Density matrix renormalization calculations of the relaxed energies and solitonic structures of polydiacetylene

The density matrix renormalization group method is applied to the Pariser-Parr-Pople-Peierls model to calculate the energies and associated structures of the low-lying states of polydiacetylene. The extrinsic dimerization of polydiacetylene, arising from the electrons in p_y orbitals in the triple bonds, is explicitly calculated. We find the following results. (i) Electronic interactions result in a twofold increase in the ground state dimerization, and a twofold decrease in the electronic correlation length, ξ. (ii) The vertical energy of the 2¹A_g⁺ state lies circa. 1 eV above the 1¹B_u^- state in long chains. (iii) The 1³B_u⁺ and 2¹A_g⁺ states undergo a sizable electron-lattice relaxation, while this is modest for the 1¹B_u^- state. As a consequence, the relaxed energy of the 2¹A_g⁺ lies circa 0.1 eV below the relaxed energy of the 1¹B_u^- state. (iv) The reduction in ξ results in a reversal in bond dimerizations in both the 1³B_u⁺ and 2¹A_g⁺ states (in contrast to the noninteracting Peierls model). However, the excitonic 1¹B_u^- state shows a polaronic distortion. We compare our results to experiment. For short oligomers the comparisons are very reasonable, but they are less satisfactory for long chains. The inclusion of solvation effects and a reparametrization of the Ohno interaction may both be necessary.