Ground state of Li andBe+using explicitly correlated functions

Abstract

We compare the explicitly correlated Hylleraas and exponential basis sets in the evaluations of ground state of Li and ${\text{Be}}^{+}$. Calculations with Hylleraas functions are numerically stable and can be performed with the large number of basis functions. Our results for ground-state energies $\ensuremath{-}7.478\text{ }060\text{ }323\text{ }910\text{ }10(32)$ and $\ensuremath{-}14.324\text{ }763\text{ }176\text{ }790\text{ }43(22)$ of Li and ${\text{Be}}^{+}$, 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 ${10}^{\ensuremath{-}9}$ relative accuracy, but the severe numerical instabilities make this basis costly in the evaluation.