Variational functionals for excited state saddle points versus traditional Hylleraas-Undheim and McDonald higher "roots," and a way to instantly improve a lowest state crude approximant

Many chemical reactions occur in excited states, so, we must know their wave functions. But the excited states are saddle points in the wave function space and cannot be located by energy minimization. The reported functional, omega n, (reducible to a self-consistent generalized eigenvalue problem, that allows simultaneous treatment with multi-configuration self-consistent field - MCSCF) locate the excited states/saddle points with the help of crude approximants of the lower lying states, without demanding any orthogonality to them, whatsoever. omega n is useful for systems (mainly large) where huge wave functions expansions (that would tend to the exact values) are impracticable, and rather small truncated (but comprehensible) wave functions are needed. omega n is checked against large wave functions of small atoms and against both large and small wave functions that implement the Hylleraas-Undheim - McDonald theorem thus locate an energy minimum near, but not the saddle point itself. Various omega n applications are given.