Ground state of Li and Be+ using explicitly correlated functions

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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.