Theoretical Study of Bipolaron Dynamics in Polyparaphenylene: II. Density Functional Theory (DFT) Calculations on Neutral Dimers and Semiempirical Hückel-Type Calculations on Neutral and Charged Model Chains

Abstract

We have derived earlier the rather lengthy formalism for time simulations in poly(p-phenylene), treating the rings as semirigid rotors. To this end the Euler-Lagrange formalism had to be used. As a first step we intended to parametrize the simplified Hückel-type hamiltonian on the basis of density functional theory (DFT) calculations on some dimeric model systems. The results of this attempt are reported here. However, calculations on much longer chains, containing up to 200 rings, show a clear tendency of our model to favor the quinoid B-phase structure over the aromatic one. Further, in doubly charged chains, the charge tends to remain unseparated and to be completely delocalized over virtually the complete part of the chain, that is in B-phase conformation. The bipolaron width turns out to be extremely small, of about 10 rings in a chain having 200 rings. This is rather unexpected and interpreted as a shortcoming of the Hückel-type nature of the hamiltonian. The reason is that in the Hückel-type model the two electrons, taken away to charge the chain, are from the same orbital, and thus charge separation is more difficult, leading, in this case, only to a delocalization, keeping the bipolaron small. We assume, that in line with Prof. Paldus' work, the inclusion of direct electron-electron interactions in the form of a Pariser-Parr-Pople (PPP) type model could overcome this difficulty. The treatment has to be done, probably, in an open shell form to make possible spin separation, if necessary. Care has to be taken for spin contaminations in such treatments and possibly even the explicit inclusion of electron correlation might be necessary. In this paper we report our model which was derived in detail in a previous paper. Then we discuss the parametrization attempts and our results on longer chains. In conclusion our suggestion is that a PPP type model must be used at least to allow for bipolaron calculations and confinement of the two like charges. Such calculations would be the content of a forthcoming paper.