  The symmetrized density matrix renormalization group approach is applied
within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond
alternation \delta) to study the ordering of the lowest one-photon
(1^{1}B^{-}_u) and two-photon (2^{1}A^{+}_g) states in one- dimensional
conjugated systems with chain lengths, N, up to N=80 sites. Three different
types of crossovers are studied, as a function of U/t, \delta, and N. The
U-crossover emphasizes the larger ionic character of the 2A_g state compared to
the lowest triplet excitation. The \delta crossover shows strong dependence on
both N and U/t. The N-crossover illustrates the more localized nature of the
2A_g excitation relative to the 1B_u excitation at intermediate correlation
strengths.
