  Using harmonic and anharmonic force constants extracted from
density-functional calculations within a supercell, we have developed a
relatively simple but general method to compute thermodynamic and thermal
properties of any crystal. First, from the harmonic, cubic, and quartic force
constants we construct a force field for molecular dynamics (MD). It is exact
in the limit of small atomic displacements and thus does not suffer from
inaccuracies inherent in semi-empirical potentials such as Stillinger-Weber's.
By using the Green-Kubo (GK) formula and molecular dynamics simulations, we
extract the bulk thermal conductivity. This method is accurate at high
temperatures where three-phonon processes need to be included to higher orders,
but may suffer from size scaling issues. Next, we use perturbation theory
(Fermi Golden rule) to extract the phonon lifetimes and compute the thermal
conductivity $\kappa$ from the relaxation time approximation. This method is
valid at most temperatures, but will overestimate $\kappa$ at very high
temperatures, where higher order processes neglected in our calculations, also
contribute. As a test, these methods are applied to bulk crystalline silicon,
and the results are compared and differences discussed in more detail. The
presented methodology paves the way for a systematic approach to model heat
transport in solids using multiscale modeling, in which the relaxation time due
to anharmonic 3-phonon processes is calculated quantitatively, in addition to
the usual harmonic properties such as phonon frequencies and group velocities.
It also allows the construction of accurate bulk interatomic potentials
database.
