Eur. Phys. J. Special Topics 218, 1-70 (2013)
https://doi.org/10.1140/epjst/e2013-01772-8

Review

Faddeev random phase approximation applied to molecules

Center for Molecular Modeling, CMM, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium

^a e-mail: matthias.degrote@ugent.be

Received: 12 November 2012
Revised: 16 January 2013
Published online: 12 March 2013

Abstract

The Faddeev Random Phase Approximation (FRPA) is a Green’s function method which couples collective degrees of freedom to the single particle motion by resumming an infinite number of Feynman diagrams. The Faddeev technique is applied to describe the two-particle-one-hole (2p1h) and two-hole-one-particle (2h1p) Green’s function in terms of non-interacting propagators and kernels for the particle-particle (pp) and particle-hole (ph) interactions. This results in an equal treatment of the intermediary pp and ph channels. In FRPA both the pp and ph phonons are calculated on the random phase approximation (RPA) level.

In this work the equations that lead to the FRPA eigenvalue problem are derived. The method is then applied to atoms, small molecules and the Hubbard model, for which the ground state energy and the ionization energies are calculated. Special attention is directed to the RPA instability in the dissociation limit of diatomic molecules and in the Hubbard model. Several solutions are proposed to overcome this problem.