Ideal dipole approximation fails to predict electronic coupling between semiconducting single wall carbon nanotubes

Single-walled carbon nanotubes (SWNTs) are highly conjugated carbon tubes that are a few nanometers in diameter and can be up to millimeters in length. The excited electronic states of semiconductor-type SWNTs are quasi-1D excitons. It is known that these spatially-extended electronic excitations can migrate among SWNTs that are bundled together, thus quenching the fluorescence owing to the presence of metallic SWNTs. Recent advances in purification and isolation have enabled studies of electronic energy transfer (EET) between SWNTs and molecular chromophores. Here we examine the electronic coupling among SWNTs in order to understand EET involving SWNTs. There are two main difficulties that need to be addressed when studying SWNT EET. The first is to obtain the electronic coupling matrix element that promotes EET. The most common method to calculate the electronic coupling between two molecules is the point dipole approximation (PDA) method, where the electronic coupling is described as the Coulombic interaction between transition dipole moments of D and A. In this approximation, each molecule is represented by a single dipole located at the center of mass for each molecule. It is well known that the PDA method fails at small separations in molecular systems. Owing to the size of SWNTs compared to typical donor-acceptor separations, it is likely that the PDA method will fail. Even when using the PDA method, however, it is difficult to obtain the dipole strength of the transition because the radiative lifetime is obscured by thermal population of dark states in the exciton band. The second difficulty is that there are a few closely spaced states associated with the lowest bright exciton transition (E{sub 11}), and each of these states might act as energy donors or acceptors. Here we will focus on the first of these challenges: the evaluation of electronic couplings between SWNTs, overcoming the limitations of the PDA method. In the last decade, sophisticated quantum-mechanical approaches to this problem have been developed which range from the calculation of the actual interaction between quantum-mechanically derived transition densities to more efficient but approximated strategies such as the distributed transition monopole approximation (TMA) method. Both these approaches are able to capture the shape of the transition density throughout the donor and the acceptor molecules, which is the origin of the well-known breakdown of the PDA method at close separations in molecular systems. Given the dimensions of the systems under study in this work, we adopt the TMA method to compute electronic couplings between SWNTs.

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