  The impact of nuclear molecular configurations on the astrophysical S-factor
for $^{16}$O + $^{16}$O is investigated within the realistic two-center shell
model based on Woods-Saxon potentials. These molecular effects refer to the
formation of a neck between the interacting nuclei and the radial dependent
collective mass parameter. It is demonstrated that the former is crucial to
explain the current experimental data with high accuracy and without any free
parameter, whilst in addition the latter predicts a pronounced maximum in the
S-factor. In contrast to very recent results by Jiang et al., the S-factor does
not decline towards extremely low values as energy decreases.
