AGP: Search for the consistent RPA reference state

The Random Phase Approximation (RPA) with exchange applied to molecular electronic structure can yield excellent excitation energies, but suffers from instabilities resulting in imaginary excitation energies when the single determinant Hartree-Fock reference state does not correspond to an absolute energy minimum. It has been shown that an Antisymmetrized Geminal Power (AGP) state is a consistent RPA reference state that cures such instabilities and permits the simultaneous calculation of ground and excited electronic states with correct energy separation over all geometries. Here we revisit this old theoretical development in the hope that new applications can be found.