  We present a new, non-variational orbital-optimization scheme for the
Antisymmetric Product of one-reference orbital Geminal wave function. Our
approach is motivated by the observation that an orbital-optimized
seniority-zero configuration interaction (CI) expansion yields similar results
to an orbital-optimized seniority-zero-plus-two CI expansion [J. Chem. Phys.,
135, 044119 (2011)]. A numerical analysis is performed for the C$_2$, LiF and
CH$_2$ molecules as well as for the symmetric stretching of hypothetical
(linear) hydrogen chains. For these test cases, the proposed
orbital-optimization protocol yields similar results to its variational orbital
optimization counterpart, but prevents symmetry-breaking of molecular orbitals
in most cases.
