Coherent exciton motion

A t the opposite end of the scale of pigment interactions is the strong-coupling or socalled exciton coupling mechanism, which also occurs through the Coulomb interaction of pigments. In this case the coupling energy is sufficiently strong, typically greater than the vibrational quantum energy h v, that it influences the shape of the absorption spectrum of the pigments involved, replacing the excited states of the individual pigments by a new set of excited states characteristic of the coupled system. Excitation energy is no longer located on a single pigment, but is delocalised over the ensemble of pigments involved in the excitonic coupling. In the simplest case of an excitonically coupled dimer made up from a pair of identical molecules, the new states are obtained by solving the Schrodinger equation for the dimer

where H1,2 are the Hamilton operators for the two pigments, V12 is the coupling energy, E the excited-state energy of the coupled system and Y the excitonic wavefunction. Solution of eq. 2.6 gives the energies and wavefunctions of the excitonically coupled system. This leads to the two excitonic excited states energies

where D is the (ground-state) energy shift due to the change in environment for each pigment (going from the gas phase into the solution environment) and is the excited-state transition energy of the uncoupled pigment. Thus excitonic coupling leads to two new excited states separated by an energy 2VI2. The result is a modification of the absorption spectrum of the dimer as compared to the monomers. The dipole moments dl,z of the two new delocalised exciton states are oriented perpendicularly to each other and depend on the orientations of the transition moments of the monomers according to

 

where do is the dipole strength of the uncoupled monomer and 8 the angle between the transition-dipole moments of the two monomers, thus conserving the total dipole strength of the combined monomers. Where more than two molecules are involved in the excitonic coupling, the relevant equations can be solved either analytically when symmetry prevails, or numerically in the general case (Pearlstein, 1982b and 1982~). While the exciton coupling determines the shape of the absorption, linear dichroism and CD spectra (Pearlstein, 1982b and 1982c), the exciton states do not live for very long at room temperature since the phase relationship of the electronic wavefunctions between the two molecules making up the coupled dimer are disturbed by thermal motions. Typically, dephasing occurs within 1 ps or less. This dephasing leads to a localisation of the excited-state energy on one of the monomers. From then on, Fiirster-type hopping transfer of energy between the two molecules may occur

 

However, during the lifetime of the excitonic states, the energy-transport dynamics are controlled by entirely different equations than for the Forster hopping mechanism, which is particularly important for larger assemblies of excitonically coupled systems. (For a modern in-depth treatment of the exciton concept in photosynthetic systems, see van Amerongen et al., 2000). It turns out that the major part of the energy transfer processes in photosynthetic systems can be quite well described using the Forster mechanism, if appropriate adaptations are made for the calculation of coupling strengths, spectral properties etc. (Yang and Fleming, 2002; Konermann et al., 1997). A rigorous excitonic description only seems necessary for larger assemblies such as the LHI or LHII complexes of purple photosynthetic bacteria, the FMO antenna complex (discussed in Section 2.4.7) and the supramolecular pigment aggregates in the chlorosomes of green sulphur bacteria (Prokhorenko et al., 2000).