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Dl

D2

D3

D4

D5

Figure 1: Structures of the compact phenylacetylene dendrimers family made of the same linear building unit. Self-similar geometry leads to unusual transport and optical properties in these Cayley tree or "Bethe lattice" structures [2-11]. Application of quantum chemistry methods to calculate the electronic structure of giant molecules is limited by computational power to small systems [12, 13]. The theoretical investigation is complicated by the delocalized nature of electronic excitations, strong electron correlations, and vibronic coupling [12, 13). The problem is simplified considerably when a molecule can be divided into a set of chromophores which are well separated in space, and their interactions are purely Coulombic. Electron 327 Mat. Res. Soc. Symp. Proc. Vol. 543 0 1999 Materials Research Society

exchange is then negligible, each chromophore retains its own electrons, and the system may be described using the Frenkel exciton Hamiltonian [14, 15]. It has been shown in [16] that optical excitations in these dendrimers do not involve charge separation between different segments. This implies that optical excitations are localized in the sense that the relative motion of electrons and holes is restricted to a single segment. However, the center of mass motion of electron-hole pairs can still be delocalized across the entire molecule. This localization allows to describe the optical response of the dendrimer using the Frenkel (rather than charge transfer) exciton Hamiltonian [14, 15, 17]: H =

'

BtBf + E JnfBtBf.

(1)

Each segment is modeled as a two-level chromophore (the ground and excited states of a single acetylene chain) [9]. B,n (Bt) are the annihilation (creation) operator of an excitation localized on the fr-th chromophore. They satisfy the commutation relations, [BA, Bt] 2 im (1 - 2BtmB,f) and [BC, Bm] = [Bi, Bt, - (Bt )2 = (Bn) = 0. The parameters of the Frenkel exciton Hamiltonian [Eq. (1)] have been computed using electronic structure calculations for D1 [16]. The Coulomb coupling between the chromophores described by Ja, leads to delocalization of energy due to the center of mass motion of the Frenkel excitons [9]. The structure of Frenkel excitons is very different for the compact and extended families of dendrimers where the linear segment length varies from generation to generation, which leads to a substantial difference in optical properties. In extended dendrimers, the segment length increases towards the center. This implies that the transition frequencies Qfj of the effective chromophores are the same only within the same generation and decrease towards the center forming an energy funnel. Since the differences between the transition frequencies in different generations are in the range 800-3200 cm- 1 whereas the Coulomb couplig J 70 cm- 1 [9], the excitons in extended dendrimers can only be delocalized within a given generation. In compact dendrimers the linear units are identical and, therefore, the excitons can be delocalized over the entire molecule. This impl