Application of New Lower-Bound Techniques to the Spectra of Li andLi+

New techniques are presented for the calculation of lower bounds to energies of atoms and ions. A combination of effective-field and intermediate-problem methods is used to seek intermediate operators which rapidly approximate the lower spectrum of the full Hamiltonian. Effectiveness of the techniques is demonstrated by showing that very small-scale calculations suffice to free the ground state of Li from the continuum, and to approximate the ${\mathrm{Li}}^{+}$ ground state within 0.8%.