Application of ’’multiple basis set technique’’ to the RPA and PVA equations

Abstract

We propose the ’’modified’’ RPA (MRPA) and ’’modified’’ PAV (MPVA) equations using the ’’modified’’ Hartree–Fock one-particle Green’s function. It is shown that when we choose the ’’modified’’ particle states in the vertex which represents a simultaneous creation (or annihilation) of two particle–hole pairs, there are two cases [(i) and (ii)]. Case (i) is what has been discussed by Ishihara and Poe, and case (ii) is an artificial exchange type of case (i). The MRPA including the contribution of particle–hole EPV ladder diagrams is derived by using case (ii). On the other hand, MPVA including the contribution of particle–hole EPV ring or ladder diagrams is derived by using case (i) or case (ii). Also, the application of case (ii) to the correlation-energy diagram, the self-energy diagram, and the augmented RPA is discussed.