Does the Traditional Band Picture Correctly Describe the Electronic Structure of n-Doped Conjugated Polymers? A TD-DFT and Natural Transition Orbital Study.

Abstract

Doped conjugated polymers have a variety of potential applications in thermoelectric and other electronic devices, but the nature of their electronic structure is still not well understood. In this work, we use time-dependent density functional theory (TD-DFT) calculations along with natural transition orbital (NTO) analysis to understand electronic structures of both p-type (e.g., poly(3-hexylthiophene-2,5-diyl), P3HT) and n-type (e.g., poly{[N,N'-bis(2-octyldodecyl)-naphthalene-1,4,5,8-bis(dicarboximide)-2,6-diyl]-alt-5,5'-(2,2'-bithiophene)}, N2200) conjugated polymers that are both p-doped and n-doped. Of course, the electronic transitions of doped conjugated polymers are multiconfigurational in nature, but it is still useful to have a one-electron energy level diagram with which to interpret their spectroscopy and other electronic behaviors. Based on the NTOs associated with the TD-DFT transitions, we find that the "best" one-electron orbital-based energy level diagram for doped conjugated polymers such as P3HT is the so-called traditional band picture. We also find that the situation is more complicated for donor-acceptor-type polymers like N2200, where the use of different exchange-correlation functionals leads to different predicted optical transitions that have significantly less one-electron character. For some functionals, we still find that the "best" one-electron energy level diagram agrees with the traditional picture, but for others, there is no obvious route to reducing the multiconfigurational transitions to a one-electron energy level diagram. We also see that the presence of both electron-rich and electron-poor subunits on N2200 breaks the symmetry between n- and p-doping, because different types of polarons reside on different subunits leading to different degrees of charge delocalization. This effect is exaggerated by the presence of dopant counterions, which interact differently with n- and p-polarons. Despite these complications, we argue that the traditional band picture suffices if one wishes to employ a simple one-electron picture to explain the spectroscopy of n- and p-doped conjugated polymers.