Orbital-optimized coupled-cluster theory does not reproduce the full configuration-interaction limit

It is shown that due to the mixing of the usual projection approach of coupled cluster with variational orbital optimization, orbital-optimized coupled cluster (OCC) fails to reproduce the full configuration-interaction (full CI) limit when the cluster operator becomes complete. It is pointed out that the fulfillment of the projected singles equations, which define the orbital gradient in Brueckner coupled cluster (BCC), is mandatory for a correct behavior. As numerical examples we present general OCC and BCC calculations up to the full CI limit on CH(2) and an active-space model of ozone. The observed deviations of OCC from full CI are of the order of the correlation error obtained in calculations with up to quadruples excitations. Thus the failure of OCC may be considered tolerable in more approximate calculations but clearly prohibitive for any benchmark application. For applications to active-space models a hybrid approach for OCC is suggested in which for active particle-hole rotations the Brueckner orbital gradient is employed, whereas for the remaining orbital rotations the variational orbital gradient is retained.