Empirical Formula of Exciton Coherent Domain in Oligomers and Application to LH2

Abstract

We investigated the mechanism by which the length of exciton coherent domain in the linear array of pigments is determined. Correctly solving a generalized master equation with memory function obtained by the secondorder perturbation of the intermolecular interaction, we obtained an empirical formula for the length of exciton coherent domain, abbreviated as coherence length. In the absence of inhomogeneity, this coherence length is expressed by a linear function of the ratio between the intermolecular coupling strength U and the destructing force γ of a coherent bond. In the presence of inhomogeneity, the coherence length is expressed by a linear function of U/γ only approximately, and its deviation becomes significant when the degree of inhomogeneity is larger than about 100 cm -1 . Applying this formula to the LH2 antenna complex of photosynthetic purple bacteria Rhodopseudomonas acidophila, we found that the coherence length of B850 is about 5 bacteriochlorophyll molecules in the absence of inhomogeneity and about 4 in the presence of inhomogeneity. The coherence length of B800 is less than 1.6, confirming that the excited state of B800 is almost localized at one bacteriochlorophyll molecule.

Intramolecular and intermolecular energy transfers in donor-acceptor linear porphyrin arrays

“…An empirical law for the coherence length for a Frenkel exciton system has been suggested. 23,34 The absorption spectrum reflects the solute/solvent configuration of the system while the molecule resides in the ground state, whereas the emission spectrum reflects the configuration of the system while the molecule resides in the excited state. The difference in solute/solvent configuration is manifested in the Stokes shift.…”

“…The energy level structure of the donor and acceptor plays a key role in the energy transfer. The nature of the donor exciton state ͑coherence length͒, which depends on the coupling strength between the chromophore units within the array relative to the fluctuation in transition frequency due to the solvent and conformational disorder, 23,34 is also a critical factor that governs the energy transfer. To this end, in addition to the fluorescence time profile at fixed detection wavelengths, we have measured TRF spectra over the entire emission region of the donor and acceptor to elucidate the energy structures and the dynamics occurring in the porphyrin arrays.…”

Excitonic Coupling Strength and Coherence Length in the Singlet and Triplet Excited States of meso–meso Directly Linked Zn(II)porphyrin Arrays

“…According to the empirical formula for one-dimensional linear arrays developed by Kakitani et al, the coherence length N c can be estimated by Equation (4). [38,39] N c 1.…”

“…This excitonic delocalization in light-harvesting systems is determined from the interpigment coupling strength (constructive factor) and line-broadening effects such as electron ± phonon coupling and site inhomogeneity (destructive factor). [38] Numerous theoretical and experimental methods have been utilized to assess the extent of exciton delocalization in LH2. These studies demonstrated that the coherence length of the strongly coupled B850 ring in LH2 is about four Bchl a molecules.…”

“…[42±44] In addition, when the empirical formula developed by Kakitani et ) are used, [2,38] the coherence length is estimated to be 4.1, even with incorporation of the inhomogeneity (ca. 150 cm…”