  The two state molecular orbital (2-MO) model of the phenyl based
semiconductors is used to calculate the low-lying spectra of the Ag and Bu
states of poly(para-phenylene) (PPP). The model parameters are determined by
fitting its predictions to exact Pariser-Parr-Pople model calculations of
benzene and biphenyl, and it is solved using the density matrix renormalisation
group method. It is shown that there exists a band of Bu (s-wave) excitons
below the band states. In the long chain limit the lowest exciton is situated
3.3 eV above the ground state, consistent 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 2Ag state, whose energy almost coincides with the charge
gap Eg. Lying just above the 2Ag state is a band Bu state (the nBu state). The
particle-hole separation of the band states scales linearly with oligomer size.
The binding energy of the 1Bu exciton is determined rigorously as 0.74 eV. The
dipole matrix elements and oscillator strengths for the transitions between the
lowest Ag and Bu 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 by the 2-MO
Hamiltonian. Only five states account for most of the calculated EA. These are
the 1Ag, 1Bu, 2Ag, nBu and another band Ag state, the kAg, thus confirming the
essential states model. An analysis of the particle excitation weight of these
states indicates that they are predominately single particle in character.
