Quantum confinement effects on the ordering of the lowest-lying excited states in conjugated polymers

The symmetrized density matrix renormalization group approach is applied within the extended Hubbard-Peierls model (with parameters U/t, V/t, and bond alternation δ) to study the ordering of the lowest one-photon (1¹B_u^-) and two-photon (2¹A_g⁺) states as well as the lowest-lying triplet 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, δ, and N. The "U - crossover" and "δ crossover" are examined for long chains, which provide a sharp contrast to the situation found previously for short chains. The "N-crossover", which only occurs for realistic intermediate correlation strength, illustrates the more localized nature of the 2A_g excitation relative to the 1B_u excitation. We also apply the quantum-chemical Pariser-Parr-Pople (PPP) model with long-range Ohno potential to the polyene molecules. We find that the 2A_g state is always below the 1B_u state for chain lengths N=4 to 40. Most interestingly, the gap between 2A_g and 1B_u first increases for N up to 16, then levels off, and finally starts to decrease. Thus, extrapolations to long chain based on short polyene data are hazardous.