Remarks On The Standard Hylleraas-Undheim And MacDonald Computation Of   Excited States
  For the computation of excited states, the standard solutions of the Schroedinger equation, using higher roots of a secular equation in a finite N-dimensional function space, by the Hylleraas-Undheim and MacDonald theorem, have several restrictions, which render them of lower quality, relative to the lowest root, if the latter is good enough. These deficiencies are reported, that prevent from comparisons with accurate experiments. 
Naoum C. Bacalis