Diagrammatic exciton-basis valence-bond theory of linear polyenes

Understanding the photophysics of pi-conjugated polymers requires a physica l understanding of the excited states involved in the photophysics. Detaile d physical understanding is difficult because of the extensive configuratio n interaction that occurs within realistic theoretical models fur these sys tems. We develop a diagrammatic exciton-basis valence-bond representation t hat is particularly suitable for the intermediate magnitude of the Coulomb interactions in these systems. We present detailed comparisons of our exact exciton-basis treatment and previous approximate approaches, focusing on t he specific many-body and single-particle interactions that have been ignor ed in the past, and the consequences thereof. Following this, we present th e results of exact numerical calculations for the noninteracting band limit , the limit of isolated dimers interacting through Coulomb interactions, an d for the Pariser-Parr-Pople Ohno Coulomb interactions with two different b ond-alternation parameters for the ten-carbon linear polyene. Simple pictor ial descriptions of the eigenstates relevant in photophysics an obtained in each case, and taken together, these results provide a systematic characte rization of both low- and high-energy excited states: in linear chain pi-co njugated systems for realistic parameters. Two different quantities, the nu mber of effective excitations within the exciton basis, and the particle-ho le correlation length for the one-excitation eigenstates are defined and ca lculated fur further quantitative comparisons between the eigenstates. A pi ctorial description of optical nonlinearity is obtained thereby. For both s mall and large bond alternation, it is found that the two-photon state that dominates third order optical nonlinearity in the low-energy region is the lowest even parity one-excitation state with a larger particle-hole correl ation length than the 1 B-u exciton. The reason for the dominance by this m A(g) state can be understood within the exciton basis from the nature of th e current operator. It is shown that the relationship between the correlate d mA(g) and the correlated 1B(u) is identical to that between the uncorrela ted 2A(g) and the uncorrelated 1 B-u. In the high-energy region of the spec trum evidence for stable biexcitons is found from the nature of the singlet -singlet two-excitation wave functions.