Contrasting Photophysical Properties of Star-Shaped vs Linear Perylene Diimide Complexes Christopher M. Pochas, ‡ Kurt A. Kistler, † Hajime Yamagata, † Spiridoula Matsika, † and Frank C. Spano* ,† † Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, United States ‡ Department of Chemistry, Pennsylvania State University, Brandywine Campus, Media, Pennsylvania 19063, United States * S Supporting Information ABSTRACT: The absorption line shapes of a series of linear and star-shaped perylene diimide (PDI) complexes are evaluated theoretically and compared to experiment. The cyclic trimer and tetrahedral complexes are part of the symmetric series, characterized by a single interchromophoric coupling, J 0 , between any two PDI chromophores. The measured spectra of all complexes show pronounced vibronic progressions based on the symmetric ring stretching mode at ∼1400 cm −1 . The spectral line shapes are accurately reproduced using a Holstein Hamiltonian parametrized with electronic couplings calculated using time- dependent density functional transition charge densities. Although the “head-to-tail” linear complexes display classic J- aggregate behavior, the star-shaped complexes display a unique photophysical response, which is neither J- nor H-like. In the symmetric N-mers (N =2−4), absorption and emission are polarized along N − 1 directions in contrast to linear complexes where absorption and emission remain polarized along the long molecular axis. In the symmetric complexes the red-shift of the 0−0 peak with increasing |J 0 |, as well as the initial linear rise of the 0−0/1−0 oscillator strength ratio with increasing |J 0 |, are independent of the number of PDI chromophores, N, and are markedly smaller than what is found in the linear series, where the shifts and ratios depend on N. Moreover, whereas the radiative decay rate, γ r , scales with N and is therefore superradiant in linear complexes, γ r scales with N/(N − 1) in the symmetric complexes. Vibronic/vibrational pair states (two-particle states) are found to profoundly affect the absorption line shapes of both linear and symmetric complexes for sufficiently large coupling. 1. INTRODUCTION Star-shaped complexes of π-conjugated chromophores are currently generating significant interest for use in optoelectronic devices, 1 which take advantage of isotropic absorption 2,3 and charge transport 4,5 without the sometimes disadvantageous effects of aggregation. Such molecules are also templates for higher-generation energy-funneling dendrimers, which are of significant interest theoretically 6−8 and practically as active materials for nonlinear optics, catalysis, drug delivery, and sensors. 8−10 We present here a theoretical analysis of the excited states and absorption spectra of a series of linear and star-shaped covalently linked perylene diimide (PDI) complexes. 11−15 PDI-based chromophores have high quantum yields and well-resolved vibronic spectra and readily self-assemble into a variety of geometries leading to both J- and H-aggregates, 16−18 making them ideal chromophores for studying the impact of aggregation on photophysical properties. Covalently linked PDI complexes also display J- and H-aggregate behavior and serve as model systems with which to study charge transport, 11,19 excimer formation, 20,21 and energy migration. 22−25 Previously, we conducted a theoretical investigation 26 of absorption and emission in a chiral PDI bichromophore, 27 using a Holstein Hamiltonian with a basis set consisting of single- and two-particle states. Electronic couplings were determined from time-dependent density functional (TDDFT) transition charge densities; that study quantitatively accounted for the Davydov splitting observed in the measured absorption spectrum 27 and showed that the spectral line shapes of the low- and high-energy Davydov components strongly resemble the line shapes expected for J- and H-aggregates, respectively. Here, we extend our investigation to include linear and higher-symmetry PDI complexes. 11−15 The simplest molecule in the linear series is a head-to-tail dimer in which the two PDI’s are covalently linked through the nitrogen head atoms. The addition of another PDI molecule using the same bonding motif results in the linear trimer. 11−13 The nonlinear complexes considered in this work include a cyclic trimer consisting of three PDI chromophores bound to a phenyl core 12,14 and a tetrahedral complex of phenyl-PDI chromophores linked to a central sp 3 -hybridized carbon atom. 12,15 In such a symmetric series of star-shaped complexes the coupling between the constituent PDI chromophores is characterized by a single Received: September 3, 2012 Article pubs.acs.org/JACS © XXXX American Chemical Society A dx.doi.org/10.1021/ja3087449 | J. Am. Chem. Soc. XXXX, XXX, XXX−XXX