  We study the electrical conductance $G$ and the thermopower $S$ of
single-molecule junctions, and reveal signatures of different transport
mechanisms: off-resonant tunneling, on-resonant coherent (ballistic) motion,
and multi-step hopping. These mechanisms are identified by studying the
behavior of $G$ and $S$ while varying molecular length and temperature. Based
on a simple one-dimensional model for molecular junctions, we derive
approximate expressions for the thermopower in these different regimes.
Analytical results are compared to numerical simulations, performed using a
variant of B\"uttiker's probe technique, the so-called voltage-temperature
probe, which allows us to phenomenologically introduce environmentally-induced
elastic and inelastic electron scattering effects, while applying both voltage
and temperature biases across the junction. We further simulate the thermopower
of GC-rich DNA molecules with mediating A:T blocks, and manifest the
tunneling-to-hopping crossover in both the electrical conductance and the
thermopower, in accord with measurements by Y. Li et al., Nature Comm. 7, 11294
(2016).
