure 2

Convergence of the ${\delta }_{\mathrm{S}},{\delta }_{\mathrm{NF}}$, and ${\delta }_{\mathrm{FCI}}$ corrections to the complete basis set limit. The correction ${\delta }_{\mathrm{NF}}$ was multiplied by $-26$ to match the scale of the plot.