Within the Tamm-Dancoff approximation, ab initio approaches describe excitons as packets of electron-hole pairs propagating only forward in time. However, we show that in nanoscale materials excitons and plasmons hybridize, creating exciton-plasmon states where the electron-hole pairs oscillate back and forth in time. Then, as exemplified by the trans-azobenzene molecule and the carbon nanotubes, the Tamm-Dancoff approximation yields errors larger than the accuracy claimed in ab initio calculations. Instead, we propose a general and efficient approach that avoids the Tamm-Dancoff approximation, correctly describes excitons, plasmons, and exciton-plasmon states, and provides a good agreement with experimental results.
Grüning, M., Marini, A., & Gonze, X. (2009). Exciton-Plasmon States in Nanoscale Materials: Breakdown of the Tamm-Dancoff Approximation. Nano Letters : a journal dedicated to nanoscience and nanotechnology, 9(8), 2820-2824. https://doi.org/10.1021/nl803717g (Original work published 2009)