  For the one-dimensional, extended Peierls--Hubbard model we calculate
analytically the ground-state energy and the single-particle gap to second
order in the Coulomb interaction for a given lattice dimerization. The
comparison with numerically exact data from the Density-Matrix Renormalization
Group shows that the ground-state energy is quantitatively reliable for Coulomb
parameters as large as the band width. The single-particle gap can almost
triple from its bare Peierls value before substantial deviations appear. For
the calculation of the dominant optical excitations, we follow two approaches.
In Wannier theory, we perturb the Wannier exciton states to second order. In
two-step perturbation theory, similar in spirit to the GW-BSE approach, we form
excitons from dressed electron-hole excitations. We find the Wannier approach
to be superior to the two-step perturbation theory. For singlet excitons,
Wannier theory is applicable up to Coulomb parameters as large as half band
width. For triplet excitons, second-order perturbation theory quickly fails
completely.
