Variational-Bound Method for Autoionization States

A variational method which provides upper bounds to energies of atomic autoionization states (QHQ eigenvalues) without requiring knowledge of target eigenstates is sought. For two-electron atoms, it is found that such a method is provided by a superposition of configurations of a single set of arbitrarily chosen orbitals, with a (physically plausible) prescribed choice of secular-equation roots. This conclusion is applicable to calculations of Hol{}ien, and explains the observed "stabilization of roots."