  We consider phononic heat transport through molecular chains connecting two
thermal reservoirs. For relatively short molecules at normal temperatures heat
conduction is dominated by the harmonic part of the molecular force-field. We
develop a general theory for the heat conduction through harmonic chains in
3-dimensions. A Landauer-type expression for the heat conduction is obtained,
in agreement with other recent studies. We use this formalism to study the heat
conduction properties of alkanes. For relatively short (1-30 carbon atoms)
chains the length and temperature dependence of the molecular heat conduction
result from the balance of three factors: (i) The molecular frequency spectrum
in relation to the frequency cutoff of the thermal reservoirs, (ii) the degree
of localization of the molecular normal modes and (iii) the molecule-heat
reservoirs coupling. The fact that molecular modes at different frequency
regimes have different localization properties gives rise to intricate
dependence of the heat conduction on molecular length at different
temperatures. For example, the heat conduction increases with molecular length
for short molecular chains at low temperatures. Similar considerations apply
for isotopically substituted disordered chains. Finally, we compare the heat
conduction obtained from this microscopic calculation to that estimated by
considering the molecule as a cylinder characterized by a macroscopic heat
conduction typical to organic solids. We find that this classical model
overestimates the heat conduction of single alkane molecules by about an order
of magnitude at room temperature. Implications of the present study to the
problem of heating in electrically conducting molecular junctions are pointed
out.
