Fast anharmonic free energy method with an application to vacancies in ZrC

We propose an approach to calculate the anharmonic part of the volumetric-strain and temperature-dependent free energy of a crystal. The method strikes an effective balance between accuracy and computational efficiency, showing a $\ifmmode\times\else\texttimes\fi{}10$ speedup on comparable free energy approaches at the level of density functional theory, with average errors less than 1 meV/atom. As a demonstration we make predictions on the thermodynamics of substoichiometric ${\mathrm{ZrC}}_{x}$, including vacancy concentration and heat capacity.