procedure is very stable for calculations with high quantum number L. This is based in the very stable two-electron integral algorithms used in the calculations. These algorithms have been described in detail by Eqs. (A.33-A.35) of Ref. [@Ruiz2e]. The accuracy of the CI calculations is $\approx 1$ mhartree ($1\times 10^{-3} a.u.$). The obtained energies are listed in Table IV. We can compare the energy values of the $S$-states obtained by the gaussoids expansion in Table II with the ones by the Hy-CI method. All the energy values are very close, the differences are in the order of few microhartrees ($1\times 10^{-6} a.u.$). The ground state energies of the Li atom and Li-like ions are slightly better by using the Gaussoids expansion, while the low-lying excited $P$-states are better by using the Hy-CI method. For the Li atom and Be$^+$ ion we compared the energies of low-lying states of $S$-, $P$- and $D$-symmetry in [@Bel1] obtaining differences in the order of few microhartrees. In this work we have calculated higher states of the Li atom and Be$^{+}$ ion using the CI method. For the ions, the literature is very scarce. We were able to compare the ground and lowest $P$-symmetry states 