Thermopower of molecular junctions is sensitive to details in the junction
and may increase, decrease, or saturate with increasing chain length, depending
on the system. Using McConnell's theory for exponentially suppressed transport
together with a simple and easily interpretable tight binding model, we show
how these different behaviors depend on the molecular backbone and its binding
to the contacts. We distinguish between resonances from binding groups or
undercoordinated electrode atoms, and those from the periodic backbone. It is
demonstrated that while the former gives a length-independent contribution to
the thermopower, possibly changing its sign, the latter determines its length
dependence. This means that the question of which orbitals from the periodic
chain that dominate the transport should not be inferred from the sign of the
thermopower but from its length dependence. We find that the same molecular
backbone can, in principle, show four qualitatively different thermopower
trends depending on the binding group: It can be positive or negative for short
chains, and it can either increase or decrease with length
