Quantifying charge transfer energies at donor-acceptor interfaces in small-molecule solar cells with constrained DFTB...

Charge transfer states around the donor-acceptor interface in an organic solar cell determine the device performance in terms of the open circuit voltage. In the present work, we propose a computational scheme based on constrained density functional tight binding theory (c-DFTB) to assess the energy of the lowest charge transfer (CT) state in such systems. A comparison of the c-DFTB scheme with Hartree-Fock based configuration interaction of singles (CIS) and with time-dependent density functional theory (TD-DFT) using the hybrid functional B3LYP reveals that CIS and c-DFTB reproduce the correct Coulomb asymptotics between cationic donor and anionic acceptor configurations, whereas TD-DFT gives a qualitatively wrong excitation energy. Together with an embedding scheme accounting for the polarizable medium, this c-DFTB scheme is applied to several donor-acceptor combinations used in molecular solar cells. The external quantum efficiency of photovoltaic cells based on zinc phthalocyanine-C60 blends reveals a CT band remaining much narrower than the density of states of acceptor HOMO and donor LUMO, an observation which can be interpreted in a natural way in terms of Marcus transfer theory. A detailed comparison with c-DFTB calculations reveals an energy difference of 0.32 eV between calculated and observed absorption from the electronic ground state into the CT state. In a blend of a functionalized thiophene and C60, the photoluminescence spectra differ significantly from neat films, allowing again an assignment to CT states. The proposed computational scheme reproduces the observed trends of the observed open circuit voltages in photovoltaic devices relying on several donor-acceptor blends, finding an offset of 1.16 eV on average. This value is similar as in polymer-fullerene photovoltaic systems where it amounts to about 0.9 eV, indicating that the photophysics of CT states in molecular donor-acceptor blends and in polymer-fullerene blends are governed by the same mechanisms.