We present improved calculations of variational energy eigenvalues for the $1s^{2}2s\hspace{0.5em}{}^{2}S$, $1s^{2}3s\hspace{0.5em}{}^{2}S$, and $1s^{2}2p\hspace{0.5em}{}^{2}P$ states of lithium using basis sets with up to 30 224 terms in Hylleraas coordinates. The nonrelativistic energies for infinite nuclear mass are $-7.478\hspace{0.5em}060\hspace{0.5em}323\hspace{0.5em}910\hspace{0.5em}143\hspace{0.5em}7(45)$ a.u. for $1s^{2}2s\hspace{0.5em}{}^{2}S$, $-7.354\hspace{0.5em}098\hspace{0.5em}421\hspace{0.5em}444\hspace{0.5em}316\hspace{0.5em}4(32)$ a.u. for $1s^{2}3s\hspace{0.5em}{}^{2}S$, and $-7.410\hspace{0.5em}156\hspace{0.5em}532\hspace{0.5em}651\hspace{0.5em}6(5)$ a.u. for $1s^{2}2p\hspace{0.5em}{}^{2}P$, 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.

• Received 31 December 2010

DOI:https://doi.org/10.1103/PhysRevA.83.034503