  The optimized random phase approximation (ORPA) for classical liquids is
re-examined in the framework of the generating functional approach to the
integral equations. We show that the two main variants of the approximation
correspond to the addition of the same correction to two different first order
approximations of the homogeneous liquid free energy. Furthermore, we show that
it is possible to consistently use the ORPA with arbitrary reference systems
described by continuous potentials and that the same approximation is
equivalent to a particular extremum condition for the corresponding generating
functional. Finally, it is possible to enforce the thermodynamic consistence
between the thermal and the virial route to the equation of state by requiring
the global extremum condition on the generating functional.
