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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.

We present improved calculations of variational energy eigenvalues for the $1{s}^{2}2s {}^{2}S$, $1{s}^{2}3s {}^{2}S$, and $1{s}^{2}2p {}^{2}P$ states of lithium using basis sets with up to 30 224 terms in Hylleraas coordinates. The nonrelativistic energies for infinite nuclear mass are $\ensuremath{-}7.478 060 323 910 143 7(45)$ a.u. for $1{s}^{2}2s {}^{2}S$, $\ensuremath{-}7.354 098 421 444 316 4(32)$ a.u. for $1{s}^{2}3s {}^{2}S$, and $\ensuremath{-}7.410 156 532 651 6(5)$ a.u. for $1{s}^{2}2p {}^{2}P$, which represent the most accurate variational upper bounds to date. An important advantage of the basis sets with multiple distance scales is their exceptional numerical stability.