Efficient first-principles approach to Gibbs free energy with thermal expansion

Abstract: We propose a method to evaluate the Gibbs free energy from constant-volume first-principles phonon calculations. The volume integral of the pressure is performed by determining the volume and the bulk modulus in equilibrium at finite temperatures, where the pressure and its volume derivative are evaluated utilizing first-principles calculations of the Gr\"{u}neisen parameter without varying the volume. We validate our method for fcc Al by comparing with the conventional quasiharmonic approximation. Furthermore, we integrate our method with self-consistent phonon theory and apply it to calculations for bcc Ti, hcp Ti, and tetragonal ZrO$_2$. We demonstrate the accuracy and computational efficiency of our method by comparing results with those obtained from directly volume-varied self-consistent phonon calculations. In all cases, our method accurately evaluates the free energy change due to thermal expansion using only constant-volume phonon calculations.