Chiral exciton wave functions in cylindrical J aggregates

Abstract

We study the exciton wave functions and the optical properties of cylindrical molecular aggregates. The cylindrical symmetry allows for a decomposition of the exciton Hamiltonian into a set of effective one-dimensional Hamiltonians, characterized by a transverse wave number k2. These effective Hamiltonians have interactions that are complex if the cylinder exhibits chirality. We propose analytical ansatze for the eigenfunctions of these one-dimensional problems that account for a finite cylinder length, and present a general study of their validity. A profound difference is found between the Hamiltonian for the transverse wave number k2=0 and those with k2 not equal 0. The complex nature of the latter leads to chiral wave functions, which we characterize in detail. We apply our general formalism to the chlorosomes of green bacteria and compare the wave functions as well as linear optical spectra (absorption and dichroism) obtained through our ansätze with those obtained by numerical diagonalization as well as those obtained by imposing periodic boundary conditions in the cylinder's axis direction. It is found that our ansätze, in particular, capture the finite-length effect in the circular dichroism spectrum much better than the solution with periodic boundary conditions. Our ansätze also show that in finite-length cylinders seven superradiant states dominate the linear optical response.

Excitons in tubular molecular aggregates

“…(5) induced by the actual long-range interactions does not diverge for long cylinders. For cylinders (of the chlorosome structure) longer than roughly 100 rings, the thus obtained states compare well to numerically obtained exact ones, and show an interesting chiral behavior of the excitation density on the cylinder's surface as a consequence of the fact that ya0 [7].…”

“…For shorter cylinders, using the ansa¨tze Eqs. (4) and (5), one finds seven superradiant states [7], one in the k 2 ¼ 0 band and three in the k 2 ¼ 1 and the k 2 ¼ À1 bands. The latter are pairwise degenerate.…”

“…This approach is rooted in a previous study of Malyshev and Moreno [9], who argued that simple standing sine waves are good approximations for the exciton wave functions of a chain with long-range point-dipole interactions. Using this idea, we have shown [7] that in the k 2 ¼ 0 band, the wave functions…”

“…In addition, we showed the validity of this approximation by calculating the ratio of the mixing matrix elements of the actual long-range interactions between different k 1 states to the difference of the diagonal matrix elements of these interactions in both states involved. We showed that generally this ratio is small (p0:1 for N 1 450 for cylinders of the chlorosome structure), and moreover, independent of the cylinder structure, this ratio decreases logarithmically for growing N 1 : For the k 2 ¼ 1 band, we used an analogous ansatz [7]:…”

“…If the effects of disorder may be ignored, the cylindrical symmetry leads to interesting optical selection rules for these states. In particular, only a few superradiant exciton transitions occur, which either are polarized parallel or perpendicular to the cylinder axis [5][6][7].…”