Comparison of density matrix renormalization group calculations with electron-hole models of exciton binding in conjugated polymers

By analogy with inorganic semiconductors such as GaAs or Si, electron-hole models may be expected to provide a useful description of the excited states of conjugated polymers. Here, these models are tested against density matrix renormalization group (DMRG) calculations. The DMRG method is used to generate nearly-exact descriptions of the ground state, 1${}^1{B}_u$ optical gap state, and the band gap of the Pariser-Parr-Pople (PPP) Hamiltonian of polyenes with between 2 and 40 carbon atoms. These are compared with both bare electron-hole (singles configuration interaction theory and the random phase approximation) and dressed electron-hole (second and third order Green’s function) methods. For the optical gap, only second-order Green’s function results were obtained. When an unscreened (Ohno) electron-electron interaction potential is used, the dressed electron-hole methods work well for the band gap. The difference between the band gap predicted by bare and dressed electron-hole methods increases with chain length, suggesting the formation of a polarization cloud around the electron and hole on long chains. Dressed electron-hole theory does not work as well for the optical gap; however, the chain-length dependence of the error is weak and thus may be partially compensated by the parameterization of a semi-empirical Hamiltonian to experimental data. These results therefore support the use of dressed electron-hole theory to parameterize a semiempirical Hamiltonian to molecular data, and then make predictions for long polymer chains. When screened electron-electron interaction potentials are used, neither the bare nor dressed electron-hole models give predictions in agreement with the DMRG results. The effects of electron correlation on the ground state are shown to be larger with screened than unscreened potentials, and this may account for the breakdown in electron-hole theory for screened potentials.