Determination of excited atomic state energies in a minimax procedure, as exemplified by the 1s2s1S state of the He atom

Problems in the use of a new variational approach to calculate excited states of multielectron systems with lower-lying states of the same symmetry are discussed. The approach is based on use of a minimax technique to determine the saddle points of the energy functional, where the energy values are upper limits on the corresponding eigenvalues of the Hamiltonian and are subject to improvement. The energy of the1s2s1S state of the He atom is calculated in a detailed example.