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

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Puchalski, Mariusz
Kedziera, Dariusz
Pachucki, Krzysztof
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Abstract
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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.
Comment: 15 pages
Keywords
Physics - Atomic Physics, Physics - Chemical Physics
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