Density-matrix renormalization-group calculations of excited states of linear polyenes

We present density-matrix renormalization-group calculations of the Pariser-Parr-Pople-Peierls model of linear polyenes within the adiabatic approximation. We calculate the vertical and relaxed transition energies, and relaxed geometries for various excitations on long chains. The triplet (1^3Bₔ^+) and even-parity singlet (2^1A₆^+) states have a 2-soliton and 4-soliton forms, respectively, both with large relaxation energies. The dipole-allowed (1^1Bₔ^-) state forms an exciton-polaron, and has a very small relaxation energy. The relaxed energy of the 2^1A₆^+ state lies below that of the 1^1Bₔ^- state. We observe an attraction between the soliton-antisoliton pairs in the 2^1A₆^+ state. The calculated excitation energies agree well with the observed values for polyene oligomers; the agreement with polyacetylene thin films is less good, and we comment on the possible sources of the discrepancies. The photoinduced absorption is interpreted. The spin-spin correlation function shows that the unpaired spins coincide with the geometrical soliton positions. We study the roles of electron-electron interactions and electron-lattice coupling in determining the excitation energies and soliton structures. Electronic interactions play the key role in determining the ground-state dimerization and the excited-state transition energies.