we use this variational expansion to determine the total energies and other bound state properties of some excited states in the Li-atom. The results obtained in Section III can also be used to correct a few mistakes and misprints made in earlier studies of three-electron atomic systems. In Section IV by using the Hylleraas-Configuration Interaction (Hy-CI) and Configuration Interaction (CI) variational expansions of the wave functions we investigate the general structure of the bound state spectra (or optical spectra, for short) of three-electron (or Li-like) atoms and ions. Section IV also contains a brief discussion of the ‘scaling’ procedure which can be used to study the electron-electron correlations in three-electron atomic systems. Concluding remarks can be found in the last Section.

Semi-exponential variational expansion
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A semi-exponential variational expansion for three-electron wave functions was developed a few years ago [@Fro2010] in order to modify the traditional Hylleraas variational expansion which has been used for three-electron atomic systems since Larsson’s work [@Lars]. Recently it became clear that the Hylleraas variational expansion of the three-electron wave functions has a very slow convergence rate. Our main idea in [@Fro2010] was to increase the total number of varied, non-linear parameters in each basis function 