  n a recent paper we proposed the expansion of the space of variations in
energy calculations by considering the approximate wave function $\psi$ to be a
functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. For
the determination of such a wave function functional, a constrained search is
first performed over the subspace of all functions $\chi$ such that
$\psi[\chi]$ satisfies a physical constraint or leads to the known value of an
observable. A rigorous upper bound to the energy is then obtained by
application of the variational principle. To demonstrate the advantages of the
expansion of variational space, we apply the constrained-search--variational
method to the ground state of the negative ion of atomic Hydrogen, the Helium
atom, and its isoelectronic sequence. The method is equally applicable to
excited states, and its extension to such states in conjunction with the
theorem of Theophilou is also described.
