  We herein present a first-principles formulation of the Green-Kubo method
that allows the accurate assessment of the non-radiative thermal conductivity
of solid semiconductors and insulators in equilibrium ab initio molecular
dynamics calculations. Using the virial for the nuclei, we propose a unique ab
initio definition of the heat flux. Accurate size- and time convergence are
achieved within moderate computational effort by a robust, asymptotically exact
extrapolation scheme. We demonstrate the capabilities of the technique by
investigating the thermal conductivity of extreme high and low heat conducting
materials, namely diamond Si and tetragonal ZrO$_2$.
