Just as the lowest eigenvalue has been shown to be an upper bound to the
exact ground-state energy, more generally, any eigenvalue 
can be
shown to be an upper bound to the corresponding exact excited state energy
[15]. In fact, one can also show that as other
N-electron basis functions are added to the CI procedure, the eigenvalues
obey the MacDonald-Hylleraas-Undheim relations
[15, 16]
where m is the number of N-electron basis functions.