  Lewis acids like tris(pentafluorophenyl)borane (BCF) offer promising routes
for efficient $p$-doping of organic semiconductors. The intriguing experimental
results achieved so far call for a deeper understanding of the underlying
doping mechanisms. In a first-principles work, based on state-of-the-art
density-functional theory and many-body perturbation theory, we investigate the
electronic and optical properties of donor/acceptor complexes formed by
quarterthiophene (4T) doped by BCF. For reference, hexafluorobenzene
(C$_6$F$_6$) and BF$_3$ are also investigated as dopants for 4T. Modelling the
adducts as bimolecules \textit{in vacuo}, we find negligible charge transfer in
the ground state and frontier orbitals either segregated on opposite sides of
the interface (4T:BCF) or localized on the donor (4T:BF$_3$, 4T:C$_6$F$_6$). In
the optical spectrum of 4T:BCF, a charge-transfer excitation appears at
lowest-energy, corresponding to the transition between the frontier states,
which exhibit very small but non-vanishing wave-function overlap. In the other
two adducts, the absorption is given by a superposition of the features of the
constituents. Our results clarify that the intrinsic electronic interactions
between donor and acceptor are not responsible for the doping mechanisms
induced by BCF and related Lewis acids. Extrinsic factors, such as
solvent-solute interactions, intermolecular couplings, and thermodynamic
effects, have to be systematically analyzed for this purpose.
