Density matrix renormalization group calculations of the low-lying excitations and non-linear optical properties of poly(para-phenylene)

The two-state molecular orbital (2-MO) model of the phenyl-based semiconductors is used to calculate the low-lying spectra of the A(g)(+) and B-1u(-) states of poly(para-phenylene) (PPP). The model parameters are determined by fitting its predictions to exact Pariser-Parr-Pople model calculations for benzene and biphenyl, and it is solved using the density matrix renormalization group method. It is shown that there exists a band of B-1(1u)- ('s'-wave) excitons below the band states. In the long-chain limit the lowest exciton is situated 3.3 eV above the ground state, consistently with experimental data. The calculated particle-hole separation of these excitons indicates that they are tightly bound, extending over only a few repeat units. The lowest band state is found to be a covalent 2(1)A(g)(+) state, whose energy almost coincides with the charge gap E-G. Lying just above the 2(1)A(g)(+) state is a band B-1(1u)- state (the n(1)B(1u)(-) state). The particle-hole separation of the band states scales linearly with oligomer size. The binding energy of the 1(1)B(1u)(-) exciton is determined rigorously as 0.74 eV. The dipole matrix elements and oscillator strengths for the transitions between the lowest (1)A(g)(+) and B-1(1u)- states are calculated and the NLO properties of PPP, such as electroabsorption (EA) and third-harmonic generation, are investigated. A comparison of the EA spectrum with the experimental data shows that the main features of the experimental spectrum are well described in the 2-MO Hamiltonian. Only five states account for most of the calculated EA. These are the 1(1)A(g)(+), 1(1)B(1u)(-), 2(1)A(g)(+), n(1)B(1u)(-) states and another band (1)A(g)(+) state, the k(1)A(g)(+) state, thus confirming the essential-states model. An analysis of the particle excitation weight of these states indicates that they are predominantly single particle in character.