用显式关联函数研究Li和Be的基态$^+$
Ground state of Li and Be$^+$ using explicitly correlated functions
摘要：
我们比较了显关联的Hylleraas基组和指数基组在计算Li和Be $^+$的基态时的结果。使用Hylleraas函数的计算在数值上是稳定的，并且可以使用大量的基函数来执行。我们对Li和Be的$^+$的基态能量$-7.478 060 323 910 10(32)$、$-14.324 763 176 790 43(22)$的计算结果是迄今为止最精确的。在小基集情况下，显相关指数函数的计算效率更高。仅用128个函数，我们就获得了大约$10^{-9}$的相对精度，但严重的数值不稳定性使这个基础在评估中代价高昂。
英文摘要：
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.
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