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- hale models may be expected to provide a useful description of the exc ited states of conjugated polymers. Here, these models are tested agai nst density matrix renormalization group (DMRG) calculations. The DMRG method is used to generate nearly-exact descriptions of the ground st ate, 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 atom s. These are compared with both bare electron-hole (singles configurat ion 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 obtai ned. 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 el ectron-hole methods increases with chain length, suggesting the format ion of a polarization cloud around the electron and hole on long chain s. Dressed electron-hole theory does not work as well for the optical gap; however, the chain-length dependence of the error is weak and thu s may be partially compensated by the parameterization of a semi-empir ical Hamiltonian to experimental data. These results therefore supper: the use of dressed electron-hole theory to parameterize a semiempiric al Hamiltonian to molecular data, and then make predictions for long p olymer chains. When screened electron-electron interaction potentials are used, neither the bare nor dressed electron-hole models give predi ctions in agreement with the DMRG results. The effects of electron cor relation on the ground state are shown to be larger with screened than unscreened potentials, and this may account for the breakdown in elec tron-hole theory for screened potentials. (C) 1998 American Institute of Physics.