Orthogonality conditions to lower-lying states and convergence of the Hylleraas-Undheim-Pekeris methods

It has been demonstrated that slow convergence of the Hylleraas-Undheim-Pekeris methods, for low-lying states of two-electron atoms, is due to the need for the wave-functions of these states to satisfy additional orthogonality conditions. A new expansion is proposed, which leads to a remarkable improvement of convergence of the variational ionization energies of the excited singlet S-states of He and Li+.