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

We propose a method to evaluate the Gibbs free energy from constant-volume first-principles 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\"uneisen parameter without varying the volume. As an example, the validity of our method is demonstrated for fcc-Al by comparing with the conventional quasiharmonic approximation that is much more computationally-demanding.