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Abstract

X-ray absorption spectroscopy (XAS) is combined with density functional theory (DFT) to determine the orbitals of one- and two-dimensional carbon π-systems (lycopene, beta-carotene, retinal, retinol, retinoic acid, coronene, triphenylene). Considerable fine structure is observed for the transition from the C 1s level to the lowest unoccupied molecular orbital (LUMO) and explained by DFT. The wave functions of the one-dimensional chain molecules display the node structure of a vibrating string. The XAS transition energy is decomposed into contributions from the C 1s core level, the π* final state, and the electron–hole interaction. For the latter, we develop a simple model that accurately represents a full Δ-self-consistent field (ΔSCF) calculation. The distortion of the LUMO because of its interaction with the C 1s hole is investigated. These results illustrate the electronic states of prototypical π-bonded carbon structures with low-dimensional character, such as those used in molecular complexes for solar cells, confined graphene structures, and molecular wires.