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The computation of small concise and comprehensible excited state wavefunctions is needed because many electronic processes occur in excited states.But since the excited energies are saddle points in the Hilbert space of wavefunctions, the standard computational methods, based on orthogonality to lowerlying approximants, resort to huge and incomprehensible wave functions,otherwise, the truncated wave function is veered away from the exact. Thepresented variational principle for excited states, Fn, is demonstrated to leadto the correct excited eigenfunction in necessarily small truncated spaces.Using Hylleraas coordinates for He 1S 1s2s, the standard method based on thetheorem of Hylleraas - Unheim, and MacDonald, yields misleading main orbitals1s1s' and needs a series expansion of 27 terms to be corrected, whereasminimizing Fn goes directly to the corect main orbitals, 1s2s, and can beadequately improved by 8 terms. Fn uses crude, rather inaccurate, lower lyingapproximants and does not need orthogonality to them. This reducessignificantly the computation cost. Thus, having a correct 1st excited state{\psi}1, a ground state approximant can be immediately improved toward anorthogonal to psi_1 function. Also higher lying functions can be found thathave the energy of psi_1, but are orthogonal to psi_1. Fn can also recognize aflipped root in avoided crossings: The excited state, either flipped or not,has the smallest Fn. Thus, state average is unnecessary. The method is furtherapplied via conventional configuration interaction to the three lowest singletstates of He 1S.

Minimization principle for non degenerate excited states (independent of orthogonality to lower lying known approximants)