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要旨

We report vibrationally broadened Franck–Condon (FC) spectra of Violaxanthin (Vx) and Zeaxanthin (Zx) for the lowest-energy 1A_g → 1B_u band that arises from the bright HOMO → LUMO single-electron excitation. Geometries were optimized using standard (1A_g) and time-dependent (1B_u) density functional theory (DFT) at the (TD-)CAM-B3LYP/6-31G(d) level, both in the gas phase and in acetone using a polarizable continuum model (PCM). DFT/MRCI multireference calculations were performed at the optimized (TD)-CAM-B3LYP structures to evaluate the energies of doubly excited states that are not accessible to linear response TD-DFT theory. The FC spectra were calculated using the time-independent (TI) scheme. The calculated spectra of Vx and Zx are very similar, with a red shift of about 0.1 eV for Zx relative to Vx, which is in agreement with the experimental data. The predicted spectral peaks of Vx and Zx deviate from experiment by less than 0.1 eV when performing the calculations in the gas phase. In the presence of acetone (PCM model), there are larger deviations so that a state specific correction scheme needs to be applied, which accounts for non-equilibrium solvent relaxation. The 1A_g → 1B_u vertical absorption energies and the corresponding vertical fluorescence energies from TD-CAM-B3LYP and DFT/MRCI agree reasonably well. The DFT/MRCI absorption and fluorescence energies for the doubly excited 2A_g and 2B_u states are found to be rather sensitive to the underlying geometry, in particular to the bond length alternation in the polyene chain. In acetone (PCM), Vx and Zx show little bond alternation, and thus the doubly excited B_u state becomes the lowest excited B_u state. (TD)-CAM-B3LYP appears to be suitable for generating realistic geometries for higher-level calculations in such molecules.