Evaluation of crystal free energy with lattice dynamics

Within the framework of density functional theory (DFT), the total energy of crystal structures is calculated at zero temperature. Herein, we briefly discuss the DFT-based lattice-dynamics approach for computing crystal free energy, the quantity needed in various non-zero-temperature contexts. We illustrate this well-established approach by examining the temperature-dependent thermodynamic stability of several crystalline materials, including ZrO${}_2$, HfO${}_2$, KBH${}_4$, and Zn(BH${}_4$)${}_2$.