Comparative application of different approaches for band structure calculations on polyparaphenylene in the Pariser-Parr-Pople model: I. The mean field (Hartree-Fock) approximation and localized Wannierfunctions

We present an investigation on the calculation of the band structure of polyparaphenylene using the one-particle Hartree-Fock method. In the ab initio case there are many calculations on this level published which are all based on different Hartree-Fock (HF) program packages and thus use different cutoff schemes for the interactions and different basis sets. Therefore the results of these studies are not directly comparable and a thorough study of different approaches based on one and the same reference is highly desirable. In two forthcoming papers we want to present a similar study on the same system using conventional correlation methods and density functional schemes, especially self interaction corrected ones. The PPP or the Hubbard model are well suited for such a purpose, since the correlation methods on top of HF use exactly the same formalisms as in the corresponding ab initio applications, however, the numerical calculations are much cheaper. In this paper we present first of all in details the formalism of the PPP and Hubbard models and its relation to the full ab initio theory. Further, we describe in detail how localized Wannierfunctions can be obtained from the delocalized canonical Bloch orbitals. Localized Orbitals are of utmost importance both for conventional correlation methods and for the Self-Interaction Correction in Density Functional Theory. Finally we derive expressions for transition dipole moments in polymer calculations and an application to the spectrum of polyparaphenylene.