  We consider a chain of atoms that are bound together by a harmonic force.
Spin-1/2 electrons that move between neighboring chain sites (H\"uckel model)
induce a lattice dimerization at half band filling (Peierls effect). We
supplement the H\"uckel model with a local Hubbard interaction and a long-range
Ohno potential, and calculate the average bond-length, dimerization, and
optical phonon frequencies for finite straight and zig-zag chains using the
density-matrix renormalization group (DMRG) method. We check our numerical
approach against analytic results for the H\"uckel model. The Hubbard
interaction mildly affects the average bond length but substantially enhances
the dimerization and increases the optical phonon frequencies whereas, for
moderate Coulomb parameters, the long-range Ohno interaction plays no role.
