Theoretical study of bipolaron dynamics in polyparaphenylene: I. Derivation of the formalism and density functional (DFT) calculations on neutral and charged model systems

Abstract

We have derived the rather lengthy formalism for time simulations in polyparaphenylene, treating the rings as semi-rigid rotors. To this end an Euler–Lagrange formalism was used. As one of the model systems to parametrize a Pariser–Parr–Pople (PPP) Hamiltonian, we have chosen an asymmetric cationic dimeric system in our model of the geometry, which allows the rings to move between aromatic A-phase and quinoidal B-phase structures. A cation was chosen, in order to avoid the presence of an unpaired spin in the model. Further, anionic models would require more extended basis sets in our Density Functional (DFT) calculations. The asymmetric structure of the model allows to scan the total potential surface between aromatic and quinoidal structures. The cation shows only one minimum on the quinoidal side. To make sure that this is not only due to the charge, around the expected minima, we also performed calculations on a quinoidal B-phase model dimer and on an aromatic A-phase model dimer (biphenyle). However, since our geometrical model is based on the central unit of the trimer, we do not find double minimum potentials in dimers, which consist of just two terminal units. But the potentials still can serve as the basis of a parameterization of the model Hamiltonian for the π-electrons, while in longer chains one has to replace the terminal units by ones which have a more appropriate geometry. The calculated DFT potentials will be compared in a forthcoming paper with the corresponding PPP potentials in order to allow a parameterization of the PPP Hamiltonian and subsequently bipolaron structure optimizations as well as simulations of the dynamics of the system. The formalism needed to this end is derived and outlined in this paper in detail. It is currently under programming.