Relaxation of the first B_u excited state in linear polyenes: From trans-butadiene to polyacetylene

We present a multiphonon approach to analyze the lattice relaxation in the first B_u excited state of linear polyenes, from trans-butadiene to polyacetylene. Within a single-electron theory including bond-length bond-order relationship, we optimize the geometries of both the ground state and the first excited state and characterize the geometry of the excited state in terms of the formation of soliton-antisoliton pairs (bipolarons). The vibrational modes are simply taken as corresponding to soliton translation and amplitude vibrations (dimerization modes) within the harmonic approximation. Photoabsorption experiments carried out on a series of linear polyenes, β-carotene, polyenals/polyenones, and polyacetylene are discussed. The Huang-Rhys factor S and the relaxation energy are calculated for polyenes with various lengths. A major result is that we find that the S value first tends to decrease with increasing chain length but after some critical length the evolution completely modifies and S starts increasing. This feature is in good agreement with the experimental data and, in the case of polyacetylene, we are able to reproduce properly the experimental subgap absorption tail. The vibronic behavior for short chains is thus markedly different from that of long chains. We therefore caution that extrapolations based on observations on short polyenes might be invalid for the polymer.