Chemical Physics 85 (1984) 73-82 73 North-Holland, Amsterdam LINESHAPES OF MOLECULAR AGGREGATES. EXCHANGE NARROWING AND INTERSITE CORRELATION E.W. KNAPP Physik-Department, Teehnisehe Universiti~t Miinchen, D 8046 Garehing, West Germany Received 20 September 1983 The influence of intersite correlation of inhomogeneities on the lineshape of exciton spectra is investigated. Starting point is a perturbation treatment, valid for strong intermolecular coupling, which is applied to one-dimensional aggregates. Analytical expressions for the linewidth are acquired for cyclic aggregates and compared with values from linear aggregates. The linewidth increases with increasing intersite correlation and exhibits an N ~1/2 dependence for long aggregates with N molecular units. For intermediate intermolecular coupling the N-value derived from the present model relates to a coherence length of the exciton. 1. Introduction Optical lineshapes of excitations in molecular crystals and aggregates are of continuous interest in many research groups [1-7]. Exciton spectra can display a set of distinct narrow lines, a set of relatively broad, merging lines or they contain only a single broad line with a characteristic shape. The structure of the spectrum is due to exciton interaction with molecular vibrations and 0igtical phonons. It splits the exciton band in a series of bands each corresponding to a specific vibronic transition. Acoustical phonons which couple to the exciton yield the phonon side band, a broad and structureless feature accompanying the individual lines. The width of a single-line spectrum or of indi- vidual lines is due to inhomogeneities introduced by lattice disorder and phonon side bands merging in the corresponding line. But, intermolecular cou- pling of the molecular excitations delocalizes the excitons which then average over the various local inhomogeneities. This exchange narrowing effect reduces the inhomogeneous linewidth. At very low temperatures and for rather perfect molecular crystals lifetime broadening may become im- portant [8]. But in general it can be neglected. Theoretical studies generally concentrate on two different aspects of exciton spectra. The first is the understanding of the vibrational structure of the exciton spectra [9-19]. The other is concerned with the shape of individual lines [20-29]. For a spec- trum of well separated lines the influence of exci- ton-phonon interaction on an individual lineshape can be included using a reduced intermolecular coupling energy V of the molecular excitons [30]. Then a simplified model can be used which does not account for the vibrational structure of an exciton spectrum. The model hamiltonian in units of h is H = ~tn)~.(nl n + v~ (In)(n + 11 + In + 1)(nl) (1) for a one-dimensional aggregate with nearest- neighbour coupling. The transition frequencies ~0 n of the local excitations In) depend on the site n in contrast to the nearest-neighbour intermolecular coupling V. The site energies E,, = h~0 n are in general corre- lated in time and space. They can be characterized by time correlation functions of the second mo-. ments (r)- =f.,m(t-- C) (2) 030!-0104/84/$03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)