Electronic Excitations of Polythiophene within Many-Body Perturbation Theory with and without the Tamm–Dancoff Approximation

Excited electronic states of small and large π-conjugated organic molecules can be described within ab initio many-body perturbation theory, notably by the GW approximation for the electron self-energy operator combined with the Bethe–Salpeter equation for correlated electron–hole excitations. In this context, the Tamm–Dancoff approximation is routinely employed to reduce the computational effort. It is known that the use of this approximation introduces errors of several 100 meV for small organic molecules but is negligible for extended systems. In this paper, we investigate how exactly the transition between these two regimes happens, by calculating the optical excitation energies of a series of polythiophene molecules of different sizes. We determine which parts of the electron–hole interaction are responsible for the deviation and show that the quantitative effects of the Tamm–Dancoff approximation depend sensitively on the size of the electronic system, in particular on the electronic conjugation length.