Relationship between the random-phase approximation ground-state total energy and GW quasiparticle energy

A connection between the random-phase-approximation (RPA) total energy E(RPA) and the GW quasiparticle energy (is an element of)GW has been pointed out. More specifically we show that: delta E(RPA)(N)/delta N=is an element of(GW), where N is the total number of electron. The variational property of the RPA total energy is also discussed and the variational equations for the orbital wave functions are derived. We argue that the RPA formalism is a method which can provide both accurate ground-state energies and single quasiparticle energies.