The standard energy functionals have their minima at the ground
state energies while they have just saddle points at the excited
state energies. Alternative functionals suitable for variational
calculations (cf. arXiv:0801.3673) are presented as possessing a
local minimum at any excited-state energy. A Helium is selected for
the test run of the resulting variational recipe.

MR2502664 Bacalis, N. C.; Xiong, Z.; Karaoulanis, D. Inherent
restrictions of the Hylleraas-Undheim-MacDonald higher roots, and
minimization functionals at the excited states. J. Comput. Methods
Sci. Eng. 8 (2008), no. 4-6, 277--285. 81Q15 (81Q05)