  We study the Seebeck effect in the $\tau$-type organic conductors,
$\tau$-(EDO-$S$,$S$-DMEDT-TTF)$_{2}$(AuBr$_{2}$)$_{1+y}$ and
$\tau$-(P-$S$,$S$-DMEDT-TTF)$_{2}$(AuBr$_{2}$)$_{1+y}$, where
EDO-$S$,$S$-DMEDT-TTF and P-$S$,$S$-DMEDT-TTF are abbreviated as OOSS and NNSS,
respectively, both experimentally and theoretically. Theoretically in
particular, we perform first-principles band calculation for the two materials
and construct a two-orbital model, on the basis of which we calculate the
Seebeck coefficient. We show that the calculated temperature dependence of the
Seebeck coefficient $S$ is semi-quantitatively consistent with the experimental
observation. In both materials, the absolute value of the Seebeck coefficient
is maximum at a certain temperature, and this temperature is lower for NNSS
than for OOSS. From a band structure viewpoint, we find that this can be traced
back to the narrowness of the band gap between the upper and the lower
pudding-mold type bands. On the other hand, the Seebeck coefficient of NNSS in
the low temperature regime steeply increases with increasing temperature, which
is due to the narrowness of the upper band. These differences in thermoelectric
properties demonstrate the effectiveness of controlling the band structure
through molecular modification.
