  We investigate the relaxation energies and excited state geometries of the
light emitting polymer, poly(para-phenylene). We solve the
Pariser-Parr-Pople-Peierls model using the density matrix renormalization group
method. We find that the lattice relaxation of the dipole-active $1^1B_{1u}^-$
state is quite different from that of the $1^3B_{1u}^+$ state and the
dipole-inactive $2^1A_g^+$ state. In particular, the $1^1B_{1u}^-$ state is
rather weakly coupled to the lattice and has a rather small relaxation energy
ca. 0.1 eV. In contrast, the $1^3B_{1u}^+$ and $2^1A_g^+$ states are strongly
coupled with relaxation energies of ca. 0.5 and ca. 1.0 eV, respectively. By
analogy to linear polyenes, we argue that this difference can be understood by
the different kind of solitons present in the $1^1B_{1u}^-$, $1^3B_{1u}^+$ and
$2^1A_g^+$ states. The difference in relaxation energies of the $1^1B_{1u}^-$
and $1^3B_{1u}^+$ states accounts for approximately one-third of the exchange
gap in light-emitting polymers.
