Variational energies and the Fermi contact term for the low-lying states of lithium: Basis-set completeness

Nonrelativistic energies for the low-lying states of lithium are calculated using the variational method in Hylleraas coordinates. Variational eigenvalues for the infinite nuclear mass case with up to 34 020 terms are $\ensuremath{-}7.478\phantom{\rule{0.16em}{0ex}}060\phantom{\rule{0.16em}{0ex}}323\phantom{\rule{0.16em}{0ex}}910\phantom{\rule{0.16em}{0ex}}147(1)$ a.u. for $1{s}^{2}2s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S$, $\ensuremath{-}7.354\phantom{\rule{0.16em}{0ex}}098\phantom{\rule{0.16em}{0ex}}421\phantom{\rule{0.16em}{0ex}}444\phantom{\rule{0.16em}{0ex}}37(1)$ a.u. for $1{s}^{2}3s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S$, $\ensuremath{-}7.318\phantom{\rule{0.16em}{0ex}}530\phantom{\rule{0.16em}{0ex}}845\phantom{\rule{0.16em}{0ex}}998\phantom{\rule{0.16em}{0ex}}91(1)$ a.u. for $1{s}^{2}4s{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}S$, $\ensuremath{-}7.410\phantom{\rule{0.16em}{0ex}}156\phantom{\rule{0.16em}{0ex}}532\phantom{\rule{0.16em}{0ex}}652\phantom{\rule{0.16em}{0ex}}41(4)$ a.u. for $1{s}^{2}2p{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}P$, and $\ensuremath{-}7.335\phantom{\rule{0.16em}{0ex}}523\phantom{\rule{0.16em}{0ex}}543\phantom{\rule{0.16em}{0ex}}524\phantom{\rule{0.16em}{0ex}}688(3)$ a.u. for $1{s}^{2}3d{\phantom{\rule{0.16em}{0ex}}}^{2}\phantom{\rule{-0.16em}{0ex}}D$. The selection of the minimum set of angular momentum configurations is discussed, with the $2P$ and $3D$ states as examples to demonstrate the impact of various configurations on the variational energies. It is shown by numerical example that the second spin function (i.e., coupled to form a triplet intermediate state) has no significant effect on either the variational energies or the spin-dependent Fermi contact term. Results of greatly improved accuracy for the Fermi contact term are presented for all the states considered.