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We study within the perturbative many-body $GW$ and Bethe-Salpeter approachthe low lying singlet charge-transfer excitations in molecular donor-acceptorcomplexes associating benzene, naphtalene and anthracene derivatives with thetetracyanoethylene acceptor. Our calculations demonstrate that such techniquescan reproduce the experimental data with a mean average error of 0.1-0.15 eVfor the present set of dimers, in excellent agreement with the besttime-dependent density functional studies with optimized range-separatedfunctionals. The present results pave the way to the study of photoinducedcharge transfer processes in photovoltaic devices with a parameter-free\textit{ab initio} approach showing equivalent accuracy for finite and extendedsystems.

Charge-transfer excitations in molecular donor-acceptor complexes within the many-body Bethe-Salpeter approach