Ground state of Li and Be$^+$ using explicitly correlated functions

TL;DR

This paper compares Hylleraas and exponential basis sets for calculating the ground states of Li and Be+ ions, achieving highly accurate results and analyzing the efficiency and stability of each method.

Contribution

It provides the most accurate ground state energies for Li and Be+ using explicitly correlated functions and compares the effectiveness of Hylleraas and exponential basis sets.

Findings

Hylleraas functions are numerically stable and suitable for large basis sets.

Exponential functions are effective with small basis sets but face numerical instabilities.

The paper reports the most accurate ground state energies for Li and Be+ to date.

Abstract

We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and Be$^+$. Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis functions. Our results for ground state energies $-7.478 060 323 910 10(32)$, $-14.324 763 176 790 43(22)$ of Li and Be$^+$ correspondingly, are the most accurate to date. When small basis set is considered, explicitly correlated exponential functions are much more effective. With only 128 functions we obtained about $10^{-9}$ relative accuracy, but the severe numerical instabilities make this basis costly in the evaluation.