Optical Responses of Conjugated Polymers by TDDFT in Real-Space and Real-Time Approach
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Optical Responses of Conjugated Polymers by TDDFT in Real-Space and Real-Time Approach Nobuhiko Akino and Yasunari Zempo Tsukuba Research Laboratory Sumitomo Chemical Co., Ltd. 6 Kitahara, Tsukuba, 300-3294 JAPAN ABSTRACT The time dependent density functional theory (TDDFT) has applied to study the optical responses of the conjugated polymers such as poly(p-phenylenevinylene) and poly(9,9-dialkylfluorene). In our study, the real-space grid representation is used for the electron wavefunctions in contrast to a conventional basis set on each atom. In the calculations of the optical responses, the real-time approach is employed, where we follow the linear responses of the systems under externally applied perturbations in the real time. Since a real polymer is too large to handle, we have calculated the oligomers with different length and observed the spectrum peak is redshifted as the length of oligomer increases. The property of the polymer is extrapolated as the infinitely long oligomer. The estimated polymer spectra agree with the experiments reasonably well. INTRODUCTION Polymer light emitting diodes (PLEDs) have been of interest for displays and other lighting applications. The low cost and the ease of processing are the advantages of the conjugated polymers over the inorganic materials and the low molecules as the former can be deposited by spin-coating over large area. Moreover, the color tuning and efficiency are considered to be controlled by the manipulation of the molecular structures. These make the conjugated polymers good candidates in the LEDs and other applications. The simplest PLED consists of the polymer layer sandwiched between the cathode and the anode. The radiative recombination of the injected electrons and holes in the polymer layer results in the emission of light. The emission color is determined by the nature of polymer and the device optimization requires us to understand the fundamental physics of the charge injection, transport, and recombination. Thus, it is essential to study from both the material design and the device optimization to achieve better LEDs. In this study, we have focus on the spectra of the polymers, which is one of the most important properties in real applications as it determines the emission frequency. To study the spectra of conjugated polymers, we have used the time dependent density functional theory (TDDFT), which has been widely used and recognized as a powerful tool in studies of the electron excitations, the dielectric properties, and the optical properties. However, since a real polymer is too large to handle, we have performed the calculations of the oligmers with different length and attempted to extrapolate the properties in the polymer. In the next section we describe the theory with our numerical details. Then, the results of its applications to poly(p-phenylenevinylene) and poly(9,9-dialkyl-fluorene) are given. In the last section, we summarize our results with discussion.
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THEORY AND NUMERICAL DETAILS The fundamental equation of time
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