1(1)B(u)(-)2 (1)A(g)(+) crossover in conjugated polymers: The phase diagram of the molecular-orbital model

Using the molecular-orbital model of conjugated polymers, a simple criterio n for the relative ordering of 1(1)B(u)(-) and 2(1)A(g)(+) states is provid ed. When the repeat unit electronic correlations increase, resulting in an increase in the triplet-singlet exchange energy, the 2(1)A(g)(+) state is e xpected to lower relative to the 1(1)B(u)(-) state. This result is confirme d by density-matrix renormalization-group calculations. Close to the phase boundary there are finite-size corrections resulting in a 1(1)B(u)(-) and 2 (1)A(g)(+) crossover as a function of chain length. The nature of this cros sover depends on the relative size of the excitons. A one-particle singlet excitation correlation function is shown to be a suitable means for evaluat ing particle-hole separations. It is further shown that the charge gap is a reliable means of determining the threshold of unbound states in the singl e-particle excitation channel. The biexciton triplet-triplet character of t he 2A(g)(+) states is investigated. The triplet-triplet separation is measu red via a two-particle triplet-triplet excitation correlation function. The triplet-triplet gap marks the threshold of unbound triplet-triplet states. [S0163-1829(99)00-424-5].