arXiv:cond-mat/9901031v1 6 Jan 1999 Molecular Orbital Models of Benzene, Biphenyl and the Oligophenylenes Robert J. Bursill 1 , William Barford 2 and Helen Daly 2 1 School of Physics, University of New South Wales, Sydney, NSW 2052, Australia. Email: ph1rb@newt.phys.unsw.edu.au 2 Department of Physics, The University of Sheffield, Sheffield, S3 7RH, U. K. Email: w.barford@sheffield.ac.uk Abstract A two state (2-MO) model for the low-lying long axis-polarised excitations of poly(p-phenylene) oligomers and polymers is developed. First we derive such a model from the underlying Pariser- Parr-Pople (P-P-P) model of π-conjugated systems. The two states retained per unit cell are the Wannier functions associated with the valence and conduction bands. By a comparison of the predictions of this model to a four state model (which includes the non-bonding states) and a full P-P-P model calculation on benzene and biphenyl, it is shown quantitatively how the 2-MO model fails to predict the correct excitation energies. The 2-MO model is then solved for oligophenylenes of up to 15 repeat units using the density matrix renormalisation group (DMRG) method. It is shown that the predicted lowest lying, dipole allowed excitation is ca. 1 eV higher than the experimental result. The failure of the 2-MO model is a consequence of the fact that the original HOMO and LUMO single particle basis does not provide an adequate representation for the many body processes of the electronic system. 1 Introduction Interest in the low-lying excitations of the phenyl based semiconductors, in particular poly(p-phenylene) and poly(p-phenylene vinylene), arises from the observation of their electroluminescence [1], [2] and the possibility of various optical and nonlinear devices. From a theoretical point of view one would like to understand how the excitations of the phenyl based semiconductors are derived from the parent excitations of benzene, how these evolve as a function of oligomer length, and how they participate in non-linear optical processes. There is now a substantial body of experimental results on the photo- and electro- luminescent properties of poly(p-phenylene vinylene) [3, 4, 5, 6, 7, 8, 9, 10], and this has generated commi- cant theoretical interest [9, 11, 12, 13, 14]. Fewer experimental results exist for poly(p-phenylene) [15, 16, 17, 2, 18], however, largely resulting from the difficulties in obtaining well characterised mate- rial. There have been a number of theoretical calculations on poly(p-phenylene). Br´ edas has used the VEH pseudopotential technique [19] and Ambrosch-Draxl et al. have performed density functional calculations using LAPW and pseudopotentials [16]. Rice et al. [13] have developed a phenomeno- logical, microscopic model based on the molecular excitations of benzene. The absorption bands are calculated using an approximate Kubo formalism. In this paper we will restrict our attention to poly(p-phenylene), and develop in full detail the model and computational techniques introduced in a recent letter [20], [21]. Our goal is to con- struct a model of poly(p-phenylene) based on the underlying Pariser-Parr-Pople (P-P-P) model of π-conjugated electron systems [22]. The P-P-P model has long been used to describe the low-lying excitations of π-conjugated systems, giving reasonable results. However, an improved parameteri- sation of this model is possible, and that was achieved in a previous paper [23]. We will use this optimised parameterisation in the current paper. We will show, at the very least, that to achieve our goal of a full description of poly(p-phenylene) a four molecular orbital (4-MO) model (as described 1