Simplified Green-function approximations: Further assessment of a polarization model for second-order calculation of outer-valence ionization potentials in molecules.

Abstract

Ab initio methods for calculating the binding-energy spectra of large molecules have traditionally been restricted to primarily either Koopmans's theorem or the density-functional transition-orbital method. The limitations of the former are well known, and the density-functional ``band-gap problem'' has led to a further realization of intrinsic difficulties with the latter. An increasingly popular alternative to these two methods is to seek a simple approximation for the Green-function self-energy. The Green-function self-energy is the optical potential seen by a scattering particle (hole). As such, the dominant many-body effects contributing to the self-energy result from polarization of the charge density at energies below the first excitation energy of the target molecule (quasiparticle regime), as well as excitations of the target at higher energies. The physical importance of polarization effects is apparent in Hedin's GW approximation, which treats the self-energy as a product of the Green function (G) and a screened interaction (W) that can be calculated (essentially) from the time-dependent linear response of the charge density. In the present paper, we examine the contribution of polarization to the usual second-order Green-function (GF2) approximation with respect to the calculation of outer-valence ionization potentials in small molecules. A simplified version (GW2) of the GW approximation is found to be an acceptable substitute for the GF2 approximation, provided a self-interaction correction is included to prevent an electron from polarizing itself.Polarization effects are further analyzed using the Coulomb-hole and screened-exchange (COHSEX) and modified-COHSEX (M-COHSEX) approximations. A second-order version (M-COHSEX2) of the M-COHSEX approximation is used to examine the origin of the incorrect ordering by Koopmans's theorem of the first three ionization potentials of the nitrogen molecule in terms of static polarization and retardation effects. Finite-basis-set errors are also explored. Although higher-order Green-function approximations must be examined before drawing final conclusions, we believe that the present work provides preliminary evidence that suitably modified versions of time-dependent density-functional, dielectric-function-based self-energy approximations can be useful for molecules.