  In this work, using the DFT and TDDFT, we have theoretically studied the
electronic and optical properties of the two recently synthesized coadsorbents
Y1 and Y2, which were aimed to enhance the efficiency of the black
dye-sensitized solar cells. To determine the solvatochromic shifts, both the
implicit and mixed implicit-explicit models have been used. The connection
between the solvatochromic shifts and the changes of dipole moments in the
excitation process is discussed. The difference in excitation charge transfer
is utilized to explain the experimentally observed difference in $J_{sc}$ for
Y1 and Y2. Investigating the interactions of I$_2$ molecules in the electrolyte
solution with the coadsorbents showed that with Y1 the recombination loss was
weakened through decreasing the I$_2$ concentration near the TiO$_2$ surface,
whereas with Y2 it was increased. As a result, the higher values of both
$J_{sc}$ and $V_{oc}$ with Y1 coadsorbent explains its experimentally observed
higher efficiency. The present study sheds light on how to design and engineer
newer coadsorbents or organic dyes for higher efficiencies.
