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

TL;DR

This paper introduces a new composite computational method combining explicitly correlated coupled cluster theory with Hylleraas basis sets and Slater orbitals to accurately calculate many-electron atom energies efficiently.

Contribution

It presents a novel approach that reduces computational complexity and improves accuracy for many-electron atoms by integrating different basis sets and correlation techniques.

Findings

Achieved better than 1 cm$^{-1}$ accuracy for beryllium atom

Eliminated need for complex nonlinear parameter optimization

Method scalable to heavier atoms without exponential cost increase

Abstract

In this work we propose a novel 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 factorisable coupled cluster theory. Instead of the usual Gaussian-type geminals for the expansion of the pair functions, we employ two-electron Hylleraas basis set. This eliminates the need for massive optimisation of nonlinear parameters and the required three-electron integrals can now be calculated relatively easily. 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 the accuracy better than $1\,$cm$^{-1}$ is obtained. We discuss in details 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 one to two orders of magnitude. The most important advantage of the method is that is does not suffer from an exponential growth of the computational costs with increasing number of electrons in the system and thus can be applied to heavier atoms preserving a similar level of accuracy.