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

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 $-7.478 060 323 910 10(32)$,$-14.324 763 176 790 43(22)$ofLiandBe$^+$ 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.