Hylleraas-Type Wave Functions for Some Excited Three-ElectronSStates

The usefulness of Hylleraas-type wave functions for variational calculation of three-electron excited $S$ states is investigated. The four lowest $\left(1\mathrm{}{s}^{2}ns\right){}_{}{}^2{}_{}{}^{}S$ wave functions for lithium are obtained in the same 57-term basis. The calculated energies are - 7.477 82, - 7.353 92, - 7.318 37, and - 7.303 39 a.u. compared to the corrected experimental results - 7.478 07, - 7.35410, - 7.318 53, and - 7.303 55 a.u. The largest part (0.000 15 a.u.) of the discrepancies is due to approximations in the core function. For the lowest ${}_{}{}^4{}_{}{}^{}S$ state for lithium a 44-term basis was used with the resulting energy - 5.212 40. The wave function was analyzed in terms of natural orbitals and found to exhibit strong $2s3s-2p3p$ "near degeneracy." The density for the Li state is significantly correlation contracted in the $3s$ region.