Upon heating, Zr undergoes HCP-to-BCC phase transition at approximately 1135 K . By the quasi-harmonic free energy of temperature-dependent (TD) phonons (F QHA ) only, the HCP phase yields lower free energy than the BCC phase from 0 K to 1500 K(∆F always positive), failing to predict the HCP-to-BCC phase transition entirely. Once anharmonic free energy correction (F anh ) is applied (see Methods for details), the differential free energies (∆F) of Zr can cross zero at around 1135 K (Figure ), demonstrating a very accurate prediction for phase transition temperature. Since Zr is a metal, we separately calculated and included electronic free energy in plotting Figure , which is computed as