Recently, impressive calculations have been achieved for the low-lying states of three-electron systems using Hylleraas-type wave functions [@Ho; @Clary; @Sims; @YD]. Such calculations are the result of developments in the methods of evaluation of the three-electron integrals. The integral methods used to perform the calculations of this work are described in Refs. [@Sims3e; @Ruiz3e; @Fro2003]. The rotationally excited states or Rydberg states of three-electron systems have attracted considerable attention and calculations have been done using theoretical methods to describe the core two-electron ion and the weakly bound excited electron [@Bhatia; @Chen]. A great theoretical interest in three-electron atomic systems can be explained by a number of facts known for such systems. First, three-electron atomic systems are very convenient objects for the study of the overall and relative contributions of the electron-electron correlations. It follows from the fact that the potential energy in the Hamiltonian, Eq.(\[Hamil\]), is represented by two sums each of which contains equal number of terms: electron-nucleus attractions and electron-electron repulsions. Therefore, by varying only one parameter $Q$ in Eq.(\[Hamil\]) we can study electron-electron correlations in such systems and relations between electron-electron and electron-nucleus correlations. Second, all three-electron atoms and ions are well known subjects in atomic physics. 