First-principles approach to efficient evaluation of Gibbs free energy with thermal expansion

The Gibbs free energy is crucial for understanding material properties such as phase transition and phase equilibria, where one of important finite temperature effects is thermal expansion. However, conventional quasiharmonic approximation (QHA) in first-principles calculations is so computationally expensive that the applicability is hard to extend to systems with dynamical instability at zero temperature. Here, we present an approach that evaluates the change in the free energy due to thermal expansion from single-volume phonon calculations. This method offers a significant advantage enabling computations that are out of reach by the QHA. Our method accurately determines the equilibrium volume and bulk modulus at finite temperatures by calculating the vibrational pressure and its volume derivative via first-principles calculations of the Grüneisen parameter. The accuracy and efficiency of our method are demonstrated for Al and Ti by comparing the results with those obtained from the conventional QHA.