The Pariser-Parr-Pople Hamiltonian is used to calculate and identify the nature of the low-lying vertical transition energies of polydiacetylene. The model is solved using the density matrix renormalisation group method for a fixed acetylenic geometry for chains of up to 102 atoms. The non-linear optical properties of polydiacetylene are considered, which are determined by the third-order susceptibility. The experimental 1B u data of Giesa and Schultz are used as the geometric model for the calculation.For short chains, the calculated E(1B u ) agrees with the experimental value, within solvation effects (∼ 0.3 eV). The charge gap is used to characterise bound and unbound states. The nB u is above the charge gap and hence a continuum state; the 1B u , 2A g and mA g are not and hence are bound excitons. For large chain lengths, the nB u tends towards the charge gap as expected, strongly suggesting that the nB u is the conduction band edge. The conduction band edge for PDA is agreed in the literature to be ∼ 3.0 eV. Accounting for the strong polarisation effects of the medium and polaron formation gives our calculated E ∞ (nB u ) ∼ 3.6 eV, with an exciton binding energy of ∼ 1.0 eV. The 2A g state is found to be above the 1B u , which does not 1 agree with relaxed transition experimental data. However, this could be resolved by including explicit lattice relaxation in the Pariser-Parr-Pople-Peierls model. Particlehole separation data further suggest that the 1B u , 2A g and mA g are bound excitons, and that the nB u is an unbound exciton.
I INTRODUCTIONPolymers, and other molecular materials, that exhibit non-linear optical properties and electroluminescence have attracted much interest amongst theorists and experimentalists, owing to their possible use in organic technology [1]- [7]. Poly(diacetylene)s (PDAs) with the general formula shown in Fig. 1. (a) are the π-conjugated organic polymers studied here: they exhibit non-linear optical properties, near-perfect crystal structure and doping-dependent transport properties. These properties make them ideally suited for use in the theorist's calculation. A full characterisation of PDA's electronic properties would mean a better understanding of π-conjugated polymers in general. In PDA with a very low polymer content (x p < 10 −3 in weight), interchain interaction is minimal and thus it can be considered an ideal one-dimensional model system. with 0 < δ < 1. This produces results that are, again, quantitatively too low; however, it does generate an energy difference of 0.48 eV between the butatriene and acetylene structures, in excellent agreement with other calculations and experiment [15]-[16]. In summary, therefore, all these models are seen to give good qualitative predictions for bond alteration, but the 3 data are seen to be consistently red-shifted owing to their single particle picture. First, in polymeric crystal form, the linear absorption spectrum is see to be symmetric and peaks at ∼ 1.8-1.9 eV. However, the onset of photoconduction occurs not at th...
