  Motivated by recent experiments [Lee et al. Nature 498, 209 (2013)], we
present here a detailed theoretical analysis of the Joule heating in
current-carrying single-molecule junctions. By combining the Landauer approach
for quantum transport with ab initio calculations, we show how the heating in
the electrodes of a molecular junction is determined by its electronic
structure. In particular, we show that in general the heat is not equally
dissipated in both electrodes of the junction and it depends on the bias
polarity (or equivalently on the current direction). These heating asymmetries
are intimately related to the thermopower of the junction as both these
quantities are governed by very similar principles. We illustrate these ideas
by analyzing single-molecule junctions based on benzene derivatives with
different anchoring groups. The close relation between heat dissipation and
thermopower provides general strategies for exploring fundamental phenomena
such as the Peltier effect or the impact of quantum interference effects on the
Joule heating of molecular transport junctions.
