  We present here a theoretical method to determine the phononic contribution
to the thermal conductance of nanoscale systems in the phase-coherent regime.
Our approach makes use of classical molecular dynamics (MD) simulations to
calculate the temperature-dependent dynamical matrix, and the phononic heat
conductance is subsequently computed within the Landauer-B\"uttiker formalism
with the help of nonequilibrium Green's function techniques. Tailored to
nanostructures, crucial steps of force constant and heat transport calculations
are performed directly in real space. As compared to conventional density
functional theory (DFT) approaches, the advantage of our method is two-fold.
First, interatomic interactions can be described with the method of choice.
Semiempirical potentials may lead to large computational speedups, enabling the
study of much larger systems. Second, the method naturally takes into account
the temperature dependence of atomic force constants, an aspect that is ignored
in typical static DFT-based calculations. We illustrate our method by analyzing
the temperature dependence of the phononic thermal conductance of gold (Au)
chains with lengths ranging from 1 to 12 atoms. Moreover, in order to evaluate
the importance of anharmonic effects in these atomic-scale wires, we compare
the phase-coherent approach with nonequilibrium MD (NEMD) simulations. We find
that the predictions of the phase-coherent method and the classical NEMD
approach largely agree above the Debye temperature for all studied chain
lengths, which shows that heat transport is coherent and that our
phase-coherent approach is well suited for such nanostructures.
